Fatigue damage control and assessment for railways bridges (FADLESS) : final report.
Date: 2014-01-31
Institutions: Directorate-General for Research and Innovation
Subjects: bridge, case study, metal structure, rail network, research report, resistance of materials, steel, transport infrastructure, urban transport

European Commission

Research Fund for Coal and Steel

Fatigue damage control and assessment  
for railway bridges

(FADLESS)

F. Lippi and W. Salvatore
Consorzio Pisa Ricerche
Corso Italia 116, 56125 Pisa, ITALY
A. Braconi, M. Finetto
RIVA Acciaio SpA
Viale Certosa 249, 20151 Milan, ITALY
H. Wenzel
VCE Holding GmbH
Hadikgasse 60, 1140 Vienna, AUSTRIA
G. De Roeck
Katholieke Universiteit Leuven
Oude Markt 13, 3000 Leuven, BELGIUM
B. Peeters
LMS International
Interleuvenlaan 68, 3001 Leuven, BELGIUM
C. Könke and V. Zabel
Bauhaus University of Weimar
Geschwister-Scholl-Str. 8, 99421 Weimar, GERMANY
A. Cunha
Faculdade de Engenharia da Universidade do Porto
Rua Dr. Roberto Frias, s/n, 4200-465 Porto, PORTUGAL

Grant Agreement RFSR-CT-2009-00027 
1 July 2009 to 30 June 2012

Final report

Directorate-General for Research and Innovation

2014 

EUR 26419 EN

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Luxembourg: Publications Office of the European Union, 2014 

ISBN 978-92-79-35043-6 
doi:10.2777/59688 

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Table of Contents 

Final Summary 

1  Introduction 

1.1  Analysis of traffic flows 
1.2  Historical development of traffic and design codes 
1.3  Standard methodology for the assessment of structural safety 
1.4  References 

2  Fatigue behaviour of steel bridges 

2.1  Analysis and classification of fatigue damages 
2.2  Distortion induced fatigue 
2.3  Vibration induced fatigue 
2.4  Fatigue damages in riveted steel bridges 
2.5  European standard for fatigue assessment 
2.6  Fatigue assessment in other National codes 
2.7  Advanced fatigue assessment procedures 
2.8  References 

3  Scopes of the research Project and adopted methodology 

3.1  Open problems 
3.2  Scope of FADLESS Project and adopted methodology 

4  Description of case studies 

4.1  Lagoscuro railway viaduct on Po river (Italy) 
4.2  Panaro bridge (Italy) 
4.3  Trezói Bridge (Portugal) 
4.4  Alcácer do Sal Bridge (Portugal) 
4.5  Saalebrücke Großheringen (Germany) 
4.6  Salzach River Bridge (Austria) 

5  Standard Fatigue Assessment 

5.1  Numerical modelling 
5.2  Experimental dynamic identification 
5.3  Vibration-based model updating 
5.4  Application to case studies 

5.4.1  Lagoscuro viaduct (Italy) 
5.4.2  Panaro Bridge (Italy) 
5.4.3  Trezói Bridge (Portugal) 
5.4.4  Alcácer do Sal Bridge (Portugal) 
5.4.5  Saalebrücke Großheringen (Germany) 
5.4.6  Salzach River Bridge (Austria) 

5.5  References 

6  Vibration/Distortion Induced Fatigue 
6.1.1  Lagoscuro viaduct (Italy) 
6.1.2  Panaro Bridge (Italy) 
6.1.3  Trezói Bridge (Portugal) 
6.1.4  Alcácer do Sal Bridge (Portugal) 
6.1.5  SaalebrückeGroßheringen 

3

5 

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6.1.6  Salzach River Bridge (Austria) 

6.2  References 

7  Guidelines for Fatigue Assessment 

8  Conclusions and Future Developments 

List of figures 

List of tables 

List of publications 

147 
158 

161 

167 

171 

183 

185 

4

 
 
Final Summary 
Fatigue is a very important failure mode for steel structures. In fact about 80/90% of failures in steel 
structures  are  related  to  fracture  and  fatigue.  In  particular,  railway  bridges  endure  million  of  stress 
cycles during their life and they are expected to be highly vulnerable to such phenomena. 
Several studies were performed in the past in order to assess the fatigue resistance of steel and steel-
concrete  composite  bridges;  such  studies  were  the  base  of  modern  codes  and  standards.  Despite  of 
these efforts, the fatigue assessment of railway bridges both considering the design of new bridges and 
the assessment of existing ones is one of the main issues in current practice. 
In  past  design  practice  of  steel  railway  bridges,  it  was  assumed  that  secondary  stresses  induced  by 
vibration/distortion  phenomena  could  be  limited  adopting  proper  detailing.  Such  objectives  were 
reached  introducing  an  high  number  of  global  and  local  stiffeners,  necessary  to  guarantee  the 
verifications of static requirements against instability as well. On the contrary, several fatigue problems 
affected and still affect steel bridges due to vibration/distortion induced effects. Also modern solutions, 
characterized  by  new  materials  with  very  high  performances  allowing  for  very  slender  structures, 
revealed to be exposed to the vibration and distortion effects which influence fatigue behaviour. By the 
way,  actual  codes  and  regulations  appear  inadequate  to  provide  effective  tools  in  order  to  obtain 
thorough information about such phenomena. 

Figure I - Examples of distortion induced fatigue crack progression. 

It  is  so  evident  the  necessity  for  a  continuous  analysis  and  review  of  current  standards  for  fatigue 
assessment,  in  order  to  guarantee  reliability  and  safety  of  steel  railway  bridges.  Modern  codes  and 
standards are based on several past studies, performed in order to assess the fatigue resistance of steel 
bridges. Such studies were realized on lines characterized by train typologies, axle loads, composition 
and design speed different from actual values and, moreover, considering only the direct effects of train 
passages  into  local  details.  Despite  of  these  efforts,  the  fatigue  assessment  of  railway  bridges  both 
considering the design of new bridges and the assessment of existing ones is one of the main issues in 
current practice. In fact, phenomena like “vibration induced” and “distortion induced” fatigue are still 
partially  uncovered  by  actual  design  codes  and  represent  a  critical  aspects  for  the  assessment  of 
existing  bridge  remaining  life  and  for  the  design  of  new  bridges.  Generally,  these  two  typologies  of 
fatigue phenomena were considered as secondary or negligible and, as a consequence, not considered 
by design codes. The possible presence of secondary stresses is ignored or not considered also in the 
evaluation of fatigue resistance of critical details by laboratory tests. By this way, proper information 
concerning  the  actual  resistance  under  the  co-presence  of  primary  and  secondary  stresses  are  not 
available.  At  least,  as  global  economy  is  continuously  changing,  a  corresponding  variation  of  trade 
volumes,  typologies  and  frequencies  is  to  be  expected.  This  development  concerns  also  the 
passenger/freight traffic on railway lines. As a consequence, railway authorities shall take into account 
a constant increase or variation of train typologies and composition, passage frequencies, volumes and 
weights  of  transported  goods,  just  to  not  underestimate  the  actual  traffic  loads  on  lines.  Thus,  a 
constant updating and review of traffic spectra is necessary to gain a reliable and safe design of new 
steel bridges and managing of existing ones. 

5

 
 
 
Main objective of the Fadless Project was the development of a modern procedure for the evaluation of 
the  structural  integrity  of  railway  steel  bridges  which  may  be  affected  by  fatigue  damage  under  the 
application of a large number of load cycles during their life-time. In particular, the Project aimed at a 
better and more accurate comprehension of actual fatigue load and resistance of principal elements and 
critical details of steel bridge typologies representative of European solutions for railway lines.  

Global Analysis of Bridge

FE Global Model

Dynamic Identification

Updated FE Global Model

Standard Fatigue 
Assessment

Identification of Critical 
Details

Monitoring System

Laboratory  Tests

Laboratory Fatigue Test

Traffic Spectra / Control of 
Critical Details

Monitoring  of Service 
Conditions

Advanced Assessment  of 
Vibration/Distortion  Induced Fatigue

Advanced Fatigue  Assessment

Local Analysis  of Critical Details

FE Local Models

Experimental Analysis of 
Critical details

Updated FE Local Model

Actual Stresses Induced by 
Vibration/Distortion

Figure II - Methodology adopted in the Fadless Project for the advanced assessment of vibration/distortion 
induced fatigue. 

In the proposed methodology, the actual fatigue loading spectra was evaluated taking into account the 
real and the expected traffic flows, also because of possible reclassification of railway lines, the global 
dynamic  train-bridge  interaction  effects  and  the  local  dynamic  vibration  and  distortional  effects. 
Moreover,  actual  fatigue  resistance  of  the  main  elements  /  critical  details  subjected  to  distortion 
induced effects was evaluated. In such a way, it was also possible to setup suitable strategies for the 
evaluation  of  vibration  induced  and  distortion  induced  fatigue  damaging  in  steel  railway  bridges,  as 
well for the control of the crack growth. 
The  adopted  approach  was  properly  calibrated  on  six  European  case  studies  representative  of  actual 
fatigue  open  problems,  i.e.  local  vibration  and  distortion  induced  effects.  Such  bridges,  including 
riveted  and  bolted  joints  for  the  connections  and  simply  supported  or  continuous  solutions  for  the 
restraining  conditions,  constituted  the  main core of the Project and were adopted as reference for all 
research activities. The bridges selected as case studies for the Project were: i) Railway viaduct on Po 
river (Italy); ii) Panaro bridge (Italy); iii) The Trezói Bridge (Portugal); iv) The Alcácer do Sal Bridge 
(Portugal); v) Saalebrücke Großheringen railway bridge (Germany); vi) Salzach River bridge (Austria) 

Figure III - Railway viaduct on Po river (Italy) 

6

 
 
 
 
 
Figure IV - Panaro bridge (Italy) 

Figure V - The Trezói Bridge (Portugal) 

Figure VI - The Alcácer do Sal Bridge (Portugal) 

Figure VII - Saalebrücke Großheringen railway bridge (Germany) 

Figure VIII - Salzach River bridge (Austria) 

7

 
 
 
 
 
 
 
 
 
 
 
 
 
The selected case studies were analyzed by means of the experimental/numerical analysis constituting 
the  innovative  and  reliable  approach  for  the  assessment  of  vibration/distortion  induced  fatigue  into 
steel bridges. Such analysis involved the following scientific/technical areas: 

•  “In field” vibration tests: by means of such tests, it is possible to obtain a reliable assessment of 
global/local vibration modes and to identify the dynamic properties necessary for the updating 
of  numerical  models.  In  particular,  the  proper  identification  of  local  modes  is  essential  for  a 
correct evaluation of vibration induced fatigue effects; 

• 

 “In field” strain tests under train passage: strain test permits a direct evaluation of actual stress 
distribution  and  intensity  into  critical  details,  thus  permitting  to  recognize  the  distortion 
mechanisms that generate the secondary stresses that influence the fatigue performances; 

•  Analytical  and  numerical  analysis:  the  development  mainly  of  numerical  models  able  to 
reproduce correctly experimental global/local dynamic behaviours and distortional phenomena 
is essential for the identification of those keypoints that will permit the proper modelling also 
of details not investigated or new structure; 

•  Laboratory  tests:  the  experimental  evaluation  of  fatigue  phenomena  in  critical  details  taking 
into account also of secondary stresses is fundamental for the estimation of actual fatigue per-
formances, as secondary stresses are generally neglected in design analysis and, consequently, 
not considered neither in laboratory tests; 

8

 
 
 
 
 
 
 
 
 
•  Assessment  of  actual  traffic:  the  estimation  of  the  real  train  spectra  by  means  of  long-term 
monitoring systems represents an important issue in fatigue assessment as it provides the nec-
essary  base  for  the  correct  calculation  of  load  cycle  acting  during  the  entire  life-cycle  of  the 
bridge. 

The  experimental/numerical  analysis,  that  constitute  the  core  of  the  proposed  methodology,  were 
interconnected to create five macro-activities aimed at analyzing extensively all those technical aspects 
that influence the fatigue performance of railway steel bridges: i) Global Analysis of Bridge, aimed at 
the investigation of actual bridge structural performance under train passage, including the assessment 
of internal forces induced by train into the critical details most subjected to vibration/distortion effects; 
ii) Local analysis of critical details, focused on the estimation of actual local stress distribution taking 
into account also of vibration/distortion effects; iii) Monitoring of Service Conditions, which objective 
was the estimation of stress spectra induced by actual traffic into critical details and of traffic spectra 
on  the  line;  iv)  Laboratory  Tests  for  the  fatigue  classification  of  critical  details  subjected  to  the  real 
stress patterns induced by vibration and distortion; v) Advanced Fatigue Assessment: for the calculation 
of  fatigue  damages  or  remaining  fatigue  life  of  critical  details  by  damage  accumulation  methods  or 
fracture mechanics approaches. The proposed methodology was successfully applied to the case studies 
and,  although  requiring  the  execution  of  experimental  and  numerical  non-standard  analysis  and  an 
additional effort with regard to current design practice, showed to be a reliable tool for the assessment 
of vibration/distortion induced fatigue. 
Main  objective  of  Fadless  research  project  was  to  clarify  the  uncertainties  concerning  vibra-
tion/distortion  induced  fatigue  into  railway  steel  bridges.  In  particular, the most important aspects of 
interest  were  the  dynamic  behaviour,  the  influence  of  train-bridge  interaction  phenomena,  the  local 
vibration/distortion effects, the actual stress patterns into critical details, the real composition of traffic 
spectra, the influence of secondary stresses on the fatigue resistance of components. 
In  the  framework  of  the  Project,  for  each  step  of  proposed  approach,  suitable  procedures  were 
developed  and  properly  calibrated  on  case  studies,  obtaining  important  information  on  the  structural 
performance  of  railway  bridges.  Results  permitted  also  to  elaborate  final  guidelines  for  the  proper 
performing  of  proposed  Methodology  and,  more  in  general,  for  a  reliable  structural  assessment  of 
railway steel bridges. 

9

 
 
 
 
1  Introduction 

Fatigue is a very important failure mode for steel structures. In fact about 80/90% of failures in steel 
structures  are  related  to  fracture  and  fatigue.  In  particular,  railway  bridges  endure  million  of  stress 
cycles during their life and they are expected to be highly vulnerable to such phenomena. 
Several studies were performed in the past in order to assess the fatigue resistance of steel and steel-
concrete composite bridges; such studies were the base of modern codes and standards [1.1; 1.2; 1.3; 
1.4]. Despite of these efforts, the fatigue assessment of railway bridges both considering the design of 
new bridges and the assessment of existing ones is one of the main issues in current practice. 
Such  eventuality  is  due  to  concurrent  events  as  for  example  the  rapid  development  of  the  European 
railway  networks  according  to  the  directives  of  the  European  Commission  [1.5]  the  increase  of 
passenger and freight railway traffic, the introduction of new high strength materials, the influence of 
particular  effects  like  distortion  and  local  vibration  not  actually  covered  by  in  fatigue  assessment 
procedures proposed by current codes and standards. 
The increase of circulation speed, the change of the vehicles geometry and masses and the increase of 
loads  that  were  observed  led  to  a  concern  in  the  understanding  of  dynamic  phenomena  and  in  their 
quantification,  thus  leading  to  the  improvement  of  safety  checking  procedures  in  structural  codes.  In 
particular,  the  evaluation  of  effective  capability  of  existing  bridges  to  guarantee  the necessary safety 
level  under  actual  traffic  conditions requires the improvement of available design procedures. Figure 
1.1  shows  a  general  framework  [1.6]  to  be  adopted  for  the  fatigue  assessment  of  existing  steel 
structures. Such an approach suggests the use of three different levels of assessment methodologies: 

•  Simplified  methods:  preliminary  evaluation  should  be  conducted  by  using  current  codes  and 
recommendations and making conservative assumptions when information is lacking or doubt-
ful; simplified models are adopted for the structures and their details; 

•  Enhanced methods: a detailed investigation should be performed, adopting a refined represen-
tation  of  the  structure  and  of  the  loads/actions;  anyway  input  data  for  model  analysis can be 
adopted from current codes; 

•  Advanced  methods:  advanced  evaluation  should  be  carried  out  to  analyze,  by  means  of  both 
numerical and experimental tools, the effective remaining fatigue life of all relevant details. 

The  application  of  different  evaluation  methodologies  requires  an  increasing  level  of  knowledge  and 
information  concerning  the  behaviour  of  structural  components  and  details.  In  particular  the  use  of 
advanced methodologies is actually limited to specialized laboratories and scientific research groups. 

Figure 1.1 - Fatigue assessment procedure for existing steel bridges [1.6]. 

11

 
 
 
 
Such  an  approach  is  mainly  due  to  the  fact  that,  traditionally,  it  was  assumed  that  the  need  for  the 
application of advanced analysis methodologies in design of steel and steel-concrete composite bridges 
can be limited adopting proper detailing that remove the secondary stresses. 
Such objectives were reached introducing an high number of global and local stiffeners, necessary to 
guarantee  the  verifications  of  static  requirements  against  instability  as  well.  On  the  contrary,  several 
fatigue problems affected and still affect steel bridges due to several reasons. 
Previous  experience  shows  that  most  cracks  found  in  bridges  were  caused  by  distortion  of  member 
cross  sections  and  out-of-plane deformation of webs that induced localized bending stresses [1.7]. In 
older  bridges,  transverse  stiffeners  and  attachment  plates  were  not  welded  to  the  tension  flange  of 
welded  I-girders  and  box  girders  for  fear  that  a  fatigue  crack  initiating in the flange would lead to a 
brittle  fracture.  This  well-intended  but  outdated  practice  originated  in  Europe  in  the  1930’s  from 
unexpected brittle fracture in the oldest welded bridges, and it was at first attributed to welding details, 
but it was primarily due to the poor quality of steel. 
This  practice  has  been  the  main  cause  of  distortion-induced  cracking,  which  can  sometime  be 
prevented by welding stiffeners to the web and to the flanges. Figure 1.2 shows a crack which formed 
along  the  fillet  weld  attaching  a  diaphragm  connection  plate  to  the  web  of  a  plate  girder  [1.7].  The 
fatigue cracking in these gaps typically occurs in a longitudinal direction along the fillet weld toe of the 
longitudinal  web-to-flange  joint, at the termination of the vertical fillet weld, or at both locations, as 
shown in Figure 1.3 [1.8]. 

Figure 1.2 - Examples of distortion induced fatigue crack progression [1.8]. 

a) 

b) 

Figure 1.3 - Web gap distortion: a) scheme of the effects; b) example in real bridge [1.8]. 

In  many  cases,  the  displacement  causing  this  distortion  is  limited  and  the  cracking  arrests  as  the 
compliance  of  the  gap  increases  and  the  stresses  are  reduced.  Because  most  of  the  cracks  are 
longitudinally oriented, there is typically no reason to be concerned about fracture of the girder unless 
the cracks turn downward and propagate across the web. It is typically a mistake to try to weld repair 
such cracks, as this restores the high stresses which originally caused the cracking and will certainly 
restart the cracking at the weld repair [1.8]. 

12

 
 
 
 
 
Besides,  distortion  and  vibration  induced  fatigue  phenomena,  typically  due  to  low  local  stiffness 
distribution  in  correspondence  of  critical  details,  can  affect  steel  and  composite  bridges.  Such 
phenomenon allows the presence of local vibration modes characterized by low frequencies (0-30 Hz) 
typically  excited  during  train  passages  which  could  produce  high  local  “modal”  stresses  causing 
relevant fatigue damages and reducing the remaining fatigue life. 
As previously stated, distortion induced or vibration induced fatigue cracking in the web gaps may be 
solved  by  a  proper  detailing  which  eliminates  the  secondary  stresses  causing  these  cracks.  In  most 
cases, the web-gap-cracking can be prevented by rigidly connecting the attachment plates to the tension 
flange. Where the distortion is displacement controlled, the stresses can be reduced by increasing the 
flexibility of the connection. If distortion is limited, holes may be drilled or cored at the crack tips to 
temporarily arrest propagation [1.8]. 
Modern design methodologies for steel and steel-concrete composite bridges adopt new materials with 
very high performances allowing for very slender structures. Such solutions, characterized by improved 
performance against static loadings, revealed to be exposed to vehicle-bridge interaction effects which 
influence fatigue behaviour. 
High  structural  slenderness  implies  that  non-structural  elements,  such  as  ballast,  retaining  walls  and 
tracks,  can  affect  bridges  dynamic  behaviour  caused  by  train  passage.  Moreover,  the  high  local 
slenderness  caused  by  the  reduction  of  plate  thickness  and  stiffeners  number,  can  increase  the 
possibility  of  obtaining  local  vibration  modes  characterized  by  low  frequencies.  As  a  consequence, 
such  local  modes  can  increase  the  possibility  of  observing  “vibration  induced”  fatigue  damage 
phenomena.  Moreover,  the  use  of  High  Performance  Steel  does  not  modify  the  results  of  fatigue 
verifications  since  fatigue  behaviour  does  not  depend  on  mechanical  or  dynamical  properties  of 
materials.  By  the  way,  actual  codes  and  regulations  appear  inadequate  to  provide  effective  tools  in 
order to obtain thorough information about such phenomena. 

1.1  Analysis of traffic flows 

By 2020, new Trans-European Transport Network (TEN-T Project) will include 94 000 km of railways, 
including  around  20  000  km  of  high-speed  rail  lines  suitable  for  speeds  of  at  least  200  km/h. 
Completing the network by 2020 involves the construction of the so-called ‘missing links’ which will 
increase  the  existing  rail  by  12  500  km.  In  addition,  12  300  km  of  rail  lines  will  be  substantially 
upgraded [1.5]. 
Completing the networks will have a huge impact in reducing journey time for passengers and goods. 
For  interregional  traffic  alone  the  benefits  are  estimated  to  be  almost  EUR  8  billion  per  year.  In 
addition, freight transport in the EU is expected to increase by more than two thirds between 2000 and 
2020, and to double in the new Member States. Freight transport between Member States is expected to 
show  the  largest  increase  overall.  Without  TEN-T  this  increase  in  transport  would  be  impossible  to 
handle, and our rate of economic growth significantly slowed. 
An  important  aspect  in  design  of  new  lines  or  in  the  evaluation  of  upgrading  operations  is  the 
convenience that the railway lines will not be restricted to their use by a limited family of trains. On the 
contrary, they should allow the transit of all vehicle typologies (both traditional, high speed and freight 
trains),  enabling  interoperability  of  the  infrastructure  by  all  possible  trains.  This  issue  is  not  only 
essential  from  a  social  and  economical  point  of  view,  but  has  also  other  implications,  such  as  to 
separate the business of the infrastructure from that of the transport operators, as suggested by the new 
European  directive  [1.9].  The  possible  presence  of  new  train  typologies,  characterized  by  several 
layouts  of  weights  and  axels  distributions,  introduces  new uncertainties on the expected traffic loads 
and  the  consequent  loading  spectra  to  be  adopted  in  fatigue  verification.  As  a  consequence,  new 
operating  conditions  of  European  Railway  Networks  require  the  assessment  of  adequacy  and 
effectiveness of actual loading spectra provided by design codes and regulations for fatigue verification 
purposes. Such spectra, derived from previous studies performed on old railway lines, could lead to an 
underestimation of actual railway traffic effects. 
The knowledge of past and current load spectra, together with predicted future loads, is essential in the 
evaluation  and  fatigue  analysis  of  existing  bridges.  In  particular,  the  information  concerning  actual 
loads is very important during rating operations according to the procedures adopted by main Railway 
Administrators. Therefore, there is a need for accurate and inexpensive methods to determine the actual 

13

 
 
loads, the strength of the bridge, and its remaining life. There is also a need for verification of live load 
used for the development of a new generation of bridge design codes. 

1.2  Historical development of traffic and design codes 

The  frequent  changing  of  train  typologies,  axel  loads  and  operating  speeds  required,  and  goes  on 
requiring, a continuous upgrading of load models, in order to represent properly actual train dynamic 
loads and effects on bridges.  
This  development  occurred  also  in  Italy  where  the  very  first  load  models,  prior  to  the  unification  of 
regional railways, were the “IV” and “V” category (Figure 1.4). These load models were adopted by 
the “Società Strade Ferrate del Mediterraneo” for the design of steel bridges in all the country. 

Figure 1.4 - Load model “IV” and “V” category. Load values are kg. 

After  the  creation  on  the  national  railway  authority  “Ferrovie  dello  Stato”,  the  first  design  code  was 
issued in 1916 and contained the following technical innovations: 

•  Railway  lines  were  subdivided  in  category  “A”,  principal  lines  with  heaviest  vehicles,  and  

category “B”, normal lines not included in category “A” and narrow-gauge lines. 

•  A new load model, “Treno normale”, heavier than “IV” and “V” category models (Figure 1.5) 
•  Bridges of line “A” had to be calculated adopting the “Treno normale” load model, while for 
lines  or  subparts  of  particular  importance  and  strongly  leaning  the  1916P  heavy train model  
had to be considered. 

•  Bridges  of  lines  “B”:  the  design  load  model  was  a  particular  train  fully  composed  of  the 

heaviest locomotives operating on the line. 

•  Sleepers,  transverse  beam  and  short  span  girders  could  be  designed  adopting  the  heavier 
between two alternative load models: i) three 18 ton axes at a distance equal to 1.5 mt; ii) a 
single 21 ton axe. 

• 

• 

In the code, the unitary strength resistance of materials were reported, with different values for 
bridge principal elements and bracings. 

It is worth noting that the limit strength resistances varied with regard to element length, with 
higher values at increasing length. 

Figure 1.5 - “Treno normale” load model (1916). 

14

 
 
 
 
In  1925,  a  design  code  specific  for  design  of  new  steel  structures,  containing  new  load  models,  was 
issued (Figure 1.6). In this code, lines were classified as normal and mountain lines (“linee di valico”). 
Different load models had to be adopted with regard to the line category: 1925N or 1916P load model 
for normal line and 1925S load model for mountain lines. Moreover, the single axis load modal value 
was increased from 21 ton up to 25 ton. At least, limit strength resistances of materials were slightly 
reduced of about 10% with respect to 1916 design code. 

Figure 1.6 - Load models of 1925 Italian design code 

A new design code for steel railway bridges was issued in 1945 and introduced two load model, type 
“A”  and  “B”  (Figure  1.7),  and  thus  confirming  the  subdivision  of  traffic  intensity  in  two  main 
categories,  “A”  and  “B”.  Also  in  this  code,  for  deck  secondary  elements  it  was  possible  to  adopt 
alternative  load  models  composed  by  a  single  axis  load  which  value  was  equal  to  30  ton  for  “A” 
category lines, and to 25 ton for “B” category lines. Main innovation of this code was the introduction 
for the first time of a dynamic amplification factor for moving loads, expressed as function of design 
velocity and theoretical length of structural elements. 

Figure 1.7 - Load model type “A” and “B” of 1945 Italian design code. 

The last design code issued by the Italian railway authority, is the 1995 "Sovraccarichi per il calcolo 
dei ponti ferroviari. Istruzioni per la progettazione, esecuzione e collaudo". In the code two different 
load models were introduced, the LM71 load model for normal railway traffic and the SW load model 
for  heavy  traffic  (Figure  1.8),  substituting  the  previous  design  code  models  and  acknowledging 
Eurocodes rules. With respect to previous codes, main innovations were constitutes by the typology of 
load modelling, not only composed by axis loads but also by distributed loads, and in the evaluation of 
dynamic amplification factors, expressed as function of element length and line maintenance level. 

15

 
 
 
 
Figure 1.8 - Load models of 1995 Italian design code. 

In Figure 1.9 a comparison between the bending effects of all aforementioned load models as function 
of  element  length  “luce”  is  reported.  In  particular,  the  values  of  the  “equivalent”  uniform  load 
producing the same maximum bending moment induced by load models are reported on ordinate axis.  

Figure 1.9 - “Equivalent” uniform loads according to load model and element length 

1.3  Standard methodology for the assessment of structural safety 

In  Europe,  National  Railway  Authorities  developed  independent  standards  for  the  assessment of the 
structural  safety  of  existing  railway  bridge,  based  on  their  own  experiences  of  infrastructure  design, 
repair and maintenance. 
In  Germany  the  Deutsche  Bahn  has  developed  the  guideline  DB  Ri  805  “Tragsicherheit  bestehender 
Eisenbahnbrücken” [1.10]. Approaches for the numerical proofs for existing steel railway bridges are 
described  in  module  805.0201  “Nachrechnen  von  Eisenbahnbrücken;  Stählerne  Eisenbahnbrücken”. 
The concept of this guideline includes four stages of assessment which have to be applied depending 
on  the  specific  situation.  Generally  the  concept  suggests  the  application  of  increasingly  complex 
investigations in stages if the structural safety cannot be proven by applying the respective concept at a 
certain stage. The most complex stage 4 includes also experimental investigations. An overview of this 
concept is given in Figure 1.10. 

16

 
 
 
 
Figure 1.10 - Scheme for the assessment of existing steel railway bridges according to the DB Richtlinie 805 
[1.10] 

1.4  References 

[1.1] EN 1993-1-9, 2002. Eurocode 3: Design of steel structures - Part 1.9: Fatigue strenght of steel 
structures. CEN European Committee for Standarsization. 

[1.2]  AREMA,  2005.  Manual  of  railway  engineering.  Washington  D.C:  American  Railway 
Engineering and 
Maintenance of Way Association (AREMA). 

[1.3] Ferrovie dello Stato, 1992. Istruzione n. 44f del 30.01.1992: Verifiche a fatica dei ponti ferroviari 
metallici. Ente Ferrovie dello Stato. 

[1.4]  Ferrovie  dello  Stato,  1997.  Istruzione  n.  I/SC/PS-OM/2298  del  2.6.1995  “Sovraccarichi  per  il 
calcolo  dei  ponti  ferroviari  -  Istruzioni  per  la  progettazione,  l’esecuzione  ed  il  collaudo”.  Ente 
Ferrovie dello Stato. 

[1.5]  European  Commission,  Energy  and  Transport  DG,  2005.  TEN-T  Trans-European  Transport 
Network: 
priority axes and projects 2005. Technical report, European Commission. (ec.europa.eu). 

[1.6] Goicolea, J., 2004. Dynamic loads in new engineering codes for railway bridges in Europe and 
Spain. In Bridges for High-Speed Railways, June 3-4; Porto. 

[1.7] Kühn, B., Lukić, M., Nussbaumer, A., Günter, H.P., Helmerich, R., Herion, S., Kolstein, M.H.,  
Walbridge, S., Androic, B., Dijkstra, O., Bucak., 2008. Assessment of Existing Steel Structures: 
Recommendations for Estimation of Remaining Fatigue Life. Report EUR 23252 EN - 2008, European 
Community. 

[1.8] Fisher, J.W., 1984. Fatigue and fracture in steel bridges: case studies. John Wiley. 

[1.9]  Fisher,  J.W.  and  Roy,  S.,  2008.  Fatigue  of  steel  infrastructure.  Proc.  of  Bridge  Maintenance, 
Safety  Management,  Health  Monitoring  and  Informatics  IABMAS08  Conference,  July  13  17  2008, 
Seoul. Korea. 

[1.10] DB Richtlinie 805: Nachrechnung bestehender Bauwerke, 2002. 

17

 
 
 
 
 
 
 
 
 
 
 
 
2  Fatigue behaviour of steel bridges  

As previously stated, fatigue performance of railway steel bridges is one of the main issue in design of 
new structures and in the assessment of existing ones. This problem is particularly complex due to the 
many uncertainties concerning the real effects of both passenger and freight traffic, and the real fatigue 
performances  of  steel  structure.  As  fatigue  damages  start  always  at  a  local  level,  the  knowledge  of 
actual fatigue resistance of details is thus fundamental for an effective assessment of such phenomena. 
The correct evaluation of loads induced by trains on bridge components together with a proper analysis 
of local details will conduct to an correct assessment of remaining fatigue life of existing structures and 
to a reliable design of new bridges. 

2.1  Analysis and classification of fatigue damages 

In general, fatigue cracks in railway steel and composite bridges may occur due to: 

•  Welding defects; 
•  Adoption of structural details with low fatigue strength; 
•  Corrosive environment; 
•  Unforeseen  stresses  and  deformations  at  joints  of  structural  members,  due  for  example  to 

secondary moments or out of plane displacements – distortion induced fatigue; 

•  Excessive vibration due, for example, to high speed railway traffic – vibration induced fatigue. 

Examples of fatigue cracks due to welding defects are the cracks at butt welded joints in the tensioned 
flange of plate girders (Figure 2.1). 
The adoption of structural details with low fatigue strength could occur in the case of old bridges not 
designed against fatigue and subjected to conditions where fatigue would occur. This is also the case of 
bridges designed according to allowable stresses that were subsequently found to be inappropriate. As 
an example, Figure 2.2 represents some details that have been re-classified in the Japanese standards, 
from the 60’s to the 90’s codes. 
It’s  also  well  known  that  corrosive  environments  increase  fatigue  damage,  because  of  cross-sections 
reduction but also because pitting corrosion plays the role of fatigue crack initiation.  

Figure 2.1 – Fatigue crack at the bottom flange of a 
plate girder 

Figure 2.2 – Examples of re-classified details 

2.2  Distortion induced fatigue 

Distortion induced fatigue and/or other unforeseen sources of stresses can frequently be found in the 
main girder to cross girder connections (Figure 2.3), on cut-out webs and on vertical stiffeners to flange 
connections  (Figure  2.4). The secondary moments and stresses arising from the connection geometry 
are  usually  not  taken  into  account  in  the  numerical  models  and  that  may  justify  the  huge  number  of 
observed  failures  caused  by  these  phenomena.  This  problem  is  also  common  in  box  girders 
diaphragms, arising for in-plane shear deformation of the diaphragms plates. 

19

 
 
 
 
a) 

b) 

Figure 2.3 – Distortion induced fatigue cracks in the 
main girder to cross girder connection 

Figure 2.4 – a) Typical Out-of-Plane Web Distortion 
Mode Concentrated in Web Gap [1.1]; b) Schematic of 
Web Crack at End of Transverse Stiffner [1.2] 

Distortion  induced  fatigue  is  also  a  well-known  problem  of  highway  bridges.  As  example,  the 
Minnesota Department of Transportation made a study of distortion-induced fatigue in a steel bridge 
located in Brooklyn Centre, Minnesota [1.3]. The case study is a typical three-span composite multi-
girder steel bridge on skew supports, susceptible to web-gap distortion (Figure 2.5). An experimental 
monitoring  program  for  the  assessment  of  the  frequency  and  magnitude  of  the  distortional  fatigue 
stresses at the web-stiffener connections and the evaluation of the impact of these stresses on fatigue 
life was implemented by infield instrumentations. A typical structural detail of a connection between 
the  transverse  stiffener  and  a  girder  tension  flange  is  reported  in  Figure  2.6.  The  out-of-plane 
deformation and rotation in the web-gap occur at stiffener ends due to the differential deformation of 
adjacent  girders.  This  rotation  of  the  diaphragm  ends  impose  large  deformations  on  the  web-gap 
leading to longitudinal cracks in the web. 

Figure 2.5 – Global view of the bridge [1.3] 

Figure 2.6 – Differential deflection of girders [1.3] 

This type of bridges will experience larger differential deflections between girders since the distance 
from applied load to the nearest support varies from girder to girder, in this context it is expected that 
skewed bridges may be more vulnerable to distortional fatigue [1.2]. 
Also,  a  finite  element  model  was  developed  to  calculate  web-gap  distortion  and  to  compare  to  the 
measured stresses on site (Figure 2.7). 
The conclusions obtained by this analysis were also confirmed by tests on two other bridges, performed 
in order to obtain information for a faster analysis of distortion induced phenomena. The first one was 
the  7th  St.  Bridge  in  St.  Paul,  Minnesota  (Figure  2.8  a)).  A  detailed  view  of  a  strain  gauge  used  to 
measure local stresses induced by out of plane bending at the connection between the stiffeners and the 
girder web can be observed in Figure 2.8 b)[1.3]. The second bridge was the Plymouth Avenue Bridge 

20

 
 
 
 
 
 
 
in  Minneapolis,  Minnesota  (Figure  2.9),  a  five-span  bridge  with  45,5º  angle  of  skew  and  X-braced 
diaphragms. 
Obtained  results  permitted  a  better  comprehension  of  the  distortional  stress  mechanism  and  the 
distortion induced fatigue in multi-girder steel bridges. 

Figure 2.7 – Local finite element model: a) global view; b) detail view of the web-stiffener connections [1.3] 

Figure 2.8 – 7th St. Bridge in St. Paul Minnesota: a) global view; b) structural detail at connection between 
stiffener and web. [1.3] 

b) 

b) 

a) 

a) 

Figure 2.9 – Plymouth Avenue Bridge in Minneapolis: a) global view; b) bottom view of the deck [1.3]. 

Distortion-induced  fatigue  cracks  were also observed during several inspection cycles of two Kansas 
highway bridges over the Little Arkansas River in Hutchinson and over the Tuttle Creek Reservoir in 
Riley [1.4].  
Constructed  in  1955,  the  Little  Arkansas  River  Bridge  is  a  17  span  steel  floor,  beam  and-stringer 
structure. As shown in Figure 2.10 a), a fatigue cracking was found in the connecting plates between 
the  stringers  and  floor  beams. In Figure 2.10 b), the retrofit scheme proposed by the authors for this 
case  is  reported.  Arkansas  River  Bridge  repairs  focused  on  reducing  restraint  in  the  damaged 
connections, after the analyses found out that additional restraint would have concentrated forces at the 
horizontal welds and exacerbated the bridge’s problems. 
The Tuttle Creek Bridge, constructed in 1962, is a 38 span structure with two girders. Typical cracking 
patterns found in the Tuttle Creek Bridge are reported in Figure 2.11. In the Tuttle Creek Bridge, steel 
angles were adopted to connect the stiffeners to the top flange of the girder, as shown in Figure 2.11. 
Threaded studs were welded to the bottom of the girder’s top flange. Steel angles were also welded to 
each side of the connection stiffener. 
Through ribs and transverse beams of orthotropic decks are also subjected to distortion phenomena, as 
illustrated in Figure 2.12 

21

 
 
 
 
 
 
 
 
Figure 2.10 – Little Arkansas River Bridge: a) damage floor 
beam to stringer connection; b) repair performed [1.4]. 

Figure 2.11 – Repair and retrofit for Tuttle Creek 
Bridge [1.4]. 

Figure 2.12 – Vibration induced fatigue cracks in orthotropic decks 

2.3  Vibration induced fatigue 

Vibration induced fatigue can occur due to intense dynamic loads such as high speed railway traffic or 
wind. Three main reasons play an important and cumulative role in the vibration induced fatigue: 

•  The dynamic response, that can lead to a high number of stress cycles; 
•  The  amplitude  of  dynamic  stress  cycles,  that  can  be  significantly  higher  than  in  the  case  of 

static loading, specially at resonance; 

•  Local vibration modes, which may have an unforeseen amplification leading to extra fatigue 

damage both in main and secondary structural elements. 

Typical  examples  of  bridge  components  subjected  to  vibration  induced  fatigue  problems  are  the 
tensioned  hangers  in  bowstring  railway  bridges  and  the  plates  of  orthotropic  decks  at  a  local  level 
(Figure 2.12). Vibration fatigue damages can also occur on hangers of relatively new arch bridge with 
truss girder, due to excessive vibrations induced by wind [1.5]. 
As example, vibration and distortion damages occurred on the Patroon Island Bridge, located in Albany 
- New York over the Hudson River [1.6] (Figure 2.13). This bridge has ten spans seven of which are 
considered as main spans and composed of steel trusses and concrete decks, while the other approach 
spans are composed of plate girders. In this case, the remaining fatigue life was estimated using strain 
measurements located in the most critical elements with respect to fatigue phenomena (Figure 2.14). 
Many experimental analysis revealed the presence of vibration fatigue problems on existing structures 
(arch  bridges,  plate  girders,  riveted  bridges),  frequently  unforeseen  due  to  errors  in  the  numerical 
models  or  to  the  structural  interaction  of  secondary  components  generally  not  considered  in  the 
analysis  (as  ballast  and  rails)  or,  more  in  general,  to  the  presence  of  distortion/vibration  phenomena 
generally neglected [1.7, 1.8, 1.9, 1.10, 1.11 and 1.12]. 

22

 
 
 
 
 
a) 

a) 

Figure 2.13 – Patroon Island Bridge: a) Overall view of the bridge, b) Structural detail. 

b) 

b) 

Figure 2.14 – Patroon Island Bridge, cracks in the structural elements: a) Crack in the upper portion of the floor 
beam; b) Crack in bearing sole plate. 

2.4  Fatigue damages in riveted steel bridges 

Existing  riveted  steel  bridges  currently  represent  the  oldest  structures  exposed  to  fatigue  phenomena 
among railway lines. Although less subjected to fatigue problems than welded solutions, they generally 
were  designed  without  the  adoption  of  rules  especially  dedicated  to  the  fatigue  resistance  of  details 
and, nevertheless, exposed to a very high number of load cycles during their long life-cycle.  
For this reasons, many old steel bridges currently on service require a continuous monitoring to avoid 
or eliminate fatigue cracks as those reported in Figures 2.15 to 2.19, occurred in old steel components 
of Italian bridges and, in most cases, repaired or substituted. 

Figure 2.15 - fatigue crack in the external component of a built-up truss 

23

 
 
 
 
 
 
 
  
 
 
  
 
Figure 2.16 - Fatigue cracks in the cover plates of deck joints 

Figure 2.17 - Fatigue cracks in the web of an upper 
transverse built-up beam  

Figure 2.18 - Fatigue cracks in the web-flange girder 
welding and on built-up flange longitudinal weldings. 

Figure 2.19 - Fatigue cracks in built-up trusses  

24

 
 
 
 
 
 
 
 
 
 
The need of keeping on-service the oldest steel bridges induced also a constant research attention on 
the  riveted  solutions  aimed  at  an  even  better  comprehension  of  their  fatigue  performance  and, 
consequently, at an optimization of maintenance and repairs. 
This attention conducted to a recent re-classification of riveted structural details by Taras and Greiner, 
in  order  to  clarify  the  actual  fatigue  resistance  of  riveted  members  [1.13].  In  this  research,  authors 
analyzed  many  experimental  results  to  create  a  database  of  fatigue  resistance  with  respect  to  detail 
type,  rivet  bearing  pressure,  stress  ratio  R,  crack  position,  used  material  and  year  of  fabrication, 
potential  pre-damage  of  the  member.  Fatigue  classes,  obtained  for  different  values  of  R,  were 
normalized to the equivalent zero stress ratio resistance and elaborated by a proper statistical approach, 
taking  into  account  also  of  run-out  tests,  i.e.  tests  interrupted  before  developing  any  crack.  Results 
permitted  to  obtain the new riveted details classification (an example is reported in Figure 2.20) and 
were also introduced in the new Austrian ONR 24008 specification. 

Figure 2.20- An example of a riveted joint fatigue class [1.13]. 

2.5  European standard for fatigue assessment 

The development of fatigue damages in railway bridge is the result of a high number of micro-damages 
induced by each single train passage on the structure along the entire life-cycle of the bridge. The entity 
of  the  final  damage  depends  on  the  composition  of  traffic  that  passed  on  the  bridge  (i.e.  the  traffic 
spectra) and on the fatigue resistance of each local detail. 
In  the  European  reference  for  the  design  of  railway  steel  bridge  (Eurocode),  the  traffic  spectra  is 
classified  as  "standard",  "heavy”  or  “light”  traffic  mixes,  depending  on  whether  the  structure  carries 
predominantly  mixed,  heavy  freight  or  lightweight  passenger  traffic  [1.14].  Such  traffic  mixes  are 
composed  of  different  combinations  of  12  fatigue  trains  as  reported  in  the  tables  of  Figure  2.21. 
Example  of  the  fatigue  trains  are  reported  in  Figure  2.22.  Moreover,  where  the  traffic  mix  does  not 
represent the real traffic an alternative traffic mix should be specified, for example a Real Trains' mix. 

Figure 2.21 – Standard, Heavy and Light Traffic mixes [1.14] 

25

 
 
 
 
 
Figure 2.22 – Train types 1 and 2 for fatigue assessment [1.14] 

L or Dt

r)  vs.  log(N) 
r)  vs.  log(N)  diagrams  for  shear  stresses.  Such  curves  are 

Fatigue  resistances  of  local  details  are  expressed  by  the  S-N  curves,  i.e.  the  log(Ds
diagrams  for  direct  stresses  and  the  log(Dt
reported in terms of characteristic values. 
Direct stress curves are characterized by 3 different levels of stress ranges: i) Ds
d (constant amplitude 
fatigue limit); ii) Ds
L (cut-off limit); iii) Ds
c (reference fatigue strength for two millions 
of  cycles).  Fourteen  direct  stress  S-N  curves  are  defined,  corresponding  to  fourteen  detail  categories 
(Figure  2.23).  Each  curve  is  defined  by  the  fatigue  strength  at  N = 2 million  cycles,  Ds
c,  which  also 
represents the corresponding detail category number (Figure 2.25). 
There  are  only  two  S-N  curves  for  shear  stress  ranges  Dt
branch with 1/5 slope and by a cut-off limit Dt
The  S-N  curve  design  values  are  obtained  by  dividing  the  corresponding  characteristic  values  by  a 
partial safety factor g Mf, which value depends on the selected assessment method, “Damage tolerant” or 
“Safe  Life”,  and  on  the  consequences  of  each  detail  failure,  "Low  consequence"  or  "High  conse-
quence", as reported in Figure 2.26 

L defined at 100 million cycles (Figure 2.24). 

i  both  characterized  by  one  single  linear 

c or Dt

Figure 2.23 - Direct stress S-N curves for structural steel 
components [1.15] 

Figure 2.24 - Shear stress S-N curves for structural 
steel components [1.15] 

26

 
 
 
 
 
 
Figure 2.25 - Generic preview of Table 8.5 [1.15] 

Figure 2.26 - Partial factor for fatigue strength, 

[1.15] 

After identifying the traffic spectra acting on the bridge and the fatigue resistance of the selected detail, 
it  is  possible  to  obtain  the  fatigue  strength  verification  by  the  Damage  Accumulation  Criteria, 
consisting on the verification of the following condition: 

=

D

n
∑ £
i
N

i

1

where: 

(2.1) 

•  D is the total damage on the detail in the entire life-cycle of the structure; 

•  ni is the expected number of stress cycles with an amplitude equal to Ds

i due to train passages: 
ni  should  be  calculated  for  the  whole  design  life  of  the  structure  and  considering  actual  and 
future traffic evolution; 

•  Ni is the fatigue resistance for a Ds

i stress range. 

The application procedure of damage accumulation methodology is composed by the following steps, 
also illustrated in Figure 2.27: 

•  a) Determination of loading events, after traffic characterization; 

•  b) Determination of stress history at the detail; 

•  c)  Cycle  counting  by  either  of  the  following  cycle  counting  methods:  rainflow  method  and 

reservoir method; 

•  d) Determination of stress range spectrum; 

• 

f) Identification of the adequate S-N curve 

•  e) Damage evaluation by the application of Palmgren-Miner rule.  

In  some  particular  cases,  when  traffic  mixes  apply  and  when  no  dynamic  analysis  needs  to  be 
performed  ,it  is  also  possible  to  adopt  the  Damage  Equivalent  Stress  Criteria,  which  consists  of  the 
verification of the following conditions: 

27

 
 
 
 
   
g

Ff

s

E

2

g

Ff

t

E

2

s

C

g

Mf

t

C

Mf

g

(2.2) 

(2.3) 

g

Ff
s

1=
 is the partial factor for fatigue loads; 
(cid:215)=
t
l

t
2
E
to N = 2 ×106 cycles, for direct and shear stress respectively; 

 and 

(cid:215)=

s

l

71

71

E

2

 are the damage equivalent stress ranges related 

and 

where: 
• 
• 

o 

o 

 is the damage equivalence factor; 

71 or D

71 are the maximum stress ranges obtained, positioning load model LM71 in 

the most unfavourable points of the track, for direct and shear stress respectively.  

The damage equivalence factor l
follows: 

 for railway bridges with a span up to 100 m, should be determined as 

l

=

l

1

l

2

l

3

l

4

4.1

(2.4) 

where: 
• 
• 
• 
• 

l 1 is the factor for the damage effect of traffic and depends on the length of the influence line; 
l 2 is the factor for the traffic volume; 
l 3 is the factor for the design life of the bridge; 
l 4 is the factor embracing the simultaneous loading of more than one track. 

Figure 2.27 - Damage accumulation method [1.15] 

2.6  Fatigue assessment in other National codes 

The  fatigue  assessment  procedures  indicated  in  other  national  codes,  such  as  IAPF  and  BS5400,  are 
similar to those present in the Eurocodes. Some of them present a different number of fatigue trains and 
different shapes and number of S-N curves (BS5400 code) [1.16].  
In the BS5400, fatigue resistances of local details are classified according to three different typologies 
(see Figure 2.28): 

•  Type 1, non-welded details; 

•  Type 2, welded details on surface; 

•  Type 3, welded details at end connections of members.  

28

 
 
D
£
D
(cid:215)
 
D
£
D
(cid:215)
  
D
(cid:215)
F
D
D
(cid:215)
F
D
l
D
s
t
£
·
·
·
   
 
 
Fatigue curves are assumed linear in the log s r - log N plane, but a bilinear curve can be adopted when 
low stress cycles have to be considered. Stress ranges are calculated by the elastic approach for welded  
and  non-welded  details.  For  non-welded  details  subjected  to  stress  reversals,  the  total  stress  range  is 
equal to the difference between the maximum tensile stress and the 60% of the minimum compressive 
stress. In this case, it is possible to take into account of the dead loads in calculating the effective stress 
range.  
The fatigue assessment can be obtained by two methods: 

•  Assessment without damage calculation, which applies in case of a permanent railway bridge 

subjected to standard loading and detail class in accordance with Code definition;  

•  Damage calculation, that can be used when stress spectra and classes of all details are known.  

In both cases, the standard RU / RL loadings or the typical trains (which general structural effects are 
assumed  to  be  represented  by  RU  /  RL  loadings)  can  be  adopted  for  stress  spectra  calculations.  In 
particular, the typical trains should be adopted when train passages produce more than one stress cycle 
on bridge components and, consequently, all the cycles must be considered in the fatigue assessment. 
In figure 2.29, the RL loading table and corresponding typical trains are reported. 
In the American Code AASHTO case, fatigue curves are also assumed to be linear (Figure 2.30) [1.17]. 
The  details  covered  are  almost  the  same  for  the  different  standards,  even  if  the  American  ASSHTO 
includes also a classification for riveted connections and for eyebar and pin plates (Figure 2.31). The 
AASHTO  specifically  distinguishes  between  vibration  induced  and  distortion  induced  fatigue 
problems. 
At least, some National codes specify more precisely the speed ranges to be considered in the analysis 
(German codes). Other relevant rules and recommendations could be found in some publications from 
the  American  Welding  Society,  the  International  Institute  of  Welding,  the  America  Railway 
Engineering Association and others. 

Figure 2.28 - BS 5400: fatigue classes of non-welded components [1.16] 

29

 
 
 
a) 

b) 

Figure 2.29 - BS 5400: RL loading table (a) and corresponding typical trains (b) [1.16] 

Figure 2.30 – S-N curves present at the AASHTO standard [1.17]. 

Figure 2.31 – Example of details’ classification at AASHTO [1.17]. 

30

 
 
 
 
 
 
2.7  Advanced fatigue assessment procedures 

The  many  limitations  of  the  S-N  curves  approach  lead  to  the  need  and  to  the  development  of  more 
sophisticated approaches. From those, probably the most well established one is the crack propagation 
approach,  based  on  Fracture  Mechanics  concepts  and  on  crack  propagation  laws  developed  from  the 
original  Paris’s  law.  This  approach  is  well  suited  for  crack  propagation.  When  dealing  with  fatigue 
crack initiation, other assessment methodologies such as the notch stress approach and the notch strain 
approach  are  better  suited.  A  recent  development  that  allows  both  for  crack  initiation  and  crack 
propagation analysis is the notch stress intensity approach. 
Finally, when the fatigue damage found in a structure is so severe that structural elements have their 
cross-sections  significantly  reduced  by  cracks  presence,  a  effective  analysis  should  be  made  to 
understand  whereas  ductile  tearing  or  sudden  collapse  is  going  to  occur.  The  European  SIN-
TAP/FITNET  “fitness-for-purpose”  procedure  is  a  recent  methodology  that  tries  to  unify  different 
methodologies and fulfill that mentioned objective [1.18]. 
The  probabilistic  approach  can  be  used  additionally,  in  all  methodologies  described  before.  It  is  a 
powerful  tool  in  the  fatigue  assessment  since  it  allows  risk  analysis  and  the  calculation  of  failure 
probability in accordance with the relevance of the structure studied. 

2.8  References 

[2.1]  Robert  E.K.  Fraser,  Gilbert  Y.  Gondin  and  Geoffrey  L.Kulak. Behaviour of Distortion-Induced 
Fatigue Cracks in Bridge Girders. Structural Engineering Report 235. December, 2000 

[2.2] Fisher, J.W. Fatigue and Fracture in Steel Bridges. John Wiley and Sons, New York,1984. 

[2.3] Rapid Assessment of Distortional Stresses in Multi-Girder Steel Bridges. 2004-48 Final Report. 
Minnesota Department of Transportation 

[2.4]  Fighting  Fatigue  in  Steel  Bridges,  Kansas  Bridge  Design  Engineers  Guide  Research  Solutions 
into  Practice. John Patrick Jones, Caroline Bennett, Adolfo Matamoros, Stan Rolfe and Kim Roddis. 
December 2008 

[2.5]  Christian  Klinger,  Gerhard  Braune,  and  Falk  Lüddecke.  Erhöhung  der  Restnutzungsdauer  an 
ermüdungsbeanspruchten  Bauteilen  einer  Stabbogenbrücke  bei  Lutherstadt  Wittenberg.  Stahlbau, 
77(12):870–879, 2008. 

[2.6]  Estimating  Fatigue  Life  of  Patroon  Island  Bridge  Using  Strain  Measurement.  Ryan  Lund, 
Sreenivas Alampalli. Transportation Research and Development Bureau. New York State Department 
of Transportation. November 2004 

[2.7]  Boulent  Imam,  Tim  D.  Righiniotis,  Marios  K.  Chryssanthopoulos,  and  Brian  Bell.  Analytical 
fatigue  assessment  of  riveted  rail  bridges. Proceedings of the Institution of Civil Engineers – Bridge 
Engineering, 159(BE3):105–116, Sept. 2006. 

[2.8] Boulent M. Imam, Tim D. Righiniotis, and Marios K. Chryssanthopoulos. Numerical modelling of 
riveted railway bridge connections for fatigue evaluation. Engineering Structures, 29(11):3071–3081, 
2007. 

[2.9]  Steffen  Marx,  Karsten  Geißler,  and  Guido  Bolle.  Die  Bestandsbrücken  der  Bahn  –  eine 
Jahrhundertaufgabe. In 16. Dresdner Brückenbausymposium, 2006. 

[2.10] Timothy D. Righiniotis, Boulent M. Imam, and Marios K. Chryssanthopoulos. Fatigue analysis 
of  riveted  railway  bridge  connections  using  the  theory  of  critical  distances.  Engineering  Structures, 
30(10):2707–2715, October 2008. 

31

 
 
 
 
 
 
 
 
 
 
 
 
[2.11]  Andreas  Taras  and  Richard  Greiner.  Versuche  an  genieteten  Brückenlängsträgern.  Stahlbau, 
77(7):507–514, 2008. 

[2.12]  Steffen  Marx,  Roland  Stein,  and  Guido  Bolle.  Monitoring-gestützte  Bauzustandsbeurteilung 
historischer  stählerner  Eisenbahnbrücken.  In  Tagungsband  33.  Darmstädter  Massivbauseminar  – 
Zukunftsfähiges Planen und Bauen, 2009. 

[2.13] Andreas Taras and Richard Greiner. Development and Application of a Fatigue Class Catalogue 
for Riveted Bridge Components. Institute for Steel Structures and Shell Structures, Graz, 5th of August 
2009. 

[2.14]  EN  1991-2:  Eurocode  1  -  actions  on  structures.  Part  2:  Traffic  loads  on  bridges.  2003, 
CEN: Brussels, Belgium. 

[2.15] EN1993-1-9: Eurocode 3: Design of steel structures, Part 1-9: Fatigue. 2004, CEN: Brussels, 
Belgium. 

[2.16]  BS5400:  Steel,  Concrete  and  Composite  Bridges.  Code  of  Practice  for  Fatigue.  1980:  B  S  I 
Standards. 

[2.17] AASHTO LRFD Bridge Design Specifications. 1994, Washington, D.C.: AASHTO. 

[2.18] Zerbst, U., Fitness-for-service fracture assessment of structures containing cracks a workbook 
based on the European SINTAP/FITNET Procedure. 2007, Amsterdam: Elsevier. XVII, 295 p.-XVII, 
295 p. 

32

 
 
 
 
 
 
 
 
 
 
 
3  Scopes of the research Project and adopted methodology 

As stated in previous chapters, the functionality maintenance of infrastructures like railway bridges is 
acquiring  more  and  more  importance  due  to  the  huge  economic  losses  related  to  the  interruption  of 
their regular service.  
This critical aspects is more stressed considering that new and existing bridges will be included in the 
new  Trans-European  Transport  Network  and,  probably,  subjected  to  traffic  spectra  (i.e.  train 
typologies,  axle  loads,  number  of  passages)  different  from  original  design  assumptions.  All  these 
changes influence also the resistance of such operas with regard to fatigue phenomena, that represents 
one of the more diffused failure modes occurred in steel bridges: in fact about 80/90% of failures in 
steel  structures  are  related  to  fracture  and  fatigue.  In  fact,  railway  bridges  endure  million  of  stress 
cycles during their life and they are expected to be highly vulnerable to fatigue effects.  
It  is  so  evident  the  necessity  for  a  continuous  analysis  and  review  of  current  standards  for  fatigue 
assessment, in order to guarantee reliability and safety of steel railway bridges.  

3.1  Open problems 

Modern codes and standards are based on several past studies, performed in order to assess the fatigue 
resistance of steel bridges. Such studies were realized on lines characterized by train typologies, axle 
loads, composition and design speed different from actual values and, moreover, considering only the 
direct  effects  of  train  passages  into  local  details.  Despite  of  these  efforts,  the  fatigue  assessment  of 
railway bridges both considering the design of new bridges and the assessment of existing ones is one 
of the main issues in current practice.  
In  fact,  phenomena  like  “vibration  induced”  and  “distortion  induced”  fatigue  are  still  partially 
uncovered by actual design codes and represent a critical aspects for the assessment of existing bridge 
remaining life and for the design of new bridges. Generally, these two typologies of fatigue phenomena 
were considered as secondary or negligible and, as a consequence, generally not considered by bridge 
design codes.  
The  possible  presence  of  secondary  stresses  is  generally  ignored  or  not  considered  also  in  the 
evaluation of fatigue resistance of critical details by laboratory tests. By this way, proper information 
concerning  the  actual  resistance  under  the  co-presence  of  primary  and  secondary  stresses  are  not 
generally available. 
At  least,  as  global  economy  is  continuously  changing,  a  corresponding  variation  of  trade  volumes, 
typologies  and  frequencies  is  to  be  expected.  This  development  concerns  also  the  passenger/freight 
traffic  on  railway  lines.  As  a  consequence,  railway  authorities  shall  take  into  account  a  constant 
increase or variation of train typologies and composition, passage frequencies, volumes and weights of 
transported goods, just to not underestimate the actual traffic loads on lines. Thus, a constant updating 
and  review  of  traffic  spectra  is  necessary  to gain a reliable and safe design of new steel bridges and 
managing of existing ones. 

3.2  Scope of FADLESS Project and adopted methodology 

The open problems concerning the assessment of fatigue performance of railway steel bridges require 
the  development  of  innovative  methodologies  for  the  correct  evaluation  of  all  those  phenomena, 
generally neglected or considered as secondary, that play an important role in the fatigue damaging. In 
particular,  such  innovative  approaches  shall  take  into  account of the real traffic spectra on European 
railway lines, and of those induced fatigue phenomena, due to imposed distortions or vibrations, that 
generate stresses which intensity can't be considered as secondary or negligible compared to primary 
stresses. 
Main objective of the Fadless Project was the development of a modern procedure for the evaluation of 
the  structural  integrity  of  railway  steel  bridges  which  may  be  affected  by  fatigue  damage  under  the 
application of a large number of load cycles during their life-time. In particular, the Project aimed at a 
better and more accurate comprehension of actual fatigue load and resistance of principal elements and 
critical  details  of  steel  bridge  typologies  representative  of  European  solutions  for  railway  lines.  For 
such  purpose,  the  actual  fatigue  loading  spectra  was  evaluated  taking  into  account  the  real  and  the 

33

 
 
expected  traffic  flows,  also  because  of  possible  reclassification  of  railway  lines,  the  global  dynamic 
train-bridge  interaction  effects  and  the  local  dynamic  vibration  and  distortional  effects.  Moreover,  
actual fatigue resistance of the main elements / critical details subjected to distortion induced effects 
was  evaluated.  In  such  a  way,  it  was  also  possible  to  setup  suitable  strategies  for  the  evaluation  of 
vibration  induced  and  distortion  induced  fatigue  damaging  in  steel  railway  bridges,  as  well  for  the 
control of the crack growth. 
In the first part of the Project, six steel railway bridges representative of actual fatigue open problems, 
i.e. local vibration and distortion induced effects, were selected as case-studies. Such bridges, including 
riveted  and  bolted  joints  for  the  connections  and  simply  supported  or  continuous  solutions  for  the 
restraining conditions, constituted the main core of the Project and were adopted as reference for the 
research activities. Selected case studies are briefly described in the following: 

•  Railway  viaduct  on  Po  river  (Italy),  composed  of  simply  supported  thought  truss  bridges 

realized both by riveted and bolted components. 

•  Panaro  bridge  (Italy),  a  double  track  welded  structure  particularly  subjected  to  distortion 

phenomena.  

•  The Trezói Bridge (Portugal), a riveted metallic bridge with three spans of 39 m, 48 m and 39 

m, totalizing 126 m length. 

•  The Alcácer do Sal Bridge (Portugal), a new composite bowstring railway bridge under final 

construction. 

34

 
 
 
 
 
 
 
 
 
 
 
•  Saalebrücke Großheringen railway bridge (Germany). This structure, of a riveted plate girder 

type, is situate on a curve of Berlin – Munich line.  

•  Salzach River bridge (Austria). This is a more than 100 year old truss bridge, single span, on a 

very busy line connecting Vienna with Innsbruck and Salzburg with Tarvisio. 

The  selected  case  studies  were  analyzed  by  means  of  experimental/numerical  analysis  to  obtain  an 
innovative  and  reliable  assessment  of  vibration/distortion  induced  fatigue  into  steel  bridges.  Such 
analysis involved the following scientific/technical areas: 

•  “In field” vibration tests: by means of such tests, it is possible to obtain a reliable assessment of 
global/local vibration modes and to identify the dynamic properties necessary for the updating 
of  numerical  models.  In  particular,  the  proper  identification  of  local  modes  is  essential  for  a 
correct evaluation of vibration induced fatigue effects; 

• 

 “In field” strain tests under train passage: strain test permits a direct evaluation of actual stress 
distribution  and  intensity  into  critical  details,  thus  permitting  to  recognize  the  distortion 
mechanisms that generate the secondary stresses that influence the fatigue performances; 

35

 
 
 
 
 
 
   
 
 
 
•  Analytical  and  numerical  analysis:  the  development  mainly  of  numerical  models  able  to 
reproduce correctly experimental global/local dynamic behaviours and distortional phenomena 
is essential for the identification of those keypoints that will permit the proper modelling also 
of details not investigated or new structure; 

•  Laboratory  tests:  the  experimental  evaluation  of  fatigue  phenomena  in  critical  details  taking 
into account also of secondary stresses is fundamental for the estimation of actual fatigue per-
formances, as secondary stresses are generally neglected in design analysis and, consequently, 
not considered neither in laboratory tests; 

•  Assessment  of  actual  traffic:  the  estimation  of  the  real  train  spectra  by  means  of  long-term 
monitoring systems represents an important issue in fatigue assessment as it provides the nec-
essary  base  for  the  correct  calculation  of  load  cycle  acting  during  the  entire  life-cycle  of  the 
bridge. 

Selected case studies, representative of typical steel railway solutions, were investigated with regard to 
the  particular  fatigue/distortion  problems  identified  in  each  structure.  To  this  aim,  research  activities 
were  properly  calibrated  and  adapted  to  the  investigated  bridges,  in  order  to  maximize  the  Project 
results. In particular, the monitoring of traffic was focused on Trezói Bridge, Alcácer do Sal Bridge, 
ans Saalebrücke Großheringen bridge, while the analysis of innovative solutions and techniques for the 
investigation of structural performances were performed with particular attention to Railway viaduct on 
Po river, Panaro bridge and Salzach River bridge. 
Extensive  experimental  and  numerical  analysis  were  performed  on  selected  case  studies,  thus 
permitting  to  obtain  exhaustive  information  concerning  the  actual  fatigue  performance  of  railway 
bridges. Moreover, obtained results permitted the development of specific guidelines for the evaluation 
and control of vibration/distortion induced fatigue effects in steel railway bridges. 

36

 
 
 
 
 
 
4  Description of case studies 

Vibration  and  distortion  induced  fatigue  damages  occurs  generally  in  different  typologies  of  steel 
railway bridges. Distortion phenomena were identified in many riveted and welded truss bridges, while 
bowstring and orthotropic desk railway bridges are more sensible to vibration induced damages.  
In order to analyze experimentally these structural typologies, six case studies were selected: 

•  Railway  viaduct  on  Po  river  (Italy),  composed  of  simply  supported  thought  truss  bridges 

realized both by riveted and bolted components; 

•  Panaro  bridge  (Italy),  a  double  track  welded  structure  particularly  subjected  to  distortion 

phenomena; 

•  The Trezói Bridge (Portugal), a riveted metallic bridge with three spans of 39 m, 48 m and 39 

m, totalizing 126 m length; 

•  The Alcácer do Sal Bridge (Portugal), a new composite bowstring railway bridge under final 

construction; 

•  Saalebrücke Großheringen railway bridge (Germany). This structure, of a riveted plate girder 

type, is situate on a curve of Berlin – Munich line; 

•  Salzach River bridge (Austria). This is a more than 100 year old truss bridge, single span, on a 

very busy line connecting Vienna with Innsbruck and Salzburg with Tarvisio. 

4.1  Lagoscuro railway viaduct on Po river (Italy) 

The Lagoscuro viaduct is a steel railway viaduct on the Bologna –Venice line and it is composed of 2 
steel  railway  viaducts  running  parallel  one  to  each  other  and  crossing  the  Po  river  (Figure  4.1).  The 
first viaduct was built in 1948 and is composed by 9 single span truss-girder bridges. Each span is 75 
meters long and 5.20 meters wide (see Figure 4.2a, b). 

Figure 4.1  - The Lagoscuro viaduct on the Po river. 

Two main truss girders support the vertical load, while X-shaped upper and lower lateral bracing assure 
the  transverse  stability.  The  upper  and  the  lower  chord,  diagonals  and  stunts  are  composed  of  4  L-
shaped  steel  elements,  riveted  together  by  means  of  plates  (Figure  4.3);  stiffening  plates  are  also 
designed to improve the transverse stiffness of the cross-section (Figure 4.4a). Stringers and additional 
elements  supporting  the  railway  lines  are  also  composed  of  riveted  steel  elements.  End  supports  are 
constituted  by  steel  bearings  directly  in  contact  with  lower  main  strings (see Figures 4.4b), so that a 
simply supported scheme is realized. 
The new Lagoscuro viaduct was recently built (2005) in order to potentiate the railway line; the same 
geometry  is  adopted  but,  differently  to  the  old  viaduct,  the  truss  girders  are  composed  by  H-shaped 
elements bolted together in the joints (see Figure 4.5). 

37

 
 
 
a) 

c) 

b) 

Figure 4.2 - Dimension of the old Lagoscuro bridge. 

a) 

b) 

Figure 4.3 - The old Lagoscuro Bridge: details of (a) L-shaped elements composing the truss girders diagonals and 
(b) a riveted joint. 

a) 

b) 

Figure 4.4 - The old Lagoscuro Bridge: details of (a) stiffening plates designed to improve the transverse stiffness 
of the cross-section (b) end supports (fixed and sliding). 

38

 
 
 
 
 
 
 
 
 
 
Figure 4.5 - The new Lagoscuro Bridge: details of bolted joints. 

4.2  Panaro bridge (Italy) 

The  bow-string  steel bridge on the Panaro river, along Bologna-Verona railway line, is the very first 
Italian  railway  bridge  constructed  adopting  welded  components  (Figure  4.6).  This  particular  bridge, 
supporting two tracks, has experienced an intense passenger and freight traffic since its construction in 
the 70's. 
The  bridge  has  a  span  length  equal  to  75.6  meters  and  its  cross  section  height  varies  from  7  to  11 
meters (Figure 4.7). All main components such as lower and upper strings, vertical and diagonal beams, 
main  cross  girders,  lower  and  upper  bracing  diagonals  at  deck  ends  are  built-up  welded  members 
(Figures  4.8  and  4.9).  All  joints  are  constituted  by  riveted  solutions,  thus  realizing  a  very  particular 
structure  among  steel  railway  bridges,  an  uncommon  mix  between  welded  components  and  riveted 
joints.  Lower  and  upper  main  bracings  are  present,  together  with  secondary  longitudinal  beams, 
directly  supporting  the  rails,  and  local  track  bracings  (Figures  4.10  and  4.11).  End  supports  are 
constituted by steel bearings directly in contact with lower main strings (Figures 4.12 and 4.13). 
During  its  exercise  life,  some  of  the  secondary  elements  of  the  structures  showed  fatigue  damages 
induced  by  distortion  and  vibration  phenomena,  as  reported  in  Figures  4.14  and  4.15  In  particular, 
almost  all  cross  beams  of  track  local  bracings  (originally  fully  fixed  to  the  secondary  longitudinal 
girders) experienced the same fatigue damage at the end restraints. Italian authority decided to cut the 
profiles  in  order  to  stop  the  crack  propagation  and  changed  beam  end  connections  into  pin  joints 
removing  the  external  bolts,  in  order  to  reduce  the  bending  forces  induced  by  distortion  phenomena 
(Figure 4.14). Moreover, the connection between sleepers and longitudinal girders, obtained by catch 
bolts anchored to steel plates welded to the upper girder flanges, experienced fatigue damages in the 
longitudinal plate-flange welding due to vibration effects (Figure 4.15). 

Figure 4.6 - Picture of Panaro bridge (Courtesy of RFI). 

39

 
 
    
 
 
 
 
BOLOGNA

PIACENZA

Figure 4.7 - Drafting of Panaro bridge (Courtesy of RFI). 

Figure 4.8 - General view of Panaro bridge 

Figure 4.9 - Riveted diagonal-lower string joint of  
Panaro bridge 

Figure 4.10 - General view of deck structure 

Figure 4.11 - General view of lower and track bracings 

Figure 4.12 - General view of unidirectional bearing 

Figure 4.13 - General view of fixed bearing 

Figure 4.14 - Typical fatigue damage and repair of 
track bracing cross beams 

Figure 4.15 - Sleepers-longitudinal girder connection 
by catch bolts  

40

 
 
 
 
 
 
 
 
 
 
 
 
4.3  Trezói Bridge (Portugal) 

The Trezói Bridge (Figure 4.16) is located in the international “Beira Alta” route that links Portugal to 
Spain, at the km 62 north of Mortágua in the village of Trezói. The bridge was constructed as part of a 
project to replace existing bridges in the “Beira Alta” route, carried out during the decade of 50, and 
was  opened  to  traffic  in  August  1956.  The  project  was  funded  by  the  Marshall  Plan,  and  the 
conception, manufacture and mounting , together with 6 other bridges of larger span of the same line, 
was of the responsibility of the German House Fried Krupp. 

Figure 4.16 - The Trezói bridge. 

The metallic riveted bridge is formed by three spans of 39 m, 48 m and 39 m, for a total length of 126 
m. The two inverted Warren truss girders that constitute the metallic deck of the bridge are 5.68 m in 
height.  The  girders  panels  are  6.50  m  wide  in  the  central  span  and  6.00  m  in  the  end  spans.  Two 
trapezoidal  shape  trusses  acting  as  columns  and  two  granite  masonry  abutments  transmit  the  loads 
carried  by  the  structure  to  the  foundation.  The  bridge  has  a  constant  width  of  4.40m  throughout  its 
length. 

Figure 4.17 -  Elevation and plan view of the Trezói bridge. 

41

 
 
 
 
 
 
 
     
The cross girders, as well as the stringers resting on them, were built using “I-shaped” sections. The 
cross girders are 71 cm in height and are connected to the lateral vertical elements with riveted plates 
as shown in Figure 4.18. The chords and diagonals of the truss girders are formed by double “U-shape” 
sections. 
The bearing supports of the superstructure are metallic and allow free rotations in the structure plane. 
At  the  east  support  the  longitudinal  displacements  are  constrained,  while  at  the  west  support 
deformations caused by longitudinal horizontal forces (thermal actions, braking, etc.) are allowed. 

Figure 4.18 - Local view of the cross-girder at the end support. 

As  can  be  observed  in  Figure  4.19  b),  the  stringers  are  aligned  with  the  rails  which  is  a  fortunate 
conception  option  since  a  misaligned  rail  normally  induces  secondary  stresses  in  the  web  of  the 
stringers. 

a) 

b) 

Figure 4.19 - Local views of structural details of the bridge: a) cross-girder above central column; b) rails resting 
above stringers. 

4.4  Alcácer do Sal Bridge (Portugal) 

The  new  Alcácer  do  Sal  railway  bridge  is  located  in  the  Lisboa  –  Algarve  connection,  in  Portugal 
(Figure 4.20).  
It is designed for passenger trains (as the Alfa Pendular tilting train and the Intercity train) running at 
speeds up to 220 km/h. Since it is also part of the main railway connection to the sea port of Sines, it is 
also designed for freight trains with up to 25 tons per axle (Figure 4.21). 
The  bridge  has  a  continuous  composite  deck  that  covers  three  spans  (160m  per  span).  The  deck  is 
suspended  from  3  arches.  Each  arch  holds  one  span  of  the deck, with 18 vertical hangers, 8 m apart 
from each other (Figure 4.22). The structure is preceded by the north and south access viaducts (with 
1115 m and 1140 m, respectively). Both viaducts and bridge are designed to hold two ballasted tracks 
even if only the upstream track is on service, at the current time.  
A reinforced concrete slab above a U-shaped steel box forms the deck (Figure 4.23a)). The 15.85 wide 
concrete slab has a maximum thickness of 0.43 m. The steel box, with sloped webs, was built up by 
welding steel plates. Maximum plate’s thickness is 120 mm. A diaphragm reinforces the deck at each 
hanger connection. Two diagonals per hanger distribute the suspension force into the deck. The arches 

42

 
 
 
 
 
 
 
present an hexagonal hollow section with variable height and width (Figure 4.23b) and Figure 4.23c)). 
Also in this case, thick steel plates assembled by welding were adopted. 
The construction process of the structure was complex (Figure 4.24). The different steel components 
were assembled in situ, and after the steel girders of the access viaducts were put in place the bridge’s 
deck steel box girder was pushed. The components of the arch and the hangers were assembled over the 
deck  and  after  that  the  concreting  of  the  deck’s  slab  was  performed.  After  the  curing  of  concrete,  a 
controlled subsidence of 1.5 m was imposed to the intermediate supports, so that compressive forces 
acted on the concrete, over that intermediate supports. 

a) Location 

b) Overview 

Figure 4.20 - New Alcácer do Sal Railway bridge 

a) Alfa Pendular train 

b) Intercity train 

c) Freight train 

Figure 4.21 - Typical traffic 

Figure 4.22 - Side view of the midspan of the bridge [4] 

43

 
 
 
 
 
 
 
 
 
b) Arch endings 

a) Deck 

c) Arch’s mid section 

Figure 4.23 – Structural elements of the bridge 

a) Sub-modules’ assemblage 

b) Steel deck’s push 

c) Arch’s assemblage 

Figure 4.24 – Construction process 

4.5  Saalebrücke Großheringen (Germany) 

One very typical solution for steel railway bridges that were erected in the first half of the 20th century 
was the riveted plate girder. Typical spans of these bridges are between 5 to 40 m. The main girders 
with I sections were assembled by connecting steel plates and rolled steel sections by rivets. Often the 
geometry of the cross section (e.g. the height of the web or the thickness of the flanges) follows the size 
of the internal forces along the beam axis. 
Between main girders, the cross beams carry the longitudinal beams that support directly the sleepers. 
In  many  cases  the  tracks  are  situated  between  the  two  main  girders.  There  are  bridges  with  ballast 
laying  on  curved  metal  sheets  while  in  other  cases  the  sleepers  are  directly  connected  to  the  steel 
structure. 
The  Saalebrücke  Großheringen  is  situated  between  Naumburg  and  Jena  at  the  junction  of  the  lines 
Erfurt  –  Halle/Leipzig  and  Jena  –  Halle/Leipzig.  The  bridge  is  part  of  the  main  connection  Berlin  – 
Munich.  The  bridge  was  constructed  between  1932  and  1935.  It  consists  of  five  35  m  to  40  m  long 
spans. Each span consists of a simply supported riveted plate girder superstructure. The two tracks are 
accommodated on separated superstructures. The 75 m long opening over the river Saale is bridged by 
simply supported riveted truss girders. The whole bridge is situated in a curve which is the reason for a 
speed limitation of the rail traffic to 90 km/h. 
Since most of the superstructures of the bridge are designed and constructed in an almost identical way 
the research was concentrated on a single span which can be considered as being representative for all 
plate  girder  superstructures  of  this  bridge.  For  the  investigations  within  the  research  Project,  the  
northern end span of the bridge was selected. It carries the southbound track and is a typical example of 
a  riveted  plate  girder  bridge.  The  typical  cross  section  of  the  considered  superstructure  is  shown  in 

44

 
 
 
 
 
 
 
 
Figure  4.25.  During  a  bridge  inspection  cracks  were  identified  which  could  be  caused  by  fatigue. 
Figure 4.26 shows several photographs of the bridge including a structural detail that was considered 
within the Project. 

Figure 4.25 - Cross section of a riveted plate girder bridge (Saalebrücke Großheringen) 

a) 

c) 

b) 

d) 

Figure 4.26 - Photographs of the Saalebrücke Großheringen: a) View of the complete bridge from South-East, b) 
View of the selected span from South-East, c) Superstructure with tracks between main girders, d) crack in a 
gusset plate at the connection of a cross beam to the main girder 

45

 
 
 
 
 
 
 
 
4.6  Salzach River Bridge (Austria) 

Salzach  River  Bridge  is  a  more  than  one  hundred  years  old  steel  railway  bridge  of  the  Salzburg-
Wörgltrack.  It  crosses  over  the  river  Salzach  at  km  68.80,  located  near  the  town  of  Schwarzach  im 
Pongau  in  the  province  of  Salzburg.  It  was  built  between  1905  and  1907  and  was  reconditioned  in 
1965. It is a riveted truss bridge with a span of 40 meters, a construction height of 4.30 meters and a 
width of 3.00 meters. The bridge’s construction material is a form of alkaline low carbon “mild” steel 
originally called: basisches Martin-Flusseisen. All connections in the bridge are done with rivets. 
The  plan  view  of  the  bridge  is  shown  in  Figure  4.28.  There  are  two  parallel  bridges  crossing  the 
Salzach.  Our  investigations  have  been  concentrated  on  the  bridge  on  the  upstream  side.  Example  of 
original design drawings are reported in Figures 4.29 and 4.30. 
Since some cracks have been already detected on the structure this object is even more interesting for 
research focused on the fatigue issue. 

Schwarzach im Pongau 

EASTERN  
BANK 

UPSTREAM 

Figure 4.27 - Salzach-bridge from the eastern river bank.Location of the bridge. 

EASTERN 
BANK 

DOWNSTREAM 

WESTERN 
BANK 

.

UPSTREAM 

Figure 4.28 - Plan view of the Salzach bridge (original blueprint). 

46

 
 
 
 
 
 
 
 
 
Figure 4.29 - Elevation of the Salzach bridge (original blueprint). 

Figure 4.30 - Section of the Salzach bridge (original blueprint). 

47

 
 
 
 
5  Standard Fatigue Assessment 

5.1  Numerical modelling 

Nowadays, numerical modelling by finite elements is the most diffused and adopted technique for the 
design  of  new  bridges  and  the  assessment  of  existing  ones.  This  approach  permits  to  obtain  easily  a 
large amount of information for the analyzed structure as, for example, deformations, internal forces or 
stresses at critical details. It is also possible to investigate the natural frequencies and mode shapes by 
modal analysis. Developers can also consider different non-linearities concerning geometry, material or 
loads and perform rapidly static or dynamic analysis to simulate almost all possible linear or non-linear 
mechanisms of the structure. 
Nevertheless, designers shall keep always in mind that finite element models, even if well defined and 
properly working, continue to be just a theoretical representation of the real structural behaviour and, 
consequently, provide approximate results. The level of approximation can be conveniently reduced by 
the  adoption  of  proper  modelling  techniques,  with  regard  to  each  analyzed  structure,  and  by  the 
execution of updating procedures, in order to calibrate the models with respect to experimental data. 
The development of effective FE models is a main issue in the fatigue assessment of railway bridge, as 
it  involves  the  correct  evaluation  of  static  and  dynamic  properties  both  for  global  and  local  models, 
often adopted for the evaluation of local stresses at critical details. Convenient static and dynamic up-
dating  procedures  can  be  performed  also  for  local  models,  thus  permitting  to  identify  and  calibrate 
accurately the boundary conditions of represented critical details and to obtain a reliable evaluation of 
local stresses. 

5.2  Experimental dynamic identification 

Experimental  tests  constitute  a  reliable  and  effective  tool  for  the  evaluation  of  structural  dynamic 
properties. They are composed of experimental acquisitions, obtained recording vibrations of suitable 
key  points  of  the  structure  subjected  to  external  excitations,  and  following  numerical  elaboration  of 
data.  Experimental  layout,  defined  by  sensor  positions,  sensibility,  acquisition  period,  sampling 
frequency and typology of excitation sources, must be defined in order to catch the specific dynamic 
properties object of the test, as for example vertical vibration modes of a simply supported bridge or 
local movements of a bracing component. 
In  case  of  bridges,  generally  experimental  dynamic  tests  are  designed  in  order  to  catch  the  global 
vibrations movements of the structure, i.e. vertical flexural, torsional and transverse modes. Moreover, 
it  is  possible  to  analyze  also  the  dynamic  behaviour  of  local  details  or  components,  in  order  to 
investigate  the  influence  of  this  local  movements  on  the  structural  performance  of  selected  element. 
Concerning  the  excitation  forces,  two  main  typologies  of  solutions  can  be  adopted:  i)  impulsive  or 
harmonic point forces, which frequency characteristics are well known; ii) ambient forces (i.e. wind, 
traffic  on  near  roads  or  highways,  movements  of  staff  members) that, in a suitable long time period, 
constitute  a  statistical  random  and  independent  set  of  actions  on  the  structure,  realizing  the  “white 
noise”  excitation  source.  This  latter  solution  is  particularly  suitable  in  case  of  bridges  because  no 
external excitation device is required to analyze the structure. Assuming ambient forces as excitation 
source,  acquired  data  can  be  elaborated  by  Operative  Modal  Analysis  techniques,  to  obtain  the 
structural identification on the basis of the “white noise” input signal. 

5.3  Vibration-based model updating 

Model  updating  is  a  method  to  improve  the  correlation  between  the  numerical  model  and  a  realistic 
structure using measured data by adjusting previously selected uncertain model input parameters. If the 
numerical  model  is  a  finite  element  model,  the  term  finite  element  model  updating  is  very  common. 
Vibration-based model updating is a type of model updating, in which the measured data is obtained by 
vibration experiments. The measured quantities are typically, time histories of accelerations, velocities, 
displacements,  or  strains.  Based  on  these  time  histories,  features  like  natural  frequencies,  modal 
damping  ratios,  mode  shapes,  or  frequency  response  functions  can  be  derived.  Suitable  modal 

49

 
 
the input parameters, sometimes called design variables; 

parameter  identification  methods  are  stochastic  subspace  identification  (SSI),  enhanced  frequency 
domain decomposition (EFDD), or poly-reference least squares complex frequency domain (p-LSCF) 
algorithm. Also certain statistical properties, like total signal energy or maximal amplitude, of the time 
histories can be used as target features. 
Due to the straightforward application of optimization methods, they are frequently applied for model 
updating problems. By defining the optimization problem for model updating six important quantities 
are needed: 
• 
• 
• 
•  parameters; 
• 
• 
• 

the function or relation to calculate the model responses depending on the model; 

the objective function that should be typically minimized; 

the target output parameters; 

the optimization method. 

the output parameters; 

In  case  of  model  updating,  the  input  parameters  are  the  uncertain  model  parameters.  Examples  are 
material  parameters,  geometrically  related  measures  of  the  model,  modelling  parameters,  boundary 
conditions, or loads. Obviously, all input parameters need to be restricted by lower bounds and upper 
bounds to avoid unreasonable identification results or to avoid numerical problems. Typical restrictions 
are  the  requirement  of  a  positive  Young’s  modulus  or  the  maximum  representative  numerical  value. 
Additional  equality  or  inequality  constrains  can  limit  the  valid  input  parameter  space.  As  only 
parameters can be derived that are sensitive with respect to the output parameters, a preselection of the 
most sensitive input parameters is recommended. This can be conducted, for instance, by a sensitivity 
analysis enhanced by engineering judgement. 
The  output  parameters  are  the  numerical  model  responses  based  on  a  certain  sample  set  of  input 
parameters.  Typical  output  parameters  are  modal  parameters  (natural  frequencies,  modal  damping 
ratios,  modal  displacements)  or  features  extracted  from  time  histories  of  displacements,  velocities, 
accelerations, strains, or stresses. 
Of  course,  to  obtain  the output parameters, a function or relation is needed between the input model 
parameters  and  the  model  responses.  This  can  be  an  analytical  function  or  another  mathematical 
description of the relation, for instance, a solution obtained from a finite element model. It would be an 
advantage, if the relation between input parameters and output parameters can be derived analytically. 
The  target  output  parameters  are  the  experimentally  obtained  features.  Evidently,  the  target  output 
parameters and the output parameters need to describe the same kind, order, and number of features. If 
experimentally  obtained  mode  shapes  are  available,  the  modal  assurance  criterion  or  energy-based 
modal assurance criterion can be applied for the assignment of numerically derived to experimentally 
obtained modes. 
To  evaluate  the  suitability  of  a  certain  input  parameter,  the  experimentally  obtained  features  and 
numerically derived model response have to be compared. Such a function is termed objective function. 
If  the  optimization  problem  is  formulated  as  positive  defined  minimization  problem,  the  objective 
function should at least satisfy the condition of positive definiteness. 
A  very  common  example  of  an  objective  function  is  the  weighted  Euclidean  distance.  If  statistical 
properties  of  the  experimentally  obtained  features  are  available,  the  Mahalanobis  distance  can  be 
suitable. If the distribution of the uncertain input parameters is of interest, measures frequently applied 
in information theory can be applied. The Kullback-Leibler distance is one example. 
By  using  the  previous  description  of  input  parameters,  output  parameters,  their  connection  by  the 
numerical  model,  and  objective  function,  any  standard  optimization  method  (e.g.,  gradient  based 
methods,  response  surface  methods,  or  nature  inspired  methods)  can  be  applied.  Depending  on  the 
number of input and output parameters and the topology of the objective function different methods are 
recommended.  Assuming  a  convex  smooth  objective  function  and  not  more  than  4  input  parameters, 
gradient-based  methods  are  suitable.  For  4  to  10  input  parameters,  and  at  least  monotone  objective 
functions,  adaptive  response  surface  methods  can  be  successfully  applied.  If  several  suboptimal 

50

 
 
positions  are  expected  and  if  more  than  10  parameters  need  to  be  detected,  genetic  algorithms  or 
particle swarm optimization methods are recommended. 
The interaction of all components of the model updating procedure is given in Figure 5.1. 

Figure 5.1 - Common procedure of model updating using experimental modal data. 

5.4  Application to case studies 

5.4.1 Lagoscuro viaduct (Italy) 

In  the  following,  results  of  the  fatigue  assessment  procedure  are  described.  First  the  results  of  the 
experimental modal identification process are reported. Then, some details about results of the model 
updating  procedure  are  briefly  shown.  Finally,  a  standard  fatigue  assessment  is  performed  and  the 
results are discussed.   

Results of the experimental identification  

Experimental  Dynamic  identification  is  performed  to  obtain  natural  frequency,  damping  ratios  and 
mode shapes of both 75 and 60 meters long Pontelagoscuro old bridges. For both, eleven accelerome-
ters were placed in a number of selected positions on the bridge deck: 6 instruments to measure vertical 
accelerations  (two  at  mid-span,  four  at  quarters,  on  both  sides  of  the  deck),  3  for  the  horizontal 
accelerations  (at  mid-span  and  at  quarters,  in  the  lower  chord)  and,  finally,  2  for  horizontal 
accelerations at mid-span and at quarter, in the upper chord (see Figure 5.2).  
Starting  from  the  recorded  data,  the  global  modes  are  identified  by  Operative  Modal  Analysis 
technique  (OMA)  [5.1-5.2],  using  the  poly-reference  Least  Squares  Complex  Frequency  domain  (p-
LSCF) algorithm, also known under its commercial name PolyMAX [5.3-5.4].  
As  for  the  60  meters  long  bridge,  nine  global  modes  of  vibration  were  clearly  identified  from  the 
experimental tests. The first frequencies and mode shapes extracted from the identification procedure 
are reported in Table 5.1. The first 4 mode shapes are shown in Figure 5.3. 
The  old  Lagoscuro  bridge  was  designed  mainly  to  support  vertical  loads.  Due to the presence of the 
vertical truss girders, the bridge has a high stiffness in the vertical plane but is quite deformable in the 
transverse  direction.  Therefore,  the  first  mode  shape  (2.14  Hz)  is  characterized  by  the  horizontal 
deformation of the bridge, with a significant cross-section distortion. The second mode shape (2.85 Hz) 
is a flexural mode with deflection in the vertical plane. The third mode shape is a torsional mode and 
the forth is the second lateral. 
Similar results are obtained also for the 75 meters long bridge. 10 modes are identified: the first two 
mode  shapes  are  characterized  by  horizontal  deformation  of  the  bridge,  involving  mainly  the  cross-
sections (1.533 and 3.112 Hz). The third mode shape is a flexural mode with deflection in the vertical 

51

 
 
 
 
plane, with at frequency of 3.321 Hz. Results are shown in Table 5.2. The corresponding mode shape 
are very similar to those shown in Figure 5.3. 

Figure  5.2 - Experimental setup with position of accelerometers. 

Table 5.1 - 60 meters long old PonteLagoscuro Bridge: 
results of experimental modal identification. 

Table 5.2 - 75 meters long old PonteLagoscuro Bridge: 
results of experimental modal identification. 

Mode n° 

1 
2 

3 

4 

5 

6 
7 
8 
9 

Frequency 
[Hz] 
2.143 
2.857 

4.307 

4.700 

7.907 

8.139 
9.804 
10.744 
11.880 

Mode Shape 

Mode n° 

I Lateral 
I Flexural (vertical)   
distortion of the 
cross section 
II lateral 
distortion of the 
cross section 
III lateral 
II Flexural 
I torsional 
III flexural 

1 

2 

3 
4 
5 
6 
7 
8 
9 
10 

Frequency 
[Hz] 
1.533 

3.112 

3.321 
4.020 
8.090 
8.324 
9.274 
11.930 
13.214 
15.860 

Mode Shape 

I Lateral 
distortion of the 
cross section 
I Flexural (vertical) 
II lateral 
III lateral 
II Flexural 
I torsional 
II torsional 
III flexural 
III torsional 

Mode  

1st - I Lateral 

2nd - I Flexural 
(vertical) 

3rd - distortion of the 
cross section 

4th - II lateral 

EXP  

FE 
model  

Figure 5.3 - Experimental and numerical first 4 mode shapes (60 meters long bridge). 

Results of the Model Updating procedure 

Global Finite Element models are used to reproduce the global dynamic behaviour of the bridge. For 
this purpose, each FE model is corrected according to a model updating procedures. The experimental 
and the numerical modes are first coupled by using the MAC (Modal Assurance Criterion) [5.5]. Then, 
the  objective  function  to  be  minimized  during  the  identification  procedure  is  defined  as  the  relative 
error  between  modal  frequencies  and  mode  shapes  obtained  adopting  a  given  set  of  identification 
parameters  (

 and the reference solution (

, i.e.: 

)

)

i φ,ω

i

i φ,ω

i

=

H

N

∑

=
1

i






w
1





2


+


i

i

i

w
2

NMD
i

2






(5.1) 

where NMD is the so called “Normalized Modal Difference” [5.6]. In Eq. (5.1), N = 4 mode shapes are 
considered. Moreover, the weight constants are taken as w1 = 1, w2 = 0.1.  

52

 
 
 
 
 
 
 
 
 
 
 
 
 
 
w
w
-
w
 
The optimization problem is solved by a global search method called DE-Q [5.7-5.8]. In this algorithm, 
the  response  surface  methodology  [5.9-5.10]  is  introduced  in  the  classical  Differential  Evolution 
algorithm  to  improve  its  performances.  Differential  evolution  (DE)  [5.11-5.12]  is  an  evolutionary 
algorithm where N different vectors collecting the parameters of the system are chosen randomly or by 
adding  weighted  differences  between  vectors  obtained  from  two  populations.  In  the  modified 
algorithm, the new parameter vector is defined as the minimum of a second-order polynomial surface, 
approximating the objective function. The performances in term of speed rate are strongly improved by 
introducing  the  second-order  approximation;  nevertheless,  robustness  of  DE  algorithm  for  global 
minimum  search  of  objective  function  is  preserved,  since  multiple  search  points  are  used  simultane-
ously. More details about the updating procedure can be found in [5.7-5.8].  
For both bridges, the parameter to be identified are: 

• 
• 

• 

the equivalent density of steel members meq (due to the large amount of plates and rivets); 
the  additional  masses  on  the  deck  m  (due  to  the  presence  of  some  secondary  elements  and 
masses that are not modelled); 
the  translational  (longitudinal)  spring  stiffness  kh  (introduced  to  simulate  the  behavior  of 
supports). 

After  the  updating  process,  the  numerical  frequencies  of  the  numerical  model  are  very  close  to  the 
experimental values. Experimental and numerical frequencies after the updating procedure are reported 
in  Table  5.3  and  Table  5.4.  It  is  shown  that  errors  are  never  greater  than  6%.  To  compare  the 
experimental  and  numerical  mode  shapes,  the  value  of  MAC  is  also  given.  In  Figure  5.4  values  of 
identification parameters and of the objective function for each iteration of all search point. 

Results of standard fatigue assessment 

Optimized FE models obtained from the updating procedure are used to perform the fatigue analysis. 
The  fatigue  assessment  is  carried  out  following  the  procedure  defined  in  the  section  6  of  EN1991  – 
Eurocode 1. In order to obtain the stress ranges on each element, dynamic analyses are performed.  

Table 5.3 - 75 meters long old PonteLagoscuro 
Bridge: Comparison between experimental and 
numerical results after the optimization process. 

Table 5.4 - 60 meters long old PonteLagoscuro 
Bridge: Comparison between experimental and 
numerical results after the optimization process. 

Experimental 
frequency 
[Hz] 
1.53 

Numerical 
frequency 
[Hz] 
1.573 

3.11 

3.32 

4.02 

3.228 

3.331 

4.025 

Mode 

1 

2 

3 

4 

1.0

0.8

0.6

0.4

0.2

-0

-0.2

-0.4

-0.6

-0.8

s
r
e
t
e
m
a
r
a
p
d
e
z

i
l

a
m
r
o
N

Experimental 
frequency 
[Hz] 
2.143 

Numerical 
frequency 
[Hz] 
2.166 

3.857 

4.307 

4.700 

3.638 

4.409 

4.749 

Error 
[%] 

MAC 
[%] 

1.07 

5.60 

2.37 

1.04 

96 

96 

75 

88 

Error 
[%] 

MAC 
[%] 

Mode 

-2.81 

-3.79 

-0.33 

-0.12 

95 

91 

96 

99 

1 

2 

3 

4 

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

i

l

]
-
[
e
u
a
v
n
o
c
n
u
f
e
v
i
t
c
e
b
O

j

-1.0

0

4

8

12
Iterations [-]

16

20

24

0.0

0

4

8

(a)

12
Iterations [-]

16

20

24

 (b) 

Figure 5.4 - (a) Values of identification parameters during the optimization process (values are normalized for 
numerical convenience); (b) values of the objective function during the optimization process. 

53

 
 
 
 
 
 
 
 
 
The fatigue assessment is then carried out on the basis of the traffic mixes ("standard traffic", "traffic 
with 250 kN-axles" or “light traffic mix”) defined in the Annex “D” of EN1991 – Eurocode 1.[5.13]. 
The fatigue strength for nominal stress ranges is represented by a series of (log ∆σR) – (log N) curves 
which  correspond  to  typical  detail  categories.  The  category  is  designated  by  a  number  which 
represents, in N/mm2, the reference values ∆σC and ∆τC for the fatigue strength at 2 million cycles. For 
riveted connections, the Italian railways company imposed a value of ∆σC = 71 N/mm2. According to 
Eurocode  3  part  1-9  [5.14],  the  fatigue  strength  values  ∆σC  is  divided  by  γMF,  so  obtaining  ∆σC  = 
71/1.35  =    52.59  N/mm2.  Adopting  this  value,  the  fatigue  strength  is  obtained  starting  from  the 
extended fatigue strength curves defined as follows: 

(

(

)
m
R N

R

(

D=

)

m

C

6102 (cid:215)

  with m=3 for 

£N

6105 (cid:215)

m

)
R N

R

(

D=

)

m

C

6102 (cid:215)

  with m=5 for 

105

6

N

101

8

=

(
/5

100

)

5/1

L

 (cutoff limit) 

D

(5.2) 

(5.3) 

(5.4) 

A  stress  history  is  determined  from  dynamic  analysis  calculations  of  the  structural  response  in  each 
structural element. Examples of displacement at midspan for train Type 1, 2 (passenger train), 4(high 
speed  train),  6  (freight  train)  are  shown  in  Figure  5.5.  Stress  histories  in  the  upper  chord  and  in  a 
diagonal member obtained from the dynamic analysis are shown in Figure 5.6.  
Then,  according  to  Eurocode  3  part  1-9,  the  stress  histories  are  evaluated  by  the  cycle  counting 
methods  (rainflow  method)  in  order  to  determine  the  stress  ranges  and  the  associated  numbers  of 
cycles.  The  stress  range  spectrum  is  determined  by  collecting  the  stress  ranges  and  the  associated 
number  of  cycles  in  descending  order.  The  damage  Dd  during  the  design  life  (100  years)  is  then 
calculated by means of the Miner’s linear damage accumulation rule [5.15-5.16]: 

D

d

∑=

E

n
N

R

(5.5) 

where nE is the number of cycles associated with the stress range 

 for band i in the spectrum and 

F

i

NR is the endurance (in cycles) obtained from S-N curves from a stress range
is based on damage accumulation by means of the following criterion: 

. The fatigue limit 

F

i

Dd  < 1,0 

(5.6) 

Finally, the Remaining Fatigue Life (RFL) of the member/detail is calculated as follows [5.14, 5.15]: 

RFL

=

1 -

D

p

D
1

f

(5.7) 

where Dp is the damage accumulated in the considered element in past periods of time and D1f is the 
damage accumulated for one year future exploitation.  
Results of fatigue assessment are reported in term of the damage accumulation index Dd over 100 years 
and  they  are  shown  in  Figure  5.7a  for  upper  and  lower  chord  elements,  in  Figure  5.7b  for  diagonal 
members, in Figure 5.8a for floorbeams and in Figure 5.8b for the bracing systems elements and the 
upper  transversal  elements.  Results  show  that  some  elements  (stringers  and  longitudinal  beams)  are 
characterized by very high value of Damage index (greater than 20) This is mainly due to the presence 
of  the  bending  moment induced by the heavy train passage (trains type 5 and 6). In the case of only 
passenger  trains,  the  stress  range  is  usually  smaller  than  the  cut-off  limit.  Damage  index  values  for 
upper and lower chords are in the range 1.6-1.7; moreover, for other members (stunts and bracings), no 
fatigue  problems  are  found.  Finally,  some  elements  are  characterized  by  very  small  values  of  Dd  (in 
particular  elements  of  the  upper  and  lower  bracing).  This  is  due  to  the  symmetric  loading  condition 
imposed during the dynamic analysis. 
An analogous procedure was performed for the 75 meters long bridge and similar results were found.  

54

 
 
s
s
D
 
s
s
D
(cid:215)
£
£
(cid:215)
 
s
D
s
D
 
 
s
D
g
s
D
g
 
Values  of  Damage  indexes  obtained  in  stringers  and  floorbeams  totally  disagree  with  investigations 
carried out on the real structure. In fact, after over 64 years of service, no visible fatigue damages have 
been found in any element or connection. This is due to the different fatigue loading spectra acting on 
the bridge than those defined by the Eurocode. In fact, mainly passenger train crosses the PonteLago-
scuro  viaduct;  moreover,  the  few  number  of  freight  train  has  weight  significantly  lower  than  those 
defined in the Eurocode. Finally, the speed of all trains crosses the bridge is strictly limited to about 
90-100 km/h.  

]

m
m

[

t
n
e
m
e
c
a
l
p
s
i
D

]

m
m

[

t
n
e
m
e
c
a
l
p
s
i
D

5

0

-5

-10

-15

-20

-25

-30

5

0

-5

-10

-15

-20

-25

-30

]

m
m

[

t
n
e
m
e
c
a
l
p
s
i
D

5

0

-5

-10

-15

-20

-25

-30

0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

Time [s]

(a) 

Time [s]

(b) 

]

m
m

[

t
n
e
m
e
c
a
l
p
s
i
D

40

30

20

10

0

-10

-20

-30

-40

-50

-60

-70

-80

0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

0

2

4

6

Time [s]

(c) 

12

14

16

18

20

8

10
Time [s]

(d) 

Figure 5.5 - Example of displacements at midspan obtained from the dynamic analysis for (a) train type 1; (b) train 
type 2; (c) train type 4; (d) train type 6. 

]

2

m
m
N

/

[

s
s
e
r
t
S

10

5

0

-5

-10

-15

-20

-25

-30

-35

-40

]

2

m
m
N

/

[

s
s
e
r
t
S

10

5

0

-5

-10

-15

-20

-25

-30

-35

-40

0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

0

1

2

3

4

5

6

Time [s]

(a) 

9

10 11 12

13 14 15

7

8
Time [s]

(b) 

Figure 5.6 - Example of  stresses due to the axial force in a upper chord (a) and in a diagonal member (b) obtained 
from the dynamic analysis. 

55

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Standard
Heavy
Light

7

17 78 80 82 119 121 123 125 127 129 131 23 25 157 159 161 163 165 167 169 171 173 175

Member

(a) 

Standard
Heavy
Light

2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0

2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0

x
e
d
n
i

e
g
a
m
a
D

x
e
d
n
i

e
g
a
m
a
D

5 29 33 54 182206 2 27 31 53 72 10718118919520521321949 68 89 10817718319019620120721422050 69 90 109178
Member

 (b)  

Figure 5.7 -  Damage index for (a) upper and lower chords and (b) diagonal members considering the standard, 
heavy and light traffic mixes. 

Standard
Heavy
Light

461 463 465 467 469 471 473 475 477 479 481 483 485 487 489 491 493 495 497 499 501 503 505 507 509 511 513 515
Member

(a) 

Standard
Heavy
Light

20.0
18.0
16.0
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0.0

x
e
d
n
i
e
g
a
m
a
D

2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0

x
e
d
n
i
e
g
a
m
a
D

1 84888435583954456849645852752773423663313333353373393413443463483503523553573593613633653683703723743761921138150133139145151134136141146148153
Member

(b)  

Figure 5.8 - Damage index for (a) floor-beams and (b) bracing and upper transversal elements considering the 
standard, heavy and light traffic mixes. 

56

 
 
 
 
 
 
5.4.2 

 Panaro Bridge (Italy) 

Two  FE  beam  models  were  developed  by  ANSYS®  software  for  the  standard  fatigue  assessment  of 
Panaro  bridge.  The  first  model  represented  the  bridge  original  resistant  scheme,  with  track  bracing 
cross  beams  fully  fixed  to  the  longitudinal  girders  (Full  Fixed  FE  Model).  The  second  model 
represented  the  actual  situation as a results of the local repair interventions, with track bracing cross 
beams connected by hinge joints to the longitudinal girders (Hinge FE Model) (Figures 5.9 and 5.10). 

HINGE/FULL FIXED 
JOINT

HINGE/FULL FIXED 
JOINT

Figure 5.9 - FEM model of the Panaro bridge 

Figure 5.10 - Track bracing cross beam connection to 
secondary longitudinal girders by full fixed/pin joints  

All girders were represented by beam elements (BEAM188), except bracing diagonals represented by 
truss  elements  (LINK8).  All  elements  were  defined  according  to  their  actual  geometrical  axis  and 
connected, where necessary, by proper internal constraints [5.17]. Those components characterized by 
variable  end  cross  sections,  as  longitudinal  girders,  track  and  upper  bracing  cross  beams,  were 
represented by I section element in central parts and T sections elements at the ends. This approach was 
necessary  to  model  properly  the  bridge  stiffness  and  to  obtain  reliable  force/stress  values,  as  end 
stiffness  greatly  influence  the  intensity  of  in-plane  and  out  of  plane  actions  induced  by  distortion 
phenomena and, consequently, the intensity of local stresses (Figures from 5.11 to 5.14). 
The evaluation of dynamic forces induced by train passages into the bridge components was performed 
according to the Eurocode rules. In particular, element stresses were calculated by incremental dynamic 
analysis  of  bridge  models  subjected  to  the  moving  loads  of  Standard  and  Heavy  train  traffic  mixes 
[5.13]. The total number of train passages was calculated assuming a life cycle of 100 years. 
As Eurocode fatigue train models are characterized by different lengths and velocities, the passage of 
each model was simulated assuming different sampling frequency in order to optimize the calculation 
times.  In  particular  analysis  frequencies,  calculated  in  such  a way that the distance covered by loads 
between two subsequent steps was equal to 1/10 of secondary longitudinal girder length for each train 
velocity, varied in the range 50-150 Hz. 

Rails and Sleepers

Main Cross
Beam

Secondary
Longitudinal
Girder

Main Cross
Beam

Figure 5.11 - Side view of secondary longitudinal girders 
with variable end cross sections 

Figure 5.12 - Local view of elements representing 
secondary longitudinal girders 

57

 
 
 
 
 
 
Upper Bracing
Cross Beam

Vertical Beam

Figure 5.13 - Side view of upper bracing cross beams with 
variable end cross sections 

Figure 5.14 - Local view of elements representing 
upper bracing cross beams 

In the dynamic analysis, damping characteristics of bridge components were represented assigning to 
each  element  a  proper  value  of  material  damping,  calculated  as  a  function  of  length  as  specified  by 
Eurocode [5.13]. Calculated girder material damping varied in the range 0.5% - 2.81%. 
Beam  element  stresses  were  extracted  from  the  FE  models  and  elaborated  in  order  to  calculate  the 
stress  time-histories  acting  on  net  cross  sections.  In  particular,  the  four  possible  combinations  of 
normal  stresses  induced  by  the  axial  force  and  the  two  bending  moments  were  considered  for  each 
element  section.  Moreover,  vertical  and  transverse  shear  stresses  acting  at  end  restraint  sections  of 
main cross girders and upper bracing cross beams were also considered. 
Normal and shear stress spectra were evaluated by rainflow counting technique. Fatigue damages were 
calculated  independently  adopting  the  linear  damage  accumulation  rule  of  Palmgren-Miner.  Fatigue 
classes  of  welded  built-up  members  were  assumed  according  to  the  indications  of  Eurocode  [5.13], 
while  for  riveted  components  the  fatigue  classes  proposed  by  Taras  and  Greiner  were  considered 
[5.18]. Fatigue classes of all bridge components are reported in Table 5.5. 

Table 5.5 - Fatigue classes adopted for Panaro bridge components 

Constructional detail 

Bridge Components 

One-shear joint with gusset plate 

Main Lower and Upper Strings; Main Vertical Beams;  
Main Diagonals Beams; Main Cross Beams at end sections; Lower 
and Upper Bracing Diagonals 

Fatigue Class 

85 for normal 
stresses 

Structural element with holes 
subject to bending and axial forces 

Main Cross Beams at intermediate sections; Secondary Longitudinal 
Girders at end sections; Upper Bracing Cross Beams at intermediate 
Sections 

90 for normal 
stresses 

Built-up sections with automatic 
fillet weld 

Secondary Longitudinal Girders at intermediate sections; Track cross 
beams at intermediate sections 

Tee-butt joints with fillet welds 

Track cross beams at end sections; Upper Bracing Cross Beams at 
End Sections 

125 for 
normal 
stresses 

36 for normal 
stresses  
80 for shear  
stresses 

For each element section, the fatigue damage Di induced by the i train type was calculated adopting the 
following simplified approach [5.13]: 

=
DD
s

i

,

max

+

D
t

v

+

D
t

h

(5.8) 

where Ds
,max is the maximum damage induced by normal stresses considering the combinations of axial 
force  and  bending  moments, Dtv is the vertical shear damage and Dth is the horizontal shear damage. 
Total fatigue damages obtained from Full Fixed and Hinge Model FE models for Standard and Heavy 
traffic mixes are reported in Figures from 5.15 to 5.18. 

58

 
 
 
 
  
Considering the Full Fixed FE Model, that represents the original resistance scheme of Panaro Bridge, 
it is possible to observe that a significant number of elements showed a fatigue damage greater than 0.1 
both for Heavy and Standard traffic mixes. Damage values between 0.1 and 1 were observed on almost 
all  vertical  beams  while  more  severe  damages,  greater  than  1,  occurred  at  the  end  cross  sections  of 
track  bracing  cross  beams  (as  really  occurred)  and  at  the  connection  joints  of  vertical  beams  with 
lower/upper  stringers  (actually  undamaged)  (Figure  5.19).  From  this  point  of  view,  more  refined 
analysis  of  identified  critical  details  seemed  to  be  necessary  for  a  proper  evaluation  of  actual  stress 
spectra. 

Full Fixed Model - Heavy Traffic Mix

200

150

100

50

l

s
t
n
e
m
e
E
d
e
g
a
m
a
D

f
o

r
e
b
m
u
N

0
0

200

150

100

50

l

s
t
n
e
m
e
E
d
e
g
a
m
a
D

f
o

r
e
b
m
u
N

0
0

l

s
t
n
e
m
e
E
d
e
g
a
m
a
D

f
o

r
e
b
m
u
N

100

80

60

40

20

0
0

0.5

Total Damage

1

1.5

Figure 5.15 - Full fixed FE model - Heavy Traffic Mix Damage 

Fill Fixed Model - Standard Traffic Mix

0.5

Total Damage

1

1.5

Figure 5.16 - Full fixed FE model - Standard Traffic Mix Damage 

Hinge Model - Heavy Traffic Mix

0.2

0.4

0.6
Total Damage

0.8

1

1.2

Figure 5.17 - Hinge FE Model - Heavy Traffic Mix Damage 

59

 
 
 
 
 
 
 
 
 
 
 
 
 
 
l

s
t
n
e
m
e
E
d
e
g
a
m
a
D

f
o

r
e
b
m
u
N

100

80

60

40

20

0
0

Hinge Model  - Standard Traffic Mix

0.5

Total Damage

1

1.5

Figure 5.18 - Hinge FE Model - Standard Traffic Mix Damage 

a)

b)

Figure 5.19 - Full Fixed FE Models - Heavy Traffic Mix: general (a) and detailed (b) graphical representation of 
damaged components (Yellow elements: -0.1 < Damage < 1 --- Red elements: Damage > 1) 

Also  for  the  Hinge  FE  Model  a  great  number  of  damaged  components  was  observed  for  Heavy  and 
Standard  traffic  mixes.  Vertical  beams  showed  damage  values  between  0.1  and  1  and  more  severe 
damages, greater than 1, occurred at the connection joints of vertical beams with lower/upper stringers. 
Nevertheless in the Hinge Model case, that represents the actual resistant scheme of Panaro bridge, the 
elements representing the end sections of track bracing cross beams did not show any fatigue damage. 
From these results, it is possible to observe that the local modification of the track bracing cross beams 
practically cancelled the distortion induced local forces while did not introduce significant variations in 
the global structural response of the bridge. 
It is important to notice in both the Full Fixed and Hinge FE Models the reliability of calculated results 
is  unknown,  as  expected  fatigue  damages  in  some  cases  really  occurred  but  in  others  didn't.  So, 
advanced  FE  models  of  critical  details  are  necessary  in  order  to  obtain  a  correct  evaluation  of  local 
stresses. From this point of view, the modelling experience of Panaro bridge confirmed the necessity of 
advanced analysis approaches in the design of new complex structures and in the assessment of older 
ones, as the use of standard techniques only could lead to an erroneous evaluation of local effects. 

Experimental Tests 

Usually  steel  bridges  show  a  real  structural  behaviour  different  from  the  theoretical  one,  as  every 
modelling  and  analysis  technique  actually  available  is  necessary  a  simplified  representation  of  more 
complex  structures.  From  this  point  of  view,  experimental  tests  are  very  effective  tools  for  the 
evaluation  of  real  forces  and  stresses  acting  into  bridge  steel  components  and,  consequently,  can  be 
adopted as a useful base for a reliable evaluation of fatigue performance. 
The experimental tests on Panaro bridge were focused on the structure dynamic identification and on 
evaluation of the effects induced by train passages. In particular, global and local vibration modes were 
identified by operative modal analysis technique (OMA) using the ambient vibrations (white noise) as 

60

 
 
 
 
 
 
 
 
excitation source. Moreover, the effects of train passages were investigated directly recording the strain 
time-histories  on  critical  details  and  the  horizontal  displacement  time-histories  of  the  deck  unidirec-
tional  bearings.  Such  tests  permitted  to  improve  the  knowledge  of  the  real  structural  behaviour  and 
constituted the base for the numerical updating of FE bridge model. 

Global/Local Experimental Dynamic Tests 

The experimental dynamic analysis on Panaro bridge was performed in order to obtain the identifica-
tion  of  the  global  vibration  modes  and,  moreover,  to  evaluate  the  dynamic  characteristics  of  track 
bracing cross beams. To this aim, accelerations in the vertical, horizontal and longitudinal directions of 
suitable structure key points were recorded assuming the ambient vibration as excitation source. 
In particular for the identification of global vibration modes, structure accelerations were recorded on 
eleven sections adopting a multi-step approach, that consists of acquiring data by moving sensors along 
the structure and keeping some of them fixed as "reference" (Figures 5.20 and 5.21). Such "reference" 
sensors are adopted as common base for merging the vibration modes identified by different recording 
configurations,  thus  providing  the  global  identification  of  the  structure  [5.19].  Accelerations  were 
recorded by PCB sensors and LMS Scadas acquisition unit adopting a sampling frequency of 400 Hz 
for time periods of 15 minutes at least. Some train passages occurred during the acquisition of ambient 
sources, nevertheless such noises were afterwards cleared from recorded signals before the numerical 
identification of natural vibration modes, obtained by PolyMAX algorithm [5.19]. 

A
A
n
o
i
t
c
e
s

1
A
n
o
i
t
c
e
s

2
A
n
o
i
t
c
e
s

R

3
A
n
o
i
t
c
e
s

4
A
n
o
i
t
c
e
s

6
A
n
o
i
t
c
e
s

Y

X

Z

8
A
n
o
i
t
c
e
s

9
A
n
o
i
t
c
e
s

R

0
1
A
n
o
i
t
c
e
s

B
B
n
o
i
t
c
e
s

PIACENZA

5
A
n
o
i
t
c
e
s

R

BOLOGNA

Figure 5.20 - Global dynamic test of Panaro Bridge: test layout 

d

a

Y

X

Z

c

b

Accelerometer - X direction

Accelerometer - Y direction

Accelerometer - Z direction

Figure 5.21 - Global dynamic test of Panaro Bridge - position / orientation of sensors on the typical cross section 

Seven  global  modes  of  vibration  were  clearly  identified  during  the  experimental  tests.  Modal 
frequencies, damping values and mode shapes are reported in Table 5.6, together with the mode phase 
collinearity  values  (MPC)  that  is  equal  to  the  unity  when  the  complex  modal  displacement  of  all 
recorded nodes have the same phase (i.e. the mode is real). The modal shape extracted for the identified 
modes are reported in Figure 5.22.  
Local dynamic tests were performed on a track bracing cross beam, recording vertical and transverse 
accelerations  of  upper  flange  at  midspan  and  lateral  sections  (Figure  5.23).  In  this  case,  a  single 
acquisition of all instrumented sections, realized adopting the same recording settings of global tests, 
permitted  to  identified  clearly  three  local  vibration  modes  of  the  cross  beam.  Modal  parameters  are 
reported in Table 5.7 while the calculated modal shapes are illustrated in Figure 5.24. 

61

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Table 5.6 - Identified global vibration mode of Panaro bridge. 

Mode n°  Frequency [Hz]  Damping [%]  MPC [%] 

Mode Shape 

1 
2 
3 
4 
5 
6 
7 

1.77 
3.65 
3.68 
4.08 
6.86 
10.93 
12.35 

0.49 
0.15 
0.65 
0.29 
0.15 
0.24 
0.25 

99.99 
99.23 
95.21 
71.70 
92.68 
90.16 
94.01 

Lateral Bending 
Torsional 
Vertical Bending 
Lateral Bending 
Distortional 
Torsional 
Vertical Bending 

1.77 Hz  Lateral

3.65 Hz  Torsional

3.68 Hz  Vertical Bending

4.08 Hz  Lateral

6.86 Hz  Distorsional

10.93 Hz  Torsional

12.35 Hz  Vertical Bending

Figure 5.22 - Panaro bridge - shapes of identified global vibration mode 

Accelerometers
Z and Y directions

X

Z

a) 

b)  

Figure 5.23: Instrumented sections (a) and sensors positioning (b) for the local cross beam dynamic tests. 

62

 
 
 
 
 
 
 
 
 
 
 
 
 
 
Table 5.7 - Identified local vibration modes of track bracing cross beam. 

Mode n°  Frequency [Hz]  Damping [%]  MPC [%]  Mode Shape 

1 

2 

3 

15.65 

44.18 

97.22 

0.82 

0.46 

0.56 

98.00 

99.96 

99.97 

Vertical Bending 

Lateral Bending 

Lateral Bending 

15.65 Vertical Bending

44.18 Hz Lateral Bending

97.22 Vertical Bending

Figure 5.24 - Panaro bridge - vibration mode shapes of track bracing cross beam 

Numerical updating 

The global vibration modes identified in the experimental dynamic tests were adopted as reference for 
the  numerical  updating  of  the  FE  Hinge  model  of  Panaro  bridge,  that  represents  the  actual  resistant 
scheme  of  the  structure.  To  this  aim,  an  automatic  optimization  procedure  was  implemented  by 
MODEFRONTIER  software  (Figure  5.25).  Objective  of  developed  procedure  was  to  minimize 
simultaneously  and  independently  the  differences between experimental and numerical eigenfrequen-
cies by the variation of suitable parameters.  
In  each  sequence  cycle,  parameter  values  were  changed  according  to  the  MOGA-II  optimization 
algorithm and transferred to the ANSYS FE model, in order to extract the first twenty eigenfrequencies 
and  vibration  mode  shapes  [5.20].  Calculated  results  were  then  elaborated  by  MATLAB  to  match 
experimental  and  numerical  mode  of  vibrations.  Mode  matching  between  ith  experimental  and  jth 
numerical vibration modes was obtained searching the highest MACij value, where MACij is the modal 
assurance criterion calculated for f

j mode shapes normalized to the unity. 

i and f

Figure 5.25 - Optimization scheme developed for the FE model updating 

After  the  optimization  procedure  was  calibrated,  suitable  mechanical  parameters  had  to  be  selected 
before  the  updating  of  Panaro  bridge  FE  Hinge  model.  From  a  preliminary  comparison  between 
numerical  and  experimental  vibration  modes,  a  large  difference  between  frequency  values  was 
observed, especially for those modes that involve transverse movements (lateral bending and torsion), 
as  reported  in  Table  5.8.  Some  modifications  were  so  introduced  into  the  FE  Hinge  model  before 
updating, in order to improve the numerical representation of bridge dynamic properties. 
The  rotation  center  of  end  bearings,  originally  assumed  at  the  contact  point  with  the  main  lower 
stringers, was moved in the downward direction, using a mass less point element (MASS21), and its 

63

 
 
 
 
 
 
 
position was assumed as an optimization parameter. This modification was due to the observation that 
the upper bearing surfaces have a circular shape with a unknown radius, with the consequence that the 
rotation center is lower than the contact point.  
Moreover, bearing stiffness were also represented into the FE model by spring elements (COMBIN14). 
In  particular,  longitudinal  and  torsional  (rotation  along  the  vertical  axis)  stiffness  of  fixed  vertical 
bearings  were  modeled,  while  for  unidirectional  bearings  only  torsional  spring  elements  were 
considered.    Bearing  stiffness  were  assumed  as  optimization  parameters  and  their  initial  values  were 
estimated  by  two  FE  models  of  fixed  and  unidirectional  bearings  subjected  to  unit  longitudinal 
displacement  or  unit  vertical  rotation  (Figure  5.26).  Spring  elements  were  directly  connected  to  the 
point  elements  representing  the  rotation  center  of  bearings.  Vertical/transverse  and  longitudinal 
rotation DOFs of point elements representing the rotation center of unidirectional bearings were fixed, 
while for fixed bearing the longitudinal DOF was also fixed. 
At  least,  also  the  values  of  dead  loads,  represented  by  equivalent  densities  of  bridge  components 
supporting secondary structures, were assumed as optimization parameters for the FE model updating. 
All selected optimization parameters are reported in Table 5.9. 

Table 5.8 - Comparison between numerical and experimental modal frequencies 

Mode n° 

1 

2 

3 

4 

5 

6 

7 

Exp. 
[Hz] 
1.77 

3.65 

3.68 

4.08 

6.86 

10.93 

12.35 

Mode Shape 

Lateral Bending 

Torsional 

Vertical Bending 

Lateral Bending 

Distortional 

Torsional 

Vertical Bending 

FE Hinge Model  
[Hz] 
2.284 

3.844 

3.989 

4.864 

7.377 

11.829 

13.763 

[%] 
29.0 

5.3 

8.4 

19.2 

7.5 

8.2 

11.4 

Modified FE Hinge Model 
[Hz] 
1.96 

3.56 

3.69 

4.15 

6.65 

10.56 

12.92 

[%] 
10.5 

2.4 

0.4 

1.8 

3.0 

3.4 

4.6 

a)  

b) 

Figure 5.26 - FE models of fixed (a) and unidirectional (b) bearings 

Table 5.9 - Selected optimization parameters for numerical updating of Panaro FE model 

Parameter n° 

1 

2 

3 

4 

5 

6 

7 

Description 
General material density of beam elements (dead weight of components, 
rivets and connecting plates) 
Material density of upper stringer elements (dead weight of components, 
rivets, connecting plates, suspended upper runaways) 
Material density of secondary longitudinal elements (dead weight of 
components, rivets, connecting plates, rails, sleepers, walking grates) 
Distance between lower stringer axis and bearing centre of rotation 

Torsional stiffness of fixed bearing 

Torsional stiffness of unidirectional bearing 

Longitudinal stiffness of fixed bearing 

Value 

9027.5 kg/m³ 

17477 kg/m³ 

16854.6 kg/m³ 

0.174 m 

124860 kN*m/rad 

230690 kN*m/rad 

1068800 kN/m 

The sensitivity functions of parameters n° 1-2-3 calculated for the 1st, 3rd and 4th vibration modes are 
reported in Figures 5.27a,b and c. The variation of such density parameters have a great influence on 
numerical values of the eigenfrequencies, while a variation of bearing stiffness parameters (n° 5-6-7) 
lower than 25% did not induced significant variations. 

64

 
 
D
D
D
D
 
D
D
D
D
M
M
M
M
 
 
 
The distance of the bearing rotation centers from lower stringer axis influenced the eigenfrequencies of 
modes  n°  1-3-5-6-7  in  the  range  0-20  m,  while  for  greater  values  the  frequencies  of  aforementioned 
vibration modes could be considered as constant (Figure 5.27d). 

Mode 1:   1.95 Hz

Mode 3:   3.68 Hz

]
z
H
[
y
c
n
e
u
q
e
r
F

]
z
H
[
y
c
n
e
u
q
e
r
F

2,12

2,07

2,02

1,97

1,92

1,87

1,82

4,6

4,5

4,4

4,3

4,2

4,1

4

3,9

3,8

Parameter 1

Parameter 2

Parameter 3

]
z
H
[
y
c
n
e
u
q
e
r
F

4

3,9

3,8

3,7

3,6

3,5

3,4

Parameter 1

Parameter 2

Parameter 3

%
5
2
-

%
0
2
-

%
5
1
-

%
0
1
-

%
5
-

%
0

%
5

Parameter Variation

%
0
1

%
5
1

%
0
2

%
5
2

%
5
2
-

%
0
2
-

%
5
1
-

%
0
1
-

%
5
-

%
0

%
5

Parameter Variation

%
0
1

%
5
1

%
0
2

%
5
2

b)

Mode 4:   4.08 Hz

Lower stringer axis - Rotation Centre Distance

Parameter 1

Parameter 2

Parameter 3

]
z
H
[
n
o
i
t
a

i
r
a
V
y
c
n
e
u
q
e
r
F

0,05

0

-0,05

-0,1

-0,15

-0,2

Mode 1
Mode 3
Mode 5
Mode 6
Mode 7

%
5
2
-

%
0
2
-

%
5
1
-

%
0
1
-

%
5
-

%
0

%
5

Parameter Variation

%
0
1

%
5
1

%
0
2

%
5
2

d)

0

5

0
1

5
1

0
2

5
2

0
3

5
3

0
4

5
4

0
5

Parameter Value [m]

Figure 5.27 - Sensitivity functions of parameter n° 1-2-3-5-6-7 calculated for vibration modes n° 1-3-4 

a)

c)

The  modeFRONTIER  procedure  converged  to  stable  parameter  configurations  after  3560  cycle 
iterations,  taking  less  than  15 seconds for each cycle for a total computation time equal to 15 hours. 
The  numerical  optimization  permitted  to  obtain  an  updated  model  characterized  by  numerical 
eigenfrequencies very similar to the experimental results (maximum difference of about 4.5%) and high 
MAC values, reported in Table 5.10. The complete MAC matrix is reported in Figure 5.28. 

Table 5.10 - Updated FE Model: initial/final values of parameters and numerical/experimental frequencies 

Parameter n° 

1 

2 

3 

4 

5 

6 

7 

Initial  
Value 
9027 kg/m³ 

Final  
Value 
7897 kg/m³ 

Mode 
n° 
1 

Numerical  
Freq. [Hz] 
1.82 

Experimental 
 Freq. [Hz] 
1.77 

17477 kg/m³ 

18735 kg/m³ 

16854 kg/m³ 

18068 kg/m³ 

0.17 m 

76.00 m 

124860 kN*m 

93645.00 kN*m 

230690 kN*m 

183270 kN*m 

1068800 kN/m 

1068800 kN/m 

2 

3 

4 

5 

6 

7 

3.64 

3.64 

4.13 

6.59 

10.66 

12.91 

3.65 

3.68 

4.08 

6.86 

10.93 

12.35 

 [%]  MAC 

2.73 

0.33 

1.06 

1.27 

4.00 

2.52 

4.53 

98.7% 

98.3% 

82.7% 

72.7% 

72.0% 

75.9% 

68.4% 

1

C
A
M

0.5

0

1

2

3

4

5

7

6

5

4

6

7

3

2

1

Figure 5.28 - Graphical representation of numerical/experimental MAC matrix 

65

 
 
 
 
 
 
 
 
 
 
 
D
D
D
D
 
Advanced Fatigue Assessment 

The Updated FE Hinge model of Panaro bridge was used for a further fatigue assessment of case study, 
comparing  results  obtained  from  an  advanced  modeling/updating  approach  with  standard  methodolo-
gies.  The  number  (Figures  5.29  and  5.30)  and  distribution  (Figure  5.31)  of  damaged  components  is 
similar  to  the  standard  results  calculated  by  the  Hinge  Model,  while  damage  intensities  are  a  little 
lower.  From  the  fatigue  assessment  point  of  view,  the  updating  process  didn't  showed  to  vary 
significantly  the  results  obtainable  from  a  global  FE  model,  thus  confirming  the  necessity  of  refined 
local analysis of critical details in order to catch properly the actual stress spectra induced by distortion 
and vibration phenomena.  

Updated Model - Heavy Traffic Mix

l

s
t
n
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m
e
E
d
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g
a
m
a
D

f
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r
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100

80

60

40

20

0
0

0.5

1

Total Damage
Figure 5.29 - Updated Model - Standard Traffic Mix Damage  

1.5

s
t

l

n
e
m
e
E
d
e
g
a
m
a
D

f

o

r
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100

80

60

40

20

0
0

Updated Model - Standard Traffic Mix

0.5

Total Damage

1

1.5

Figure 5.30 - Updated Model - Standard Traffic Mix Damage  

a)

b)

Figure 5.31 - Updated FE Models - Heavy Traffic Mix: general (a) and detailed (b) graphical representation of 
damaged components (Yellow elements: -0.1 < Damage < 1 --- Red elements: Damage > 1) 

66

 
 
 
 
 
 
 
 
 
 
 
 
5.4.3 

 Trezói Bridge (Portugal) 

A first numerical study was conducted based on a simple FE model using the software SOLVIA [5.21] 
to evaluate the dynamic behaviour of the bridge using a discretisation of the structure in 3D beam and 
truss elements (Figure 5.32). Due to the relatively low computational effort required by this model, it 
was possible to make a first calculation of natural frequencies and modal shapes, and to run simulations 
of  train  crossing,  introducing  also  the  train-bridge  interaction  effect,  and  using  the  resulting  nominal 
stresses to obtain a preliminary fatigue assessment.  

Figure 5.32 - Global view of the mesh of the 3D beam finite element model. 

Due  to  localised  vibration  effects  detected  in  these  analyses,  more  detailed  models  were  further 
developed. In subsequent stages, global and local finite element models using shell elements were built 
in order to capture local phenomena, like distortion induced fatigue and out-of-plane bending. 
In the former FE model, the deck and the lateral exterior elements of the columns were simulated with 
beam elements, while truss elements were used to represent the inner members that form a triangular 
geometry of the columns. The connection of these columns to the bridge deck is hinged, since there are 
mechanical  devices  that  allow  free  rotation  in  the  vertical  longitudinal  plane  of  the  bridge.  Several 
point  masses  were  distributed  along  the  deck  and  the  columns  to  simulate  the  metallic  connections, 
rivets and wood sleepers. The same elasticity modulus of 200 GPa was adopted for the deck and for the 
columns. 
The  bearings  of  the  deck  at  the  abutments  allow  the  rotation  in  the  vertical  plane.  Longitudinal 
movement is allowed in the east bearing and constrained in the west bearing. However, for low levels 
of  excitation,  as  is  the  case  during  ambient  vibration  tests,  the  behaviour  of  these  supports  can  be 
different,  since  friction  forces  can  prevent  displacements  or  rotations.  As  a  consequence,  for 
comparison with the frequencies and modal configurations obtained experimentally, restraining of  the 
longitudinal displacements in both supports was introduced. 
The natural frequencies and shapes of the most relevant modes provided by this initial global model are 
presented in Table 5.11. 

Table 5.11. Modal parameters calculated numerically 

Mode 

Freq. [Hz] 

Mode shape 

1st lateral bending mode 

2.99 

2nd lateral bending mode 

4.25 

3rd lateral bending mode 

4.53 

1st vertical bending mode 

5.33 

67

 
 
 
 
 
 
 
Mode 

Freq. [Hz] 

Mode shape 

1st torsion mode 

5.87 

2nd vertical bending mode 

6.76 

The first extracted modes, with frequencies defined in the range 0.6 Hz to 2.3Hz are associated with the 
bending of the two trapezoidal shape trusses that act as columns. The frequencies of these modes are 
very  distant  from  the  frequency  content  of  the  train  loading  and  are  not  important  for  the  fatigue 
evaluation for that reason . 
Numerical  simulations  were  conducted  in  order  to  evaluate  the  structural  response  due  to  train 
crossing. The calculations made, including the interaction effect between the bridge and the train, led 
to the conclusion that for this specific structure the effects due to the inertia of the vehicle are much 
inferior to the effects of its weight. In this case, the phenomenon of energy transfer between the bridge 
and the suspension of the vehicles showed to be of negligible importance for the range of circulation 
velocities that are possible and allowed in this bridge. To reach those conclusions, two methodologies 
were implemented within the dynamic calculations: the moving load methodology, which allows a fast 
and  reliable  way  to  obtain  dynamic  stresses  and  deformations;  and  a  methodology  that  uses  contact 
surfaces to simulate not only the dynamic behaviour of the bridge, but also its interaction with the train 
structure and mass. 
The first methodology consists in varying the vertical forces applied to the nodes belonging to the path 
of the train, creating a set of punctual loads that simulate the space variation of the load through a time 
variation  of  its  value.    To  include  the  interaction  effect,  the  train  was  modelled  as  an  independent 
structure  that  interacts  with  the  bridge.  This  was  achieved  using  a  specific  algorithm  included  in 
SOLVIA software [5.21] which allows the use of contact surfaces. This algorithm is described in detail 
in  Bathe  [5.22].  Taking  into  account  the  conclusions  of  these  previous  studies,  the  calculations 
presented  in  the  next  sections  were  made  using the less time consuming methodology of the moving 
load technique. 
For the purpose of adjusting and validating the numerical finite element model, an ambient vibration 
test  was  conducted.  The  adjustment  was  made  modifying  when  necessary  the  model’s  mechanical 
characteristics, the distribution of mass and the support conditions. 
Seismographs fitted with triaxial accelerometers were chosen for the field measurements because they 
appeared to be the most adequate, since these units are completely independent between them and of 
any  external  source,  they  possess  internal  batteries,  the  collected  information  is  kept  in  an  internal 
memory  card  and  their  synchronisation  is  assured  by  GPS,  thus  eliminating  the  necessity  of  electric 
cables. 
Accelerations due to ambient excitation were measured according to three orthogonal directions at 19 
sections at the top of one of the main beams. In each setup of 12 minutes, a seismograph was placed at 
a reference point located 6 m apart from the middle of the central span in a location where the majority 
of the modal coordinates would be different from zero, and two others were placed successively at the 
18 remaining points of measurement. For the identification of torsion modes, the ambient response was 
measured simultaneously at both edges of one section (upstream and downstream). 
With  the  time  series  obtained  in  each  setup,  average  normalised  power  spectra  (ANSPD)  for  the 
vertical and transversal directions were calculated (Figure 5.33). The selection of peaks of these spectra 
permitted the identification of the natural frequencies of the structure in the frequency range of interest. 
Figure 5.34 to Figure 5.36 present a comparison between identified and calculated mode shapes related 
to  the  most  relevant  natural  frequencies.  It’s  worth  noting  that  the  modes  identified  experimentally 
show  that  the  deck  does  not  undergo  longitudinal  movements.  Therefore,  the  hypothesis  of  fixing 
longitudinal movements in the abutments is correct. 
Table  5.12  summarises  the  frequencies  and  modal  configurations  identified  by  the  Peak  Picking 
method. These results are compared with the values obtained from the finite element model. 

68

 
 
 
 
 
Figure 5.33 - ANPSD: vertical and transversal direction. 

Experimental mode shapes 

Numerical mode shapes 

f=5.42 Hz

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95 100 105 110 115 120 125

0.5

0

0

-0.5

-1

-1.5

f=6.84 Hz

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95 100 105 110 115 120 125

Figure 5.34 - Lateral view of the first 2 identified (left) and calculated (right) vertical bending modes. 

Experimental mode shape 

Numerical mode shape 

f=2.95 Hz

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95 100 105 110 115 120 125

Figure 5.35 - Top view of the first identified (left) and calculated (right) lateral bending mode. 

Experimental mode shape 

f=6.01 Hz

Numerical mode shape 

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95 100 105 110 115 120 125

5

0

-5

-10

0

-0.5

-1

-1.5

0

-0.5

-1

-1.5

Figure 5.36 - Lateral view of the first identified (left) and calculated (right)  torsion mode. 

From  the  analysis  of  Table  5.12  and  of  Figure  5.34  to  Figure  5.36,  it  can  be  concluded  that  the 
correlation between identified and calculated natural frequencies is very good. 
An  initial  field  strain  measurement  campaign  was  conducted  at  Trezói  Bridge  using  electrical  strain 
gauges,  in  order  to  validate  the  numerical  simulations  of  the  crossing  of  the  trains  and  to  evaluate 
fatigue damage assessment of the principal structural elements. In Figure 5.37 the layout of the bridge 
instrumentation  is  shown.  Fourteen  sensors  were  applied  to  cross  sections  of  members  which 
experience  the  highest  tensile  stresses  and  four  strain  gauges  in  rails  sections  in  the  vicinity  of  both 
abutments outside the bridge in order to estimate traffic information.  In some cases, the location of the 

69

 
 
 
 
 
 
 
 
 
  
 
 
  
 
  
 
 
   
 
sensors  was  defined  to  capture  the  local  enhancement  effect  due  to  geometry  stress  concentration. 
These  stress  enhancements  were  foreseen  using  a  local  shell  finite  element  model  developed  in 
software Ansys [5.17], as illustrated in Figure 5.37 c). 

Table 5.12 - Calculated and identified natural frequencies. 

Identified 
(Hz) 

frequency 

Calculated 
(Hz) 

frequency 

Mode type 

Variation % 

2.95 

5.42 

6.01 

6.84 

2.99 

5.33 

5.87 

6.76 

1st transv. bending 

1st vert. bending 

1st torsional 

2nd vert. bending 

1.34% 

1.69% 

2.39% 

1.18% 

b) 

c) 

a) 

Figure 5.37 - Instrumentation layout: a) Location of the 14 instrumented sections and corresponding distribution of 
the sensors; b) strain gauges at a node with high stress concentrations; c) corresponding finite element model. 

The  acquisition  system  was  composed  by  a  PXI/SCXI  platform  from  National  Instruments.  A 
continuous  recording  of  the  readings  was  made  with  sampling  rate  of  100Hz,  which  is,  in  this  case, 
sufficient for dynamic observations. The timeframe chosen to measure stresses in this structure was set 
in two days that historically have higher traffic volume, though the measured traffic volume wasn´t so 
high as in previous years. However, during that period, 8 freight trains and 16 passenger trains crossed 
the bridge. 
The  local  model  illustrated  by  Figure  5.37  c)  was  validated  using  nominal  stresses  measured  at  the 
midspan of the structural element and the peak stresses near the joint. The stress magnitudes and the 
corresponding  stress  concentration  were  compared  and  the  average  calculated  stress  concentration 
factor  of  1.40  was  obtained  and  confronted  with  the  stress  concentration  factor  of  1.388  obtained 
through the measurements. These results increased the confidence in this local model hence allowing a 
more extensive fatigue analysis using numerical simulations. 
Real data obtained from the Portuguese railway agencies CP and Refer were used in order to compare 
calculated and measured stresses. The geometrical characteristics and loads of the vehicles that crossed 
the bridge during the measurement period were used to simulate these trains crossing using the global 
finite  element  model.  The  first  train  analysed  was  composed  by  a  locomotive  and  four  passenger 
wagons  with  270  tons  of  total  weight.  The  circulation  speed  was  estimated  using  the  measurements 
made in the rails and it was also possible to evaluate if a particular train was accelerating, breaking or 
maintaining a constant speed. An example of the speed estimation is presented in Figure 5.38, where 
each  peak  corresponds  to  a  single  axle.  The  distance  between  strain  gauges  was  divided  by  the  time 
difference  between  peaks  of  the  same  axle  to  obtain  the  velocity  per  axle.  In  the  present  case,  the 
average  estimated  velocity  was  30.5km/h.  An  automatic  processing  of  the  data  was  performed  using 
routines developed in Matlab.  

70

 
 
 
 
 
 
 
Figure 5.38 - Strain measured in rails sections in the vicinity of both abutments outside the bridge (east and west). 

Despite  some  difficulties  in  estimating  the  axle  loads,  which  may  be  influenced  by  the  dynamic 
component  enhanced  by  possible  wheel  defects,  the  vehicle  loads  were  estimated  using  the 
methodology  described  in  [5.23],  [5.24]  and  [5.25].  This  analysis  led  to  good  agreement  between 
estimated and known axle loads. 
In Figure 5.39, a comparison is made between measured and calculated stresses in the lower chord at 
the centre of the bridge, which is the element subjected to the highest tensile stress. The stress spectra 
were also compared, since they are a very useful representation of the stress history in the context of 
fatigue analysis. These were calculated using the Rainflow counting algorithm [5.26] implemented in 
Matlab. 

Stress Spectrum (calculated vs  measured)

ncalc

nmed

s
e
l
c
y
c

f
o

r
e
b
m
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N

10
9.5
9
8.5
8
7.5
7
6.5
6
5.5
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0

2 3 4 5 6 7 8 9

0
1

1
1

2
1

3
1

4
1

5
1

6
1

7
1

8
1

9
1

0
2

1
2

2
2

3
2

4
2

5
2

6
2

Stress Range (MPa)

                              a)                                                                           b)  

Figure 5.39 -  Comparison between numerical and calculated results: a) Measured vs. calculated stresses; b) 
Measured vs. calculated fatigue stress spectra. 

It  was  concluded  that  the  agreement  between  measured  and  calculated  stresses  and  stress  spectra  is 
good in both cases. The small differences between the stress histories may be due, in particular, to the 
geometry effect of the rivets and steel plates that are not modeled in this FEM and out of plane bending 
moments also not detected with these numerical simulations. Nevertheless these results increased the 
confidence in the numerical simulation made and in the train characteristics obtained. 
The  European  codes  prescriptions  include  the  possibility  of  implementation  of  dynamic  analysis  for 
simulation  of  specific  real  trains,  the  Eurocode  fatigue  trains  [5.13].  The  European  norm  EN1993-9 
[5.14] defines the rules for the calculation of fatigue resistance using the Whöller curves.  
However, the absence of a specific curve for the analysis of riveted details is a major drawback of the 
Eurocode 3. Taras and Greiner [5.18] conducted a research where several Whöler curves for different 
structural details were studied and, particularly, the riveted details were analysed in order to conclude 
about the best curve to represent its fatigue behaviour. The conclusion was that the Eurocode curve 71 
fitted best the details and was the most adequate for the analysis of such riveted components. 
In this context, the stress spectra of all the elements of Trezói Bridge were calculated using the EN1991 
fatigue trains and the three traffic mixed and, following the recommendations of [5.18], damage was 
calculated using fatigue curve 71 of EN1993-9. 

71

 
 
  
 
 
 
 
A  total  of  256  structural  elements  were  analysed  in  order  to  identify  the  most  sensitive  elements  to 
fatigue loading. Figure 5.40 summarises the damage indices obtained for all the elements considering 
the present age of the bridge and assuming the EN1991 Heavy Traffic scenario. A first conclusion can 
be made: there is a high number of elements with a damage index higher than 1.0, which means that 
they  would  collapse  under  the  conditions  specified  in  this  code.  The upper and lower chords are the 
elements  with  the  highest  stresses.  However  the  highest  damage  values  clearly  occur  at  the  cross 
girders. These elements have typically the highest damage values, since they suffer direct influence of 
each train axle, which leads to at least one stress cycle for each axle. For this reason, they are submitted 
to greater number of cycles than other principal structural elements. 

Figure 5.40 -  Fatigue damage indices for all structural elements for the EN1991 Heavy Traffic scenario. 

The  same  calculations  were  made  using  real  traffic  data  obtained  from  records  of  the  Portuguese 
railway  agencies  CP  and  Refer  for  this  specific  bridge  in  the  period  of  2001  to  2006,  assumimg  the 
traffic  conditions  in  this  period  as  conservative  in  terms  of  the  bridge  lifetime.  The  corresponding 
present  damage  indices  are  shown  in  Figure  5.41  and  clearly  a  difference  in  the  magnitude  of  the 
damage  is  observed  with  regard  to  the  one  obtained  based  on  the  EN1991  Heavy  traffic  scenario. 
Damages are lower than the ones obtained from the calculations based on the Eurocodes, certainly due 
to the fact that the real traffic is significantly lower than the assumed in EN1991. 

Figure 5.41 -Fatigue damage indices for all structural elements for real traffic scenario. 

To  enhance  the  confidence  in  these  results,  fatigue  damage  was  calculated  using  the  stress  histories 
measured  during  the  developed  temporary  monitoring  campaign.  Since  the  strain  gauges  were  then 

72

 
 
 
 
placed only in the main structural elements (upper and lower chords), it was not possible to evaluate 
the damage in the cross-girders. However, comparisons in the chords were conducted.  
All  14  instrumented  sections  of  the  bridge  were  analysed  for  each  train  passage.  The  corresponding 
results are presented in Figure 5.42 for the 1st day of measurements, where it can observed that damage 
is highest at sensors 1 to 6 which correspond to the chords.  
For  validation  purposes,  the  corresponding  damage  at  those  locations  was  also  calculated  using 
numerical simulations of the trains that crossed the bridge during the measurement campaign. 

a)                                                                            b) 

Figure 5.42 -  Damage per crossing in measured sections for the 1st day of measurements: a) using 
measured stresses; b) using numerical simulations. 

There  is  a  reasonable  agreement  between  damage  indexes  calculated  from  measured  strains  and 
calculated from simulations made with the FEM with beam elements. However, some discrepancies are 
observed in some locations of strain gauges close to the connection between chords and other structural 
elements. These are probably related to the influence of the geometry in the stress calculations. This 
difference was expected since the complex geometry of these areas was not reproduced in this model. 

5.4.4  Alcácer do Sal Bridge (Portugal) 

The first step of the fatigue analysis was the identification and classification of bridge’s fatigue prone 
details. This classification was based on the design information and also on visits to the bridge, during 
its construction phase. The most relevant details are: 

•  The extremities of the diagonals of the bridge (Figure 5.43); 

•  The welded elements transverse to the deck, such as diaphragms and stiffeners (Figure 5.44a); 

•  The  connections  between  transverse  beam  and  top  side  flanges,  at  each  diaphragm  (Figure 

5.44b). 

a) Top of the diagonal 

b) Bottom of the diagonal 

Figure 5.43 - Extremities of the diagonals 

73

 
 
 
 
 
 
a) Welded elements transverse to the deck 

b) Transverse beam 

Figure 5.44 - Elements perpendicular to the longitudinal direction of the deck 

Among all these details, the top connection of the diagonals of the last diaphragm of the bridge (Figure 
5.45) revealed to be the most critical one. 

Figure 5.45 - Critical detail 

The different details were analysed according to the damage linear accumulation method, described in 
the Eurocode 3. Figure 5.46 illustrates the different stress history responses of the critical detail of the 
bridge to the passage of the 12 standard fatigue trains. In this case the most conditioning train was the 
FT 5. 

Figure 5.46 - Stress histories in the critical detail, due to standard fatigue trains 

Since  the  structure  can  hold  2  tracks,  the  simultaneous  crossing  of  trains  over  the  bridge  was  also 
attended. A uniform probability distribution of the crossing points was considered.  

74

 
 
 
 
 
 
 
In  Figure  5.47  and  Figure  5.48,  the  stress  histories,  at  the  critical  detail,  due  to  the  simultaneous 
passage  of  two  Standard  Fatigue  Trains,  are  presented.  The  difference  between  the  two  cases  is  the 
point where both trains cross each other. 

Figure 5.47 - Stress history in the critical detail: crossing in the central span 

Figure 5.48 - Stress history in the critical detail: crossing in the last span 

Since different crossing points lead to different stress histories, the damage will also vary. That can be 
recognized by the different stress range histograms shown in Figure 5.49. In those histograms, the red 
line  is  the  adequate  Design  Fatigue  Strength  Curve,  according  to  Eurocode  3.  The  dashed  line 
highlights  the  design  value  of  the  constant  amplitude  fatigue  limit,  ∆σD.  A  summary  of  the  fatigue 
damage obtained at the critical detail as a function of the crossing point of the two Standard Fatigue 
Trains is presented in Figure 5.50. 
Assuming  that  the  crossing  point  has  an  uniform  probability  distribution,  an  average  value  of  the 
damage  for  simultaneous  crossings  can  be  computed,  Dcross.  Total  damage,  D,  including  12%  of 
crossing events occurrence can then be computed by the following equation:  

  D = (100%-12%) Dno cross + 12% Dcross                                                                                                                         (5.9) 

75

 
 
 
 
 
Equation  (5.9)  was  used  to  compute  the  total  damage  at  the  critical  detail,  for  the  different  traffic 
scenarios  present  in  Eurocode  3.  Each  traffic  scenario  is  defined  in  terms  of  variety  and  number  of 
standard fatigue trains per day. In all cases, the annual damage obtained is very low (Figure 5.51). 

a) Crossing at central span 

b) Crossing at last span 

Figure 5.49 - Stress range histograms for different crossing points 

Figure 5.50 - Damage in the critical detail as a function of the crossing point 

Figure 5.51 - Damage in the critical detail for different traffic scenarios 

76

 
 
 
 
 
 
The different modes of vibration of the bridge have different impacts on its total dynamic response. In 
order  to  assess  the  contribution  of  higher  frequency  modes,  the  total  response  (for  Standard  Fatigue 
Train 5), at the critical detail, obtained with the modal superposition method was decomposed into its 
different components (Figure 5.52).  

Figure 5.52 - Contribution of different modes of vibration modes to the total response 

The maximum stress range was then computed for an increasing number of modes, up to 30 Hz (Figure 
5.53). It was observed that, in this case, the maximum stress range is controlled mainly by the global 
modes of vibration, with lower frequencies. 

Figure 5.53 - Contribution of different modes of vibration modes to the maximum stress range 

5.4.5  Saalebrücke Großheringen (Germany) 

Finite element model for preliminary studies 

To  obtain  a  first  overview  of  the  global  structural  behaviour  of  the  bridge  a  relatively  simple  finite 
element model was created. This model was formed by beam elements with respective cross sections 
and  material  properties  of  the  main  girders,  the  cross  beams,  the  longitudinal  beams  and  the  main 
lateral bracings. With this model the natural frequencies and mode shapes of the lowest modes, which 
are also supposed to be the most relevant in the context of fatigue, were calculated. In Figure 5.54 the 
first three calculated global mode shapes and natural frequencies are summarized. 
As the considered structure consists of many slender structural elements, such as the bracings, it was 
expected,  that  also  local  modes  of  specific  elements  could  have  an  influence  on  vibration  induced 
fatigue.  These  effects  could  not  be  represented  sufficiently  well  by  the  first  finite  element  model. 
Additionally, a numerical model was needed that allowed for the calculation of local structural stresses. 
This gave reason for the creation of more refined finite element models. 

77

 
 
 
 
3.863 Hz 

5.707 Hz 

7.696 Hz 

Figure 5.54 - First model consisting of beam elements: first three calculated global modes. 

Finite element models for numerical simulations 

A  more  detailed  finite  element  model  of  the  complete  superstructure  of  the  bridge’s  end  span  was 
created in several stages. In the first refined model all primary steel members were modelled by 4 node 
shell elements. A graphic representation of this model is shown in Figure 5.55. 

Figure 5.55 - Refined finite element model of the whole superstructure consisting of shell elements 

To identify locations of concentrated stresses under live load, the movement of a constant vertical axel 
load along the longitudinal beams was simulated by means of the first refined model. The axel load was 
placed at several positions along the track. For each loading location the static response of the structure 
was computed. Figure 5.56a) indicates the von Mises stresses for load locations close to the cross beam 
that is connected to the main girder at the support. An interesting finding is that there is a significant 
stress concentration at the connection of the cross beam to the main girder.  

a)

b)

Figure 5.56 - a) Stress concentrations at the connection of cross beam and main girder at the pier support, b) 
influence line of von Mises stresses at the hot spot with respect to the load’s distance from the cross beam’s axis. 

The influence line of the stresses at the location of the stress concentration with respect to the distance 
of the axel load to the cross beam is given in Figure 5.56b). In this curve the maximal stresses occur 
shortly before the axel reaches the axis of the cross beam. This observation supports the hypothesis that 
an  eccentric  loading  on  the  cross  beam  results  in  torsion  of  the  cross  beam  which  leads  to  stress 
concentrations in the respective structural connection. 
The described results supported the initial assumption that the identified crack in the gusset plate was 
caused by fatigue due to cyclic loading during the passages of trains. Nevertheless a further refinement 
of the model was required for a detailed stress analysis. 
A  third  finite  element  model  of  the  complete  superstructure  of  the  first  span  of  the  Saalebrücke was 
created with the FE program ABAQUS. The superstructure of the unballasted bridge consists of two 

78

 
 
 
 
 
 
 
 
main  plate  girders and two longitudinal stringers interconnected with cross-girders (see Figure 5.57). 
The flange of the main girder was divided into 5 segments with different thicknesses ranging from 14 
mm to 70 mm (indicated as S1-S5 in Figure 5.57). In the model, all steel members were modelled by 
shell elements assuming linear elastic behaviour with a Young’s modulus of 205 GPa and a Poisson’s 
ratio  of  0.3.  This  global  FE  model  of  the  bridge  has  55541  elements  and  56100  nodes.  The  detailed 
mesh of some parts of the model is shown in Figure 5.58. 

Figure 5.57 - Geometry and mesh of the detailed finite element model of the whole superstructure 

a)

b)

Figure 5.58 - Detailed views of the mesh a) at the end section and b) in the central section 

This model allowed also for the representation of the local modal behaviour. The first 100 calculated 
modes clearly showed that the majority are local rather than global modes. This means that most modes 
are characterized by vibrations of several structural elements such as web plates of the main girders or 
bracings.  The  first  three  global  mode  shapes  and  examples  for  local  mode  shapes  which  are 
characterized by bending of bracing elements and web plates, respectively, are shown in Figure 5.59, 
while a selection of typical local modes is represented in Figure 5.60. 

a)

b)

c)

f = 3.61 Hz 

f = 5.46 Hz 

f = 8.01 Hz 

Figure 5.59 - Third FE-model: first three global modes 

79

 
 
 
 
 
 
 
 
Mode 7: 10.92 Hz 

Mode 8: 11.01 Hz 

Mode 9: 11.95 Hz 

Mode 10: 12.17 Hz 

Mode 14: 13.6 Hz 

Mode 30: 16.69 Hz 

Figure 5.60 - Third FE-model: selected local modes 

Experimental modal analyses - First campaign 

A  first  experimental  modal  analysis  was  performed  to  obtain  information  about  the  global  modal 
behaviour of the considered span. In total 18 measurement points on the top flanges of the main girders 
were  instrumented  with  3D-accelerometers  to  measure  the  accelerations  in  vertical  ,  lateral  and 
longitudinal direction. Additionally one measurement point in the adjacent span (MP 10 in fig. 5.61) 
was  taken  into  account.  Figure  5.61  shows  the  measurement  points  while  the  photographs  in  Figure 
5.62  give  an  impression  of  the  used  equipment.  From  this  first  experimental  modal  analysis  the  five 
global modes shown in Figure 5.63 were identified. 
From these results two major conclusions could be drawn: 
1. 
solutions. 
2. 
Two  of  the  identified  mode  shapes  show  very  small  amplitudes  of  the  first  span  but  maximal 
values for the sensor placed in the second span. I could be expected that these are mainly characterized 
by deflections of the second span. 

The first three identified global modes of the first span agree very well with the calculated modal 

80

 
 
 
 
 
 
 
 
 
 
Figure 5.61 - Measurement points in the first experimental campaign 

a) 

b) 

Figure 5.62 - Accelerometers located on the top flange of the main girder 

a) f1 = 3.60 Hz, ζ1 = 0.71 % 

b) f2 = 4.16 Hz, ζ2 = 2.15 % 

c) f3 = 5.26 Hz, ζ3 = 1.26 % 

d) f4 = 5.84 Hz, ζ4 = 2.87 % 

e) f5 = 7.91 Hz, ζ5 = 3.41 % 

Figure 5.63 - Global modes identified from the first experimental campaign: a) first lateral bending of the first 
span, b) lateral bending of the second span, c) vertical bending of the first span, d) vertical bending of the second 
span, e) torsion of the first span. 

Experimental modal analyses - Second campaign 

As  described  in  the  previous  section,  the  identified  modal  behaviour  showed  a  coupling  of  the  two 
adjacent  spans  even  though  both  spans  are  actually  separate  simply  supported  beams.  To  investigate 
this  coupling  of  adjacent  spans  as  well  as  to  identify  several  local  modes,  a  second  experimental 
campaign was carried out. 
With  respect  to  the  local  modal  behaviour  four  typical  elements  were  selected  for  the  local  modal 
analyses: 
• 

a longitudinal beam, 

81

 
 
 
 
 
 
• 

• 

• 

a web plate of the main girder, 

a rod of the lower bracings and 

a cross beam. 

For the identification of the global modal behaviour wireless force-balance accelerometers were placed 
at the upper flanges of the main girder while conventional piezoelectric accelerometers were installed 
at the lower flanges. To provide the possibility of a combination of the incomplete mode shapes from 
both  measurement  systems  reference  sensors  of  both  types  were  placed  at  two  common  locations. 
Figure 5.64 shows the used wireless and piezoelectric wired sensors at a reference point on the upper 
flange. 
The  locations  of  the  measurement  points  of  the  first  two  spans  are  illustrated  in  Figure  5.65  While 
sensors were placed in the first span both at the upper and the lower flange, the second span was only 
instrumented along the top flange. 

Figure 5.64 - Wireless sensors with piezoelectric sensors at a reference point on the upper flange 

Figure 5.65 - Sensor locations at spans I and II 

Piezoelectric  accelerometers  were  also  applied  to  the  selected  structural  elements  for  local  modal 
analyses.  These  sensors  were  connected  to  the  same  measurement  system  as  the  piezoelectric 
accelerometers  installed  at  the  lower  flange  of  the  main  girder.  All  measurement  setups  and  further 
specifications are given in the following sections. 
The photographs in Figure 5.66 give an overview about the measurement points at a longitudinal beam, 
a cross-beam, one of the lower bracings and a web plate of one of the main girders. 
At all setups vibration tests were performed with both ambient and impulse excitation. In several setups 
also measurements were acquired during train passages. 

82

 
 
 
 
a) 

c) 

b) 

d) 

Figure 5.66 - Measurement points at a) a longitudinal beam, b) a cross beam, c) a lower bracing  and d) a web 
plate of the main girder 

Operational modal analysis for the second test campaign 

The  modal  parameters  of  the  main  girders  were  extracted  from  the  measured  ambient  vibration  data 
using  the  covariance-driven  reference-based  Stochastic  Subspace  Identification  (SSI-cov/ref)  method 
[5.27].  Data  preprocessing,  system identification and modal analysis were performed using MACEC, 
which  is  a  MATLAB  toolbox  developed  for  Experimental  and  Operational  Modal  Analysis  by  the 
Structural Mechanics division of K.U. Leuven [5.28]. 
The  first  5  identified  global  mode  shapes  are  summarized  in  Figure  5.67  together  with  the  averaged 
natural frequencies, modal damping ratios and mode descriptions. One can deduce from several mode 
shapes  that  the  adjacent  superstructures  are  weakly  coupled.  Moreover,  a  good  correspondence  was 
found between the experimental results and the numerical results provided by the detailed FE model. 

Mode 1: f = 3.62 Hz, ζ = 0.38 %: lateral bending mode of span 1 

Mode 2: f = 4.20 Hz, ζ = 0.56 %: lateral bending mode of span 2 

Mode 3: f = 5.28 Hz, ζ = 0.36 %: vertical bending mode of span 1 

Mode 4: f = 5.93 Hz, ζ = 0.71 %: vertical bending mode of span 2 

Mode 5: f = 7.90 Hz, ζ = 0.53 %: torsional mode 

Figure 5.67 - Second test campaign: The first five identified global modes 

83

 
 
 
 
 
  
 
 
 
 
 
Figure 5.68 and 5.69 compare the modal displacements on the upper flanges of the main girders of the 
considered span for modes 1 and 2, respectively. The experimental mode shapes correspond very well 
with the calculated results conforming to high MAC values, exceeding 0.96. And the relative difference 
Df  defined  by  Df  =(fc- fe)/ fe between the numerical fc and experimental frequencies fe is less than 
3%. 
Several local modes of the selected structural elements were identified in the frequency range below 20 
Hz. Shown in Fig. 5.70 are two local modes identified on the selected web plate. Both are characterized 
by local plate bending. And shown in Fig. 5.71 (left) is the first vertical bending mode of the selected 
longitudinal beam. In addition, Fig. 5.71 (right) shows one of the local modes of the selected rod of the 
lower bracing, characterized by its vertical bending. Note that global modes as shown in Fig. 5.67 were 
also identified at the selected elements. In Fig. 5.72 the global modes 1 and 3 combined with the local 
deformation  identified  on  the  selected  web  plate  are  shown.  The  web  plate’s  local  deformation  is  in 
agreement with the global deformation. Similar results are found for the selected longitudinal beam. 

Figure 5.68 - Comparison of the identified mode 1 to the FE results (Df = 3%, MAC = 0.97) 

Figure 5.69 - Comparison of the identified mode 2 to the FE results (Df = 2%, MAC = 0.96) 

84

 
 
 
 
Figure 5.70 - Local modes identified on the selected web plate (f = 17.81Hz and f = 19.66 Hz) 

Figure 5.71 - Local modes identified on the selected longitudinal beam at f = 16.69Hz (left) and on the selected 
rod of the lower bracing at f = 17.88Hz (right) 

Figure 5.72 - Global mode 1 and mode 3 combined with the local deformation at the web plate. 

Operational Standard fatigue assessment 

The standard approach for the estimation of the remaining lifetime that has in practice to be applied to 
existing steel railway bridges in Germany is described in guideline 805 of Deutsche Bahn (DB, German 
Railways) [5.29]. The algorithm is structured into four steps: 

1) 

Calculation of the fatigue relevant coefficient for the loading capacity 

b

UICD,

b

,
UICD

=

zul

s

k
Be
,
s
max

g

B

UIC

where 

zulD

s

k
,Be

g

B

dynamic amplification factor, 
permitted  value  of  the  double  amplitude  of  the  stress  in  N/mm2  under 
consideration of the notch type, the material and the ratio of stresses  k  
and 
partial  safety  factor  for  the  structural  condition  (considering  cor- 
rosion). 

k

=

s
s

G

G

Q+
Q+

min
max

s
s

UIC

UIC

85

 
 
 
 
 
 
 
 
(cid:215)
Q
(cid:215)
D
 
Q
 
 
 
(cid:215)
(cid:215)
 
with 
s

G

smin

UIC

smax

UIC

stress in N/mm2 due to dead load, 

minimal  stress  in  N/mm2  from  traffic  load  UIC  71  (LM71  from  EN 
1991-2) and 
maximal stress in N/mm2 from traffic load UIC 71. 

2) 

Calculation of the total damage of the past for the reference year 1876 (fictive damage): 

VergD

,
1876

(cid:215)=
a






b

1

UICD
,

5






where 
VergD

,
1876

a  

accumulated  damage  sum  caused  by  traffic  from  the  past  to  the  year 
1996 for non-welded structures for the fictive year of construction 1876 
and a yearly gross tonnage of 25 × 106 t and 
coefficient depending on the decisive length l from [5.30]. 

3) 

4) 

Calculation  of the damage for the time period since first operation with underlying values of 
precise traffic conditions (precise damage): 
r

=

r

r

r

D

Verg

1

2

3

4

Verg

,
1876

D

with 
r  
r

1

2

r

3

r

4

correction factor to consider the construction year of the bridge, 

correction factor to consider the yearly gross tonnage per track 

=r
2

tbrutto
year

1
6
10

t

,

25

correction factor for multiple-tracks with the estimation of a meeting rate 

of 12.5 % depending on the ratio of stresses 

=

a

+
21
correction factor to consider the permitted train speed. 

s

1

and 

s

Calculation of the service life expectancy: 
D
+

1
01,0

R

=

Verg
D

Zuk

<

A

50

years

where 
ZukD  
A  
In case that measures to enhance or strengthen the structure are taken 

annual accumulated damage in the future and 

difference between the current year and the year 1996. 

ZukD  is calculated as 

D

Zuk

=

,0

025

r

r

,2

Zuk

,2

Verg

r

r

,4

Zuk

,4

Verg

b

b






,
UICD

,
Verg

UICD
,

,

Zuk

5






D

Verg

These  four  steps  of  the  standard  approach  were  applied  to  both  the  main  structural  members  of  the 
superstructure  and  the  gusset  plate  that  was  identified  to  be  critical with respect to fatigue action by 
numerical investigations. Due to a lack of information about the loads that were applied to the bridge in 
  was  set  to  1.  This  assumption  is  considered  as  conservative.  The 
the  past,  the  correction  factor 

r

2

86

 
 
 
 
 
 
 
 
 
(cid:215)
(cid:215)
(cid:215)
(cid:215)
 
 
·
(cid:215)
 
 
D
D
 
 
-
-
 
(cid:215)
(cid:215)
(cid:215)
(cid:215)
 
 
results  of  the  calculations  following  the  standard  approach  given  in  [5.30]  are  summarized  in  Table 
5.13. 

Table 5.13. Estimated remaining lifetime R for the year 2012 and the considered structural elements according to 
[5.29]. 

Structural element 

Longitudinal beam 
Cross beam 
Main girder 
Detail: Gusset plate 

max/

smin
[N/mm2] 

UIC

b

UICD,

k  

68.58 
90.94 
90.22 
170.00 

0.00 
0.00 
0.00 
0.00 

1.204 
0.964 
1.120 
0.681 

0.036 
0.075 
0.139 
0.027 

VergD  
[10-3] 
0.052 
0.158 
0.075 
0.904 

ZukD  
[10-3] 
1.31 
3.94 
1.88 
15.80 

R  

[years] 
50 
45 
50 
-12 

The  results  in  Table  5.13  show  that  all  main  structural  components  have  a  remaining  service  life 
expectancy of more than 30 years according to the standard assessment approach described in [5.29]. 
On  the  contrary  the  calculations  for  the  gusset  plate  result  in  a  negative  remaining  life  expectancy, 
which  means  that  the  life  time  has  already  expired.  This  result  agrees  with  the  identification  of  the 
crack at the existing structure. 

5.4.6  Salzach River Bridge (Austria) 

FE Global Models 

In the following section the initial modeling procedures for the selectedtruss bridge are presented. The 
geometry is taken from the design drawings.The numerical analysis is performed with the commercial 
Finite  Element  code  ANSYS  (SAS  IP).  A  numerical  model  representing  the  three-dimensional  mass 
and  stiffness  distribution  of  the  bridge  is  used.  The  implemented  model  is  shown  in  Figure  5.73  to 
Figure  5.75.The  elastic  modulus  for  the  structural  iron  is  assumed  98000  N/mm2.The  mass  per  unit 
volume of the material is assumed 7800 kg/m3.  

Y 

DOWNSTREAM 

Z 

X 

UPSTREAM 

Figure 5.73 - Solid view of the model. 

Y 

X 

Figure 5.74 - Solid view of the model in the YZ plane. 

DOWNSTREAM

UPSTREAM

Figure 5.75 - Solid view of the model in the XZ plane. 

87

 
 
 
 
 
 
 
 
 
 
 
Mass Distribution and Permanent Loads 

In order to accurately describe the torsion behavior of the structure and the distribution of the vertical 
loads, the non-structural mass (sleepers, rails, etc.) is distributed over the swelling trusses and the top 
belt of the Bridge. Also the overhanging pedestrian’s bridge on one side of the main bearing structure 
is modeled with MASS 21 elements and is distributed on the upstream bottom chord. 

Structural mass: 

•  Self-weight:  

Non-structural masses: 
•  Consoles:  
•  Wooden bar  

on the consoles:  

•  Rails:    
•  Wooden beams   

the mass per unit volume of the material was assumed 7800 kg/m³ 

the mass of all the consoles is approximately 1050 kg. 

the mass of the bar on the consoles is approximately 2508 kg. 
the mass of the rails is approximately 8960 kg. 

(swells for the rails):  the mass of the all the wooden beams is approximately 6080 kg 

Modal analysis 

Selected mode shapes are shown for the first approximate numerical model. 

Figure 5.76 - First lateral bending mode at 2.101Hz; First vertical bending mode at 4.668Hz. 

Figure 5.77 - Second lateral bending mode at 5.112Hz; Torsional mode at 5.705Hz. 

Experimental Dynamic Identification 

The choice of sensor positions was such that the global and local structural behavior could be analyzed 
both in vertical and horizontal directions. Altogether 14 sensors were used and 3 measurements with 3 

88

 
 
 
 
 
 
 
 
 
 
 
different layouts have been performed. In all 3 layouts 11 of these sensors were placed along the bridge 
on  the  overhanging  pedestrian  overpass  on  the  side  of  the  main  truss.  The remaining 3 sensors were 
placed  on  the  steel  plates  of  the  truss  nodes  under  the  top  deck  or  at  the  downstream  side.  These 
sensors provided information about the torsional motion of the bridge. 

DOWNSTREAM 

UPSTREAM 

Figure 5.78 - Sensor positioning. First set of three. 

Figure 5.79 - Brimos wireless on the walkway. EpiSensor on the joint. 

Natural Frequencies and Mode Shapes 

The identified mode shapes are given below. This identification was carried out on the data ridded of 
the transient signal parts which record train passing. 

Vertical mode at 3.74Hz – torsion 

Vertical mode at 4.89Hz – bending 

Vertical at 6.64Hz – bending /w lateral torsion 

Vertical mode at 7.81Hz – lateral torsion 

Figure 5.80 - Natural frequencies and mode shapes identified from data excluding railway traffic. 

89

 
 
 
 
 
 
 
 
 
For  the  data  including  transient  signal  parts  during  railway  traffic  the  first  six  modes  retrieved  are 
presented below. 

Vertical mode at 4.79Hz – bending 

Vertical mode at 5.15Hz – bending 

Vertical mode at 5.45Hz – bending  

Vertical at 6.44Hz – bending /w lateral torsion 

Figure 5.81 - Natural frequencies and mode shapes identified from data including railway traffic. 

Model Updating 

As  the  initial  model  showed  poor  coherence  with  the  outcome  of  the  tests  it  was  need  to  revisit  the 
model  and  direct  more  attention  to  questionable  inputs  like  supports  and  material  properties. 
Additionally, the model has been extended to allow for proper simulation of train-bridge interaction. 
The basic geometry of the bridge was left unchanged from the original model. 
In the last revision the numerical model of the bridge intended for the transient analysis was improved. 
The wooden sleepers have been introduced to the model to simulate the connection of the rails and the 
bridge  more  precisely.  The  rails  were  modeled  along  the  length  of  the bridge, plus 400m before and 
after  it  to  facilitate  a  full  transient  train-track  interaction  analysis.  The  connection  of  the  rails  to  the 
sleepers was assumed rigid. 
The actual supports of the bridge had to be checked on site. This inspection revealed the incorrectness 
of  the  initial  assumption.  There  are  fixed  supports  at  the east bank while the west bank supports are 
movable in the longitudinal direction. Moreover, the bridge is supported only at the bottom chords. 
The track-soil interaction is modeled according to Eurocode EN 1991-2:2003, 6.5.4.4, P.102. The rails 
off  the bridge were supported every 0.65m with non-linear spring-elements. The spring stiffness was 
chosen  for  the  vertical  supports  and  the  horizontal  supports  (simulating  the  creep  resistance  of  the 
rails).  

Figure 5.82 - Supports of the bridge at the east (left) and west (right) ends. 

90

 
 
 
 
 
 
 
 
 
 
EASTERN
RIVER BANK

WESTERN
RIVER BANK

Y

Z

X

Figure 5.83 - Supports of the modeled bridge at the east (left) and west (right) ends. 

Table 5.14 - Spring stiffness for creep resistance. 

u0 
[mm] 
0.5 

Creep resistance for each rail 
support [kN] 
39.00 

Creep resistance for every 1 m of 
track [kN/m] 
60.00 

Table 5.15 - Vertical support stiffness. 

Vertical support stiffness  
compression stiffness 

tension stiffness 

loaded track [kN/mm] 
20.14 

21.20 

Figure 5.84 - Scheme of the track-soil interaction. 

Permanent Loads 

The rails and sleepers have become an integral part of the model. Thus, the list of permanent loads has 
changed as follows. 

Structural mass: 

•  Self-weight:  
Non-structural masses: 

•  Consoles:    
•  Wooden bar  

the mass per unit volume of the material was assumed 7850 kg/m³ 

the mass of all the consoles is approximately 1050 kg. 

on the consoles:   the mass of the bar on the consoles is approximately 2508 kg. 

91

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Modal Analysis 

In  the  table  below  the  numerical  eigenfrequencies  are  compared  to  the  test  results.  They  show  an 
acceptable agreement which means the model can be used for further analysis. For the last entry of the 
table it was difficult to find a unison match. The two closest numerical modes could both harmonize 
with the experimental frequency as this was identified as a combination horizontal and vertical bending 
and torsion. 

Table 5.16 - Comparison of numerical and tested natural frequencies. 

Mode shapes 

Numerical [Hz] 

Tested [Hz] 

1 

2 

3 

4 

1. vertical bending 

3. horizontal bending 

2. vertical bending 

4.78 

12.74 

15.76 

4. horizontal bending / torsion 

18.23 / 19.76 

4.79 

12.96 

15.54 

19.26 

After  careful  matching  of  the  numerical  and  tested  modes  a  final  graphical  comparison  is  presented 
here. 

4.781Hz 

4.79Hz 

12.741Hz 

12.96Hz 

15.757Hz 

15.46Hz 

18.227Hz 

19.88Hz 

19.762Hz 

19.88Hz 

Figure 5.85 - Comparison of numerical and experimental mode shapes. 

92

 
 
 
 
 
 
 
 
 
 
With  this  model  an  interaction  analysis  has  been  run  and  the  output  force  and  stress  histories  also 
seems to support the aptness of the model for in depth analysis of the ongoing phenomena. 

Trend charts 

Figure 5.86 and Figure 5.87 show charts of the eigenfrequency characteristics. In these charts the red 
and  lighter  colours  represent  peaks  of  the  mode  shapes  viewed  from  above.  In  Figure  5.86  one  can 
clearly see that beginning from 4.8 Hz to around 7.5 Hz the first order mode shapes are concentrated. 
At around 13 Hz to 16.5 Hz the second order mode shapes and at around 20 Hz the third order mode 
shapes can be found. 

Figure 5.86 - Charts of normedeigenfrequency characteristics over the test stations (horizontal axis: along the 
bridge), vertical, 0-25Hz; with railway traffic (left), withoutrailway traffic (right). 

Figure 5.87 - Charts of the eigenfrequency characteristics over the measurement stations (horizontal axis: along the 
bridge) transversal, 0-25Hz, with railway traffic (left), withoutrailway traffic (right). 

If Figure 5.86 left and right are compared, it is possible to notice the influence of the train mass on the 
eigenfrequencies of the bridge. In the right chart of Figure 5.86  the related peaks one can see in the left 
appear to be one to two hertz higher in frequency. This additional mass of the trains leads to one to two 
hertz higher natural frequencies.  

Swing intensity 

Figure 5.88 shows the swing intensity for each frequency, with and without railway traffic. It can be 
seen that the swing intensity in vertical direction with railway traffic reaches zone III. That means this 
structure is exposed to such a high dynamic strain that fatigue problems can appear. 
Figure 5.89 shows the swinging amplitude per sensor. In this way, it is possible to evaluate the critical 
locations where high amplitudes occur leading to possible fatigue problems. 

93

 
 
 
 
 
 
 
10000

e
d
u
t
i
l

p
m
A

1000

100

III

IV

I

II

1.EF
2.EF
3.EF
4.EF
5.EF

6.4 mm²/s²
64 mm²/s²
2000 mm²/s²

e
d
u
t
i
l

p
m
A

6.EF
7.EF
8.EF
9.EF
10.EF

10

0.1

1

10

100

1000

10000

1000

100

10

0.1

III

IV

I

II

1

10

100

1000

Figure 5.88 - Swing intensity in vertical direction, without railway traffic (left), with railway traffic (right). 

Figure 5.89 - Maximum swing intensity sensor location for frequency 4.8Hz,10.16Hz and 12.96Hz. 

5.5  References 

[5.1]  C. Rainieri, G. Fabbrocino, G.M. Verderame, E. Cosenza, Modal analysis of the Tower of the 
Nations  in  Naples,  Proceedings  of  “XIV  World  Conference  on  Earthquake  Engineering”,  Beinjin, 
China, 2008. 

[5.2]  L.  Zhang,  T.  Wang,  Y  Tamura,  A  Frequency-Spatial  Decomposition  (FSDD)  Technique  for 
Operational  Modal  analysis.  In  Proceedings  of  the  “1st  International  Operational  Modal  Analysis 
Conference (IOMAC)”, April 26-27, Copenhagen, Denmark, 2005 

[5.3]  B. Cauberghe, Applied frequency-domain system identification in the field of experimental and 

94

 
 
 
 
 
 
 
 
operational modal analysis. PhD thesis, Vrije Universiteit Brussel, 2004 

[5.4]  R.  Pintelton,  J.  Schoukens,  System  Identification  –  a  Frequency  Domain  Approach,  IEEE 
Press, New York, 2001. 

[5.5]  D.J. Ewins, Modal Testing: Theory and Practice, New York, John M. Wiley & Sons, 2000. 

[5.6]  C. Gentile, F. Matinez y Cabrera, Dynamic assessment of a curved cable-stayed bridge at the 
Malpensa 2000 Airport, Milan, Italy. Structural Engineering International, 1, 52-58, 2001. 

[5.7]  L.  Vincenzi,  M.  Savoia,  Coupling  of  Differential  Evolution  algorithm  and  Quadratic 
Approximation  for  dynamic  identification,  Proceedings  of  “ICOSSAR  -  International  conference  of 
structural safety and reliability”, Osaka, Japan, 2009. 

[5.8]  L.  Vincenzi,  M.  Savoia,  Improving  the  speed  performance  of  an  evolutionary  algorithm  by 
second-order  cost  function  approximation.  Proceedings  of  “2nd  International  Conference  on 
Engineering Optimization”, September 6-9, Lisbon, Portugal, 2010. 

[5.9]  G.E.P. Box, K.B. Winson, On the experimental attainment of optimum conditions. J. R. Statist. 
Soc., B13, 1-45, 1951. 

[5.10]  A.  Khuri,  J.A.  Cornell,  Response  Surfaces.  Designs  and  Analyses,  Marcel  Dekker  Inc.,  New 
York, 1996. 

[5.11]  R.  Storn,  K.  Price,  Differential  Evolution  -  a  simple  and  efficient  heuristic  for  global 
optimization over continuous spaces. J. of Global Optimization, 11(4), 341-359, 1997. 

[5.12]  M. Savoia, L. Vincenzi, Differential evolution algorithm for dynamic structural identification. 
Journal of Earthquake Engineering, 12(5), 800-821, 2008 

[5.13]  EN 1991-2, Eurocode 1 - Actions on structures - Part 2: Traffic loads on bridges, 2003. 

[5.14]  EN 1993-1-9, Eurocode 3: Design of steel structures –Part 1-9: Fatigue, 2004. 

[5.15]  R.I. Stephens, A. Fatemi, R.R. Stephens, and H.O. Fuchs, Metal Fatigue in Engineering, 2nd 
edition, John Wiley & Sons, Inc., New York, 2001. 

[5.16]  N.E.  Dowling,  Mechanical  Behavior  of  Materials,  Prentice  Hall,  (3rd  Edition)  New  Jersey, 
USA, 2006. 

[5.17]  ANSYS  Inc.  (2005).  ANSYS  User  Manuals  Version  10.  ANSYS  Inc.  Global  Headquarters, 
Canonsburg, PA. 

[5.18]  Taras, A. and Greiner, R., 2009. Development and Application of a Fatigue Class Cata-logue 
for Riveted Bridge Components. Report ECCS TC6 - 2009 - xxx, Institute for Steel Structures and Shell 
Structures - Graz University of Technology, Graz. Austria. 

[5.19]  LMS International (2005). LMS TestLab Rev6A: Operational Modal Analysis User Manual 

[5.20]  ESTECO srl (2007). modeFRONTIER User Manual Version 4.0b. 

[5.21]  SOLVIA, Finite element system. http://www.solvia.com/ 

[5.22]  Bathe K. A solution method for planar and axisymetric contact problems. International Journal 
For Numerical Methods in Engineering 1985; 21:65-88 (1985). 

[5.23]  Moses  F.  Weigh-in-motion  system  using  instrumented  bridges.  Transportation  Engineering 
Journal (ASCE) 1979; 105:233–249. 

[5.24]  Liljencrantz  A,  Karoumi  R,  Olofsson  P.  Implementing  bridge  weigh-in-motion  for  railway 
traffic. Computers and Structures 2007; 85:80-88. 

[5.25]  Project  co-ordinator:  Norwegian  Geotechnical  Institute  (NGI).  Sustained  Performance  of 
Railway Tracks (SUPERTRACK). Final Report 2005. 

[5.26]  Kühn B, Lukić M, Nussbaumer A, Günther H-P, Helmerich R, Herion S et al. Assessment of 
Existing  Steel  Structures:  Recomendation  of  Remaining  Fatigue  Life.  Technical  Report  under  JRC  – 

95

 
 
 
ECCS. February 2008 

[5.27]  B.  Peeters,  G.  De  Roeck,  Reference-based  stochastic  subspace  identification  for  output-only 
modal analysis, Mechanical Systems and Signal Processing, 13 (6): 855–878, 1999. 

[5.28]  E.  Reynders,  M. Schevenels, G. De Roeck, MACEC: A Matlab toolbox for experimental and 
operational analysis, Report BWM-2008-07, April 2008. 

[5.29]  Richtlinie 805, Tragsicherheit bestehender Bauwerke, Deutschen Bahn AG, Germany, 2002. 

[5.30]  Richtlinie  804,  Eisenbahnbrücken  (und  sonstige  Ingenieurbauwerke)  planen,  bauen  und 
instand halten, Deutschen Bahn AG, Germany, 2010. 

[5.31]  D.  Ribeiro,  R.  Calçada,  R.  Delgado,  Fatigue  on  metallic  railway  bridges:  Methodology  of 
analysis and application to Alcácer do Sal Bridge, IABMAS, Porto, Portugal, 2006. 

[5.32]  C.  Vale,  N.  Ribeiro,  R.  Calçada,  R.  Delgado,  Dynamics  of  a  precast  system  for  high-speed 
railway tracks, COMPDYN, 3rd ECCOMAS, Corfu, Greece, May 2011. 

96

 
 
6  Vibration/Distortion Induced Fatigue 

The correct assessment of vibration/distortion phenomena into steel railway bridges is one of the main 
issue in current design as it concerns with the identification and evaluation of local effects generally 
neglected or simply not consider by standard mechanical modelling. The main effort is thus constituted 
by the identification of critical details most exposed to such phenomena and by the correct evaluation 
of secondary stresses induced by vibration/distortion mechanisms. 
The critical details can be successful identified by a preliminary analysis of bridge structural behaviour, 
by means of standard analysis properly refined in order to catch a qualitative indication of local fatigue 
behaviour.  In  case  of  existing  bridges,  experimental  dynamic  identification  of  structure  shall  be 
performed  in  order  to  calibrate  the  numerical  global  models  on  experimental  data  by  updating 
procedures. 
Once critical details are identified, en effective evaluation of local stresses can be obtained by means of 
numerical  local  models  able  to  represent  properly  the  vibration/distortion  phenomena  that  influence 
intensity  and  distribution  of  stresses.  In  order  to  provide  reliable  results,  local  models  shall  be 
calibrated  according  to  experimental  dynamic  data,  obtained  by  the  identification  of  local  vibration 
modes, or according to strain patterns recorded at train passage. 
Updated global/local models can be used for the calculation of stress spectra at critical details induced 
by the passage of every train type and composition, in case taking into account also of the train-bridge 
interaction  effects.  Fatigue  stress  spectra  shall  then  be  defined  according  to  actual  traffic  spectra  on 
railway line, i.e. real train typology, composition, speed and frequency. Long-term monitoring systems 
can  be  conveniently  adopted  for  the  evaluation  of  actual  train  traffic  and,  moreover,  for  the 
experimental evaluation of stress spectra into bridge components. 
At  least,  stress  spectra  shall  be  compared  with  fatigue  resistance  of  selected  detail  to  assess  its 
performance,  in  case  realizing  proper  fatigue  tests  of  the  component  able  to  reproduce  also  the 
identified vibration/distortion induced effects. The experimental evaluation of fatigue resistance shall 
be adopted when the real mechanical behaviour of selected detail is different from ideal one or in case 
of innovative solutions not expressly covered by design codes. 
A  reliable  vibration/distortion  fatigue  assessment  require  the  realization  of  extensive  and  advanced 
numerical  analysis,  generally  not  performed  at  design  stage,  together  with  experimental  tests  on 
constructed  structure  in  order  to  confirm  or  modify  the  design  assumptions.  Results  obtained  from 
research  analysis  on  case  studies  permitted  to  clarify  and  optimize  the  execution  of  experimental 
activities and numerical analysis for the typologies of railway steel bridges selected for the Project. 

6.1.1  Lagoscuro viaduct (Italy) 

From the results obtained by the standard fatigue assessment described in section 5, the critical details 
were identified (see Figure 6.1). The connections between floor-beams and stringers were identified as 
possible  critical  details  for  fatigue.  The  identified  critical  members  and  details  for  fatigue  are  the 
connections  between  the  floorbeams  and  (longitudinal)  stringers  and  the  connection  between  floor-
beams and the main truss girders. Fatigue on the first 2 diagonals and upper and lower chord were also 
investigated.  Moreover,  the  main  lower  bracings  (see  Figure  6.2)  were  identified  as  the  more  prone 
elements to local vibrations.  

Figure 6.1 - Bridge critical points where fatigue 
phenomena could arise. 

Figure 6.2 - Lower bracings, floorbeam and stringers. 

97

 
 
 
 
This system is composed by X bracings, spanning the whole width of the bridge in one direction and 
two  panels  in  the  other  direction.  Each  bracing  is  composed  by  two  L-shaped  elements  connected 
together by stiffening plates. All the other details are not critical for fatigue. Substructures containing 
the specific member were then studied. Local models developed to better investigate the connections 
behaviour are described in the next section. 

FE local models 

Local  detailed  substructures  were  modelled  (see  Figure  6.3-6.4).  In  all  the  models,  the  presence  of 
rivets  was  represented  by  rigid  links  connecting  elements  or  it  was  assumed  they  guarantee  the 
structural continuity.  
Substructure  “a”  models  the  bracing  system  and  it  is  able  to  gives  accurate  results  for  the  local 
vibrations  of  X  bracing  elements  and  stringers.  The  model  is  composed  by  4600  nodes,  4400  shell 
elements and 136 links (see Figure 6.3a). In all bridges, only two type of bracings are present. For the 
local  analysis,  the  most  recurrent  one  was  chosen.  The  main  natural  modes  are  obtained  by  modal 
analysis and the first bending mode shape  of bracings is found at 5.6 Hz. In the further analyses, the 
higher modes were neglected due to their very low vibration amplitudes and high frequency. 
The  model  “b”  aims  to  faithfully  reproduce  the  connections  between  floor-beams  and  stringers,  and 
floor-beams  with  the  two  main  truss  girder  (Figure  6.3b).  From  this  model,  information  about  stress 
history of floor-beams will be obtained. All floor-beams have the same section; the local model is then 
representative for the whole old viaduct. In the model “b”, about 5000 nodes, 5000 shell elements and 
200 links are used. 
The  model  “c”  (Figure  6.4)  is  an  accurate  model  of  the  connection  between  a  floorbeam  and  a 
longitudinal stringer. Brick elements are used. Also the presence of rivets are taken into accout and the 
mesh of each steel plate is carefully refined close to each rivet. In model “c”, about 24000 nodes and 
15000 brick linear elastic elements are used.  

18:43:15

Y
Y

Z
Z

X
X

Z
Z

X
X

Y
Y

(a) 

(b) 

Figure 6.3 - Local mode (a) for stringers and bracings and (b) for floor-beams. 

(a) 

(b) 

Figure 6.4 - Local mode (a) for stringers and bracings and (b) for floor-beams. 

98

 
 
 
 
 
 
 
 
An  advanced  fatigue  assessment  is  carried  out  on  the  Old  PonteLagosuro  viaduct.  After  having 
identified the members potentially subject to fatigue or local vibrations (see section 6.1), a substructure 
finite element model containing the specific member was studied. The detailed substructure model has 
been  then  excited  by  prescribing  at  the  boundaries  the  displacement  time  histories  obtained  in  the 
corresponding  nodes  of  the  optimized  global  model.  The  train  transits  on  the  bridge  were  simulated 
considering a 3-dimensional Vehicle Bridge Interaction model.  
From the stresses obtained in the local FE model, the fatigue assessment was carried out following the 
procedure  proposed  in  [6.1].  In  order  to  obtain  the  stress  ranges  on  each  element,  dynamic  analyses 
were  performed  with  train  masses  defined  according  to  EN  1991  -  Eurocode  1  [6.2].  The  damage 
indexes were evaluated according to the Miner role.  

Dynamic analysis with 3D –vehicle bridge interacting model 

The  train  transits  on  the  bridge  were  simulated  in  order  to  detect  the  presence  of  local  vibrations  in 
structural  members.  In  the  dynamic  analysis  of  a  railway  bridge,  moving  loads  are  traditionally 
represented  as  a  series  of  moving  axle  loads.  This  approach  is  adopted  by  the  design  codes  (the 
Eurocode 1 [6.2]) and it was adopted in the standard fatigue assessment procedure. In this model, the 
global dynamic behaviour of the bridge caused by the moving action of the vehicle can be described 
with  a  sufficient  degree  of  accuracy.  However,  the  effect  of  interaction  between  the  bridge  and  the 
moving load is neglected. For this reason, the moving load model gives good results only if the mass of 
the vehicle is small relative to that of the bridge, or when the vibration frequencies of the bridge are 
well separated to those of the vehicle [6.3].  
The  dynamic  interaction  between  a  bridge  and  the  moving  vehicles  represents  a  special  discipline 
within  the  structural  dynamics  field  [6.4].  In  order  to  simulate  the  train-bridge  interactive  dynamics 
many kinds of two-dimensional and three-dimensional models for train carriages have been presented 
and adopted [6.5-6.8], in which the springs and the dashpots are used to describe the interactive effects 
between  wheels  and  primary  suspensions  as  well  as  primary  and  secondary  suspensions.  The 
subsystems  interact  through  the  contact  forces,  the  forces  induced  at  the  contact  points  between  the 
wheels and the rails surface (of the railway bridge) or the pavement surface (of the highway bridge). 
Such a problem is nonlinear and time-dependent [6.9] due to the fact that the contact forces may move 
from time to time, while their magnitudes do not remain constant, as a result of the relative movement 
of the two subsystems. 
Following the procedure described in [6.10], a 3-dimensional Vehicle Bridge Interaction (VBI) model 
was  applied  to  the  global  model  of  the  Pontelagoscuro  bridges  to  obtain  the  displacements  in  both 
vertical  and  horizontal  directions.  In  all  models,  the  car  bodies,  the  bogies  and  the  wheels  were 
assumed to be rigid and connected by means of springs and dashpots to represent the two suspensions 
systems [6.10-6.11]. Dynamic analyses were conducted considering a three dimensional model for cars 
and bridge. Data regarding the suspensions system of the high-speed train ETR500Y given in [6.10] are 
used. The masses of cars were defined according to the Eurocode [6.1]. 
To solve the bridge vehicle interacting problem, a set of ordinary differential equations of motion must 
be written to represent the dynamic behaviour of the bridge as: 

ɺɺ

+

vKvCvM
b

b

b

b

b

+

ɺ

=

P
b

b

(6.1) 

bC   and 

bM , 
bvɺɺ

bK are  the  mass  matrix,  damping  matrix  and  stiffness  matrix,  respectively; 
 represent the displacement, velocity and acceleration vectors of the bridge DOFs, and 

where 
bvɺ and 
the force vector transferred to the bridge.  
In some finite elements models, thousands of nodes and elements are used, therefore the Equation (6.1) 
could  be  a  system  of  thousands  equations.  Due  to  the  fact  that  it  is  often  possible  to  describe  an 
approximate  dynamic  response  with  just  a  few  modes,  the  system  of  equations  can  be  substantially 
reduced.  In  fact,  rewriting  the  equations  of  motion  in  modal  coordinates  and  normalizing  the  mode 
shapes in respect to the mass matrix, the set of equations assume the following form: 

bv , 
bP is 

ɺɺ
ɺ
qKqCq
b

+

+

*
b

*
b

b

=

*
P
b

b

(6.2) 

where the matrices 

*
bC , 

*

bK  and the vector 

*

bP  are defined as follows: 

99

 
 
 
 
C

*
b

x=
2

=
*
*
PΩKΩ
b
b

;2

;

F=

T

P
b

(6.3) 

and  F

 is the 

N DOF

0N

 mode shapes matrix and  Ω  is the 

N ·

0 N

0

diagonal matrix that collects the 

frequencies of the considered modes. 
bP  is determined knowing the position along the bridge of the 
wheel axles at each time step. In this case the first four optimized modes are considered to describe the 
motion of the bridge, so that Equation (7.2) results in a set of only four uncoupled equations. 
Vehicle models with a varying degree of sophistication can be found in literature (see for instance [6.4, 
6.5,  6.8])  to  account  for  the  dynamic  effect  between  train  and  bridge.  In  all  cases,  to  solve  the 
interacting problem, a set of ordinary differential equations of motion can be written as:  

ɺɺ
vM
v

v

+

+
vKvC

ɺ

v

v

v

=

P
v

v

(6.4) 

vM , 

vC   and 

vK   are  the  mass,  damping  and  stiffness  matrices; 

  are  the 
where 
vP  is the vector that collects 
displacement, velocity and acceleration vectors of the vehicle system; and 
the dynamic force on the vehicle. In this work, a sophisticated vehicle model, proposed in [6.10] and 
represented in Figure 6.5, was implemented. Instead of a 2D model, using the 3D model also horizontal 
and torsional modes can be involved and taken into account. The vehicle–bridge dynamic interaction 
problem  can  be  solved  with  an  iterative  procedure  within  each  time  step  coupling  the  two  sets  of 
equations enforcing compatibility conditions in terms of displacements at the contact points: 

vv , 

vvɺ and 

vvɺɺ

b

ɺɺ
ɺ

*
*
qKqCq
bb
bb

+
+
vKvCvM

v

+
ɺɺ

+
ɺ

=

v

v

v

v

*
P
b
=

v

P
v

(6.5) 

t
The  equations  of  motions  are  solved  using  Newmark’s  method.  Therefore,  assigning  a  time  step 
and  knowing  the  velocity  v,  the  weight  W  and  the  relative  distances  of  all  the  axles  of  each  train, 
Equation  (6.5)  can  be  solved.  Then  the  interaction  forces  on  the  bridge  and  on  the  vehicle  can  be 
computed  for  each  time  step,  and  so  nodal  loads  time  history  can  be  obtained.  Furthermore, 
accelerations, velocities and displacements time history for each degree of freedom both for bridge and 
vehicle can be calculated for the given crossing train. More details are given in [6.13, 6.14].  

1
h

2
h

3
h

CH

CV

K H

RX2

Y2

Z 2

2b2

CHH

CVV

K VV

RX1

Z1

Y1

K V

YW1

Z W1

RXW1

2b1

K VV

CVV

RY1

Z1

CV

W2

K V

W1

K HH

RY1

Y1

RY2

Z 2

RY2

Y2

2s

W3

RY3

W4

Z 3

2q0

RY3

Y3

Figure 6.5 - Vehicle models with 15 DOFs [6.10] 

Figures 6.6 compare the displacements time history at mid span node obtained using the moving load 
model and the VBI model for Train type 1 and Train type 3. Small differences between the two train 
models are obtained during the train passage and in the free vibrations after the train has left the bridge. 
The maximum displacement of the bridge is about 25 mm for the moving loads model and 27 mm for 
the  VBI  model  when  the  train  type  1  crosses  the  bridge.  Similar  results  can  be  obtained  for  all 
passengers trains. 
Some  representative  results  obtained  with  the  3D  VBI  model  are  shown  in  Figure  6.7  for equivalent 
train Type 5 and 7. As shown, the 3D VBI model is able to obtain also a dynamic interaction between 
the cars and the bridge in the horizontal direction. To excite horizontal and torsional modes, dynamic 

100

 
 
 
·
 
 
D
 
 
analyses  were  carried  out  imposing  a  initial  condition  (displacement)  to  the  cars.  As  expected,  very 
small oscillations amplitude is obtained in the horizontal direction, being the railway track centred in 
respect to the axis of the bridge, but sufficient to load the X bracings and to excite the torsional mode 
shape. In order to better understand the dynamic behaviour of the mid span transversal cross-section of  
Figure 6.8a, the horizontal time history displacement of the nodes 989 and 1093 and the vertical time 
history displacement of the nodes 3448 and 3888 regarding the train type 5 are plotted in Figure 6.8b 
and 6.9c, respectively. 
Figure  6.8b  shows  the  counter  phase  motion  of  the  nodes  3448  and  3888  suggesting  that  torsional 
vibration  is  involved.  Finally,  in  Figure  6.9,  the  horizontal and vertical acceleration time histories of 
the lower mid span node 989 of the bridge (see Figure 6.8a) due to the passage of the freight train type 
5  are  shown.  Higher  values  of  the  accelerations  are  predicted  in  the  horizontal  direction  with  values 
bounded between 1.2 and -1.2 m/s2, in comparison to the accelerations in the vertical direction which 
are included within 0.3 and -0.3 m/s2. 

]

m
m

[

t
n
e
m
e
c
a

l

p
s
D

i

5

0

-5

-10

-15

-20

-25

-30

0

]

m
m

[

Moving loads model
VBI model

t
n
e
m
e
c
a
l
p
s
i
D

2

4

6

8

Time [s]

10

(a) 

5

0

-5

-10

-15

-20

0

Moving loads model
VBI model

2

4

6

Time [s]

8

10

(b) 

Figure 6.6 - Comparison between moving loads and 3D VBI models for (a) train type 1 and (b) train type 3 

]

m
m

[

t
n
e
m
e
c
a
l

p
s
i
D

5

0

-5

-10

-15

-20

-25

-30

-35

-40

-45

0

]

m
m

[

t
n
e
m
e
c
a
l

p
s
i
D

Horizontal
Vertical

5

10
Time [s]

15

20

(a) 

5

0

-5

-10

-15

-20

-25

-30

0

Horizontal
Vertical

2

4

6

8

10

Time [s]

(b) 

Figure 6.7 - 3D VBI analyses: horizontal and vertical displacement for (a) train type 5 and (b) train type 7 

1093 

]

m
m

[

t
n
e
m
e
c
a
l
p
s
i
D

]

m
m

[

3448 

3888 

989 

(a) 

t
n
e
m
e
c
a
l
p
s
i
D

4

3

2

1

0

-1

-2

-3

-4

0

5

0

-5

-10

-15

-20

-25

-30

-35

-40

Node 989
Node 1093 

2

4

6

8
10
Time [s]

12

14

16

18

(b) 

Node 3448
Node 3888

Figure 6.8 - (a) Bridge transversal cross–section; (b) horizontal displacement time history of the nodes 989 and 
1093; (c) vertical displacement time history of the nodes 3448 and 3888; (d) lower scale view of (c) 

-45

0

2

4

6

10
8
Time [s]

12

14

16

18

(c)   

101

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1.5

1

0.5

0

-0.5

-1

]

2

s
/
m

[

n
o

i
t
a
r
e
l
e
c
c
A

0.4

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

]

2

/

s
m

[
n
o

l

i
t
a
r
e
e
c
c
A

-1.5

0

2

4

6

8
10
Time [s]

12

14

16

18

(a) 

-0.4

0

2

4

6

8
10
Time [s]

12

14

16

18

(b) 

Figure 6.9 - (a) horizontal acceleration time history and (b) vertical acceleration time history of the mid span node 
of the bridge 

The  detailed  substructure  model  has  been  then  excited  by  prescribing  at  the  boundaries  the 
displacement time histories obtained in the corresponding nodes of the global model. A linear dynamic 
transient  analysis  has  then  been  performed  and  stress  histories  are  obtained.  Results  are  given  for  7 
selected points, where the fatigue phenomena could mainly arise:  
-  Points no. “1” and “2” are located in the bottom chord, as indicated in Figure 6.10a; 
-  Point no. “3” is on the stringer, at midspan, placed in the bottom chord, as indicated in Figure 6.10a; 
-  Points no. “4” and “5” are on the floor-beam, see Figure 6.10b; 
-  Points no. “6” and “7” are on the main bracing system, Figure 6.10a. 
The investigated points are selected considering the results obtained in the global fatigue analysis and 
results  of  stress  intensity  in  the  local  models.  The  stress  history  of  some  of  the  selected  points  are 
shown in Figure 6.12-6.15.  
The  maximum  stress  for  truss  girder  members  attains  about  25  MPa  in  the  case  of  transit  of  a 
passengers train (see Figure 6.10a), 18 MPa for high speed trains (Figure 6.10b) and 65 MPa for freight 
trains (Figure 6.10c). Very high stress are obtained for stringers (see Figure 6.11): the maximum stress 
range is greater than 180 MPa when the train type 6 transits on the bridge. As far as the bracings are 
concerned  (Figure  6.13),  the  stress  history  is  clearly  due  to  the  superposition  of  low  frequency 
excitation, due to the quasi-static displacements, and higher frequency stresses probably caused by the 
local vibrations of the member.  
From  the  stresses  obtained  in  the  detailed  FE  model,  the  fatigue  assessment  is  carried  out  with  the 
procedure described in the following. 

1

NODAL SOLUTION

STEP=1
SUB =10
TIME=.1
UY       (AVG)
RSYS=0
DMX =.001673
SMN =-.209E-03
SMX =.001265

2 

1 

3 

Y

Z

X

MX

SEQV     (NOAVG)
DMX =.541E-06
SMN =15553
SMX =.489E+08

JAN 29 2012
18:56:56

MN

6 

7 

4 

5 

MX

MN

Z

XY

-.209E-03

-.454E-04

.118E-03

.282E-03

.446E-03

.610E-03

.774E-03

.938E-03

.001101

.001265

15553

.545E+07

.109E+08

.163E+08

.217E+08

.272E+08

.326E+08

.380E+08

.435E+08

.489E+08

Figure 6.10 - Monitored points for fatigue assessment. 

102

 
 
 
 
                                                                                
 
                                                                                
 
 
 
 
2

4

6
Time [s]

8

10

12

(a) 

2

4

6

8

10

Time [s]

(b) 

]

a
P
M

[

s
s
e
r
t

S

]
a
P
M

[

s
s
e
r
t

S

80

60

40

20

0

-20

-40

0

60

40

20

0

-20

-40

0

200

150

100

50

0

-50

]
a
P
M

[

s
s
e
r
t

S

2

4

6
Time [s]

8

10

12

(a) 

2

4

6

8

10

Time [s]

(b) 

]
a
P
M

[

s
s
e
r
t

S

]
a
P
M

[

s
s
e
r
t

S

]
a
P
M

[

s
s
e
r
t

S

30

25

20

15

10

5

0

-5
0

20

15

10

5

0

-5

0

80

60

40

20

0

-20

0

5

10
Time [s]

15

20

(c)  

Figure 6.11 - Stress history of the lower chord at 
midspan for: (a) train type 1, (b) train type 3, (c) train 
type 6. 

-100

0

5

10
Time [s]

15

20

(c)  

Figure 6.12 - Stress history in a stringer for: (a) train 
type 1, (b) train type 3, (c) train type 6. 

10

0

-10

-20

-30

]

a
P
M

[

s
s
e
r
t

S

-40

0

2

4

6
Time [s]

8

10

12

(a) 

2

4

6

8

10

Time [s]

(b) 

.

]

a
P
M

[

s
s
e
r
t

S

5

0

-5

-10

-15

-20

-25

0

20

0

-20

-40

-60

]
a
P
M

[

s
s
e
r
t

S

-80

0

5

10
Time [s]

15

20

(c)   

Figure 6.13 - Stress history of a floor-beam for: (a) 
type 1 train, (b) type 3 train, (c) type 6 train, (d) type 7 
train 

]
a
P
M

[

s
s
e
r
t

S

]
a
P
M

[

s
s
e
r
t

S

]
a
P
M

[

s
s
e
r
t

S

5

0

-5

-10

-15

0

5

0

-5

-10

-15

0

10

0

-10

-20

-30

-40

0

2

4

6
Time [s]

8

10

12

(a) 

2

4

6

8

10

Time [s]

(b) 

5

10
Time [s]

15

20

(c)   

Figure 6.14 - Stress history of the bracing for: (a) type 
1 train, (b) type 3 train, (c) type 6 train, (d) type 7 train. 

103

 
 
 
 
 
 
 
 
 
 
 
 
 
 
Advanced fatigue assessment 

Information in design standards is sometimes insufficient for a reliable estimation of fatigue behaviour 
of the riveted details in old steel bridges. In most cases, standards give the lower boundary of the test 
results for a set of specified riveted details, which is not always reasonable when estimating Remaining 
Fatigue Life (RFL). In [6.1], S-N lines and their parameters are proposed for frequently used riveted 
details  in  old  steel  bridge  riveted  connections.  The  influence  of  mean  stresses  and  stress  ratio  on 
fatigue strength category is taken into account by function f (R) as follows: 

(

R

)

c

=

Rf
(

)

c

0,

(6.6) 

where ∆σc(R) is the fatigue strength category for the considered detail as a function of the stress ratio 
R, σc,0   is the fatigue strength category for the considered detail for stress ratio R = 0 and f (R) is the 
correction  function  which,  for  mild  steels  (low  carbon  steels  with  carbon  level  under  0,25%),  is 
determined by the following formula [6.1]: 

Rf
(

)

=


R
1

6.01

R
1


4.01

R

R

when

R

>

0

when

1

R

0

(6.7) 

Using  Eurocode  S-N  line  model  and  stress  ratio  correction  f(R),  number  of  cycles  to  failure  (fatigue 
crack initiation) may be obtained as a function of stress range and stress ratio R as follows: 

(

s

)

m

R

N

R

(

=

Rf
(

)

s

C

0,

)

m

102

6

  with m=5 for 

£N

8101 (cid:215)

s

L

=

(
/2

)
100

5/1

s

D

 (cutoff limit) for 

‡N

8101(cid:215)

(6.8) 

(6.9) 

A  stress  history  is  determined  from  dynamic  analysis  calculations  of  the  structural  response  in  each 
structural  element  .  Then,  according  to  Eurocode  3  part  1-9,  the  stress  histories  are evaluated by the 
cycle  counting  methods  (rainflow  method)  in  order  to  determine  the  stress ranges and the associated 
numbers  of  cycles.  The  stress  range  spectrum  is  determined  by  collecting  the  stress  ranges  and  the 
associated number of cycles in descending order. The damage Dd during the design life (100 years) is 
then calculated by means of the Miner’s linear damage accumulation rule. 
As for the evaluation of the Remaining Fatigue Life, the past life of the old bridge is assumed 64 years.  
Two different models for determining the fatigue strength of the investigated details are used: 
-  Fatigue  strength  model  (F1),  based  on  Eurocode  [6.9].  The  detail  category  for  the  investigated 

details is 71. The influence of stress ratio and mean stresses is neglected; 

-  Fatigue  strength  model  (F2),  based  on  Eurocode,  but  with  the  influence  of  stress  ratio  using  the 

correction function f (R) (Eqns 6.7-6.9). 

Damage indexes over 100 years are reported in Figure 6.15; it is show that for point “1” and “2” the 
damage indexes are Dd = 0. All stiffening plates introduced in the detailed local model are subject to 
cycles over the cutoff limit. 
Damage  index  for  point  “3”  is  very  high,  with  value  of  about  15.  For  Point  “3”,  it  is  interesting 
compare  the  procedure  defined  in  Eurocode  (Fatigue  strength  model  F1),  with  that  proposed  by 
Georgiev (Fatigue strength model F2, [6.1]). Due to many cycles with stress ratio less than zero (and 
consequently with values of function f(R) moderately greater than 1), the damage index decrease from 
15.4 to 8.80. The Remaining Fatigue Life (RFL) is respectively -57 years and  -31 years. Finally, as far 
as the bracing system is concerned (points n. 6 and n. 7), only small-amplitude stress histories due to 
both  local  vibrations  and  global  effects  are  found.  The maximum stress is under the cutoff limit; for 
this reason, the Damage index is zero and the RFL is infinity.  
In conclusion, critical members and details for fatigue are found in stringers, due to high stress range 
rather  than  vibration  induced  and/or  distortion  induced.  All  other  details  seem  to  be  not  critical  for 
fatigue. 
As  underline  for  the  standard  fatigue  procedure,  values of Damage indexes obtained in stringers and 
floorbeams are unreliable. In fact, after over 64 years of service, no visible fatigue damages have been 
found in any element or connection. As mentioned before, this is due to the different fatigue loading 
spectra acting on the bridge than those defined by the Eurocode. In fact, mainly passenger train crosses 

104

 
 
s
D
(cid:215)
s
D
 
£
£
-
-
-
-
-
 
(cid:215)
D
D
 
D
D
 
the PonteLagoscuro viaduct; moreover, the few number of freight train has weight significantly lower 
than those defined in the Eurocode. 

x
e
d
n

i

e
g
a
m
a
D

16

14

12

10

8

6

4

2

0

Eurocode 3
Georgiev [2]

1

2

3

4

5

6

7

Figure 6.15 - Damage index for  Fatigue strength model F1, based on Eurocode 3, and for Fatigue strength model 
F2 [6.1] 

6.1.2  Panaro Bridge (Italy) 

Results  of  standard  fatigue  assessment  and  fatigue  damages  actually  occurred  on  Panaro  bridge 
permitted to select two critical details concerning distortion/vibration induced fatigue: 

•  Cross beams of track local bracings at the end restraints; 

•  The steel plates welded to the upper girder flanges connecting sleepers to longitudinal girders 

by catch bolts. 

FE local models 

In order to better understand the behaviour of these critical details, two local models were developed 
by the ANSYS software (Figures 6.16 and 6.17).  

Boundary 
Nodes

Boundary
Nodes

Figure 6.16 - Local model of the track bracing cross 
beam 

Figure 6.17 - Local model of the connection plate 
between sleepers and longitudinal girders 

Track bracing cross beam was originally full fixed to longitudinal girders then, after the discovery of 
extensive  fatigue  damages,  end  connections  were  modified  in  pin  joints.  The  model  representing  the 
original resistant scheme of the cross beam was developed using shell elements (Figure 6.16) assuming 
the bolted connection between the cross beam and the longitudinal girder as continuous (no bolt was 
modelled).  

105

 
 
 
 
 
 
 
 
The model that represent the connection plate between wooden sleepers and longitudinal girders was 
developed  using  shell  elements  for  the  bridge  structural  elements  and  beam  elements  for  wooden 
sleepers,  rails  and  for  the  track  bracing  (Figure  6.17).  In  particular,  the  welded  connection  between 
longitudinal  girders  and  the  plate  was  modelled  using  rigid  links.  Other  rigid  connections  were 
introduced in order to represent bolted connection between the plate and the wooden sleepers and to 
schematize the joint between rails and wooden sleepers. 
In both models, shell elements were defined adopting the material densities obtained from the updating 
procedure (described in chapter 5) to take into account of additional masses. 

Advanced fatigue assessment 

A  fatigue  assessment  of  such  critical  details  with  a  standard  approach,  i.e.  following  the  procedure 
defined in the section 6 of EN1991 – Eurocode 1, was performed in order to identify the initial crack 
positions that were actually observed on the bridge.  
For this purpose local analyses were performed by the imposition of displacements obtained from the 
dynamic analyses of the global FE model (performed using Eurocode 1 train models - Figure 4.85) to 
the boundary nodes of local models in order to study the distortional patterns on such details. 
In  Figures  6.18  and  6.19  the  Von  Mises  stress  maps  resulting,  respectively,  for  one  passage  of  train 
model 1 and train model 2, are reported for the track bracing cross beam. It is possible to note that the 
maximum stress value is located in correspondence of the observed start crack position, but values of 
stress  cycles  are  quite  low  and  under  the  cut-off  limit  of  this  detail.  Indeed  the  cut-off  limit  for  this 
detail was calculated as:  

L = 16.83 MPa 

(6.1) 

following  Eurocode  prescriptions,  adopting  a  fatigue  class  of 
=  36  MPa  for  this  welded 
component. As reported in Figures 6.21 and 6.22, the maximum amplitude of stress cycles was nearly 3 
MPa for train 1 and 2 MPa for train 2 (blue curve is related to Point A of Figure 6.20 and violet curve 
is related to Point B of Figure 6.20). 

C

sD

Figure 6.18 - Von Mises Stress Map for one passage of 
train 1 

Figure 6.19 - Von Mises Stress Map for one passage of 
train 2 

Point A

Point B

Figure 6.20 - Locations of Points A and B on the local model of the track bracing cross beam 

106

 
 
D
s
 
 
 
[Pa]

[Pa]

Figure 6.21 - Track bracing cross beam - Stress cycles 
for one passage of train 1(points A and B) 

Figure 6.22 - Track bracing cross beam - Stress cycles for 
one passage of train 2 (points A and B) 

Different stress values calculated for Point A and Point B underlined some distortional phenomena in 
this  detail,  but,  on  the  other  hand,  the  low  values  of  such  stresses  didn't  permit  to  observe  the  crack 
initiation in this numerical model. More refined numerical models representing the prestressed bolted 
connection  by  contact  elements  may  be  necessary  for  a  correct  evaluation  of  the  hot-spot  fatigue 
phenomena (Figure 6.23).  

Figure 6.23 - Example of refined model representing also prestressed bolts or rivets. 

In Figures 6.24 and 6.25 the Von Mises stress maps resulting for one passage of train 1 are reported for 
the  connection  plate  local  model.  It  is  possible  to  note  that  the  maximum  Von  Mises  stress  value  is 
located  in  the  end  of  such  plate,  but  this  point  doesn't  correspond  to  the  experimentally  observed 
starting crack position. 
In Figure 6.26 stress cycles for one passage of train 1 in correspondence of the maximum Von Mises 
stress  location  on  the  longitudinal  girder  (blue  curve)  and  on  the  connection  plate  (violet  curve)  are 
reported.  Also  for  this  detail  a  more  refined  solid  local  model  is  under  realization,  in  order  to  fit 
numerical results with the observed ones. 

Figure 6.24 - Von Mises Stress Map for one passage of 
train 1 (Top view) 

Figure 6.25 - Von Mises Stress Map for one passage of 
train 1 (Bottom view) 

107

 
 
 
 
 
 
 
[Pa]

Figure 6.26 - Connection Plate - Stress cycles for one passage of train 1 

Vehicle bridge interaction analysis 

An analysis of the interaction phenomena between train and bridge was realized in order to verify the 
amplification  of  the  dynamic  response  of  Panaro  bridge  and  to  highlight  the  possible  presence  of 
resonance phenomena in some bridge elements. 
To  this  purpose,  the numerical procedure developed by Chellini [3, 4] was applied considering three 
models  representing    the  Italian ETR500Y high speed train: i) a simplified model with six degree of 
freedom;  ii)  a  more  refined  model  with  ten  degree  of  freedom;  iii)  a  complex  model  with  thirty-one 
degree of freedom. Aims of this numerical procedure were the evaluation of the global model response 
under the train passages, the evaluation of displacements fields in bridge details and the evaluation of 
train-bridge interaction forces. 
In  Figures  6.27  and  6.28  time  histories  of  bridge  modal  displacements  and  bridge  modal  velocities 
calculated  are  reported.  These  analyses  were  performed  using  seven  natural  vibration  modes  of  the 
bridge  in  the  motion  equations,  and  assuming  the  contact  between  vehicle  and  bridge  in  correspon-
dence of the track as rigid, thus neglecting rail imperfections. Results are presented for the simulation 
performed using a six degree of freedom train model with a train velocity of 160 Km/h. 

0.025

0.02

0.015

0.01

0.005

0

(cid:8)
☯(cid:4)
]
m
(cid:18)
(cid:5)(cid:17)
[
t
(cid:4)
n
(cid:5)
e
(cid:16)
m
(cid:13)(cid:12)
e
(cid:15)
c
(cid:3)(cid:7)
a
l
(cid:14)
p
(cid:12)(cid:13)
s
i
(cid:11)
D
(cid:10)
(cid:9)

-0.005

0

]
s
/
m

[
y
t
i
c
o
l
e
V

0.2

0.15

0.1

0.05

0

-0.05

-0.1

0

Mode 1

Mode 2

Mode 3

Mode 4

Mode 5
Mode 6

Mode 7

2

4

6

8

10

12

14

16

18

(cid:2)(cid:3)(cid:4)(cid:5)☯(cid:7)(cid:8)

Time [s]

Figure 6.27 - Time history of modal displacement 

Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Mode 7

2

4

6

8

10

12

14

16

18

Time [s]

Figure 6.28 - Time history of modal velocity 

108

 
 
 
 
 
 
 
 
 
 
 
Looking at these figures is possible to note that the third bridge mode (the first vertical bending mode) 
gives the major contribution to the bridge dynamics during a train passage. 
In Figure 6.29 time histories of accelerations of points on the quarter and on the midspan of the bridge 
are reported. From these figures it is possible to note that the maximum value of vertical acceleration at 
midspan is higher than at quarters. 

0.25

0.2

0.15

0.1

0.05

0

-0.05

-0.1

-0.15

-0.2

-0.25

A3a Y
A3b Y
A5a Y
A5b Y

0.25

0.2

0.15

0.1

0.05

0

-0.05

-0.1

-0.15

-0.2

-0.25

A3a Y
A3b Y
A5a Y
A5b Y

a)

0

5

10

15

20

b)

25

0

5

10

15

20

25

Figure 6.29 Time history of accelerations for a) points on the quarter and b) on the mid of bridge span 

Finally a comparison between the results obtained from the three train models was developed in order 
to understand the sensitivity to such variable in terms of fatigue assessment. From these analyses it was 
found that the time histories of point displacements were affected by the train model and so the load 
cycles  were  influenced by this choice in terms of average stress (Figure 6.30). On the contrary, time 
histories of point accelerations weren't greatly affected by the train model choice (Figure 6.31).  
With  regard  to  the  fatigue  assessment,  the  necessity  of  train-bridge  interaction  analysis  shall  be 
evaluated  considering  the  influence  on  displacement  time-histories  at  local  details  rather  than  the 
vertical accelerations at midspan. 

-3

x 10

5

4

3

2

1

0

]

m

[

t
n
e
m
e
c
a
l
p
s
i
D

6DOF

31DOF

10DOF

0.15

0.1

0.05

0

-0.05

-0.1

]
2
s
/
m

[
n
o

i
t
a
r
e
l
e
c
c
A

(cid:8)
(cid:21)(cid:7)
☯(cid:4)

(cid:7)

(cid:16)(cid:16)(cid:5)(cid:13)(cid:5)(cid:20)(cid:12)(cid:18)(cid:3)(cid:10)(cid:17)

(cid:19)

6DOF

31DOF

10DOF

-1

0

2

4

6

8

10

12

14

16

18

0

2

4

6

8

10

12

14

16

18

Time [s]

Time [s]

Figure 6.30 - Sensitivity to the train model - time history 
of point displacement 

Figure 6.31 - Sensitivity to the train model - time history 
of point acceleration  

Experimental tests on critical details 

As results of the standard fatigue assessment of the Panaro bridge, the following details were selected 
as critical for distortion/vibration induced fatigue phenomena: i) the track bracing cross beam (Figure 
6.32a); ii) the connection plate between wooden sleepers and longitudinal girders (Figure 6.32b); iii) 
the connection joint between the vertical beam and the upper stringer (Figure 6.32c).  
In particular, for the track bracing cross beam and for the connection plate between wooden sleepers 
and  longitudinal  girders,  such  experimental  tests  were  performed  in  order  to  obtain  the  structural 
dynamic identification and to evaluate local stresses under the train passages; while for the connection 
joint between the vertical beam and the upper stringer the tests were executed measuring only the local 
strain pattern. 

109

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
                              a)                                                          b)                                                    c) 

Figure 6.32 - Critical details of the Panaro Bridge 

Track bracing cross beam 

The  experimental  campaign  on  the  track  bracing  cross  beam  consisted  in  the  recording  of  the 
accelerations in three points (Positions A, B, C on figure 6.33) in horizontal and vertical direction, in 
order to perform the Operational Modal Analysis for the dynamic identification of this detail. A single 
acquisition of all instrumented sections, realized adopting a sampling frequency of 400 Hz, permitted 
to identify three local vibration modes of the cross beam. Modal parameters and shapes obtained by the 
PolyMAX algorithm are illustrated in the figure 6.34. 

Sleeper

Pos.A

Pos.B

Pos.C

Track Bracing Cross Beam

Pos.G

Pos.D

Pos.E

Pos.F

Secondary Longitudinal Girder

Y

X

Z

Sensors Position/Type: A) Accelerometers Z and Y directions, Strain guages; B) Accelerometers Z and Y 
directions; C) Accelerometers Z and Y directions 

Figure 6.33 - Instrumented section and sensors positioning for the local cross beam modal tests 

15.65 Hz Vertical Bending  

44.18 Hz Lateral

97.22 Hz Vertical Bending 

Figure 6.34 - Panaro bridge - vibration mode shapes of track bracing cross beam 

Moreover, the measurement of local stresses under train passages, by strain gauges according to the test 
configuration reported in Figure 6.35, was also performed. By the analysis of strain data, as reported in 
the Figures 6.36 and 6.37, it was possible to observe that the local repair intervention on track bracing 
cross beam reduced the stress field (the maximum stress variation was equal to about 5 MPa under a 
freight train passage). 

110

 
 
 
 
 
 
 
 
 
 
 
Point 3

Point 1

Point 4

Point 2

Figure 6.35 - Panaro bridge – Test layout and strain gauges installation of track bracing cross beam 

]
a
P
M

[

s
s
e
r
t

S

1

0

-1

-2

-3

-4

-5

Point 4
Point 5

Point 3 - Vertical Dir.
Point 1 - Vertical Dir.

]
a
P
M

[

s
s
e
r
t

S

2

1.5

1

0.5

0

-0.5

-1

-1.5

-2

3900

4000

4100

4200

4300

4400

4500

4600

4700

4800

N° of Samples

N° of Samples

4000

4100

4200

4300

4400

4500

4600

4700

Figure 6.36 - Panaro bridge – Measured stresses under a 
freight train passage, Point 1 and 3, vertical direction 

Figure 6.37 - Panaro bridge – Measured stresses under a 
freight train passage, Point 2 and 4 

Wooden sleepers/longitudinal girders connection plate 

The  measurement  of  local  stresses  under  train  passages,  by  strain  gauges  according  to  the  test 
configuration reported in Figure 6.38, was performed in order to measure local stress fields under train 
passages in the connection plate. 

Test Layout - Side 1 

Catch bolts
Point 7

Point 8

Point 6

Point 5

Welding

a)

Side 1

  b)

c) 

Figure 6.38 - Panaro bridge – Test layout and strain gauges installation of the connection plate between wooden 
sleepers and longitudinal girders 

By the analysis of strain data, it was possible to observe that the welding between the connection plate 
and the longitudinal girders was subjected to intense stress variations, and then to fatigue phenomena. 
For example, the maximum stress variation due to a freight train passage is nearly equal to 45 MPa, as 
reported in the figure 6.39. 
The  impact  testing  technique  was  applied  to  perform  the  structural  dynamic  identification  the 
connection plate between longitudinal girders and wooden sleepers, as reported in the Figure 6.40. 

111

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Point 8 - dir.y
Point 5 - dir.y
Point 6 - dir.y
Point 7 - dir.y

15

10

5

0

-5

-10

-15

-20

-25

-30

4000

4100

4200

4300

4400

4500

4600

4700

Figure 6.39 - Panaro bridge – Measured stresses under a freight train passage, Point 5, 6, 7 and 8 

P5 (+Y)
P6 (-Y)
P8 (-Y)
P9 (+X)
P7 (+Y)

F
R
F
n
o
i
t
a
r
e
l
e
c
c
A

0.045

0.04

0.035

0.03

0.025

0.02

0.015

0.01

0.005

0

0

a) 

b) 

50

100

150

200

250

300

Frequency Bandwidth

Figure 6.40 - a) Impact testing on the connection plate between longitudinal girders and wooden sleepers; b) 
Frequency Response Functions (FRF). 

Vertical beam/upper stringer connection joint 

The  measurement  of  local  stresses  under  the  train  passages,  by  the  application  of  strain  gauges  in 
accordance with the test configuration reported in Figure 6.41, was performed to measure local stress 
fields under train passages in the connection joint. 

Point 4

Point 2

Point 3

Point 1

Point 6

Point 5

 a)

b)

Figure 6.41 - Panaro bridge – Test layout and strain gauges installation on the connection joint between vertical 
beam and upper stringer 

By  the  evaluation  of  strain  data,  it  was  possible  to  analyze  the  stress  field  in  the  connection  joint 
between  vertical  beams  and  upper  stringers.  For  example,  a  peak  stress  value  due  to  a  freight  train 
passage nearly equal to 18 MPa was found, as reported in the Figure 6.42. 

112

 
 
 
 
 
 
 
 
 
 
 
 
]

a
P
M

[

s
s
e
r
t

S

0

-2

-4

-6

-8

-10

-12

-14

-16

-18

Point 1- dir x

Point 2 - dir x

Point 3 - dir x

Point 4 - dir x

Point 5 - dir x

Point 6 - dir x

1

1.005

1.01

1.015

1.02

1.025
N° of samples

1.03

1.035

1.04

1.045

4
x 10

Figure 6.42 - Panaro bridge – Measured stresses under a freight train passage, Point 1, 2, 3, 4, 5, and 6 

Long-term monitoring 

A long-term monitoring system was developed in order to evaluate actual fatigue loading spectra (i.e. 
train  axle  loads,  composition  and  velocities)  and  to  estimate  the  train-bridge  interaction  forces. 
Moreover,  system  was  also  designed  to  analyze  the  effects  of  distortions  and  local  vibrations  on  the 
fatigue resistance of identified critical details (Figure 6.43). 

Pos.A

Y

X

Z

Pos.B
1
A

Pos.C

Instrumented Sleeper
Traversina Strumentata

Strain Gauge

Enstensimetro

Mobotix® Camera

Mobotix Camera
Biaxial accelerometer

Pos.D

Figure 6.43 - layout of the developed long-term monitoring system. 

Monitoring system is composed by: four instrumented sleepers, for the evaluation of train axle loads, 
train  compositions  and  train  velocities  (Position  A  and  Position  D)  and  for  the  evaluation  of 
train/bridge dynamic interaction forces (Position B and Position C); strain gauges installed on the main 
lower  longitudinal  girders  for  the  evaluation  of  global  effects  on  the  bridge  due  to  train  passages;  a 
biaxial accelerometer located on the quarter span length of the main lower longitudinal girder, for the 
evaluation  of  global  mode  frequencies  during  the  monitoring  period  analyzing  free  vibrations  after  a 
train passage; two Mobotix® cameras for the visual estimation of train types; a National Instruments® 
acquisition unit connected to the aforesaid sensors types and controlled by an host computer via local 
network.  In  the  Figure  6.44  a  graphical  representation of the local network installed on the bridge is 
reported. 
Data acquisition and data storage are executed by a LabVIEW® procedure performed by the acquisition 
unit.  This  procedure  is  composed  by  the  running of three parallel tasks: with reference to the Figure 
6.45, after the buffer initialization (Point 0), the first task (Point 1) consists in the acquisition of sensor 
data with a sampling frequency of 800 Hz and in their storage in the buffer; the second task (Point 2) 
consists in the buffer reading every half second, writing in a file every 800 samples; and the third task 
(Point  3)  is  composed  by  the  file  transfer  to  the  host  computer  deleting  the  original  file  on  the 
acquisition unit after file transfer itself. 
In  order  to  evaluate  local  dynamic  behaviour  and  distortional  strain  patterns  under  train  passages  in 
critical details (i.e. vibration/distortion induced fatigue), the monitoring system foresaw the installation 
of three accelerometer and eight strain gauges for the local monitoring of the track bracing cross beam 

113

 
 
 
 
 
 
 
and the connection plate between longitudinal girders and wooden sleepers, as reported in the Figure 
6.46, and the installation of six strain gauges for local monitoring of the joint between vertical beams 
and upper stringers, as reported in the Figure 6.47. 

Data Transfer

Connection to the 
Local Network

Setting operations

Mobotix®
Cameras

Local Network

1

Host
Computer

Network Port

NI ®
Acquisition
Unit

Laptop

0

…

……

Sensors
(Accelerometers, 
Strain Gauges)

2

3

Figure 6.44 - monitoring system local network 

Figure 6.45 - LabVIEW® procedure performed by the 
acquisition unit 

Accelerometro
Accelerometer

Estensimetro
Strain Gauge

Y

X

Z

Figure 6.46 - local monitoring system of the track bracing cross beam/connection plate between longitudinal 
girders and wooden sleepers. 

Strain gauges

Figure 6.47 - local monitoring system of the joint between vertical beams and upper stringers. 

The train axle loads are investigated by an instrumented wooden sleeper containing two load cells, one 
for  each  rail,  designed  to  measure  directly  the  vertical  load  transferred  from  rail  to  sleepers.  In 
particular, load cells are positioned in direct contact with the lower surfaces of rail anchoring plates. 
Such  plates  are  not  in  contact  with  other  part  of  the  sleepers,  thus  transferring  all  vertical  forces 
thought  load  cell  only.  Machined  steel  plates  and  regulating  screws  permit  a  correct  installation  and 
vertical  regulation  of  load  cells.  The  first  version  of  the  instrumented  sleeper  (Rev.1)  is  reported  in 
Figure 6.48. 
A  load  test  of  instrumented  sleeper  Rev.1  was  performed.  A  test  rail,  supported  by  two  traditional 
wooden sleepers at lateral positions and by the instrumented sleeper in central position, was subjected 
to an increasing vertical load by an hydraulic jack (see Figure 6.49a)). The comparison between applied 
load and force measured by load cell is reported in Figure 6.49b). Two main results were obtained by 

114

 
 
 
 
 
 
 
load test: i) the proposed instrumented sleeper guarantees a linear response; ii) a suitable calibration on 
field is necessary to estimate correct values of train axle loads. 
A  revised  version  of  instrumented  sleeper,  developed  to  increase  resistance  of  machined  steel  plates 
supporting the load cells and a better regulation capabilities, was approved by Rete Ferroviaria Italiana 
S.p.A.,  the  Italian  railway  infrastructures  manager  society,  for  the  installation  on  the  Panaro  bridge, 
without any restriction on train velocities (see Figures 6.50 and 6.51). 

Load Cell

Wooden Sleeper

Vertical load on cell

Steel Pins

a) 

Rail Anchoring Plate

Plates-conic wedges for the 
instrumentation setting

b)

Figure 6.48 - a) Rev.1 of the developed weighting in motion system and b) instrumentation setting system of the 
load cell 

a) 

Measured load by instrumented sleeper [kN]
Measured load by instrumented sleeper [kN]
Measured load by instrumented sleeper [kN]

Figure 6.49 - a) global layout of the validation test; b) a particular of the hydraulic jack; c) test load cycle on 
instrumented sleeper. 

Rev.1

Rev.2

Figure 6.50 - main changes in instrumentation setting 
system. 

Figure 6.51 - Rev.2 of the instrumented sleeper 

6.1.3  Trezói Bridge (Portugal) 

Inspection of the results of the global fatigue assessment clearly shows that there are some structural 
elements with much higher damage, which are the cross-girders at the extreme supports and above the 
columns.  The  location  of  these  elements  is  better  characterised  in  Figure  6.52.  This  was  expected 
because the train loads are almost directly applied to these elements, which implies a high sensitivity to 

115

 
 
 
 
 
 
 
 
cycle variation and local loading effect. On the other hand, the structure works as a low-pass filter for 
the  main  elements  (chords,  diagonals,  etc.)  which,  for  that  reason,  don’t  exhibit  a  high  number  of 
response cycles. 

Figure 6.52 - Characterization of the elements more affected by fatigue according to the global fatigue 
assessment results using a bar FEM (yellow – cross-girders; blue – diagonals; red – bottom chords) 

In general, the majority of fatigue problems arise from bad conception of structural details. This leads 
to  out-of-plane  loading,  secondary moments, vibration fatigue and distortion. In particular, the cross-
girders are prone to such problems. In old bridges, the common misalignment of the rails with the axle 
of the stringers leads to an eccentric loading outside the plane of these elements, which creates stresses 
not foreseen in the cross-girders and cracks due to load path detectable only with more complex finite 
element  models.  Also  the  vibrations  that  occur  in  these  elements  induce  stress  cycles  that  cannot  be 
evaluated with simple models. In the particular case of Trezói Bridge, the first natural frequencies of 
the  cross-girders  fall  in  the  range  of  the  loading  frequencies,  increasing  the  concern  to  adequately 
characterise the structural behaviour of these elements. Therefore, an additional FEM was developed 
with a more elaborated definition of these elements. 
The finite element model developed in the previous stage using beam elements was enhanced in order 
to  capture  local  vibration  modes.  A  FEM  was  developed  using  shell  elements  to  simulate  the  cross 
girders above the columns and the cross-girders at the extremity supports. In Figure 6.53 this model is 
schematically represented. 
In these two regions, all secondary elements were conveniently discretised in order to characterise the 
real behaviour of these structural details. A special attention was given to the joints of the cross girders 
in  order  to  capture  local  vibration  modes,  the  effect  of  secondary  bending  moments  and  eventual 
distortion. 

Figure 6.53 -  FEM mesh using beam and shell elements – local view above the main columns. 

116

 
 
 
 
 
The  longitudinal  girders  that  support  the  rails  were  also  discretised  with  shell  elements,  so  that  the 
connection  between  the  flange  of  these  elements  and  the  flange  of  the  cross  girders  was  correctly 
modelled  in  order  to  capture  distortion  effects.  Rigid  links  were  introduced  between  the  nodes 
connecting  the  bar  elements  with  the  corresponding  shell  elements  that  constitute  the  top  chord,  to 
simulate accurately the continuity between structural joints. This model was also calibrated using the 
results  from  the  initial  ambient  vibration  test.  The  global  vibration  modes  were  compared  and  some 
slight  modifications  were  made  in  terms  of  mass  distribution  and  boundary  conditions  in  order  to 
achieve greater agreement between the calculated and identified modal shapes and frequencies. 
In  order  to  preliminary  estimate  dominant  frequencies  of  local  modes  of  the  cross  girders,  an 
experimental  campaign  was  conducted  using  piezoelectric  accelerometers  PCB  connected  to  a  2-
channel Fourier analyzer APS Signalcalc with interposition of signal conditioning units, to measure the 
dynamic  response  of  these  elements.  These  uni-axial  sensors,  with  a  sensitivity  of  100mV/g  ,  were 
chosen due to their particular characteristic of not needing specific power supply, operating with linear 
response over the frequency range of interest, having also a strong magnetic base which allows an easy 
and reliable fixation to the structure (Figure 6.54 b)). 
The recording of the time series of acceleration was made during one day with a sampling frequency of 
320Hz and the excitation was induced manually by impact with a timber beam. The Fourier Analyzer 
incorporates filtering capacity and averaged FFTs of 6 time records were made in the range 0-120Hz, 
with a frequency resolution of 0.0098Hz. Accelerations were measured in the vertical direction in three 
locations at the top flange of the extremity cross girder (R5, R12, R8), and the horizontal acceleration 
was  also  measured  at  midspan  of  this  element  (R13)  perpendicularly  to the element axis, in order to 
capture vibration modes with lateral movement. The different locations of the sensors can be observed 
in Figure 6.54 a). 
A similar test was conducted at the cross girder above the column. 

                                            a)                                                                         b) 

Figure 6.54 - Layout: a) locations of the accelerometers at the extremity cross-girder; b) un-iaxial accelerometer 

Figure  6.55  shows  the  Average  Normalised  Power Spectra (ANPSD) obtained for the cross girder at 
the extremity support. A moving average is also added in order to clearly identify peaks since it can be 
used  as  a  low-pass  filter  to  remove  some  of  the  measurement  noise.  The  local  frequencies  can  be 
related to the peaks of these spectra and different types of local modes can be also identified if taking  
into  account  the  location  of  the  measured  acceleration.  For  the  vertical  direction,  the  frequencies 
30.5Hz and 24.4 Hz are only present in the results for location R5, this meaning that only these modes 
have a modal coordinate with a significant value in this location. 
The  analysis  of  the  Average  Power  Spectrum  for  position  R13  allows  to  conclude  that  some  local 
modes have significant horizontal components. 
A  monitoring  program  was  designed  to  reduce  the  uncertainties  associated  with  fatigue,  namely  in 
terms  of  the  structural  dynamic  response  and  the  trains’  characteristics.  One  of  the  most  important 
aspects in the assessment of old structures is the estimation of real loadings,  which may enable a more 
precise fatigue life estimation in the presence of more realistic stress spectra. With this purpose and as 
stated  above,  the  monitoring  system  was  also  designed  to  allow  the  collection  of  data  on  vehicle 
characteristics,  including  velocity  spectra,  number  of  axles,  axle  loads  and  their  spacing,  moving 
directions and traffic density. 
In this context, strain gauges were applied in the cross girders located at the top of the columns and at 
one support in the abutment in accordance with the critical locations previously identified. In addition, 
rails sections in the vicinity of both abutments, but outside the bridge, were instrumented with strain 

117

 
 
   
 
gauges in order to estimate the axle loads of the real trains and the corresponding velocity. The general 
layout of the instrumented sections is presented in Figure 6.56. 

Figure 6.55 - Average Normalised Power Spectra. 

Figure 6.56 - Global view of the location of strain gauges. 

Four strain gauges were placed in the flanges of each instrumented cross-girder in order to capture the 
highest  stress  ranges  at  the  detail  with  the  lowest  fatigue  strength.  They  were  placed  near  the 

118

 
 
 
  
 
connection between the cross girder and the gusset at the vicinity of the rivets in order to capture the 
stress enhancement due to the presence of rivets. 
The  acquisition  system  is  a  platform  from  National  Instruments  and  is  composed  by  a  computer 
responsible  for  high  performance  signal  conditioning,  which  integrates  two  SCXI  modules  able  to 
operate with 16 different channels. 
The results from dynamic monitoring of local vibration effects on the cross girders were subsequently 
correlated with the numerical results achieved with the more sophisticated FEM modelling developed 
with  the  purpose  of  analysing  the  contribution  of  local  modes.  In  this  context,  Figure  6.57  shows  a 
comparison  between  calculated  and  identified  frequencies using an ANPSD for the vertical direction 
obtained  from  the  field  test  using  accelerometers.  The  frequency  values  in  red  are  associated  to  this 
field test, the ones in blue are obtained via numerical model, and the green ones were obtained with the 
ANPSD  calculated  from  strains  measured  with  the  strain  gauges  (see  Figure  6.56).  Also,  some  local 
modes are represented in Figure 6.58 in correspondence with the frequencies presented in Figure 6.57 
Generally a significant number of local modes with relevant dynamic contribution to the response can 
be observed, and a good agreement between numerical and experimental frequencies is found. 

Figure 6.57 – Comparison between calculated and measured frequencies (ANPSD for the vertical 
direction): red - frequencies from the accelerometers, blue – frequencies from the FEM and green – 
frequencies from ANPSD of measured strains. 

a)                                                                             b) 

Figure 6.58 - Local modes of the cross-girder at the extremity support: a) vertical bending mode; b) 
lateral bending mode. 

Further  correlation  analyses  were  made  in  order  to  get  additional  confidence  in  the  developed  FEM 
using  the  numerical  simulations  of  the  trains´  crossings  and  the  data  from  the  field  measurement 
campaign  with  strain  gauges.  To  achieve  this  goal,  the  stresses  measured  at  the  cross-girder  at  the 
vicinity of one of the columns were compared with the corresponding calculated stresses. Figure 6.59 
a) present a partial view of the structure with indication of the location of this strain gauge. The train 
that  crossed  the  bridge  at  the  time  of  measurement  was  composed by a Locomotive and 7 passenger 
vehicles. 
The results obtained are presented in Figure 6.59 b), where the red graphic corresponds to the measured 
stresses and the blue one to the calculated. The agreement between both graphics is very good and it 
was concluded that there was no need for further refinement of the mesh of the FEM model, in order to 
capture a good definition of the stress variation. 
The  methodology  used  in  this  work  to  estimate  axle  loads  was  developed  by  Moses  and  his  team  in 
1979 for road bridges [6.16]. Since then it has been evolving and several studies have been developed 
for the case of railway bridges [6.16]. 

119

 
 
 
 
  
 
 
The  automatic  analysis  of  the  raw  data  obtained  from  the  field  measurements  was  assured  again  by 
routines developed in Matlab. 
Due  to  the  relatively  low  velocity  of  the  trains  in  this  bridge  (bellow  90km/h),  which  implies  lower 
dynamic  effects  due  to  wheel  irregularities,  it  was  possible  to  estimate  the  axle  loads  using  strains 
measured in the rails. For that purpose, and as referred previously, four strain gauges were placed at the 
rail sections at the vicinity of the abutments at the beginning of the bridge and at the end.  
To estimate the velocity of the train, the distance between strain gauges was divided by the time that 
each axle takes to cross from one strain gauge to another. If the train is accelerating or braking it will 
be obtained a different velocity for each axle. It was possible to observe that some trains crossed the 
bridge at a higher velocity that the maximum permitted velocity by the railway authorities (90km/h). 
The  majority  of  the  trains  have  a  velocity  close  to  this  limit,  suggesting  that  those  are  freight  trains 
since there is a train station close to the bridge thus implying that a great number of passenger trains 
stop before entering the bridge. 

a) 

b) 

Figure 6.59 - Validation of the FEM using strain gauges: a) location of strain gauges; b) comparison between 
measured and calculated stresses in the cross-girder. 

The load spectra estimated from the strain measured is presented in Figure 6.60 a) were a comparison 
with the EC1 traffic loads is also made. In general, the axle loads have a realistic value since typically 
the minimum axle loads in Portuguese trains is around 5 tons and the maximum around 35 tons. We 
can observe that there are some estimations that are bellow and above these limits. This may be due to 
some dynamic effect (due to the some defects on the wheels for example) that leads to an underestima-
tion  of  the  loads  in  the  first  case  and  an  overestimation in the second case. Fortunately only a small 
number  of  axle  loads  fall  bellow  or  above  these  limits  which allows us to analyze these results with 
higher  confidence.  In  order  to  increase  the  confidence  in  these  estimations,  a  comparison  was  made 
with the real data that was available to us from the railway administrations and it was concluded that 
the majority of the load estimated fall within the official ranges. 
In Figure 6.60 b) the damage per crossing of 1533 trains is presented for the 8 locations of the strain 
gauges in the cross-girders. These values of damage have the same order of magnitude of the damage 
calculated numerically. 

a) 

b) 

Figure 6.60 – Load spectra and damage calculations: a) axle load spectra; b) Damage calculations. 

120

 
 
 
 
 
 
 
The  structural  node  6,  as  illustrated  in  Figure  6.61,  was  selected  as  a  potential  fatigue  critical  node. 
This node is located just over the pier of the bridge and connects a cross girder to the upper stringer, 
side diagonals and the post. Also, some bracing members are connected to the node, as illustrated by 
Figure  6.62  a).  A  local  model  of  the  node  was  built  using  20  node  solid  finite  elements.  Continuity 
between the parts making the node was assumed. Figure 6.62 b) illustrates the finite element mesh of 
the  investigated  node.  The  members  connected  in  the  node  were  cut  as  illustrated  in  Figure  6.63.  In 
order to define the boundary conditions of the node, the Multi-point constraints (MPC) technique was 
used.  In  particular,  pilot  nodes  (reference  points)  were  placed  at  the  end  of  each  member,  at  the 
centroid position of the cross section of the members. The displacements and rotations, coming from 
the  global  dynamic  analysis  are  applied  directly  to  these  pilot  nodes  (Figure  6.64a)  which  are  later 
transformed into translations to be applied directly to the nodes of the respective cross sections (Figure 
6.64b). The local analysis of the node was performed in the ABAQUS® commercial code. The local 
stress distributions, over time, will be evaluated for a train crossing. Resulting local stress spectra will 
be  assessed  using  the  rainflow  cycle  counting  technique  and  fatigue  damage  computed  using  the 
Basquin [6.17] relation of the material and the Miner’s linear damage summation rule [6.18]. 

Figure 6.61 – Location of the critical node to be assessed by local fatigue analysis. 

a) 

b) 

Figure 6.62 – Potential critical node: a) photo and b) continuum finite element model based on solid finite 
elements. 

Figure 6.63 – Local model of the node 6 of the Trezói bridge: members dimensions. 

121

 
 
 
 
 
 
Section  2

Section  4

Section  8

Section  3

Section  5

Section  1

a) 

Section  7

Section  6

Section  9

b) 

Figure 6.64 – Boundary conditions procedure: a) MPC definition and b) sections numbering. 

In order to simulate the behaviour of the node 6 of the Trezói bridge, using the local model described 
above, the displacement/rotation history to be applied at the sections of the local model, were derived 
from  the  global  model,  for  a  time  step  increment  of  0.002  seconds,  resulting a total number of 4275 
steps, corresponding to the train crossing in a total time of 8.548 seconds. A locomotive-hauled freight 
train as illustrated in Figure 6.65 was considered in this analysis, with a weight of 21.5 tons per axle for 
the  locomotive  and  10  tons  per  axle  for  the  freight  cars.  Figure  6.66  illustrates  the  resulting 
displacement/rotation histories, for each section. Section 4, which corresponds to a horizontal bracing, 
exhibits a very high vibrating pattern. Section 6, which is a side diagonal, apparently shows significant 
vibration, in terms of z rotation, but the amplitude of the vibration is one order of magnitude bellow the 
vibration experienced by the horizontal bracing. 
All 4275 steps that defined the displacement/rotation history were applied to the local model (refer to 
Figure  6.64),  concerning  a  train  crossing  the  bridge  The  stress  histories  were  evaluated  at  several 
fatigue potential critical locations for fatigue damage analysis. 
Figure  6.67  shows  the  von  Mises  stress  distribution  for  the  time  equal  to  3.5  seconds  which 
corresponds to a critical loading scenario over the node. The analysis of the figure reveals maximum 
von  Mises  stress  levels  in  the  order  of  245  MPa,  which  represents  high  values.  These  maximum 
stresses are observed on the top of the cross-girder members.  
The  boundary  conditions  considered  to  validate  the  local  finite  element  model  was  a  passenger train 
crossing. However, the cargo train crossing was considered in the fatigue assessment, since it results in 
higher loads levels, as plotted in Figure 6.68. The cargo train crossing was considered more sever load 
case for fatigue computation. 

Figure 6.65 – Locomotive-hauled freight train. 

The  local  stress  spectra  was  subjected  to  the  rainflow  cycle  counting  method  in  order  to  extract  the 
stress  ranges  histogram  for  a  train  crossing  and  then  the  linear  damage  summation  rule  [6.17]  was 
applied  to  compute  the  damage  corresponding  to  the  train  crossing.  The  number  of  train  crossings 
required to initiate a crack (D=1) was computed. The stress components used in damage computations 
were  obtained  for  the  direction  along  the  member’s  geometrical  axis.  The  fatigue  damage  was 
computed using the Basquin’s relation [6.18], which is available for the bridge material [6.19]: 

s

2

=

s

(
2

N

f

)

b

'

f

=

(
.
26
609

N

)

f

0

.

092

(6.10) 

122

 
 
 
 
 
 
 
-
D
 
f's

  is  the  stress  range, 

  is  the  cyclic  fatigue  strength  coefficient,  b  is  the  fatigue  strength 

where  Ds
exponent and Nf is the number of cycles to failure. In general, the fatigue damage values are very low 
for the points investigated. Figure 6.69 plot the number of train crossings until cracking, computed at 
four locations also indicated in Figure 6.69. The critical spot is located at the corner of the stringer-to-
gusset connection.  

Figure 6.66 – Displacement/rotations history for sections 1 to 9 of node 6 from the Trezói bridge. 

Figure 6.67 – Critical spot located at the cross-girder to gusset connection. 

123

 
 
 
 
 
 
 
 
 
]
a
P
M

[

,
s
s
e
r
t

S

80

60

40

20

0

-20

-40

-60

80

60

40

20

0

]
a
P
M

[

 s
,
s
s
e
r
t

S

-20

-40

-60

]
a
P
M

[

,
s
s
e
r
t

S

60

40

20

0

-20

-40

-60

-80

60

40

20

]
a
P
M

[

0

0

 s
,
s
s
e
r
t

S

-20

0

5

10

Time [s]

15

Sever case - location 1

Validation FE model (1)

0

5

10

15

Time [s]

Sever case - location 3

Validation FE model (3)

-40

-60

-80

Sever case - location 2

Validation FE model (2)

0

5

10

Time [s]

15

Sever case - location 4

Validation FE model (4)

5

10

Time [s]

15

Figure 6.68 – Comparison of stress spectra between a passenger train crossing, used to validate the local finite 
element model (red line), and a cargo train crossing, defined as the severe case (blue line). 

)
1
=
D

i

(
g
n
k
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a
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u

s
e
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1.E+08

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1.E+04

1.E+02

1.E+00

1

4

3

2

1

2

3

4

Nodes

FE mesh 2

FE mesh 1

Figure 6.69 – Number of train crossings until fatigue crack initiation, computed at the top of the stringer-to-gusset 
connection. 

6.1.4  Alcácer do Sal Bridge (Portugal) 

The Alcácer do Sal bridge is a composite structure, composed of a welded steel box girder as illustrated 
in Figure 6.70a). Welded joints are potential fatigue critical details which have to be assessed in detail, 
through  a  local  modelling.  Local  modelling  is  required  to  assess  the  local  stresses  and  to  look  for 
potential  fatigue  cracking  hot  spots,  as  presented  in  Figure  6.70b).  The  assessment  efforts  were 
concentrated in a section under a hanger, as pointed out in the global finite element model illustrated in 
Figure 6.71. The section is reinforced with welded ribs all around the section forming a diaphragm.  

124

 
 
 
s
 
 
s
 
 
 
 
 
 
 
 
 
 
The  boundary  conditions  of  the  local  models  were  defined  using  a  shell-to-solid  sub-modelling 
technique, available through the ANSYS. The boundary conditions are computed from the results of a 
global shell model of the bridge. Figure 6.72 illustrates the relative locations of the local models with 
respect to the global model. The shells of the global model should fit the mid thickness of the plates of 
the local models, in order to be able to assess an accurate sub-modelling process. Figure 6.73 illustrates 
the  finite  element  models  of  the  investigated  welded  details.  Global  overviews  of  the  meshes  are 
illustrated as well as some local aspects of the mesh at the welded joints. Solid 20-noded elements were 
used  to  build  the  models  and  regular  mapped  meshes  were  preferably  proposed.  These  models  were 
built in the ANSYS® code.  

a) 

b) 

Figure 6.70 - welded steel box girder: a) diaphragm 51; b) critical welded detail. 

Figure 6.71 – Location of the critical section under investigation. 

Figure 6.72 – Relative locations of the local models with respect to the global model. 

125

 
 
 
 
 
 
 
 
 
 
a) 

b) 

Figure 6.73 - Local finite element model of a critical detail of the Alcácer do Sal railway bridge. 

The local models of the welded details of the box girder of the Alcácer do Sal bridge were submitted to 
displacements  at  the  cutting  boundaries  which  were  computed  with  the  global  model,  for  the  Alfa 
Pendular passengers train (Figure 6.74), at the traveling speed of 230 Km/h. A total of 1200 time steps 
were simulated with time increments of 0.002 seconds, resulting a total crossing time of 2.556 seconds. 
In order to better understand the distortion effects resulting from the train crossing, the displacements 
at a module 8 meters in length of the box girder was analyzed. Figure 6.75 illustrates the module of the 
box girder, pointing out the reference nodes. Figure 6.76 illustrates the displacements history for some 
reference  points.  The  analysis  of  the  displacement  spectra  shows  that  vibration  is  reduced.  The 
distortion of the box girder section seems relative small, which reflects a very high stiff construction. 

Figure 6.74 – Alfa Pendular passengers train. 

Figure 6.75 – Section of the box girder of the Alcácer do Sal bridge. 

Fatigue assessment was performed using the solid finite element presented in Figure 6.73. An approach 
based on S-N curves using the net stress definition was considered. Based on experimental S-N curves 
previously assessed, the number of cycles to failure of the actual welded detail of the Alcácer do Sal 
bridge  was  computed.  Net  stresses  were  assessed  as  the  linearized  stresses  at  the  critical  location. 
Stresses along the diagonal axis were computed. In order to reduce computational costs, only few steps 
were  selected  for  damage  computation.  Figure  6.77  plots  the  stress  history  resulting  from  the 

126

 
 
 
 
 
 
experimental  validation  of  the  local  finite  element  model.  Figure  6.77  shows  selected  times 
corresponding to important load history events near the hot spot. These times were used to compute the 
net stress spectra. The net stress spectra was subjected to the rainflow cycle counting method in order 
to extract the stress ranges histogram for a Alfa Pendular train crossing the bridge. Figure 6.78 plots net 
stress  ranges  resulting  from  a  rainflow  cycle  counting.  The  mean  S-N  curves  resulting  from 
experimental campaign was used to compute the number of cycle to failure of the welded detail: 

D s

net

=

.
213

E

+

21

.
303

N

f

(6.11) 

Using the equivalent stress computation applied to the net stress spectra presented in Figure 6.78, the 
number  of  cycles  to  failure  was  computed  as  5.12E+8  crossings.  This  number  reveals  a  very  small 
damage induced by each Alfa Pendular crossing the bridge. 

)

m

(

s
t
n
e
m
e
c
a
l

p
s
i
D

)

m

(

s
t
n
e
m
e
c
a
l

p
s
i
D

)

m

(
s
t
n
e
m
e
c
a
l
p
s
i
D

1.80E-03

1.60E-03

1.40E-03

1.20E-03

1.00E-03

8.00E-04

6.00E-04

4.00E-04

2.00E-04

0.00E+00

-2.00E-04

0

7.00E-04

6.00E-04

5.00E-04

4.00E-04

3.00E-04

2.00E-04

1.00E-04

0.00E+00

-1.00E-04

1.00E-02

5.00E-03

0.00E+00

-5.00E-03

-1.00E-02

-1.50E-02

Ux1

Ux5

Ux7

Ux11

Ux13

Ux17

2.00E-05

1.50E-05

1.00E-05

5.00E-06

0.00E+00

)

m

(

s
t
n
e
m
e
c
a
l
p
s
i
d
e
v
i
t
a
l
e
R

Ux1-Ux5

Ux7-Ux11

Ux13-Ux17

0

400

800

1200

Time steps

-5.00E-06

Time steps

400

800

1200

Uy1

Uy5

Uy7

Uy11

Uy13

Uy17

0

400

800

1200

Time steps

0

400

800

1200

Time steps

Uz1

Uz5

Uz7

Uz11

Uz13

Uz17

-1.00E-05

5.00E-05

4.00E-05

3.00E-05

2.00E-05

1.00E-05

0.00E+00

-1.00E-05

-2.00E-05

)

m

(

s
t
n
e
m
e
c
a
l
p
s
i
d
e
v
i
t
a
l
e
R

6.00E-03

)

m

(

n
o
i
t
r
o
t
s
i

d
/
s
t
n
e
m
e
c
a
l
p
s
i

d
e
v
i
t
a
l
e
R

5.00E-03

4.00E-03

3.00E-03

2.00E-03

1.00E-03

0.00E+00

Uy1-Uy5

Uy7-Uy11

Uy13-Uy17

0

400

800

1200

Time steps

Uz1-Uz5

Uz7-Uz11

Uz13-Uz17

Time steps

0

400

800

1200

Figure 6.76 – Displacement histories for some reference points. 

127

 
 
·
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Numerical data

Strain gauges data

9

8

7

6

5

4

3

2

1

0

]
a
P
M

[

,
s
s
e
r
t

S

50

-1

100

0
8
1

4
8
1

0
9
1

200

1
1
2

5
1
2

1
2
2

150

Step

6
2
2

1
3
2

6
3
2

250

Figure 6.77 – considered load step for damage computation. 

]
a
P
M

[

,
e
g
n
a
r

s
s
e
r
t
s

t
e
N

30

25

20

15

10

5

0

Figure 6.78 – Net stress range resulting from rainflow cycle counting. 

Also, in order to perform the crack growth prevision, in the critical details of the bridge, in an efficient 
way,  a  new  methodology  was  developed  and  validated.  The  scope  of  the  proposed  methodology  is 
illustrated in Figure 6.79. 

Figure 6.79 – Data needed for crack propagation analysis 

128

 
 
 
s
 
 
 
 
D
s
 
 
 
 
Generically, K can be represented as (Eq. (6.12)): 

( )
tK

=

σaπC

(6.12) 

where C is a function of the geometry of the structure and of the crack dimensions, σ is the nominal 
stress acting on the detail and a is the crack dimension.  
Consider a structure containing a crack with the dimension an. Static loading acting on the structure (eg 
structure’s self-weight or internal residual stresses due to manufacturing) induce a certain stress state 
on it, σsta, originating a stress intensity factor, Ksta, through the crack front, according to: 

( )

=

σaπCtK
n

sta

n

sta

(6.13) 

If the same structure is subjected to a dynamic loading, the latter will produce a stress field variable in 
time, σdyn(t). Admitting that, during each loading event, the crack remains with approximately constant 
dimensions, then, it can be written: 
( )t

σaπCtK
n

(6.14) 

( )

=

dyn

dyn

n

Considering the simultaneous action of the static and dynamic loadings, the total stress intensity factor 
acting on the structure, through time, becomes: 

K

*
total

( )
t

=

K

sta

+

( )tK

dyn

(6.15) 

where K*
total is the total stress intensity factor before a “signal” correction presented in later paragraphs. 
The process of crack opening and crack closure is a non-linear phenomenon, namely due to the contact 
between the crack faces. Nevertheless, for small cracks, the referred non-linear phenomenon does not 
induce a global non-linear behavior. Thus, in that cases, the determination of the temporal evolution of 
the  stress  intensity  factor,  Kdyn(t),  through  the  crack  front,  can  be  achieved  using  the  modal 
superposition method. 
The application of the modal superposition method allows writing: 

( )
t

=

σ

dyn

∑ (cid:215)

( )
tYσ

j

j

j

(6.16) 

where the j subscript refers to the number of each mode of vibration, σj is the nominal stress in the jth 
mode  shape  and  Yj(t)  is  the  modal  coordinate  of  the  jth  mode  of  vibration.  The  number  of  modes  of 
vibration  to  consider  can  be  determined  by  a  convergence  analysis,  after  adopting  a  convenient 
convergence criterion. 
Replacing the Eq. (6.16) in the Eq. (6.14) it becomes: 

( )
tK
dyn

=

aπC

n

n

∑

j

( )
tYσ

j

j

( )
tYσaπC
n

n

j

j

=

∑

j

=

∑

j

( )
tYK

j

j

(6.17) 

In the previous equation, the modal stress intensity factor, Kj, is the stress intensity factor obtained with 
the configuration of the jth mode shape. 
Replacing the Eq. (6.17) in the Eq. (6.15) it finally becomes: 
∑ (cid:215)

( )
tYK

( )
t

*
total

K

K

+

=

sta

j

j

(6.18) 

j

In conclusion, to obtain the temporal evolution of K only the calculation of Ksta and of the different Kj 
is required. The calculation of K for each time step of the analysis is, then, avoided. 
An  important  reflection  to  consider,  relates  to  the  “signal”  of  Ksta  and  of  the  several  Kj.  As  it  is 
generally accepted, disregarding the crack closure effects due to local plasticity in the surroundings of 
the crack front, the stress intensity factor associated to rupture mode I, KI, only  takes positive values 
when the crack is open, assuming a null value when it is closed and/or under compression. 
Nevertheless,  a  numerical  analysis  with  a  linear  elastic  finite  element  model,  built  without  contact 
elements  at  the  crack  faces,  will  not  detect  the  overlap  between  the two crack faces, when the crack 
surroundings are subjected to compression. Consequently, two opposite loading situations, eg a tension 
nominal stress of σ and a compression nominal stress of –σ will lead to the same positive value of the 

129

 
 
(cid:215)
 
(cid:215)
 
(cid:215)
 
 
 
(cid:215)
(cid:215)
(cid:215)
(cid:215)
(cid:215)
 
 
energy release rate, G. As K is generally obtained from G, as a function of its square root, also the same 
positive value of K will be obtained in the two opposite situations.  
Not taking the above mentioned effect into account would mislead the obtained results. For the modal 
superposition of stress intensity factors to be possible the determination of the signal of Ksta and of each 
Kj is fundamental.  
Two different and alternative criteria can be used to distinguish between both situations: 

1.  The relative displacement between the crack faces, measured in two points located near the 
crack front, δ, will be positive if the crack is open and will be negative if the crack is closed 
(overlapping); 

2.  The stress component perpendicular to the crack plane, in a node belonging to the crack front, 

σct, is positive if the crack is open and is negative if it is closed (overlapping). 

The application of any of these criterion allow for the definition of the signal of Ksta and of each Kj. 
Once Ksta and each Kj are defined, the final expression of the total value of K through time is defined as 
follows (Eq. 6.19): 

( )
t

=

K

total









K

sta

+

∑

( )
tYK

j

j

j

0

K

sta

+

∑

j

K

sta

+

∑

j

( )
tYK

j

j

( )
tYK

j

j

0

<

0

(6.19) 

It  can  be  concluded  that,  when  a  fatigue  crack  is  present  in  a  structure,  the  calculation  of  the  stress 
intensity  factor  through  time,  at  the  crack  front,  when  it  is  subjected  to  a  dynamic  loading,  can  be 
summarized on the following steps: 

1.  Calculation of the displacement field of the structure due to the static loading, Φsta, and 

extraction of Ksta and the corresponding signal.  

2.  Modal analysis of the structure and obtaining, for each jth mode of vibration, the value of Kj 

and the corresponding signal. Modal frequencies, ωj, modal masses, mj, and mode shapes, Φj, 
are also computed. Modal damping ratios, ξj, are generally defined based on standards or on 
experimental results. 

3.  Characterization of the dynamic loading, F(t), and calculation of the modal forces, Fj(t). 

4.  Obtaining the time histories of the modal coordinates, Yj(t). 

5.  Obtaining Ktotal(t) by application of the Eq. (6.8.4.9). 

These steps may include, or not, the application of submodeling techniques (Figure 6.80). 
The presented method has three main advantages: 

1.  For a structure which dynamic behavior is well characterized by N vibration modes, the stress 
intensity factor has to be computed only N+1 times. The time history of the modal coordinate 
of each mode of vibration may be determined subsequently, in an efficient way, solving each 
one of the single degree-of-freedom problems. 

2.  The contribution of each mode of vibration to the value of Ktotal(t), at each time step, can be 
obtained directly, allowing to understand which modes of vibration contribute more decisively 
to the crack propagation. 

3.  Consideration of different dynamic loads only implies the recalculation of the modal coordi-

nates Yj(t). 

In contrast, a traditional analysis would imply the analysis of the whole structure through time and the 
calculation of K for each time step (typically thousands of times). 
In  parallel,  in  order  to  perform  more  reliable  crack  growth  previsions,  tests  were  performed  to 
characterize the steel used in the bridge’s construction regards its fatigue crack propagation behaviour 
[6.17].  

130

 
 
(cid:215)
(cid:220)
‡
(cid:215)
(cid:220)
(cid:215)
 
 
a) With submodeling 

b) Whithout submodeling 

Figure 6.80 – Flow chart for the application of the proposed methodology 

The tests were conducted according to ASTM E647. CT specimens were machined from welded plates 
approximately 1 m long and 230 mm wide. A butt weld with a double V preparation joined the plates 
along  their  longer  side.  According  to  the  welding  procedure  qualification  followed  for  the  bridge 
mentioned,  the  welding  process  was  the  flux-cored  wire  metal-arc  welding  with  active  gas  shield 
(welding process 136, according to EN ISO 15614-1:2004), with a 100ºC preheating and an inter-run 
temperature lower than 250ºC. The welding sequence included multi-run welding on alternate sides of 

131

 
 
 
 
the plate and the filler metal was the MEGAFIL 710 M. The preparation dimensions were a thickness 
of root face of 2 mm, a gap of 3 mm and a bevel angle of 60º. The welds were ground flushed during 
the machining process.  
The CT specimens were extracted from three different locations, sampling base material (BM), weld 
metal (WM) and heat affected zone (HAZ), always with the initial notch (and cracking plane) parallel 
to  the  weld  line.  A  test  matrix  of  nine  cases  was  adopted,  in  order  to  characterize  the  fatigue  crack 
propagation of the base material, welded material and heat affected zone, under three different R ratios, 
0.1, 0.4 and 0.7. 
The dimensions were a thickness (B) of 32 mm, a width (W) of 132 mm, an overall width of 165 mm 
and  an  overall  height  of  158.4 mm.  The  double  V  preparation  of  the  original  plates  implied  that  the 
specimens called HAZ actually sample the heat affected zone close to the original plate’s free surfaces 
and base metal in the mid thickness. The specimen geometry used is presented in Figure 6.81, whereas 
Figure 6.82 schematically shows the location of the WM and HAZ specimens. 

Figure 6.81 – CT specimen 

Figure 6.82 – Location of specimens containing weldments  (schematic). 

The notch used was obtained using two different techniques; up to a certain distance from the load line 
the notch was machined by simple milling with a tool perpendicular to the specimen face, and the last 
3.5  mm  of  the  initial  notch  were  obtained  using  a  wire  electrical  discharge  machining  (EDM) 
equipment leaving a final notch tip radius of 0.15 mm. A fatigue pre-crack was grown starting from this 
EDM notch, making sure that the maximum loads were low enough in order to limit crack tip plastic 
deformation, in accordance with ASTM E647. Pre-cracking was performed under R = Pmin/Pmax = 0.1, 
where P is the applied load.    
The servo-hydraulic MTS testing machine used had a 250 kN load capacity, and the testing frequency 
was  chosen  to  be  between  6  and  10  Hz  depending  on  the  actual  load  of  each  specimen.  Travelling 

132

 
 
 
 
 
microscopes (20x magnification) were used on each side of the specimen to make periodic readings of 
current crack length a as a function of number of cycles N. 
The base material used was the steel grade S355NL according to EN 10025, EN 10029 and EN 10163.  
The results obtained for base material, tested under the three values of R, are presented in Figure 6.83, 
where each straight line corresponds to the best fit of Paris’ Law. The data was determined according 
to the ASTM E647 standard. 

Figure 6.83 - Base material da/dN vs. D K data for the three R values tested. 

However,  when  testing  specimens  containing  welds  (either  WM  or  HAZ  specimens),  a  rather  more 
complicate behaviour was found and corrections were required in order to account for the crack closure 
effects observed. The final results are presented in Figure 6.84 and Figure 6.85. 

Figure 6.84 - Weld material da/dN vs. D K data for the three R values tested (‘cor’ - D Keff). 

Figure 6.85 - Heat affected zone material da/dN vs. D K data for the three R values tested (‘cor’ - D Keff). 

133

 
 
 
 
 
6.1.5  SaalebrückeGroßheringen 

Identification of train types, speed and acceleration 

Using the strains measured on the rail over the abutment and over the pier, the average speed of each 
axle can be estimated. For this purpose an algorithm was developed that detects corresponding peaks in 
the  two  measured  signals  and  calculates  the  average  speed  of  each  axle  during  its  passage  of  the 
considered  superstructure  based  on  the  extracted  time  lag  between  two  corresponding  peaks  and  the 
known distance between the two measurement locations. Figure 6.86 shows a time series of measured 
strains  at  one  location  at  the  track  together  with  the  derived  average  speeds  for  the  axles.  From  this 
diagram the increasing speed of the train can be well observed. 

Figure 6.86 –  Time series of measured strains at a track during a train passage (top) and corresponding average 
axle speeds (bottom). 

After  calculating  the  speed  of  each  axle,  the  distances  between  all  axles  can  be  derived.  Based  on 
knowledge about the axle patterns for some typical vehicles, such as locomotives and wagons used for 
passenger  trains  such  as  ICE,  Intercity  and  double  decker  trains,  the  respective  train  type  can  be 
identified. Figure 6.87a) summarizes the relative occurrences of the detected train types in one and a 
half  years  based  on  almost  25,000  detected  trains.  The  diagram  shows  that  the  majority  of  trains 
passing the bridge are freight trains. Figure 6.87b) confirms that most trains pass the bridge at a speed 
of 80 to 90 km/h, i.e. close to the speed limit. Only a small number of trains travel at comparatively low 
speeds, especially freight trains, mostly after having stopped at a rail signal in front of the bridge such 
as the train for which the diagrams in Figure 6.86 were recorded. 

(a)

(b)

Figure 6.87 – Identification of passing trains in one year and a half: (a) distribution of identified train types, (b) 
speed histogram showing the relative frequency for different train types 

Estimation of axle loads 

The wheel loads were estimated based on strain measurements on one rail close to the abutment. For 
the  estimation  of  the  axle  load  it  is  assumed  that  the  derived  wheel  loads  are the same for one axle. 
Accordingly, the estimated wheel loads are doubled to derive the respective axle load. Due to the fact 
that the axle loads are derived from measurements of strains in the rail during train passages, the results 
are also influenced by dynamic effects. Several vehicle types regularly pass the bridge, such as regional 
trains  with  double  decker  wagons  and  a  locomotive  of  type  BR  143,  which  makes  statistical 
assessments possible. 

134

 
 
 
 
 
For  locomotives  the  nominal  axle  loads  can  be  extracted  from  respective  data  sheets  such  as  [6.20]. 
This  gives  a  very  good  opportunity  to  assess  the  estimated  axle  loads.  Figure  6.88a)  summarizes  all 
estimated mean axle loads which are calculated as the average of the four respective values identified 
for each locomotive of type BR 143with respect to train speed. The boxes mark the range from 25 % to 
75 % of all respective mean values of the four locomotive axles. From the diagram can be derived that 
for speeds up to 70 km/h the identified average axle loads coincide well with the nominal axle load of 
210 kN with a deviation range of approximately ± 5 %. For higher speeds the average mean axle loads 
tend to decrease, while the scatter of the mean axle loads increases. This observation gives reason to 
assume  that  dynamic  effects  such  as  bridge–vehicle  interactions  have  an  increasing  influence  on  the 
axle load estimates with increasing train speed. 
Another observation that was made for the majority of vehicles, such as locomotives, that have boogies 
with two axles, is that the load identified for the respective second axle was usually slightly higher than 
the  one  corresponding  to  the  first  axle  of  the  boogie.  6.88b)  illustrates  the  statistics of the identified 
axle loads for all detected locomotives of type BR 143 with a speed of up to 70 km/h. The boxes mark 
the range from 25 % to 75 % of all respective samples for one axle. The observed deviations of axle 
loads  between  adjacent  axles  agree  with  the  assumption  that  the  longitudinal  force  that  has  to  be 
generated  to  move  the  train  leads  to  an  additional  moment  about  the  boogie  horizontal  axis  and 
consequently  to  differences  between  the  vertical  forces  transmitted  through  the  wheels.  Respective 
theoretical derivations were developed for example in [6.21]. 
Using the estimated axle loads the total mass of the trains that passed the bridge during the investigated 
time period of 1.5 years can be calculated.The calculation yields17.3 Mt., where80% of the total mass 
is associated with freight trains, 14%with high speed trains, and 6% only with regional trains. 

a)

b)

Figure 6.88 – Axle load identification: (a) statistics of the mean values of the identified axle loads of the 
locomotives of type BR 143 with respect to speed, (b) statistics of the identified axle loads for the four axles of 
locomotives of type BR 143 with speeds up to 70 km/h; the boxes include all samples from  25 to 75 %, the 
dashed lines extend to the most extreme data points not considered as outliers, outliers are plotted individually (red 
cross).  

Local strain measurements 

Strain data was recorded from two strain gauge rosettes located on two gusset plates: one with and one 
without a visual crack. Principal stresses and hence von Mises effective stresses were calculated from 
the  strain  time  series  for  each  rosette.  Subsequently,  a  rainflow  algorithm  was  applied  to  these  von 
Mises stresses. Stress cycles with amplitudes of less than 10 N/mm2 were excluded from the rainflow 
statistics. 
The results obtained from a one and a half year long monitoring on the Saalebrücke Großheringen are 
shown in Figure 6.89 and Figure 6.90 for the gusset plate with and without a crack, respectively. The 
depicted  rainflow  histograms  are  grouped  according  to  the  regular  passing  train  types.  As  it  can  be 
clearly seen for both gusset plates, load cycles at higher stress levels are associated with passing freight 
trains. This observation can be expected due to the higher loads of freight trains. 

135

 
 
 
Figure 6.89 – Rainflow cycle histogram of the strain 
gauge rosette with a crack grouped for different kind of 
trains (RB – regional, IC/ICE – high speed, Cargo – 
freight train), calculated for the time of one year and a 
half 

Figure 6.90 – Rainflow cycle histogram of the strain 
gauge rosette without a crack grouped for different kind 
of trains (RB – regional, IC/ICE – high speed, Cargo – 
freight train), calculated for the time of one year and a 
half 

 is noted that the gusset plate without the crack seems to experience much higher load cycles than the 
one  without  the  crack.  On  the  other  hand,  the  number  of  rainflow  cycles  in  the  low  cycle  amplitude 
regime is up to one order of magnitude higher for the undamaged gusset plate. Figure 6.91 shows the 
comparison  of  the  rainflow  cycle  histograms  and  emphasis  this  observation.  This  result  justifies  the 
assumption of higher stresses in the cracked gusset plate close to the crack due to resulting stress re-
distributions. 

Figure 6.91–Rainflow cycle histogram of the strain gauge rosette with and without a crack, calculated for the time 
of one year and a half 

Laboratory fatigue test of the detail gusset plate 

As  described  in  chapter  5,  the  fatigue  life  expectancy  of  the  critical  detail  expired already as can be 
assumed also by the presence of the crack in the real structure. This finding is also supported by the 
numerical results that showed stress concentrations at the location of the identified crack. 
By means of laboratory fatigue tests S/N curves will be derived to improve the estimations of damage 
accumulation due to fatigue and resulting remaining life time expectancies for this detail. To prepare 
the design of the laboratory tests, first a loading situation had to be defined that 

• 

• 

leads to a similar stress distribution as in the gusset plate on the bridge and 

can be generated with reasonable technical effort in the laboratory. 

After an iterative process of investigations considering different boundary conditions, loading locations 
and  directions,  a  configuration  was  found  that  allows  for  the  application  of  a  unidirectional  load. 

136

 
 
 
 
 
Figure  6.92a)  shows  the  numerical  model  of  the  gusset  plate  while  in  Figure  6.92b)  the  stress 
distribution is given if translational displacements along line L8 are applied to the plate which is fixed 
along lines L1, L2 and L9. The stress distributions are very similar to those calculated for the gusset 
plate in the bridge model during a train passage. 
Based on these results an experimental setup was developed. The assumed displacements along line L8 
in Figure 6.93a) were not in the direction of one global coordinate axis. Accordingly a respective force-
controlled  setup  had  to  be  designed.  To  simplify  the  structure  of  the  test  bed  the  gusset  plate  was 
rotated such that the force can be applied in the vertical direction. A respective structure was designed 
and  manufactured.  The  numerical  model  is  shown  in  Figure  6.93  whereas  a  design  drawing  an  a 
photograph of the test bed are shown in Figure 6.94 

(a)

(b)

(a)

(b)

Figure 6.92 – Numerical model of the gusset plate: (a) 
geometry, (b) stress distribution due to translational 
displacements along line L8. 

Figure 6.93 – Numerical model of the fatigue test: (a) 
side view, (b) isometric view. 

(a)

(b)

Figure 6.94 – Setup for fatigue tests: (a) design drawing, (b) test bed in the laboratory. 

The frequency of the cyclic loads was 3 Hz in average and 5 Hz maximum for the lower load levels. 
The specimens had been equipped with linear strain gauges and strain gauge rosettes at the location of 
the highest stress levels, known from the numerical model. 
A  crack  length  sensor  was  developed  and  installed  at  the  predicted  crack  location  on  specimens  (cf. 
Figure 6.95): A plastic foil equipped with 1 cm separated conducting paths perpendicular to the crack 
path. The cut of a conducting path was detected by the control system, which and could be programmed 
to stop the machine at that time. Additionally, the crack growth could be monitored without being at 
the test bed.  
The  crack  lengths  as  function  of  the  applied  load  cycles  are  shown  in  Figure  6.96  for  two  different 
loads (stress values). It is noted, that on one hand the crack starts to form much earlier than in the high 
stress level specimen. On the other hand, different numbers of load cycles were recorded for the same 
stress level. One reason could be that the crack sensor foil was not positioned exactly at the same point 
for all plates. 
The  slope  of  the  crack  length  as  a  function  of  load  cycle  number  is  much  higher  in  the  case  of  500 
N/mm2, which is a plausible result. 

137

 
 
   
   
 
 
 
Figure 6.97 shows the S/N curves 71 and 160 from [6.22] and the results obtained during the fatigue 
laboratory test. All experimental data points were found above the highest S/N-curve in [6.22]. Since 
not all plate specimens have been processed yet, it was renounced to calculate a linear regression curve 
for the time being, due to the limited regime of stress levels and number of load cycles that could be 
covered in a reasonable time during the experiment. 

(a)

(b)

Figure 6.95 – Setup for fatigue tests: (a) crack length sensor and strain gauges, (b) measurement control program. 

Figure 6.96 – Fatigue test: crack length as a function of 
the load cycles for two different stress values (pk-pk): 
300 N/mm2: Blech02, Blech03, Blech02 manual; 500 
N/mm2: Blech04 

Figure 6.97 – S/N diagram of the fatigue test: 
Experimental data from seven specimens, S/N curves 71 
and 160 from [6.22] 

Fatigue loading spectra 

Based on the numerical model developed, a dynamic analysis is subsequently performed to predict the 
response of the bridge under the train passage. The train type considered in the analysis is the German 
high speed train ICE3 (Figure 6.98). 

Figure 6.98 - Loading scheme of the high speed train ICE3. 

138

 
 
 
 
 
 
 
It  is  composed  of  a  locomotive  followed  by  7wagons.The  length  of  the  wagon  is  24.775  m.  Each 
vehicle  is  considered  as  an  independent  entity  with  1  car  body,  2  bogies,  and4  wheel  sets.  Both  the 
primary  and  the  secondary  suspension  system  are  modelled  as  linear  elastic  system  represented  by 
springs and dampers. At each side of each wheel set and bogie are horizontal and vertical springs and 
dampers. A 3 DOF’s vehicle model (Figure 6.99), including the vertical motion for both the car body 
and the bogies, is used for dynamic train-bridge interaction analysis. The static axle loads (4 axles for 
each  wagon)  of  the  train  are  listed  in  table  6.1  and  the  dynamic  characteristics  of  the  vehicle  are 
presented in Table 6.2. 

Figure 6.99 - A 3-DOF vehicle model for dynamic train-bridge interaction analysis. 

Table 6.1 - Axle loads of ICE3. 

Table 6.2 - Characteristics of the suspension 
system of ICE3. 

  Wagon 

Axle loads (t)  Car body M2 (kg)  Bogie 
M1 (kg) 

Wheel-set 
MW (kg) 

Wagon 

1 

2 

3 

4 

5 

6 

7 

8 

55.61 

59.90 

53.47 

56.00 

53.48 

53.47 

59.90 

55.61 

37410 

42200 

35270 

38300 

35780 

35270 

42200 

42200 

6040 

6550 

6040 

6550 

6550 

6040 

6550 

6040 

1530 

1150 

1530 

1150 

1150 

1530 

1150 

1530 

1 
2 
3 
4 
5 
6 
7 
8 

Stiffness  (N/m) 
KVV 
KV 
240000 
1080000 
240000 
900000 
240000 
900000 
240000 
900000 
240000 
900000 
240000 
900000 
240000 
900000 
240000 
1080000 

Damping  (Ns/m) 

CV 
10000 
10000 
10000 
10000 
10000 
10000 
10000 
10000 

CVV 
10000 
10000 
10000 
10000 
10000 
10000 
10000 
10000 

The mass matrix of a 3-DOF vehicle model is taking the form of: 

=
M diag{

v

M M M

,

,

1

2

}

1

The stiffness matrix of the vehicle system is expressed as: 

+

2

K

VV

=

K

v

4

K







V
2

VV

K
0

2

K

VV

K
4
VV
K
2

VV

0

2
+
V

K
VV
K
2

VV

4

K





  

(6.20) 

(6.21) 

The damping matrix Cv can be obtained by replacing the stiffness coefficients in equation (6.21) by the 
corresponding damping coefficients. 
Table 6.3 summarizes the eigenfrequencies of the high speed train ICE3. The natural frequencies of the 
car body and the bogie are estimated from the following equations: 

=

f

vc

1
2π

K K
V VV
M K K
+

8
(2

V

2

=

f

vb

1
2π

K

VV

4

K

+2
V
M

1

)

VV

(6.22) 

The natural frequencies of the vehicle are found in the frequency range between 0.54 Hz and 3.17 Hz 
as listed in Table 6.3. 
Based on the numerical model of the bridge and the vehicle model, a train-bridge interaction analysis is 
performed  using  the  developed  MATLAB  toolbox  DATIS.  The  first  78  modes  of  the  bridge,  with 
natural frequencies ranging from 3.61 Hz to 30.02 Hz, consisting of both global and local modes, are 
used in the dynamic analysis. A value of 0.43% is assumed for the damping ratio, which is the mean 

139

 
 
 
 
 
 
 
 
-
-
-
-
 
value of the identified modal damping ratio of the global modes. A train speed of 89 km/h is considered 
in  the  analysis  according  to  the  recorded  train  passage  data.  Figure  6.100  shows  the  computed  time 
history of the vertical displacement at mid span (mid-point at the lower bracing, see Figure 6.101).The 
two vertical lines t=t1 and t=t2 indicate the time when the train enters and leaves the considered span, 
respectively. The maximum absolute value of the displacement is about 11 mm. The contribution of the 
first  5  modes  is  presented  as  well.  It  can  be  observed  that  the  2nd  mode,  which  is  the  first  vertical 
bending  mode,  contributes  the  most  to  the  deflection  of  the  bridge,  while  the  contribution  of  higher 
modes can be neglected. 

Table 6.3 - Computed natural frequencies of the vertical mode of ICE3. 

Wagon 

Frequency (Hz) 

1 

2 

3 

4 

5 

6 

7 

8 

Car body 
Bogie 
Car body 
Bogie 
Car body 
Bogie 
Car body 
Bogie 
Car body 
Bogie 
Car body 
Bogie 
Car body 
Bogie 
Car body 
Bogie 

0.5408 
3.1725 
0.5042 
2.8088 
0.5515 

2.9249 

0.5293 

2.8088 

0.5476 

2.8088 

0.5515 
2.9249 
0.5042 

2.8088 

0.5408 
3.1725 

t=t1

t=t2

5

10

15

Time [s]

20

25

30

35

-3

x 10

2

0

-2

-4

-6

-8

-10

-12
0

]

m

[

t
n
e
m
e
c
a
p
s
D

l

i

Z

Y
2

X

1

3

4

5

Figure 6.100 - Time history of the displacement at mid span. 

Span I b

Span II b

A

C

6

G

8

10

12

14

16

18 20

22

24

26

28

30

32

34

36

Span III b

E

7

9

35740

11

13

15

17 19

21

D

B

23

F

25

27

35180

29

31

33

35

37

38

39

40

42

43

44 45

41

35180

Mid point

Figure 6.101 - Sensor layout in one of the measurement setups. 

Figures 6.102a) compares the measured and predicted time history of the vertical acceleration at point 
7on the first span (see Figure 6.101) after the application of a low-pass filter with a cut-off frequency 
of 10 Hz. A good agreement is obtained between the experimental and predicted results with a similar 
value  for  the  maximum  acceleration.  Figure  6.102b)  shows  the  results  in  the  frequency  domain.  The 
dominant frequencies near 3 Hz, 4 Hz, 5-6 Hz, 8 Hz are well predicted by the numerical model, which 

140

 
 
 
 
 
 
 
 
indicates that the dynamic behaviour of the bridge is well represented by the FE model, and the fatigue 
loading spectra estimated from the dynamic train-bridge interaction analysis for the critical details are 
reliable for the fatigue analysis.  

0.3

0.2

0.1

0

-0.1

-0.2

-0.3
0

2

]

s
/
m

[

n
o
i
t
a
r
e
e
c
c
A

l

(a)

t=t1

t=t2

]
z
H

2

/

s
/
m

5

10

15

Time [s]

20

25

30

35

[

n
o
i
t
a
r
e
e
c
c
A

l

(b)

0.5

0.4

0.3

0.2

0.1

0
0

1

2

3

4
5
Frequency [Hz]

6

7

8

9

Figure 6.102 - Predicted (black line) and measured(red line) acceleration at point 7 during the passage of high 
speed train ICE3 at a speed of 89 km/h: (a) time history and (b) frequency content 

Fatigue analysis of the critical details 

During the inspection of the bridge, cracks are found at the connection plate between cross beam and 
main girder at the support in between the first and the second span as shown in Figure 6.103. The plate 
connects the main girder, the cross girder, and the lower bracing. 

Figure 6.103 - View the crack. 

As  this  was  the  main  observed  crack,  the  study  was  focused  on  the  propagation  of  the  crack  on  the 
connection plate and the remaining fatigue life. For this aim, a fracture mechanics analysis is carried 
out. The global FE model is enhanced at the location where cracks are found by introducing detailed 
connection geometry. A close-up view of the global-local model at the connection plate is depicted in 
Figure 6.104. The connection plate and part of the low bracing, the cross girder, and the main girder are 
modelled with solid elements. The thickness of the connection plate is 12 mm and it is connected to the 
main structure through the riveted holes as described in chapter 4. The mesh at the vicinity of the crack 
tip is shown in Figure 6.105. A crack length of a=130 mm is introduced according to the measurement. 

Figure 6.104 - Local model of the connection plate with solid elements. 

141

 
 
 
 
 
 
 
  
 
 
Figure 6.105 - Mesh at the vicinity of the crack tip. 

In  fracture  mechanics,  there  are  three  modes  describing  different  patterns  of  crack  displacements: 
Mode I, opening or tensile mode; Mode II, sliding or in-plane shear; and Mode III, tearing or anti-plane 
shear. Figure 6.106 shows a schematic representation of each of these three modes. The crack growth 
rate at the crack tip da/dN can be calculated as given in equation (6.23) : 

a
d
N
d

=

C K
(

)

m

(6.23) 

Where  da  is  the  change  in  the  crack  length  for  dN  number  of  stress  cycles,  C  and  m  are  materials 
constants, which take the value of 10-11 and 3 for the steel, respectively. KD
is the range of the stress 
intensity factor, which is a very important parameter that measures of the change in stress within the 
vicinity of the crack tip fracture mechanics. 
There are different techniques to calculate the stress intensity factor, such as displacement extrapola-
tion,  force  method,  J  integral,  Virtual  Crack  Closure  Technique,  etc..  In  the  present  work,  the 
displacement  extrapolation  method  is  used.  To  obtain  a  good  representation  of  the  crack-tip  field, 
quarter-point isoparametric elements are adopted. The displacements at the crack tip field are linearly 
extrapolated  by  the  displacements  of  four  nodes  around  the  crack  tip,  A,  B,  A0,and  B0  indicated  in 
Figure 6.107. The following equations are given: 

K t
( )
I

=

p
2

G
+

K

1

lim
r
0

v

r

K t
( )
II

=

p
2

G
+

K

1

lim
r
0

K t
( )
III

=

p
2

G
+

1

K

lim
r
0

u

r

w

r

(6.24) 
Where  u(t),  v(t),  w(t)  are  dynamic  displacements  in  a  local  cartesian  coordinate  system  as  shown  in 
Figure  6.108,  r  is  the  radius  of  element  at  the  crack  tip  in  a  local  coordinate  system,  G  is  the  shear 
modulus, K=3− 4µ if plane strain or axisymmetric or (3-µ)(1+ µ) if plane stress, µ is Poisson's ratio. 

Figure 6.106 - Three modes of crack 
displacement. 

Figure 6.107 - Finite 
elements and nodes near 
crack tip. 

Figure 6.108 - Local coordinate 
system of the crack. 

142

 
 
 
D
                           
ﬁ
D
 
ﬁ
D
 
ﬁ
D
 
 
 
 
Figure 6.109 - The flowchart for the fatigue life prediction of a railway bridge based on the fracture mechanics 
method. 

Figure  6.109  gives  a  flow  chart  for  the  fatigue  life  prediction  procedure  based  on  the  fracture 
mechanics method. The procedure can be summarized by the following steps:  

1.  Create the numerical model of the bridge including a crack model with an initial crack length 

of a0. 

2.  Modal analysis of the bridge. Perform train-bridge interaction analysis to obtain the displace-

ments of the nodes around the crack tip. 

3.  Compute the stress intensity factor based on the nodal displacements according to equation 

6.24. 

4.  Convert the time history of the stress intensity factor during the passage of a train into stress 

intensity factor range spectra using the rainflow cycle-counting method.  

5.  The crack growth rate da/dN after one train passage can be calculated according to Paris law as 

given in equation (6.25).  
k

da dN
/

=

D∑
(
n C K
i

)

i

m

i

 (6.25) 

6.  A hypotheses is made that the stress intensity K remains the same when the total crack incre-

ment is smaller than the element size ae around the crack tip in the crack model. The total num-
ber of the train cycles for the crack length grows from a0 to a0+ae can be determined as follows: 

=
N a

e

/(

da dN
/

)

(6.26) 

7.  Remeshing the crack model and update the stress intensity factor K after N number of train 

cycles. Repeat steps 5 and 6. 

143

 
 
 
  
           
8.  The procedure ends until the crack grows to a critical size of acr which is calculated using the 

residual strength diagram of the cracked structure, considering material toughness and ultimate 
strength. 

Based on the aforementioned procedure, the crack growth rate of the Saalebrücke bridge is computed. 
The train type considered is a freight train passes the bridge. It consists of 140 axles and the identified 
axle loads are presented in Figure 6.110. The train speed is 84 km/h. When the train passes the bridge, 
it  is  found  that  the  connection  plate  is  under  multiaxle loading and under in-plane compression. The 
crack  mode  is  therefore  characterized  as  mode  II  and  mode  III  dominant  and  mixed-mode  fracture. 
Figures 6.111 and 6.112 present the computed time history of the dynamic stress intensity factor during 
the  passage  of  the  freight  train  at  a  speed  of  84  km/h  for  the  shearing  mode  and  the  tearing  mode, 
respectively. It can be observed that during the train passage, various of stress intensity factor cycles 
with different amplitudes are generated. 
As the crack mode of the connection plate is characterized as a mixed-mode, the equivalent stress 
intensity factor Keff  is computed according to equation (6.26) and the result is presented in Figure 
6.113. 

eK

4
ff

=

(

K

2
I

+

K

2
II

+

K

2
III

/(1

m

+
2

))

4

2
K K
I

2
II

(6.26) 

The rainflow counting method is then applied to count the cycle range for the stress intensity 
factor.  Base  on  equation  (6.25),  the  crack  growth  increment  after  one  freight  train  passage  is 
predicted as 1.4175e-007 m. 

Figure 6.110 - Identified axle load of one freight train. 

Figure 6.111 - Time history of the stress intensity factor 
KII for the shearing mode. 

Figure 6.112 - Time history of the stress intensity factor 
KIII for the tearing mode. 

Figure 6.113 - Time history of the equivalent stress 
intensity factor. 

144

 
 
-
                   
 
 
 
 
Continuous monitoring 

A continuous monitoring system was installed in the Saalebrücke bridge from May 2011. The locations 
of  the  measurement  points  are  illustrated  in  Figure  6.114  in  green  colour,  known  as  #  7  and  #  25. 
Thermometers were installed to monitor the air temperature and the steel frame temperature. 

Figure 6.114 - Measurement layout of the continuous health monitoring. 

An automatic modal analysis procedure, based on stochastic subspace identification, has been applied 
that  is able to extract the modal parameters from stabilization diagrams without any user interaction. 
Figures 6.115 to 6.117 show the variation of the natural frequencies of the first three modes during the 
measured  period  from  September  2011  to  May  2012.The  solid  line  in  the  figures  indicates  the 
identified  frequency  in  the  short  term  monitoring  campaign  on  27  and  28  May  2010.  Significant 
variability  in  the  identified  natural  frequencies  is  observed.  During  the  measured  period,  measured 
temperatures ranged from minus 20 degree to 40 degree. It is observed that in February the temperature 
drops below freezing point. The identified natural frequencies of the bridge are observed to vary by 5-
14  percent  in  the  time  period  considered.  This  is  surprising  since  the  Saalebrücke  Bridge  is  a  steel 
railway bridge which is often expected to be less influenced by the environment.  

Figure 6.115 - Variation of the frequency of the first lateral bending mode and temperature between 2011.08.14 
and 2012.05.30. 

Figure 6.116 - Variation of the frequency of the first vertical bending mode and temperature between 2011.08.14 
and 2012.05.30. 

145

 
 
 
 
 
Figure 6.117 - Variation of the frequency of the first torsion bending mode and temperature between 2011.08.14 
and 2012.05.30. 

Figures 6.118 to 6.120 plot the identified natural frequencies versus the temperature. From this figure, 
it is evident that the natural frequency and temperature are strongly correlated and that the relationship 
is nonlinear: low temperatures correspond to higher modal frequencies. It is observed that the identified 
natural frequencies of the bridge increased at colder temperatures with a very sharp increase near the 
freezing point. 
Because  of  this  inherent  variability  in  the  natural  frequencies,  a  model  of  the  relationship    between 
temperature and natural frequency must be developed before the dynamic characteristics of the bridge 
can be used for condition assessment. This can be done through development of a mathematical model 
correlating  the  modal  parameters  (e.g.,  natural  frequencies)  to  environmental  effects  (e.g.,  tempera-
ture).  It  is  worth  noting  that  the  modeling  of  the  relationship  between  the  frequencies  and  the 
temperature is the subject of ongoing research. 

Figure 6.118 - Natural frequency of first lateral bending 
mode versus temperature. 

Figure 6.119 - Natural frequency of first vertical 
bending mode versus temperature. 

Figure 6.120 - Natural frequency of first torsion mode 
versus temperature. 

146

 
 
 
 
 
 
 
 
6.1.6  Salzach River Bridge (Austria) 

Critical Details 

There is visible damage on the Salzach bridge. The main idea behind this investigation is to determine 
if fatigue could be the source of the damage. The visible cracks are located in the connection between 
the  cross  girders  and  the  vertical  main  beams.  In  the  Figure  6.121  below  a top view of the bridge is 
shown where the location of the cracked cross-girders is marked with orange frames. Open cracks are 
present  in  the  first  three  cross-girders  from  the  east  support  and  the  first  two  from  the west support. 
Cracks exist on both sides of the cross-girders.  

Figure  6.121 - Top view of the bridge with the damaged cross-girder connections framed in orange.  

In Figure 6.122 a detailed view of the connection between the cross girder and the vertical main beam 
is  shown.  The  location  of  the  crack  is  marked  with  a  red  ellipse.  The  damages  appear  in  the  10 mm 
thick connection plate that is highlighted in the figure below. The question of the origin of the crack 
arises as the joint seems to be a case of bad detailing. 

Figure 6.122 - Detail of the connection between cross-girder and vertical main beam with damaged element 
highlighted in red. Crack location marked by ellipse. 

Figure 6.123 and Figure 6.124 show detailed photographs of two different visible cracks on the cross-
girders. The cracks have been mitigated by hole drilling.  

147

 
 
 
 
Figure 6.123 - Detail photograph of the damage at position U03 (compare Figure ) 

Figure 6.124 - Detail photograph of the damage at position U10 (compare Figure ) 

In the selected detail the significant stress type is the shear stress. For assessing fatigue of a structural 
element stress histories are required. The BEAM44 element that was used for modeling the cross-girder 
does not support the option to output shear stress as a result. Thus the transient shear force record was 
extracted and this was then converted to a shear stress record.  

Local Model 

The model of the connection detail was created in Ansys based on the true geometry. 

148

 
 
 
 
Figure 6.125 - Joint detail of cross-girder and vertical beam. Solid finite element model: axonometric view, front 
view. 

Train-Structure Interaction 

To  further  the  knowledge  of  loading  of  the  bridge  on  one  hand  and  in  depth  analysis  of  structural 
details  on  the  other  we  opted  for  a  train-bridge  interaction  analysis.  The  approach  is  henceforth 
described. 

Figure 6.126 - Moving ICE 3 train. 

Model of the ICE 3 Train 

For  the  transient  analysis  we  chose  to  model  an  ICE  3  train  due  to  the  availability  of  a  detailed 
description. Although the very same type of train does is not in operation on this line it is comparable 
to the passenger trains operated on the line and so can yield a realistic picture about the loading of the 
bridge. The dimensions of the locomotive and the in-between wagons are given in Figure 6.127. 

149

 
 
 
 
Figure 6.127 - ICE 3 train length properties. 

Figure 6.128 - ICE3 train model full length (above), one wagon (below) 

The  following  table  gives  detailed  information  about  the  masses  of  the  train  for  each  wagon.  For 
modeling  only  part  of  the  total  weight  was  used  as  wheels  and  bogies  were  modeled  with  their 
respective weights included. 

Table 6.4 - Example of masses of the ICE3 type train. 

Wagon  Axis 
No 

No 

Load 

[kN] 

axis (2 wheels) 

bogie  wagon 

[ton] 

[ton] 

[ton] 

total 

[ton] 

passenger 

[ton] 

total 
[ton] 

1 

1 

1 

1 

2 

2 

2 

2 

… 

16 

16 

16 

16 

1 

2 

3 

4 

5 

6 

7 

8 

149.40 

149.40 

148.40 

148.40 

166.30 

166.30 

163.30 

163.30 

… 

… 

61 

62 

63 

64 

148.40 

148.40 

149.40 

149.40 

1.53 

1.53 

1.53 

1.53 

1.15 

1.15 

1.15 

1.15 

… 

1.53 

1.53 

1.53 

1.53 

6.04 

18.50 

6.04 

18.91 

6.55 

21.05 

6.55 

21.15 

55.61 

3.95 

59.56 

59.90 

6.02 

65.92 

… 

… 

… 

… 

… 

6.04 

18.50 

6.04 

18.91 

55.61 

3.95 

59.56 

TOTAL 

9926.40 

992.64 

The total length of the ICE3 train with 16 wagons is 393.70m. The whole mass of the reference vehicle 
(train plus max. loading) is 992.64 tons. The mass per meter is approximately 2.5 t/m and axle loads 
range from 142.50kN up to 170.9kN. 
In  the  numerical  Model  of  the  ICE3  train  the  coaches  are  approximated  by  rigid  bodies.  These  rigid 
bodies are modeled with BEAM44 elements which have been assigned a stiff material. The mass of the 
ICE3 train is distributed on the horizontal BEAM44 elements. The longitudinal coupling between the 
coaches is simulated with spring elements COMBIN14 with the stiffness of 10kN/mm. 

150

 
 
 
 
 
 
 
 
  
  
  
  
  
  
 
 
Primary suspension

Wheel mass

Hertzian spring

Secondary suspension 

Figure 6.129 - Combined train and bridge model. Detail of wheel suspension. 

Figure 6.130 - Coupling between the coaches. 

COMBIN14 

Also  the  bogies  of  the  train  were  modeled.  In  Figure  6.131  the  principle  of  the  numerical  model  is 
shown. A Hertzian spring is representing the contact between the rail and the wheel. The mass of the 
wheels are modeled by the MASS21 elements. The damping of the primary and secondary springs was 
assumed 1kN at 0.1m/s. In the following table the spring stiffnesses of the train suspension are summed 
up. 

Table 6.5 - Spring stiffness of the train suspension. 

Spring stiffness [N/m] 

Hertzian spring 

vertical 

Primary spring 

Secondary spring 

1310e6 

1.08e6 

wagon at end 

wagon – intermediate 

0.9e6 

vertical 

horizontal 

0.24e6 

0.12e6 

Parameters of the Analysis 

The train passes the bridge with at a velocity of 120km/h. Various time stepping has been used to get a 
comparison of the output and an indication of the necessary step size. The time step of 0.002s equals to 
a  forward  displacement  of  6.67cm.  With  an  element  size  of  about  15cm  this  is  the  lowest  allowable 
time step already allowing the tying of the wheel node to the same node of the rail in two consecutive 

151

 
 
 
 
 
 
 
steps.  The  results  show  that  this  phenomenon  does  not  have  significant  influence  on  the  results  as 
compared to the time step of 0.005s. 
The analysis was solved with the Newmark time integration scheme. An overall damping of 3% was 
applied. 

ti 

t

i+1

Figure 6.131 - Scheme of the connection between rail and wheel nodes in each time step by constraint equations. 
The contact nodes of the wheels are constrained to have the same vertical displacement as the closest rail node. 
Nodes of the same color are coupled vertically for one time step. 

Solution Scheme 

At any given time step by the application of constraint equations a bond is formed between the nodes 
representing the wheel of the train and the closest located node of the rails. Only the vertical degrees of 
freedom  are  bonded  not  to  transmit  any  numerically  generated  horizontal  acceleration,  which  stems 
from the forward shifts of the train in each time step. After the solver has found the equilibrium for the 
given  time  step  the  bonds  are  removed,  the  train  is  shifted  forward  and  new  constrain  equations  are 
defined to the closest nodes of the rail in this newly updated position. Then the next time step is solved. 
Figure  6.132  shows  the  result  of  time  step  number  150,  which  means  the  train  has  already  moved 
forward 10m. 

Figure 6.132 - Showing the position of the train in time step 150. 

It  is  noteworthy,  that  the  afore  mentioned  solution  procedure  is  valid  only  until  no  loss  of  contact 
occurs  between  the  interacting  systems.  Once  the  wheel  forces change direction to uplift, clearly the 
solution becomes incorrect. However, to verify the corectness of the solver while contact is maintaned 
an alternative uncoupled, iterative solver has been developed. In this approach the two systems (train 
and  bridge)  are  not  connected  in  any  degrees  of  freedom  but  influence  each  other  by  trasmittion  of 
interaction forces on the wheels and the resulting displacements of the rails. At any given time step first 
the train forces are computed on a supported train system. In a second solution the wheel contact forces 
are applied on the rail, which then yields the rail deformations. This is the end of one iteration step. 
The resulting deformations are then applied to the supports of the train to compute and updated set of 
wheel forces which in turn are applied to the track. Iterations are repeated until convergence is reached. 

152

 
 
 
 
  
  
 
  
  
  
  
  
 
 
 
Afterwards the train is moved forward. This analysis is extremely time consimung as the analysis has 
to be restarted after each partial solution and so information exchange must be realized through files 
saved  on  the  hard  drive.  For  these  reasons  only  a  short  time  of  the  train  passing  was  analysed  to 
compare the two solvers. Figure 6.133 shows this comaprison. 

Figure 6.133 - Comparison of the two solvers for train-track interaction. 

To keep the postprocessing procedure in a reasonable timespan, a substet of elements and nodes was 
chosen at both end of the bridge, see Figure 6.134.  

East 

West 

Figure 6.134 - Top view of the bridge; the two selected joints highlighted with red circles. 

Initial Conditions 

In  getting  the  correct  response  in  time  the  initial  conditions  play  a  crucial  role.  For  the  described 
analysis  the  train  starts  off  in  level  position  acquired  from  its  own  weight.  No  impulse,  i.e.  initial 
velocity or acceleration was applied to the wagons. The static displacement of the wagons due to self-
weight is about 52cm. Care must be taken in properly defining an initial time step. In this step we want 
to let the train reach its nonzero vertical displacement butintroduce zero velocity and acceleration. This 
can be achieved by running the first step as steady-state in two substeps with time integration turned 
off. After establishing such an initial step the time integration can be turned on and carried out over the 
required time frame. 

Loading Outcome 

In this section the results of the train-bridge interaction analysis are presented. First the force history in 
a selected point is given. Later the shear force and axial stresses are shown. 

Figure 6.135 - Load force record upon passing of the train under a selected sleeper. 

153

 
 
 
 
 
 
 
Figure 6.136 - Load force histogram from the previous plot in 12 classes. 

Figure 6.137 - Shear force in the cross-girder at the joint during passing of the train. 

Figure 6.138 - Shear stress in the cross-girder at the joint during passing of the train. 

154

 
 
 
 
 
Figure 6.139 - Normal stress in the cross-girder at the joint during passing of the train. 

Rainflow Counting 

For  computing  the  fatigue  curves  the  rainflow  counting  algorithm  was  be  used.  The  algorithm  has 
several  stages.  First  peaking  is  performed.  In  this  phase  the  signal  is  cleared  of  intermediate  values 
between  local  peaks  which  are  defined  by  the  change  of  the  slope  of  the  curve.  In  the  second  phase 
filtering is done, however not in the traditional sense, simply values below a threshold are eliminated. It 
is  to  get  rid  of  unwanted  small  perturbations  and  noise.  Finally  the  actual  rainflow  counting  is 
performed.  The  procedure  counts  full  and  half  loops  based  on  the  criteria  of  inter-relation  of  four 
points in the series (see Figure 6.140). In the end classes are set up based on their desired number and 
the number of cycles for each class is determined. Half-loops are counted as ½ cycle. 
The  daily  events  once  prepared  in  terms  of  stresses  were  ready  to  be  processed  by  the  rainflow 
counting  algorithm.  Initially  all  the  events  were  appended  to  one  vector  to  allow  for  fast  unified 
processing.  The  threshold  for  the  filtering  was  chosen  0.1%  of  the  maximum  amplitude.  The  cycle 
counts for a typical day are plotted in Figure 6.141. The preparation of the signal for the cycle counting 
does  have  its  nuances.  An  engineering  judgment  on  the  peaking  and  filtering  is  advisory.  As  the 
peaking and filtering greatly depend on the sampling of the data, intermediate checks are beneficial to 
the final results. 

Figure 6.140 - Criteria for loop counting in rainflow algorithm. a) full loops   b) half loops 

155

 
 
 
 
What one must have in mind is that the filtering of the data should not affect the overall extremes and 
thus should yield consistently the same classes regardless of the filtering threshold. The cycles counted 
for the select day are presented in 10 classes. The positive behavior of the processing is that the low 
magnitude  cycles  are  greatly  affected  by  increasing  the  threshold  value  while  with  increasing  cycle 
magnitudes this effect decreases.  
From  observations  we  could  extrapolate  the  approximate  number  of  trains  per day that are using the 
bridge.  We  estimated  53  trains  per  day  passing  the  bridge.  With  the  shear  stress  records  from  our 
numerical analysis we could create now cycle counts for both investigated cross-girder joints. 
Originally the numerical model of the bridge lacked some stiffening plates exactly at the problematic 
joints. The results for this case are given here first. 

Figure  6.141  -  Cycle  counts  by  rainflow  algorithm  onone  typical  day.  East  cross-girder;  filtering 
threshold 0.1%. 

Figure 6.142 - N-S curve for the joint compared to class 36 (EN 1993-1-9); east cross-girder. 

At  this  point  it  seemed  that  the  fracture  of  the  cross-beam  at  the  joint  could  have  suffered  from  bad 
detailing.  Simply  calculating  the  maximum  shear  stresses  in  the  cross-girders  in  the  damaged  region 
seems to support this conclusion. For mild steels of the era we have found the yield strengths of 
240MPa  (1922)  and 
comparison 

370MPa  (1908).  If  we  assume  the  lower  value  of  the  two  we  arrive  at  the 

,  with 

 , 

MPa

 MPa. 

(6.27) 

156

 
 
 
 
 
This  equates  to  a  safety  factor  of  1.036.  The  requirement  is  very  close  to  the  material  strength  and 
assuming  that  heavier  freight  trains  operate  on  the  line  the  limit  strength  of  the  material  could  have 
been exceeded.  
However, upon closer examination of the original blueprints additional stiffening plates were found at 
the joint. Its inclusion does decrease the overall stress ranges at the joint. These results follow here. 

Figure 6.143 - Cycle counts for one day. East cross-girder, dt=0.002s. 

Figure 6.144 - N-S curve for the joint compared to class 80 (EN 1993-1-9); east cross-girder; dt=0.002s. 

Figure 6.145 - Cycle counts forone day. East cross-girder, dt=0.005s. 

157

 
 
 
 
 
 
Figure 6.146 - N-S curve for the joint compared to class 80 (EN 1993-1-9); east cross-girder; dt=0.005. 

Finally,  the  cycles  calculated  from  numerical  data  can  be  matched  with  normative  restrictions  (EN 
1993-1-9) [6.28]. For this task the joint is assumed to be of class 80 and the computed cycle counts are 
taken  from  Figure  6.143  and  Figure  6.144.  In  the  figures  below  one  can  see  that  the  one  year  cycle 
counts are not touching the curve from the code as in the old model. By assuming a life expectancy of 
onehundred  years  and  adding  up  the  cycles  over  this  time  period  one  can  see  that  this  final  curve 
reaches  the  normative  curve  for  class  80.  This  leads  us  to  believe  that  fatigue  could  have  caused 
cracking of the element at the joint. 
Moreover, we may state that the difference in time stepping is not significant. The smaller time step of 
0.002  seconds  gives  more  low  level  perturbations,  which  can  be  filtered  out,  however  these  are  not 
critical for the fatigue assessment of the joint. Nonetheless for a fatigue assessment of this type a time 
step of 0.005 seconds is sufficient. 

Remarks 

The Salzach Bridge is an old riveted bridge. It has had some cracks on its cross-girders for about 20 
years.  They  were  mitigated  by  the  standard  method  of  hole  drilling.  It  is  unclear  what  caused  this 
damage.  The  two  forerunning  candidates  are  incompetent  detailing  or  fatigue.  The  analysis  pointed 
rather towards an erroneous design of the detail. Nonetheless, additional investigation showed that the 
answer is not clearly straightforward and that fatigue could have played a more or less significant role 
in the development of the damage. Thinking about the inaccuracies in the loading history of the bridge 
no definitive statements can be made about the damaged joints. 

6.2  References  

[6.1]  L. Georgiev. Fatigue life analysis of an old riveted bridge based on S-N lines. Proceedings of 
“7th International Conference on Bridges across the Danube”. Sofia, Bulgaria October 14-15, 2010.  

[6.2]  Eurocode 1, Actions on structures – Part 2: Traffic loads on bridges, European committee for 
standardization, EN 1991-2, 2003. 

[6.3]  L. Fryba. Dynamics of railway bridges. London: Thomas Telford; 1996. 

[6.4]  F.  Yang,  G.A.  Fonder.  An  iterative  solution  method  for  dynamic  response  of  bridge-vehicles 
systems. Earthquake Eng Struct Dynam 25, 195–215, 1996. 

[6.5]  Y.B. Yang, B.H. Lin. Vehicle-bridge interaction analysis by dynamic condensation method. J 
Struct Eng, 121(11), 1636–43, 1995. 

[6.6]  Y.S.  Cheng,  F.T.K.  Au,  Y.K.  Cheung.  Vibration  of  railway  bridges under a moving train by 
using bridge–track–vehicle element. Eng Struct 23, 1597–606, 2001. 

[6.7]  Q.  Zhang,  A.  Vrouwenvelder,  J.  Wardenier.  Numerical  simulation  of  train-bridge  interactive 
dynamic, Computer and Structure 79: 1059-1075, 2001. 

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[6.8]  Y.S. Wu, Y.B. Yang. Steady-state response and riding comfort of trains moving over a series 
of simply supported bridges. Eng Struct 25, 251–65, 2003. 

[6.9]  B. Biondi, G. Muscolino, A. Sofi. A substructure approach for the dynamic analysis of train-
track-bridge system, Computer and Structure 83: 2271-2281, 2005. 

[6.10]  K.  Liu,  G.  De  Roeck,  G.  Lombaert,  The  effect  of  dynamic  train-bridge  interaction  on  the 
bridge response during a train passage, Journal of Sound and Vibration 325, Elsevier, 2009. 

[6.11]  K.  Liu,  E.  Reynders,  G.  De  Roeck,  G.  Lombaert,  Experimental  and  numerical  analysis  of  a 
composite bridge for high-speed trains, Journal of Sound and Vibration 320, Elsevier, 2008. 

[6.12]  K. Liu, E. Reynders, G. De Roeck, Experimental validation of the dynamic interaction analysis 
between high-speed trains and the Sesia viaduct, Leuven University, Belgium. 

[6.13]  L. Vincenzi, M. Savoia, W. Salvatore, Experimental modal analysis and fatigue assessment on 
the Lagoscuro viaduct, in Proceeding of “IABMAS 2012”, Como Lake, Italy, 2012 

[6.14]  Vincenzi  L.,  Savoia  M.  Salvatore  W.  Experimental  analysis  and  fatigue  assessment  on  a 
railway  steel  viaduct.  11th  International  Conference  on  Computational  Structures  Technology 
(CST2012), Dubrovnik, Croatia, 4-7 September 2012. 

[6.15]  Vincenzi  L.,  Savoia  M.  Rossi  F.  Vehicle-bridge  interactive  analyses  on  the  PonteLagoscuro 
viaduct.  11th  International  Conference  on  Computational  Structures  Technology  (CST2012), 
Dubrovnik, Croatia, 4-7 September 2012. 

[6.16]  Cunha  A,  Caetano  E,  Magalhães  F,  Moutinho  C.  Recent perspectives in dynamic testing and 
monitoring of bridges. Journal of Structural Control and Health Monitoring 2012. 

[6.17]  Miner,  M.A.,  1945,  Cumulative  Damage  in  Fatigue,  Journal of Applied Mechanics, Vol. 67: 
A159-69. 

[6.18]  Basquin O. H., 1910, The exponential law of endurance tests. Proc. Annual Meeting, American 
Society for Testing Materials,Vol. 10, pp. 625-630. 

[6.19]  Jesus,  A.M.P.  [et  al.],  2011,  Strain-life  and  crack  propagation  fatigue  data  from  several 
Portuguese old metallic riveted bridges, Engineering Failure Analysis, 18, p.148–163. 

[6.20]  Krupp, www.eisenbahnfieber.de, Krupp, Udo, 2010, URL http://www.eisenbahnfieber.de. 

[6.21]  A. Steimel, Elektrische Triebfahrzeuge und ihre Energieversorgung, Oldenbourg Industriever-
lag, Munich, 2nd edition, 2006.  

[6.22]  A. Taras, R. Greiner, Development and Application of a Fatigue Class Catalogue for Riveted 
Bridge Components, ECCS TC6 Reports, 2009. 

[6.23]  C. Esveld, A.W.M. Kok, Interaction between moving vehicles and railway track at high speed, 
Rail Engineering International, 27, 3, 14-16, 1998. 

[6.24]  I.  Faria,  R.  Delgado,  R.  Calçada,  Bridge-vehicles  dynamic  interaction:  numerical  modelling 
and practical applications, Bridges for High-Speed Railways, 159-179, 2008. 

[6.25]  Eurocode 3: Design of steel structures, Part 1-9: Fatigue. 

[6.26]  Ansys Inc., Theory Reference, release 10.0 

[6.27]  Ansys Inc., Structural Analysis Guide, release 10.0 

[6.28]  Ansys Inc., Advanced Analysis Techniques Guide, release 10.0 

159

 
 
7  Guidelines for Fatigue Assessment 

The  correct  assessment  of  fatigue damages induced by vibration/distortion phenomena is particularly 
complex as it involves the local analysis of secondary effects generally neglected or not represented in 
the calculation of main components.  
Standard design of steel structure, in the past and nowadays, is frequently composed by two subsequent 
levels of analysis: i) a global assessment of internal forces induced by loads into main components; ii) 
design of connections by means of the previously calculated results.  
In case of railway bridges, typically this approach leads to the developing of a global mechanical model 
representing the bridge deck or superstructure, composed in most cases by beam elements, adopted for 
the  design  of  members  and  for  the  calculation  of  joint  forces.  By  this  way,  it  is  possible  to  obtain  a 
reliable evaluation of internal forces acting into bridge components that can be modelled by beams, but 
it is not possible to evaluate the local effects into critical details, thus neglecting such secondary effects 
as vibration and distortion that induce additional fatigue damages 
The  mechanical  models  are  then  subjected  to  external  loads,  generally  constituted  by  distributed  or 
point  forces.  In  railway  bridge  case,  trains  are  modelled  by  the  moving  load  approach,  i.e.  series  of 
point loads (axle weight) moving over the bridge at design speed, or as an equivalent static load. In the 
first case a dynamic analysis is required, while by the second approach it is possible to perform just a 
static  analysis.  In  both  cases,  the  models  adopted  to  represent  the  effects  of  trains  are  composed  by 
vertical  loads  only,  not  considering  at  all  the  horizontal  forces  induced  by  trains  on  bridges  that,  in 
some cases,  could be amplified by resonance with bridge vibration modes characterized by horizontal 
displacements (as torsional or horizontal modes). Such effects, generally neglected, could increase the 
local stresses and induce unexpected fatigue damages. Furthermore, the dynamic analysis with moving 
loads  do  not  take  into  account  of  the  possible  train-bridge  interaction  phenomena  that,  in  resonance 
case, could modify the bridge dynamic response. 
At least, stress spectra induced into local details by all trains passing on the bridge is calculated and 
adopted for the fatigue assessment of selected component. The stress spectra, obtained from the design 
traffic spectra assumed for the line, could be different from real spectra due to differences in the traffic 
composition. This could lead to an erroneous estimation of actual fatigue performance both for existing 
and newly designed bridges. 
Moreover,  the  conventional  fatigue  resistances  adopted  for  bridge  components  and  details,  i.e.  the 
fatigue  classes,  could  not  representative  as  obtained  by  ideal  laboratory  specimens  subjected  to  load 
conditions that didn't consider the possible presence of secondary effects. 
The results obtained by the Fadless Project permitted the development of an advanced approach for the 
proper  assessment  of  vibration  and  distortion  induced  fatigue.  The  proposed  methodology  aims  at 
evaluating  correctly  the  stress  spectra  induced  by  trains  into  bridge  details  most  exposed  to 
vibration/distortion  phenomena,  and  at  estimating  properly  the  fatigue  resistance  of  investigated 
components. 
The  adopted  approach  is  based  on  a  complex  mix  of  different  typologies  of  experimental  and 
theoretical analysis as reported in Figure 7.1. The fatigue assessment is obtained by the composition of 
four macro-activities: 

•  Global  Analysis  of  Bridge:  the  objective  of  the  global  analysis  is  the  investigation  of  actual 
bridge structural performance under train passage. To this aim, results obtained from numeri-
cal analysis and experimental dynamic tests are mixed together to obtain a reliable assessment 
of internal forces induced by train into bridge components, thus identifying also those critical 
details most subjected to vibration/distortion effects; 

•  Local analysis of critical details: an extensive assessment of local stress induced by trains into 
the critical details identified in the global analysis is performed by means of numerical mod-
els,  properly  calibrated  with  regard  to  experimental  tests  on  investigated  components.  Cali-
brated local models will provide a reliable estimation of actual local stress distribution taking 
into account also of vibration/distortion effects; 

•  Monitoring of Service Conditions: the identification of critical details will constitute the base 
for  the  development  of  a  monitoring  system,  aimed  at  estimating  the  real  stress  spectra  in-

161

 
 
duced by actual traffic into critical details and, more in general, at identifying the traffic spec-
tra on the line, i.e. train typology, composition, axle loads, speed. The knowledge of the criti-
cal details and of the real dynamic characteristics of the bridge will permit the optimization of 
monitoring  capabilities  and  the  control  of  those  components  most  exposed  to  vibra-
tion/distortion effects; 

•  Laboratory  Tests:  the  actual  fatigue  resistance  of  critical  details  subjected  to  the  real  stress 
patterns  obtained  by  calibrated  local  models  will  be  evaluated  by  proper  laboratory  fatigue 
tests. It will be so possible to classify exactly the fatigue behaviour of such components taking 
into account also of those secondary effects induced by vibration and distortion generally not 
considered in laboratory tests. 

•  Advanced  Fatigue  Assessment:  the  identification  of  real  traffic  spectra,  the  developing  and 
calibration by updating of Global and Local models and the experimental evaluation of fatigue 
resistance  by  laboratory  tests  will  compose  the  main  core  of  the  final  advanced  fatigue  as-
sessment.  Standard  or  advanced  damage  accumulation  methods  shall  be  adopted  for  the 
evaluation  of  fatigue  performance  of  undamaged  or  repaired  components,  while  existing 
cracks shall be analyzed by fracture mechanic approaches. 

Global Analysis of Bridge

FE Global Model

Dynamic Identification

Updated FE Global Model

Standard Fatigue 
Assessment

Identification of Critical 
Details

Monitoring System

Laboratory Tests

Laboratory Fatigue Test

Traffic Spectra / Control of 
Critical Details

Monitoring of Service 
Conditions

Advanced Assessment  of 
Vibration/Distortion  Induced Fatigue

Advanced Fatigue Assessment

Local Analysis of Critical Details

FE Local Models

Experimental Analysis of 
Critical details

Updated FE Local Model

Actual Stresses Induced by 
Vibration/Distortion

Figure 7.1 - Methodology for the advanced assessment of vibration/distortion induced fatigue. 

The proposed methodology was successfully applied to the case studies selected for the Faldess Project 
and,  although  requiring  the  execution  of  experimental  and  numerical  non-standard  analysis  and  an 
additional effort with regard to current design practice, showed to be a reliable tool for the assessment 
of vibration/distortion induced fatigue. 

Global analysis of bridge deck or superstructure 

The  global  analysis  of  bridge  deck  or  superstructure  shall  be  obtained  by  finite  element  models, 
representing the main structural components as longitudinal girders, transverse beams or bracing. Both 
beam and shell elements can be used depending on bridge typology (for example: beam elements for 

162

 
 
 
girder bridge; shell elements for composite deck with steel box sections). Particular attention shall be 
made at the respect of actual geometry and position of modelled components: for example, the common 
misalignment in old bridges of the rails with the axle of the stringers, leading to an eccentric loading 
outside the plane of these elements, shall be correctly represented in the model. 
All  non-structural  permanent  loads  as  rails, sleepers or gratings shall be represented in the model by 
additional  permanent  loads  or  by  equivalent  densities  of  supporting  elements.  In  both  cases,  the 
dynamic properties shall be calculated assuming all permanent loads as mass sources. 
External  restraints  shall  be  modelled  taking  into  account  of  the  following  aspects:  i)  the  geometrical 
position  of  the  contact  surfaces  between  bridge  and  supports;  ii)  the  stiffness  of  supports  along  the 
different degrees of freedom; iii) the continuity of rails over bridge ends. Spring elements can be used 
to represent support stiffness and the effects of rail continuity on bridge ends. 
The bridge dynamic identification shall be designed in order to catch the global vibrations movements 
of the structure, i.e. vertical flexural, torsional and transverse modes. Ambient actions (i.e. wind, traffic 
on near roads or highways, movements of staff members) that, in a suitable long time period, constitute 
a  statistical  random  and  independent  set  of  forces  on  the  structure,  can  be  adopted  as  “white  noise” 
excitation source, thus avoiding the use of external excitation device to analyze the structure. Assuming 
ambient  forces  as  excitation  source,  acquired  data  can  be  elaborated  by  Operative  Modal  Analysis 
techniques, to obtain the structural identification on the basis of the “white noise” input signal. 
Developed numerical models shall be updated with regards to experimental dynamic data, i.e. natural 
frequencies and mode shapes, obtaining the calibration of those mechanical or geometrical parameters 
(such  as  material  densities,  external  constraint  conditions,  loads)  which  estimation  is  unclear  or 
subjected to wide range of values. At least the following parameters shall be considered in the updating 
process: 

•  Non-structural permanent loads (such as rails, sleepers, bolts and steel plates); 

•  External supports: geometrical position, stiffness; 

•  Bridge ends: stiffness of spring elements representing rail continuity. 

The updated global model shall then be used for the standard fatigue assessment of the bridge, aimed at 
identifying  those  critical  details  most  subjected  to  vibration/distortion  phenomena.  To  this  aim,  a 
proper evaluation of the influence of train-bridge interaction phenomena on the local stresses shall be 
realized. 
Trains  passing  on  railway  bridges  are  typically  considered  just  as  external  moving  loads  and 
represented  by  series  of  point  forces  or,  when  a  dynamic  analysis  is  not  required,  by  an  equivalent 
static load model. This approach can be considered correct when the weight of the train is negligible 
with regard to the weight of the bridge, as in case of concrete bridges. Nevertheless, in case of steel 
bridges the influence of train-bridge interaction phenomena and the possible amplification of stresses 
induced by train passage into local details due to resonance effects between the train and the natural 
vibration modes of the structure shall be evaluated. In particular, with regard to the effects induced by 
vibration/distortion  phenomena,  the  interaction  analysis  shall  take  into  account  also  of  the  lateral 
effects  induced  by  train  on  the  bridge.  This  aspect  is  generally  neglected  as  standard  moving  load 
models  are  constituted  by  vertical  loads  only,  thus  not  considering  in  any  way  the  presence  also  of 
lateral  contact  forces  between  wheels  and  rails.  By  train-bridge  interaction  analysis  it  is  possible  to 
estimate also the possible resonance effects of lateral forces with those bridge natural vibration modes 
characterized by horizontal displacement (like transversal or torsional modes). Interaction analysis can 
be performed adopting different mechanical models of the train with a variable number of degrees of 
freedom. As more complex models require a higher calculation effort, it is advisable to perform some 
preliminary  analysis  in  order  to  identify  the  train  model  complexity  level  required  for  a  reliable 
evaluation of local stresses. Generally, the complexity of train model is increased since a stable bridge 
response  is  found  and  further  increase  do  not  modify  the  results.  Typically,  vertical  accelerations  of 
particular points are adopted as reference for the choice of model complexity. In case of steel bridge, 
for a proper evaluation of vibration/distortion induced fatigue, displacements at boundaries of critical 
details shall be adopted as reference instead of accelerations, as they define the calculated stresses into 
local models. 

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Local analysis of critical details 

After  the  identification  of  critical  details  by  global  analysis,  the  evaluation  of  local  stresses  shall  be 
obtained by finite element local models representing the actual geometry of the selected component or 
joint. All secondary steel plates used for the connections and, in case, bolts or riveted shall be included 
in  the  models  .  Shell  or  brick  elements  shall  be  adopted  for  the  development  of  such  models.  Local 
model shall be calibrated with regard to experimental data (constituted by natural dynamic properties 
or  strain  patterns  induced  by  train  passage)  in  order  to  provide  a  reliable  representation  of  vibra-
tion/distortion  phenomena.  The  numerical  local  models  shall  be  developed  according  to  the  two 
following approaches: 

• 

Independent FE local model: the local model is developed independently from the global one. 
In  this  case,  the  displacement  time-histories  obtained  from  the  global  model  under  the  train 
passage shall be transferred to the boundary nodes of the local model; 

•  Local model included into the global model: the connection or component object of the local 
analysis  is  properly  modelled  by  shell  or  brick  elements  directly  into  the  global  model.  The 
refined local model shall be extended to all the area that may influence the stress patterns into 
the  investigated  component.  Continuity  of  local  and  global  elements  shall  be  guaranteed  by 
rigid connections on boundary nodes. 

The  updated  local  models,  providing  reliable  estimation  of  actual  strain  patterns  into  critical  details, 
will be used also for the design of proper laboratory fatigue tests in order to evaluate experimentally 
the  fatigue  resistance  of  investigated  components  subjected  also  to  vibration/distortion  induced 
stresses.  Moreover,  updated  models  will  be  adopted  for  the  final  advanced  fatigue  assessment  of 
investigated bridge. 

Monitoring of Service Conditions 

The  fatigue  assessment  of  railway  bridges  can  be  obtained  adopting  the  standard  traffic  spectra 
reported by design codes. By this approach, local stress spectra are calculated according to a theoretical 
traffic that could be significantly different from real one, as design spectra were defined according to 
past  studies  on  railway  lines  and  do  not  take  into  account  of  the  actual  train  composition,  typology, 
axle  loads  and  frequency.  Moreover,  in  case  of  the  fatigue  assessment  of  old  structure,  as  riveted 
bridges, the effects induced by trains during all the life-cycle prior to the definition of current design 
codes shall be evaluated adopting proper "past" traffic spectra. 
Past traffic spectra shall be evaluated considering the train load models reported in past design codes, 
as such models reflect the evolution of train technologies including vehicle composition and axle loads. 
Reliable  information  on  the  traffic  spectra  actually  passed  on  an  existing  bridge  can  be  provided  by 
National railway authorities only. In case such data are not available, it is possible to adopt the actual 
code  traffic  spectra  but  calculated  results  could  be  unreliable  and  high  fatigue  damages  not  actually 
present on the structure could be obtained.  
In case reliable estimation of past traffic spectra is not possible, a structural health monitoring program 
for  the  control  of  bridge  performance  shall  be  considered.  To  this  aim,  results  obtained  from  the 
updated  global  model  will  permit  the  optimal  design  of  monitoring  systems  aimed  at  the  control  of 
critical  details  and,  also,  at  the  evaluation  of  traffic  spectra.  In  case  of  damaged  components,  it  is 
possible  to  realize  an  experimental  estimation  of  strain  patterns  at  fatigue  cracks  or  at  repairs,  for  a 
direct  monitoring  of crack growth or control of remaining life-cycle. Moreover, actual traffic spectra 
can be conveniently evaluated by sensors and procedures for the automatic identification of axle loads 
and train speeds.  
By this approach, it will possible to obtain a reliable and effective structural health monitoring system 
for the control of real bridge service conditions, and the evaluation of actual traffic spectra necessary 
for the advanced assessment of fatigue performances. 

Laboratory Tests 

Actually,  the  fatigue  resistances  of  steel  components  and  details  are  expressed  by  the  S-N  curves 

164

 
 
 
adopting the results of laboratory tests on specimens subjected to ideal load conditions that did not take 
into account of the possible presence of secondary effects. Moreover, riveted solutions are considered 
equivalent  to  bolted  solutions  with  regard  to  fatigue  resistance,  neglecting  the  inherent  difference 
between these two construction techniques. 
In case of riveted components, as experimental tests could be particularly complex due to the supply 
difficulties of riveted specimens, it is possible to adopt the fatigue classification reported by the railway 
National  authorities  standards,  that  were  constantly  updated  just  for  the  monitoring  of  the  many 
existing riveted bridges still on service among all European countries. 
The  actual  fatigue  resistance  of  investigated  detail  shall  be  evaluated  by  laboratory  tests  designed  in 
order  to  reproduce  the  real  stress  patterns  calculated  by  local  FE  models  taking  into  account  also  of 
vibration/distortion induced effects. It is so possible to obtain a reliable experimental evaluation of the 
real fatigue resistance and, as a consequence, of the fatigue performance under the effects induced by 
the actual traffic spectra. 

Advanced Fatigue Assessment  

The  final  fatigue  assessment  will  be  obtained  by  the  composition  of  advanced  investigation  on  the 
global/local mechanical structural behaviour, on the real traffic spectra on selected railway line and on 
the  actual  fatigue  resistance  of  critical  details  under  the  effects  induced  also  by  vibration/distortion 
phenomena.  The  results  of  this  final  step  are  the  calculation  of  fatigue  damages  into  undamaged 
components or the estimation of remaining fatigue life-cycle of damaged components. 
In case of undamaged details, the fatigue assessment shall be performed adopting a standard damage 
accumulation method law like Miner's law or advanced approaches. If sufficient information on future 
traffic  spectra  are  available,  it  will  be  also  possible  an  estimation  of  remaining  life  for  the  most 
exposed critical detail up to the achievement of 100% fatigue damage. 
Concerning  the  estimation  of  the  remaining  life-cycle  of  a  damaged  component,  the  following  two 
situations can occur: 

•  Repair interventions were realized: in this case, the local FE models shall represent the actual 
geometry of the component including also the repair intervention. Remaining fatigue life can 
be estimated by damage accumulation methods like Miner's rule; 

•  No  repair  interventions  were  realized:  in  this  case,  fatigue  cracks  identified  into  the  bridge 
components are still present. The crack growth rate can be evaluated by fracture mechanic ap-
proaches developing proper numerical model representing the actual crack geometry in order 
to evaluate correctly the local stress intensity factors. 

The advanced fatigue assessment will provide reliable and extensive information concerning not only 
the  actual  situation  of  fatigue  damages  into  bridge  components,  but  also  a  prevision  of  future 
development  in  case  of  existing  damages  or  an  estimation  of  remaining  life  for  undamaged 
components.  

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8  Conclusions and Future Developments 

Main objective of the Fadless project was the analysis of vibration/distortion effects on the fatigue life-
cycle  of  existing and new railway steel bridges. As fatigue still represents the most frequent damage 
cause  in  such  structures,  the  development  of  advanced  fatigue  assessment  procedures  taking  into 
account also of vibration/distortion effects was necessary for an effective design of new bridges and a 
reliable assessment of existing ones. 
During the Project, it was extensively shown that vibration/distortion phenomena can cause significant 
fatigue damages in railway steel bridges. The two effects can occur, simultaneously or independently, 
in bridges characterised by different structural solutions or loads. In fact, each case study selected for 
the  Project  showed  a  different  sensibility  to  such  phenomena  depending  on  its  own  dynamic 
characteristics, on the building technology (welded, riveted or bolted), on the geometry of local details, 
on the traffic spectra passing on the line. This different sensibility was highlighted also by the presence 
of  minor  or  extensive  fatigue  damages.  Generally,  it  was  evident  that  the  influence  of  vibra-
tion/distortion  effects  on  the  actual  fatigue  performance  of  investigated  structure  varied  for  each 
particular case, depending also on the ratio between the secondary stresses induced by such phenomena 
and  the  primary  stresses  induced  directly  by  applied  loads.  From  this  point  of  view,  it  was  clear  the 
impossibility  of  defining  practical  rules  (i.e.  without  extensive  analysis)  for  the  evaluation  of  the 
"exposure level" of existing steel bridges to vibration/distortion effects. 
Nevertheless, a reliable and advanced fatigue assessment was obtained by the application of the Project 
methodology,  aiming  at  a  correct  evaluation  of  all  parameters  influencing  the  actual  fatigue 
performance  of  steel  bridges.  All  aspects  that  contribute  at  defining  local  stress  spectra  and  fatigue 
resistances were extensively investigated by means of experimental/numerical analysis, identifying into 
the  global  structure  such  critical  details  most  exposed  to  vibration/distortion  fatigue  damages.  The 
proposed  methodology  was  composed  of  three  main  parts:  i)  the  evaluation  of  actual  structural 
behaviour,  for  a correct estimation of internal stresses induced by trains; ii) the identification of real 
traffic spectra passing on the bridge; iii) the experimental fatigue classification of critical details. The 
advanced fatigue assessment was finally obtained by the comparison between the internal stress spectra 
induced  by  actual  train  traffic  passing  on  the  bridge  and  the  real  fatigue  resistance  of  investigated 
component.  In  case  of  existing  cracks,  the  remaining  fatigue  life  was  conveniently  evaluated  by 
fracture mechanic approaches. 
Moreover,  the  application  of  proposed  Methodology  showed  that  vibration/distortion  fatigue  effects 
were  so  dependent  on  the  own  characteristics  of  each  case  study  (structural  typology,  geometry  of 
connections,  traffic  spectra,  et.)  to  make  it  impossible  the  development  of  reliable  and  effective 
guidelines  covering  all  possible  cases.  This  was  due  to  the  fact  that  the  fatigue  damages  induced  by 
vibration and distortion depended on a large number of parameters, each one characterized by a great 
variability and uncertainties, in such a way that each investigated bridge showed its own characteristic 
fatigue  performance  not  extendible  as  general  result  to  other  bridges  of  same  typology.  In fact, even 
considering  similar  solutions,  fatigue  resistance  was  defined  by  million  cycle  repetitions  of  single 
events  that  could  damage  or  not  a  specific  component  depending  on  small  variations  of  specific 
exercise conditions, i.e. all those parameters defining the structural bridge response. 
In  particular,  main  results  obtained  by  proposed  Project  Methodology  were  constituted  by  the 
successful  interconnections  of  experimental  and  numerical  analysis  that  permitted  an  extensive 
investigation of all parameters affecting the fatigue performances of railway bridges, as summarized in 
the following:  

i)  Global  dynamic  behaviour  of  superstructures:  the  structural  dynamic  response  of  bridge 
decks  depended  on  construction  typology,  bridge  geometry,  interaction  with  contiguous 
structures (as in case of multi-span viaducts), supporting conditions defined by piers and 
abutments.  Project  results  showed  that  standard  mechanical  models  adopted  to  represent 
the bridge dynamic behaviour, both in case of analytical and/or finite element approaches, 
were not sufficiently refined to describe properly the real performance of case studies and 
that proper calibrations, with regard to the experimental data specific of each case study, 
were always necessary; 

167

 
 
ii) 

iii) 

iv) 

v) 

vi) 

vii) 

viii) 

ix) 

Local details and connections: existing steel bridges currently on exercise among European 
lines covered a wide and complex range of construction techniques from 19th century riv-
eted  solution  to  modern  bow-string  steel-concrete  composite  superstructures.  The  fatigue 
resistance of local details and connections reflected the same wide and complex behaviour. 
In the Project, reliable evaluations of remaining life were obtained considering the histori-
cal  exercise  conditions  of  each  case  study  including  past/actual  traffic  spectra,  structural 
modifications  and/or  repairs  due  to  fatigue  damages  and/or  overload  events,  and the real 
fatigue resistance of critical details obtained by experimental data; 

Train-bridge dynamic interaction phenomena: deck dynamic response could be influenced 
by train-bridge dynamic interaction, i.e. the structural response of the coupled mechanical 
system  constituted  by  the  bridge  superstructure  and  the  moving  train  exchanging  contact 
forces  along  rail  contact  surfaces.  The  intensity  of  interaction  effects  depended  on  train 
composition, passing speed, weight and spacing of axels, stiffness and damping properties 
of  axle  suspensions.  Each  case  study,  characterized  by  different  structural  configuration 
and traffic property, required a specific evaluation of interaction effects with regard to the 
intensity of internal forces induced by passing trains; 

Rail defects or misalignments: in case of rail defects the dynamic effects of passing trains 
could be amplified, thus generating an unexpected variation of internal forces with regard 
to theoretical calculation. Experimental analysis of exercise conditions could identify such 
phenomena and provide suitable basis for proper calibration of mechanical models  

Secondary components: the secondary components as rails or ballast, generally not consid-
ered  in  the structural analysis, could modify significantly the external support conditions 
from  theoretical  hypothesis  depending  on  the  specific  structural  configuration  of  investi-
gated bridge. The influence of such phenomena on structural performance could be evalu-
ated by experimental analysis and calibration of mechanical models; 

Traffic  spectra:  the  composition  of  train  traffic  was  essential  for  a  correct  evaluation  of 
past,  actual  and  future  fatigue  cycle  internal forces into critical details. Result of Project 
activities showed that actual traffic was significantly different among European countries 
from  the  indication  of  Euro  design  code.  In  particular,  main  differences  concerned  the 
weight of axles, the composition of trains and the passing speeds. From this point of view, 
assuming the design code spectra could lead to erroneous fatigue assessment and to non-
optimized management of railway infrastructure; 

Bridge history: in case of repairs and/or modifications of bridge components due to dam-
ages, variation/modification of train traffic or deterioration the fatigue response cloud vary 
from original assumptions, also considering the possible interaction of different construc-
tion techniques adopted for bridge components along structure life-cycle. It was so evident 
the necessity of an historical reconstruction of maintenance activities performed by railway 
authorities on each case studies that permitted to evaluated correctly the fatigue load cycles 
really occurred on bridge components; 

Local  stresses:  the  uncertainties  concerning  the  stress  distribution  at  local  non-standard 
details or connections, either damaged and undamaged, lead to extensive investigation by 
numerical  models  and  experimental  analysis.  Such  advanced  analysis  were  necessary  to 
clarify the real mechanisms of internal stress distribution and to identify correctly the fa-
tigue resistance class of non-standard components; 

Stress  spectra  into  critical  details:  the  real  fatigue  spectra  acting  into  critical  details  de-
pended  on  the  local  dynamic  behaviour  in  exercise  conditions  including  vibra-
tion/distortion  effects.  Local  experimental  analysis  and  calibration  of  numerical  models 
were necessary to clarify the great uncertainties concerning the local mechanical behaviour 
and boundary conditions of investigated details under train passages; 

168

 
 
x) 

Local  defects  or  damages:  remaining  fatigue  life  of  bridge  components  was  significantly 
influenced by the presence of local defects or damages due to unexpected or unregistered 
overload events. Indeed the presence of such local singularities could lead to unexpected 
fatigue  failure  with  regard  to  an  equal  undamaged  component.  Also  in  this  case,  it  was 
clear  the  necessity  of  visual  inspection  and  identification  of  such  possible  damages  for 
each investigated structure. 

In spite of the great number and variability of such factors, the Project Methodology was successfully 
applied  to  selected  case  studies  thus  obtaining  the  confirmation  of  its  validity  and  reliability  as  an 
effective tool for the proper evaluation of all aspects defining the fatigue behaviour of a steel railway 
bridge.  From  this  point  of  view,  the  proposed  Methodology  could  be  adopted  as  reference  for  the 
development  of  extensive  investigations  on  European  railway  steel  bridges.  By  the  analysis  of  a 
statistically  based  number  of  case  studies,  the  typical  vibration/distortion  mechanisms  that  induce 
fatigue damages on each bridge typology could be identified and, finally, design rules for the control of 
vibration/distortion  phenomena  into  new  railway  steel  bridges  could  be  defined.  In  particular, 
innovative  constructive  solutions  for  the  reduction  or  removal  of  vibration/distortion  effects  shall  be 
proposed by design codes. 
Eventually, starting from Project results, future developments shall be focused on the development of 
unified European approach for the fatigue assessment of existing and new bridges, taking into account 
of vibration/distortion phenomena and of improved traffic load models representative of past and actual 
European train effects on railway lines. 

169

 
 
 
List of figures 

Figure I - Examples of distortion induced fatigue crack progression. 

Figure II - Methodology adopted in the Fadless Project for the advanced assessment of vibra-
tion/distortion induced fatigue. 

Figure III - Railway viaduct on Po river (Italy) 

Figure IV - Panaro bridge (Italy) 

Figure V - The Trezói Bridge (Portugal) 

Figure VI - The Alcácer do Sal Bridge (Portugal) 

Figure VII - Saalebrücke Großheringen railway bridge (Germany) 

Figure VIII - Salzach River bridge (Austria) 

Figure 1.1 - Fatigue assessment procedure for existing steel bridges 

Figure 1.2 - Examples of distortion induced fatigue crack progression 

Figure 1.3 - Web gap distortion: a) scheme of the effects; b) example in real bridge 

Figure 1.4 - Load model “IV” and “V” category. Load values are kg 

Figure 1.5 - “Treno normale” load model (1916) 

Figure 1.6 - Load models of 1925 Italian design code 

Figure 1.7 - Load model type “A” and “B” of 1945 Italian design code 

Figure 1.8 - Load models of 1995 Italian design code 

Figure 1.9 - “Equivalent” uniform loads according to load model and element length 

Figure 1.10 - Scheme for the assessment of existing steel railway bridges according to the DB 
Richtlinie 805 

Figure 2.1 – Fatigue crack at the bottom flange of a plate girder 

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Figure 2.3 – Distortion induced fatigue cracks in the main girder to cross girder connection 

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Figure 2.4 – a) Typical Out-of-Plane Web Distortion Mode Concentrated in Web Gap;  
b) Schematic of Web Crack at End of Transverse Stiffner 

Figure 2.5 – Global view of the bridge 

Figure 2.6 – Differential deflection of girders 

Figure 2.7 – Local finite element model: a) global view; b) detail view of the web-stiffener  
connections 
Figure 2.8 – 7th St. Bridge in St. Paul Minnesota: a) global view; b) structural detail at  
connection between stiffener and web. 

Figure 2.9 – Plymouth Avenue Bridge in Minneapolis: a) global view; b) bottom view  
of the deck 

Figure 2.10 – Little Arkansas River Bridge: a) damage floor beam to stringer connection;  
b) repair performed 

Figure 2.11 – Repair and retrofit for Tuttle Creek Bridge 

Figure 2.12 – Vibration induced fatigue cracks in orthotropic decks 

Figure 2.13 – Patroon Island Bridge: a) Overall view of the bridge, b) Structural detail. 

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Figure 2.14 – Patroon Island Bridge, cracks in the structural elements: a) Crack in the upper  
portion of the floor beam; b) Crack in bearing sole plate. 

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171

 
 
Figure 2.15 - Fatigue crack in the external component of a built-up truss 

Figure 2.16 - Fatigue cracks in the cover plates of deck joints 

Figure 2.17 - Fatigue cracks in the web of an upper transverse built-up beam 

Figure 2.18 - Fatigue cracks in the web-flange girder welding and on built-up flange  
longitudinal welding. 

Figure 2.19 - Fatigue cracks in built-up trusses 

Figure 2.20- An example of a riveted joint fatigue class 

Figure 2.21 – Standard, Heavy and Light Traffic mixes 

Figure 2.22 – Train types 1 and 2 for fatigue assessment 

Figure 2.23 - Direct stress S-N curves for structural steel components 

Figure 2.24 - Shear stress S-N curves for structural steel components 

Figure 2.25 - Generic preview of Table 8.5 
Figure 2.26 - Partial factor for fatigue strength, g Mf 

Figure 2.27 - Damage accumulation method 

Figure 2.28 - BS 5400: fatigue classes of non-welded components 

Figure 2.29 - BS 5400: RL loading table (a) and corresponding typical trains (b) 

Figure 2.30 – S-N curves present at the AASHTO standard 

Figure 2.31 – Example of details’ classification at AASHTO 

Figure 4.1 - The Lagoscuro viaduct on the Po river 

Figure 4.2 - Dimension of the old Lagoscuro bridge 

Figure 4.3 - The old Lagoscuro Bridge: details of (a) L-shaped elements composing the  
truss girders diagonals and (b) a riveted joint 

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Figure 4.4 - The old Lagoscuro Bridge: details of (a) stiffening plates designed to improve the 
transverse stiffness of the cross-section (b) end supports (fixed and sliding) 

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Figure 4.5 - The new Lagoscuro Bridge: details of bolted joints 

Figure 4.6 - Picture of Panaro bridge (Courtesy of RFI) 

Figure 4.7 - Drafting of Panaro bridge (Courtesy of RFI) 

Figure 4.8 - General view of Panaro bridge 

Figure 4.9 - Riveted diagonal-lower string joint of Panaro bridge 

Figure 4.10 - General view of deck structure 

Figure 4.11 - General view of lower and track bracings 

Figure 4.12 - General view of unidirectional bearing 

Figure 4.13 - General view of fixed bearing 

Figure 4.14 - Typical fatigue damage and repair of track bracing cross beams 

Figure 4.15 - Sleepers-longitudinal girder connection by catch bolts 

Figure 4.16 - The Trezói bridge. 

Figure 4.17 - Elevation and plan view of the Trezói bridge. 

Figure 4.18 - Local view of the cross-girder at the end support. 

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Figure 4.19 - Local views of structural details of the bridge: a) cross-girder above central  
column; b) rails resting above stringers. 

Figure 4.20 - New Alcácer do Sal Railway bridge 

Figure 4.21 - Typical traffic 

Figure 4.22 - Side view of the midspan of the bridge 

Figure 4.23 – Structural elements of the bridge 

Figure 4.24 – Construction process 

Figure 4.25 - Cross section of a riveted plate girder bridge (Saalebrücke Großheringen) 

Figure 4.26 - Photographs of the Saalebrücke Großheringen: a) View of the complete  
bridge from South-East, b) View of the selected span from South-East, c) Superstructure  
with tracks between main girders, d) crack in a gusset plate at the connection of a cross  
beam to the main girder 

Figure 4.27 - Salzach-bridge from the eastern river bank.Location of the bridge. 

Figure 4.28 - Plan view of the Salzach bridge (original blueprint). 

Figure 4.29 - Elevation of the Salzach bridge (original blueprint). 

Figure 4.30 - Section of the Salzach bridge (original blueprint). 

Figure 5.1 - Common procedure of model updating using experimental modal data. 

Figure 5.2 - Experimental setup with position of accelerometers. 

Figure 5.3 - Experimental and numerical first 4 mode shapes (60 meters long bridge). 

Figure 5.4 - (a) Values of identification parameters during the optimization process  
(values are normalized for numerical convenience); (b) values of the objective function  
during the optimization process. 

Figure 5.5 - Example of displacements at midspan obtained from the dynamic analysis  
for (a) train type 1; (b) train type 2; (c) train type 4; (d) train type 6. 

Figure 5.6 - Example of stresses due to the axial force in a upper chord (a) and in a  
diagonal member (b) obtained from the dynamic analysis. 

Figure 5.7 - Damage index for (a) upper and lower chords and (b) diagonal members  
considering the standard, heavy and light traffic mixes. 

Figure 5.8 - Damage index for (a) floor-beams and (b) bracing and upper transversal elements 
considering the standard, heavy and light traffic mixes. 

Figure 5.9 - FEM model of the Panaro bridge 

Figure 5.10 - Track bracing cross beam connection to secondary longitudinal girders by  
full fixed/pin joints 

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Figure 5.11 - Side view of secondary longitudinal girders with variable end cross sections 

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Figure 5.12 - Local view of elements representing secondary longitudinal girders 

Figure 5.13 - Side view of upper bracing cross beams with variable end cross sections 

Figure 5.14 - Local view of elements representing upper bracing cross beams 

Figure 5.15 - Full fixed FE model - Heavy Traffic Mix Damage 

Figure 5.16 - Full fixed FE model - Standard Traffic Mix Damage 

Figure 5.17 - Hinge FE Model - Heavy Traffic Mix Damage 

Figure 5.18 - Hinge FE Model - Standard Traffic Mix Damage 

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Figure 5.19 - Full Fixed FE Models - Heavy Traffic Mix: general (a) and detailed (b)  
graphical representation of damaged components (Yellow elements: -0.1 < Damage < 1  
--- Red elements: Damage > 1) 

Figure 5.20 - Global dynamic test of Panaro Bridge: test layout 

Figure 5.21 - Global dynamic test of Panaro Bridge - position / orientation of sensors  
on the typical cross section 

Figure 5.22 - Panaro bridge - shapes of identified global vibration mode 

Figure 5.23: Instrumented sections (a) and sensors positioning (b) for the local cross beam  
dynamic tests. 

Figure 5.24 - Panaro bridge - vibration mode shapes of track bracing cross beam 

Figure 5.25 - Optimization scheme developed for the FE model updating 

Figure 5.26 - FE models of fixed (a) and unidirectional (b) bearings 

Figure 5.27 - Sensitivity functions of parameter n° 1-2-3-5-6-7 calculated for vibration  
modes n° 1-3-4 

Figure 5.28 - Graphical representation of numerical/experimental MAC matrix 

Figure 5.29 - Updated Model - Standard Traffic Mix Damage 

Figure 5.30 - Updated Model - Standard Traffic Mix Damage 

Figure 5.31 - Updated FE Models - Heavy Traffic Mix: general (a) and detailed (b)  
graphical  representation of damaged components (Yellow elements: -0.1 < Damage < 1  
--- Red elements: Damage > 1) 

Figure 5.32 - Global view of the mesh of the 3D beam finite element model. 

Figure 5.33 - ANPSD: vertical and transversal direction. 

Figure 5.34 - Lateral view of the first 2 identified (left) and calculated (right) vertical  
bending modes. 

Figure 5.35 - Top view of the first identified (left) and calculated (right) lateral  
bending mode. 

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Figure 5.36 - Lateral view of the first identified (left) and calculated (right) torsion mode. 

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Figure 5.37 - Instrumentation layout: a) Location of the 14 instrumented sections and  
corresponding distribution of the sensors; b) strain gauges at a node with high stress  
concentrations; c) corresponding finite element model. 

Figure 5.38 - Strain measured in rails sections in the vicinity of both abutments outside  
the bridge (east and west). 

Figure 5.39 - Comparison between numerical and calculated results: a) Measured vs.  
calculated stresses; b) Measured vs. calculated fatigue stress spectra. 

Figure 5.40 - Fatigue damage indices for all structural elements for the EN1991 Heavy  
Traffic scenario. 

Figure 5.41 -Fatigue damage indices for all structural elements for real traffic scenario. 
Figure 5.42 - Damage per crossing in measured sections for the 1st day of measurements:  
a) using measured stresses; b) using numerical simulations. 

Figure 5.43 - Extremities of the diagonals 

Figure 5.44 - Elements perpendicular to the longitudinal direction of the deck 

Figure 5.45 - Critical detail 

Figure 5.46 - Stress histories in the critical detail, due to standard fatigue trains 

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Figure 5.47 - Stress history in the critical detail: crossing in the central span 

Figure 5.48 - Stress history in the critical detail: crossing in the last span 

Figure 5.49 - Stress range histograms for different crossing points 

Figure 5.50 - Damage in the critical detail as a function of the crossing point 

Figure 5.51 - Damage in the critical detail for different traffic scenarios 

Figure 5.52 - Contribution of different modes of vibration modes to the total response 

Figure 5.53 - Contribution of different modes of vibration modes to the maximum  
stress range 

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Figure 5.54 - First model consisting of beam elements: first three calculated global modes. 

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Figure 5.55 - Refined finite element model of the whole superstructure consisting of  
shell elements 

Figure 5.56 - a) Stress concentrations at the connection of cross beam and main girder  
at the pier support, b) influence line of von Mises stresses at the hot spot with respect to  
the load’s distance from the cross beam’s axis. 

Figure 5.57 - Geometry and mesh of the detailed finite element model of the whole  
superstructure 

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Figure 5.58 - Detailed views of the mesh a) at the end section and b) in the central section 

Page 79 

Figure 5.59 - Third FE-model: first three global modes 

Figure 5.60 - Third FE-model: selected local modes 

Figure 5.61 - Measurement points in the first experimental campaign 

Figure 5.62 - Accelerometers located on the top flange of the main girder 

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Figure 5.63 - Global modes identified from the first experimental campaign: a) first  
lateral bending of the first span, b) lateral bending of the second span, c) vertical  
bending of the first span, d) vertical bending of the second span, e) torsion of the first span.  Page 81 

Figure 5.64 - Wireless sensors with piezoelectric sensors at a reference point on the  
upper flange 

Figure 5.65 - Sensor locations at spans I and II 

Figure 5.66 - Measurement points at a) a longitudinal beam, b) a cross beam, c) a lower  
bracing and d) a web plate of the main girder 

Figure 5.67 - Second test campaign: The first five identified global modes 

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Figure 5.69 - Comparison of the identified mode 2 to the FE results (Df = 2%, MAC = 0.96)  Page 84 

Figure 5.70 - Local modes identified on the selected web plate (f = 17.81Hz and  
f = 19.66 Hz) 

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Figure 5.71 - Local modes identified on the selected longitudinal beam at f = 16.69Hz (left)  
and on the selected rod of the lower bracing at f = 17.88Hz (right) 

Page 85 

Figure 5.72 - Global mode 1 and mode 3 combined with the local deformation  
at the web plate. 

Figure 5.73 - Solid view of the model. 

Figure 5.74 - Solid view of the model in the YZ plane. 

Figure 5.75 - Solid view of the model in the XZ plane. 

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Figure 5.76 - First lateral bending mode at 2.101Hz; First vertical bending mode at 4.668Hz.  Page 88 

Figure 5.77 - Second lateral bending mode at 5.112Hz; Torsional mode at 5.705Hz. 

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Figure 5.78 - Sensor positioning. First set of three. 

Figure 5.79 - Brimos wireless on the walkway. EpiSensor on the joint. 

Figure 5.80 - Natural frequencies and mode shapes identified from data excluding  
railway traffic. 

Figure 5.81 - Natural frequencies and mode shapes identified from data including  
railway traffic. 

Figure 5.82 - Supports of the bridge at the east (left) and west (right) ends. 

Figure 5.83 - Supports of the modeled bridge at the east (left) and west (right) ends. 

Figure 5.84 - Scheme of the track-soil interaction. 

Figure 5.85 - Comparison of numerical and experimental mode shapes. 

Figure 5.86 - Charts of normed eigenfrequency characteristics over the test stations  
(horizontal axis: along the bridge), vertical, 0-25Hz; with railway traffic (left), without  
railway traffic (right). 

Figure 5.88 - Swing intensity in vertical direction, without railway traffic (left), with  
railway traffic (right). 

Figure 5.89 - Maximum swing intensity sensor location for frequency 4.8Hz,10.16Hz  
and 12.96Hz. 

Figure 6.1 - Bridge critical points where fatigue phenomena could arise. 

Figure 6.2 - Lower bracings, floorbeam and stringers. 

Figure 6.3 - Local mode (a) for stringers and bracings and (b) for floor-beams. 

Figure 6.4 - Local mode (a) for stringers and bracings and (b) for floor-beams. 

Figure 6.5 - Vehicle models with 15 DOFs 

Figure 6.7 - 3D VBI analyses: horizontal and vertical displacement for (a) train type 5  
and (b) train type 7 

Figure 6.8 - (a) Bridge transversal cross–section; (b) horizontal displacement time history  
of the nodes 989 and 1093; (c) vertical displacement time history of the nodes 3448 and  
3888; (d) lower scale view of (c) 

Figure 6.9 - (a) horizontal acceleration time history and (b) vertical acceleration time history  
of the mid span node of the bridge 

Figure 6.10 - Monitored points for fatigue assessment. 

Figure 6.11. Stress history of the lower chord at midspan for: (a) train type 1,  
(b) train type 3, (c) train type 6. 

Figure 6.12. Stress history in a stringer for: (a) train type 1, (b) train type 3,  
(c) train type 6. 

Figure 6.13. Stress history of a floor-beam for: (a) type 1 train, (b) type 3 train,  
(c) type 6 train, (d) type 7 train 

Figure 6.14.Stress history of the bracing for: (a) type 1 train, (b) type 3 train,  
(c) type 6 train, (d) type 7 train. 

Figure 6.15. Damage index for Fatigue strength model F1, based on Eurocode 3, and  
for Fatigue strength model F2 

Figure 6.16 - Local model of the track bracing cross beam 

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Figure 6.17 - Local model of the connection plate between sleepers and longitudinal girders  Page 105 

Figure 6.18 - Von Mises Stress Map for one passage of train 1 

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Figure 6.19 - Von Mises Stress Map for one passage of train 2 

Page 106 

Figure 6.20 - Locations of Points A and B on the local model of the track bracing cross beam  Page 106 

Figure 6.21 - Track bracing cross beam - Stress cycles for one passage of  
train 1 (points A and B) 

Figure 6.22 - Track bracing cross beam - Stress cycles for one passage of  
train 2 (points A and B) 

Figure 6.23 - Example of refined model representing also prestressed bolts or rivets. 

Figure 6.24 - Von Mises Stress Map for one passage of train 1 (Top view) 

Figure 6.25 - Von Mises Stress Map for one passage of train 1 (Bottom view) 

Figure 6.26 - Connection Plate - Stress cycles for one passage of train 1 

Figure 6.27 - Time history of modal displacement 

Figure 6.28 - Time history of modal velocity 

Figure 6.29 Time history of accelerations for a) points on the quarter and  
b) on the mid of bridge span 

Figure 6.30 - Sensitivity to the train model - time history of point displacement 

Figure 6.31 - Sensitivity to the train model - time history of point acceleration 

Figure 6.32 - Critical details of the Panaro Bridge 

Figure 6.33 - Instrumented section and sensors positioning for the local cross beam  
modal tests 

Figure 6.34 - Panaro bridge - vibration mode shapes of track bracing cross beam 

Figure 6.35 - Panaro bridge – Test layout and strain gauges installation of track bracing  
cross beam 

Figure 6.36 - Panaro bridge – Measured stresses under a freight train passage,  
Point 1 and 3, vertical direction 

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Figure 6.37 - Panaro bridge – Measured stresses under a freight train passage, Point 2 and 4  Page 111 

Figure 6.38 - Panaro bridge – Test layout and strain gauges installation of the connection  
plate between wooden sleepers and longitudinal girders 

Figure 6.39 - Panaro bridge – Measured stresses under a freight train passage,  
Point 5, 6, 7 and 8 

Figure 6.40 - a) Impact testing on the connection plate between longitudinal girders and  
wooden sleepers; b) Frequency Response Functions (FRF). 

Figure 6.41 - Panaro bridge – Test layout and strain gauges installation on the connection  
joint between vertical beam and upper stringer 

Figure 6.42 - Panaro bridge – Measured stresses under a freight train passage,  
Point 1, 2, 3, 4, 5, and 6 

Figure 6.43 - layout of the developed long-term monitoring system. 

Figure 6.44 - monitoring system local network 

Figure 6.45 - LabVIEW® procedure performed by the acquisition unit 

Figure 6.46 - local monitoring system of the track bracing cross beam/connection  
plate between longitudinal girders and wooden sleepers. 

Figure 6.47 - local monitoring system of the joint between vertical beams and  
upper stringers. 

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Figure 6.48 - a) Rev.1 of the developed weighting in motion system and b) instrumentation  
setting system of the load cell 

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Figure 6.49 - a) global layout of the validation test; b) a particular of the hydraulic jack;  
c) test load cycle on instrumented sleeper. 

Figure 6.50 - main changes in instrumentation setting system. 

Figure 6.51 - Rev.2 of the instrumented sleeper 

Figure 6.52 - Characterization of the elements more affected by fatigue according to the  
global fatigue assessment results using a bar FEM (yellow – cross-girders; blue – diagonals;  
red – bottom chords) 

Figure 6.53 - FEM mesh using beam and shell elements – local view above the main  
columns. 

Figure 6.54 - Layout: a) locations of the accelerometers at the extremity cross-girder;  
b) uniaxial accelerometer 

Figure 6.55 - Average Normalised Power Spectra. 

Figure 6.56 - Global view of the location of strain gauges 

Figure 6.57 – Comparison between calculated and measured frequencies (ANPSD for the  
vertical direction): red - frequencies from the accelerometers, blue – frequencies from the  
FEM and green – frequencies from ANPSD of measured strains.  

Figure 6.58 - Local modes of the cross-girder at the extremity support: a) vertical bending  
mode; b) lateral bending mode.  

Figure 6.59 - Validation of the FEM using strain gauges: a) location of strain gauges;  
b) comparison between measured and calculated stresses in the cross-girder. 

Figure 6.60 – Load spectra and damage calculations: a) axle load spectra; b) Damage  
calculations. 

Figure 6.61 – Location of the critical node to be assessed by local fatigue analysis. 

Figure 6.62 – Potential critical node: a) photo and b) continuum finite element model  
based on solid finite elements. 

Figure 6.63 – Local model of the node 6 of the Trezói bridge: members dimensions. 

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Figure 6.64 – Boundary conditions procedure: a) MPC definition and b) sections numbering.  Page 122 

Figure 6.65 – Locomotive-hauled freight train. 

Figure 6.66 – Displacement/rotations history for sections 1 to 9 of node 6 from  
the Trezói bridge. 

Figure 6.67 – Critical spot located at the cross-girder to gusset connection. 

Figure 6.68 – Comparison of stress spectra between a passenger train crossing, used to  
validate the local finite element model (red line), and a cargo train crossing, defined as  
the severe case (blue line). 

Figure 6.69 – Number of train crossings until fatigue crack initiation, computed at the  
top of the stringer-to-gusset connection. 

Figure 6.70 - welded steel box girder: a) diaphragm 51; b) critical welded detail. 

Figure 6.71 – Location of the critical section under investigation. 

Figure 6.72 – Relative locations of the local models with respect to the global model. 

Figure 6.73 - Local finite element model of a critical detail of the Alcácer do Sal railway  
bridge. 

Figure 6.74 – Alfa Pendular passengers train. 

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Figure 6.75 – Section of the box girder of the Alcácer do Sal bridge. 

Figure 6.76 – Displacement histories for some reference points. 

Figure 6.77 – considered load step for damage computation. 

Figure 6.78 – Net stress range resulting from rainflow cycle counting. 

Figure 6.79 – Data needed for crack propagation analysis 

Figure 6.80 – Flow chart for the application of the proposed methodology 

Figure 6.81 – CT specimen 

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Figure 6.82 – Location of specimens containing weldments  (schematic). 
Figure 6.83 - Base material da/dN vs. D K data for the three R values tested. 
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Figure 6.84 - Weld material da/dN vs. D K data for the three R values tested (‘cor’ - D Keff).  Page 133 
Figure 6.85 - Heat affected zone material da/dN vs. D K data for the three R values tested  
(‘cor’ - D Keff). 

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Figure 6.86 –  Time series of measured strains at a track during a train passage (top) and  
corresponding average axle speeds (bottom). 

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Figure 6.87 – Identification of passing trains in one year and a half: (a) distribution of  
identified train types, (b) speed histogram showing the relative frequency for different  
train types 

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Figure 6.88 – Axle load identification: (a) statistics of the mean values of the identified  
axle loads of the locomotives of type BR 143 with respect to speed, (b) statistics of the  
identified axle loads for the four axles of locomotives of type BR 143 with speeds up to  
70 km/h; the boxes include all samples from  25 to 75 %, the dashed lines extend to the  
most extreme data points not considered as outliers, outliers are plotted individually  
(red cross).  

Figure 6.89 – Rainflow cycle histogram of the strain gauge rosette with a crack grouped  
for different kind of trains (RB – regional, IC/ICE – high speed, Cargo – freight train),  
calculated for the time of one year and a half 

Figure 6.90 – Rainflow cycle histogram of the strain gauge rosette without a crack grouped  
for different kind of trains (RB – regional, IC/ICE – high speed, Cargo – freight train),  
calculated for the time of one year and a half 

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Figure 6.91–Rainflow cycle histogram of the strain gauge rosette with and without a crack,  
calculated for the time of one year and a half 

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Figure 6.92 – Numerical model of the gusset plate: (a) geometry, (b) stress distribution  
due to translational displacements along line L8. 

Figure 6.93 – Numerical model of the fatigue test: (a) side view, (b) isometric view. 

Figure 6.94 – Setup for fatigue tests: (a) design drawing, (b) test bed in the laboratory. 

Figure 6.95 – Setup for fatigue tests: (a) crack length sensor and strain gauges,  
(b) measurement control program. 

Figure 6.96 – Fatigue test: crack length as a function of the load cycles for two different  
stress values (pk-pk): 300 N/mm2: Blech02, Blech03, Blech02 manual; 500 N/mm2:  
Blech04 

Figure 6.97 – S/N diagram of the fatigue test: Experimental data from seven specimens,  
S/N curves 71 and 160 from Taras et Greiner 

Figure 6.98 - Loading scheme of the high speed train ICE3. 

Figure 6.99 - A 3-DOF vehicle model for dynamic train-bridge interaction analysis. 

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Figure 6.100 - Time history of the displacement at mid span. 

Figure 6.101 - Sensor layout in one of the measurement setups. 

Figure 6.102 - Predicted (black line) and measured(red line) acceleration at point 7 during  
the passage of high speed train ICE3 at a speed of 89 km/h: (a) time history and  
(b) frequency content 

Figure 6.103 - View the crack. 

Figure 6.104 - Local model of the connection plate with solid elements. 

Figure 6.105 - Mesh at the vicinity of the crack tip. 

Figure 6.106 - Three modes of crack displacement. 

Figure 6.107 - Finite elements and nodes near crack tip. 

Figure 6.108 - Local coordinate system of the crack. 

Figure 6.109 - The flowchart for the fatigue life prediction of a railway bridge based  
on the fracture mechanics method. 

Figure 6.110 - Identified axle load of one freight train. 

Figure 6.111 - Time history of the stress intensity factor KII for the shearing mode. 

Figure 6.112 - Time history of the stress intensity factor KIII for the tearing mode. 

Figure 6.113 - Time history of the equivalent stress intensity factor. 

Figure 6.114 - Measurement layout of the continuous health monitoring. 

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Figure 6.115 - Variation of the frequency of the first lateral bending mode and temperature  
between 2011.08.14 and 2012.05.30. 

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Figure 6.116 - Variation of the frequency of the first vertical bending mode and temperature  
between 2011.08.14 and 2012.05.30. 

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Figure 6.117 - Variation of the frequency of the first torsion bending mode and temperature  
between 2011.08.14 and 2012.05.30. 

Figure 6.118 - Natural frequency of first lateral bending mode versus temperature. 

Figure 6.119 - Natural frequency of first vertical bending mode versus temperature. 

Figure 6.120 - Natural frequency of first torsion mode versus temperature. 

Figure  6.121 - Top view of the bridge with the damaged cross-girder connections framed  
in orange. 

Figure 6.122 - Detail of the connection between cross-girder and vertical main beam with  
damaged element highlighted in red. Crack location marked by ellipse. 

Figure 6.123 - Detail photograph of the damage at position U03 (compare Figure ) 

Figure 6.124 - Detail photograph of the damage at position U10 (compare Figure ) 

Figure 6.125 - Joint detail of cross-girder and vertical beam. Solid finite element model:  
axonometric view, front view. 

Figure 6.126 - Moving ICE 3 train. 

Figure 6.127 - ICE 3 train length properties. 

Figure 6.128 - ICE3 train model full length (above), one wagon (below) 

Figure 6.129 - Combined train and bridge model. Detail of wheel suspension. 

Figure 6.130 - Coupling between the coaches. 

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Figure 6.131 - Scheme of the connection between rail and wheel nodes in each time step  
by constraint equations. The contact nodes of the wheels are constrained to have the same  
vertical displacement as the closest rail node. Nodes of the same color are coupled vertically  
for one time step. 

Figure 6.132 - Showing the position of the train in time step 150. 

Figure 6.133 - Comparison of the two solvers for train-track interaction. 

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Figure 6.134 - Top view of the bridge; the two selected joints highlighted with red circles. 

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Figure 6.135 - Load force record upon passing of the train under a selected sleeper. 

Figure 6.136 - Load force histogram from the previous plot in 12 classes. 

Figure 6.137 - Shear force in the cross-girder at the joint during passing of the train. 

Figure 6.138 - Shear stress in the cross-girder at the joint during passing of the train. 

Figure 6.139 - Normal stress in the cross-girder at the joint during passing of the train. 

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Figure 6.140 - Criteria for loop counting in rainflow algorithm. a) full loops   b) half loops 

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Figure 6.141 - Cycle counts by rainflow algorithm on one typical day. East cross-girder;  
filtering threshold 0.1%. 

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Figure 6.142 - N-S curve for the joint compared to class 36 (EN 1993-1-9); east cross-girder.  Page 156 

Figure 6.143 - Cycle counts for one day. East cross-girder, dt=0.002s. 

Figure 6.143 - N-S curve for the joint compared to class 80 (EN 1993-1-9); east cross-girder; 
dt=0.002s. 

Figure 6.144 - Cycle counts for one day. East cross-girder, dt=0.005s. 

Figure 6.145 - N-S curve for the joint compared to class 80 (EN 1993-1-9); east  
cross-girder; dt=0.005. 

Figure 7.1 - Methodology for the advanced assessment of vibration/distortion induced  
fatigue. 

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List of tables 

Table 5.1 - 60 meters long old PonteLagoscuro Bridge: results of experimental modal  
identification. 

Table 5.2 - 75 meters long old PonteLagoscuro Bridge: results of experimental modal  
identification. 

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Table 5.3 - 75 meters long old PonteLagoscuro Bridge: Comparison between experimental  
and numerical results after the optimization process. 

Page 41 

Table 5.4 - 60 meters long old PonteLagoscuro Bridge: Comparison between experimental  
and numerical results after the optimization process. 

Table 5.5 - Fatigue classes adopted for Panaro bridge components 

Table 5.6 - Identified global vibration mode of Panaro bridge. 

Table 5.7 - Identified local vibration modes of track bracing cross beam. 

Table 5.8 - Comparison between numerical and experimental modal frequencies 

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Table 5.9 - Selected optimization parameters for numerical updating of Panaro FE model 

Page 52 

Table 5.10 - Updated FE Model: initial/final values of parameters and  
numerical/experimental  frequencies 

Table 5.11. Modal parameters calculated numerically 

Table 5.12 - Calculated and identified natural frequencies. 

Table 5.13. Estimated remaining lifetime R for the year 2012 and the considered  
structural elements according to Richtlinie 805 

Table 5.14 - Spring stiffness for creep resistance. 

Table 5.15 - Vertical support stiffness. 

Table 5.16 - Comparison of numerical and tested natural frequencies. 

Table 6.1 - Axle loads of ICE3. 

Table 6.2 - Characteristics of the suspension system of ICE3. 

Table 6.3 - Computed natural frequencies of the vertical mode of ICE3. 

Table 6.4 - Example of masses of the ICE3 type train. 

Table 6.5 - Spring stiffness of the train suspension. 

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List of publications 

EN  1993-1-9,  2002.  Eurocode  3:  Design  of  steel  structures  -  Part  1.9:  Fatigue  strenght  of  steel 
structures. CEN European Committee for Standarsization. 

Cunha,  A.,  Caetano,  E.,  Moutinho,  C.  &  Magalhães,  F.,  2013.  Continuous  dynamic  monitoring  of 
bridges: different perspectives of application. Keynote Lecture, 6th ECCOMAS Conference on Smart 
Structures and Materials, SMART 2013, Torino, Italy;  

Cunha, A., Caetano, E., Magalhães, F. & Moutinho, C., 2012. Monitorização Dinâmica e Identificação 
Estrutural  de  Pontes  e  Estruturas  de  Grande  Vão,  XXXV  Jornadas  Sul-Americanas  de  Engenharia 
Estrutural, Keynote Lecture, Rio de Janeiro, Brasil.  

Marques,  F.,  Moutinho,  C.  &  Cunha,  A.,  2012.  Local  fatigue  analysis  using  a  long-term  monitoring 
system  at  Trezói  railway  bridge,  Eighth  International  Conference  on  Engineering  Computational 
Technology Dubrovnik, Croatia.  

Moutinho,  C.,  Marques,  F.  &  Cunha,  A.,  2012.  Implementation  of  a  dynamic  monitoring  system  at 
Trezói railway bridge, 5th European Conference on Structural Control, EACS 2012, Genoa, Italy.  

Moutinho,  C.,  Marques,  F.  &  Cunha,  A.,  2012.  Instrumentation  of  a  metallic  railway  bridge  and 
implementation  of  a  dynamic  monitoring  system  for  local  fatigue  analysis,  15th  International 
Conference on Experimental Mechanics, Porto, Portugal.  

Cunha,  A.,  Caetano,  E.,  Moutinho,  C.,  Magalhães,  F.,  Hu,  W.-H.  &  Marques.  F.,  2011.  Dynamic 
Monitoring  of  Bridges  at  ViBest/  FEUP:Ongoing  applications,  4th  Int.  Conf.  on  Experimental 
Vibration Analysis for Civil Engineering Structures, EVACES'2011, Varenna, Italy.  

Marques, F., Hu. W.-H., Moutinho, C, Magalhães, F. & Cunha, A., 2011. Evaluation of dynamic effects 
and  fatigue  assessment  of  a  railway  bridge  supported  by  temporary  monitoring,  EURODYN'2011, 
Leuven, Belgium.  

Marques, F., Cunha, A., Caetano, E., Moutinho, C. & Magalhães, F., 2013. Análise de fadiga associada 
a  vibrações  locais  na  ponte  ferroviária  de  Trezói,  3º  Congresso  sobre  Segurança  e  Conservação  de 
Pontes, ASCP2013, FEUP, Porto.  

Marques,  F.,  Moutinho,  C.,  Cunha,  A.  &  Caetano,  E.,  2013.  Implementação  de  um  sistema  de 
monitorização dinâmica na ponte ferroviária de Trezói, 3º Congresso sobre Segurança e Conservação 
de Pontes, ASCP2013, FEUP, Porto.  

Albuquerque, C., Pinto, N, Calçada, R. and Gabriel, J., 2013. Monitorização contínua do tráfego e da 
fadiga de componentes estruturais críticos da nova ponte ferroviária sobre o rio Sado, 3º Congresso 
sobre Segurança e Conservação de Pontes, ASCP2013, FEUP, Porto.  

Albuquerque, C., Silva, L, Calçada, R., Castro, P.T. and Fernandes, A.A., 2013. Aplicação de técnicas 
inovadoras  na  análise  de  fadiga  da  nova  ponte  ferroviária  sobre  o  rio  Sado,  3º  Congresso  sobre 
Segurança e Conservação de Pontes, ASCP2013, FEUP, Porto.  

Albuquerque,  C.,  Calçada,  R.,  Pinto,  N.  and  Gabriel,  J.,  2011.  Experimental  characterization  of  the 
dynamic  behaviour  of  the  new  railway  bridge  over  the  river  Sado.  EVACES'11  -  4th  International 
Conference on Experimental Vibration Analysis for Civil Engineering, Varenna, Italy.  

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Albuquerque, C., Calçada, R. and Castro, P., 2012. Fatigue assessment of a bowstring railway bridge. 
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Infrastructure 

Structure 

railway 

Panaro 

bridge, 

steel 

and 

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187

 
 
 
 
 
 
 
 
 
European Commission

EUR 26419 —  Fatigue damage control and assessment for railway bridges (FADLESS)

Luxembourg: Publications Office of the European Union

2014 — 187 pp. — 21 × 29.7 cm

ISBN 978-92-79-35043-6
doi:10.2777/59688