Applied Mechanics and Materials Vol. 82 (2011) pp 344-349
Online available since 2011/Jul/27 at www.scientific.net© (2011) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMM.82.344

Effects of Outrigger Truss Systems on Collapse Initiation Times ofHigh-Rise Towers Exposed to Fire
Daigoro Isobe1,a and Le Thi Thai Thanh2,b1

Associate Professor, Univ. of Tsukuba, 1-1-1 Tennodai, Tsukuba-shi, Ibaraki 305-8573, Japan
2

Graduate student, Univ. of Tsukuba, 1-1-1 Tennodai, Tsukuba-shi, Ibaraki 305-8573, Japanaisobe@kz.tsukuba.ac.jp, be0712356@edu.esys.tsukuba.ac.jp

Keywords: Outrigger truss system, Collapse initiation time, High-rise towers, Fire, Progressive
collapse, ASI-Gauss technique.

Abstract. In this paper, progressive collapse analyses were performed on a 30-story, seven-span
tower that was exposed to fire. The Adaptively Shifted Integration (ASI)-Gauss technique was used todemonstrate the effects of fire patterns and structural parameters on collapse initiation time: theduration from the beginning of the fire until collapse initiation. Specifically, an outrigger truss system
was placed on the roof of a model, and the influence of the system on the structural vulnerability of thetower was verified. The structural parameters that were varied in the analyses included the axial force
ratio, the member joint strength ratio and the member strength ratio of the outrigger trusses to thestrength of the beams on the first floor. From the numerical results, it is confirmed that collapse
initiation times are significantly affected by the member joint strength ratio if the axial force ratio issmall (floor loads are low) on the condition that the fire pattern is nearly symmetrical, and the load
paths to and from the outrigger truss system are sufficiently protected.
Introduction
Studies on the resistance of buildings to collapse are becoming increasingly prominent because thenumber of decrepit buildings has increased worldwide. The desire of researchers to assess theperformance of buildings under stress has been increasing since the 9.11 terrorist attacks on the World
Trade Center (WTC) towers in 2001. To determine the true cause of the total collapse of these towers,
we conducted an aircraft impact analysis [1] followed by fire-induced collapse analyses to investigate
how fire patterns, the structural weakness of member joints, and the outrigger trusses on roof tops
influenced the collapse behavior of the high-rise towers [2]. The analytical results of the latter
analyses, which were obtained using the Adaptively Shifted Integration (ASI)-Gauss finite element
code [3], showed a clear difference between each fire pattern, between the models with strong andweak member-joint strengths, and between the models with and without outrigger trusses. In general,
the strongly designed models withstood total collapse, whereas the weak models began to collapse
when the temperature was highest, which eventually resulted in total collapse. The models withoutrigger trusses tended to withstand collapse longer due to their catenary action only if their load
paths were protected. In this paper, we focused on the change of collapse initiation time: the durationfrom the beginning of the fire until the beginning of the collapse, when structural parameters such as
the axial force ratio, the member joint strength ratio and the member strength ratio of the outrigger
trusses to the strength of beams on the first floor were varied. An outline of the numerical code is firstdescribed, followed by numerical results and discussion.
Numerical Methods
Relationship between the location of the numerical integration point in a linear Timoshenko beam
element and the stress evaluation point where a plastic hinge is formed in a rigid bodies-spring model(RBSM) is expressed asr = -s,(1)

All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,
www.ttp.net. (ID: 220.209.116.199-16/08/11,14:50:19)

Applied Mechanics and Materials Vol. 82

345

where s is the location of the numerical integration point and r is the location where the stress andstrain are evaluated or the location of a plastic hinge in the plastic stage. The s and r terms are
dimensionless quantities with values between -1 and 1.
In both the ASI and ASI-Gauss techniques, the numerical integration point is shifted adaptively if afully plastic section is formed within an element. When the plastic hinge is unloaded, thecorresponding numerical integration point shifts back to its original position. Here, the original
position represents the location where the numerical integration point is placed if the element behaveselastically. Therefore, the plastic behavior of the element is simulated appropriately, and a converged
solution is achieved using only a small number of elements per member. However, in the ASI
technique, the numerical integration point is placed at the midpoint of the linear Timoshenko beam
element, which is considered to be optimal for one-point integration if the entire region of the element
behaves elastically. Therefore, solutions in the elastic range are not sufficiently accurate if the numberof elements per member is very small because a low-order displacement function is applied for the
linear Timoshenko beam element.
MemberMember

-1

-1/2

0

1/2

1

-1

1

0

-1 -1

0

1

1

Element 1

Element 2

Numerical integration point

Stress evaluation point-1/√3

rg 0 sg
Element 1

0

1/√3

1

-1 -1

sg 0 rg

1

Element 2

sg = 1-(2/√3), rg = -1+(2/√3)(b) ASI-Gauss technique(a) ASI techniqueFig. 1 Location of numerical integration and stress evaluation points in the elastic range

The primary difference between the ASI and ASI-Gauss techniques is the original position of thenumerical integration point as shown in Fig. 1. In the ASI-Gauss technique, two consecutive elementsthat form a member are considered to be a subset, and the numerical integration points of anelastically deformed member are located such that the stress evaluation points coincide with theGaussian integration points (±1/√3 in dimensionless coordinate) of the member. Thus, the stress andstrain are evaluated at the Gaussian integration points of the elastically deformed members. The
Gaussian integration points are optimal for two-point integration, and the accuracy of the bending
deformation is mathematically guaranteed [4]; therefore, the ASI-Gauss technique takes advantage of
two-point integration while utilizing one-point integration in the actual calculations.
Figure 2 shows the location of the numerical integration points for each stage of the ASI-Gauss
technique. A plastic hinge is typically generated before it develops into a member fracture, and theplastic hinge is expressed by shifting the numerical integration point to the opposite end of the fully
plastic section according to Eq. 1. For instance, if a fully plastic section initially occurs at the right endof an element (r = 1) as shown in Fig. 2, then the numerical integration point shifts immediately to theleft end of the element (s = -1). At the same time, the numerical integration point of the adjacentelement that forms the same member is shifted back to its midpoint where it is appropriate for
one-point integration. A member fracture is expressed by reducing the sectional forces of the element
immediately after the occurrence of a fractured section on either end of the element.
The yield condition used in the analyses is expressed as follows:222 My 
 Mx 
 +  N  − 1 = f y − 1 = 0,
 + 
f = 
 C M M x0 
 N0 
 C M M y0 

(2)

346

Performance, Protection and Strengthening of Structures under Extreme
Loadings=sg

s=0

Plastic hinge

Fracture

s=－1
s=sg

s=0

s=0

Numerical integration point

Node(a) Elastic stage(b) Plastic stage(c) Member fracture

Fig. 2 Location of numerical integration points for each stage of the ASI-Gauss technique

where fy is the yield function, Mx, My and N are the bending moments around the x and y axis and theaxial force, respectively. The terms with the subscript 0 are values that result in a fully plastic section
in an element if they act on the cross section independently. The parameter CM, which represents theratio of the member joint strength to the strength of the member itself, is used to explicitly express theinfluence of the member joint strength. The values of the ratio are fixed on the basis that the member
joint strengths of some of the columns in the WTC towers were weak compared to those of themembers [5].
The fracture condition of the member joints is considered by examining the bending strains, axial
tensile strain and shear strains in a member as follows:κx−1 ≥ 0κ x0orκy−1 ≥ 0
κ y0

or

γ xz
−1 ≥ 0γ xz 0or

γ yz−1 ≥ 0γ yz 0or εz 
 − 1 ≥ 0 , ε z0 (3)where κx, κy, γxz, γyz, εz, κx0, κy0, γxz0, γyz0 and εz0 are the bending strains around the x and y axis, theshear strains for the x and y axis, the axial tensile strain and the critical values for these strains,respectively. We used critical fracture strains, which were obtained from experiments on
high-strength joint bolts [6].
Elemental contact is considered in the numerical code by connecting gap elements between thepairs of elements that are determined to be in contact by their geometrical relationships. More details
regarding the code can be found in [3] and [7].
Fire-Induced Progressive Collapse Analyses for the High-Rise Towers
Fire-induced collapse analyses were performed on a 30-story, seven-span tower as shown in Fig. 3.
An outrigger truss system was placed on the roof of the model, and the influence of the system on the
structural vulnerability of the tower was verified. Several structural parameters were varied todetermine their contribution to the collapse behavior: the axial force ratio of the columns to thestructural strength capacity varied from 0.1 to 0.5, which was determined by varying only the floorloads; the member joint strength ratio CM at every member connection in the model varied from 0.1 to
0.6; and the member strength ratio of the outrigger trusses to the strength of beams on the 1st floor
varied from 0.0 (no outrigger truss system placed) to 2.0. The tower model consisted of 9,360 linear
Timoshenko beam elements, 6,644 nodes and 39,600 degrees of freedom. For example, the columns
used on the 1st floor were 700 mm × 700 mm box-section-type steel columns with 28-mm-thickplates. Two fire patterns were applied: three rows of sections in the middle and the sections in theouter area, from the 21st to the 24th floors were assumed to be on fire, as shown in Fig. 4, to determine
how the fire patterns affected the collapse initiation time. The aircraft collision followed by

Applied Mechanics and Materials Vol. 82

347

Outrigger truss system

28m

120m
Core
structureZ

Pattern A

28m
Y

Upper viewY

Pattern B

X

0.9
0.8
0.7
0.6
0

200

400 600 800 1000
Temperature [ C](a) Elastic modulus

Fig. 4 Assumed fire patterns (21F-24F)

1

1000

0.8

800

Temperature [℃]1

Yield strength reduction factor

Elastic modulus reduction factor

Fig. 3 30-story, seven-span tower model

0.5

X

Front view

0.6
0.4
0.2
0

600
400
200

200

400 600 800 1000
Temparature [ C](b) Yield strength

Fig. 5 Strength reduction curves of raw steel due to elevatedtemperatures [8]0200

400 600
Time [s]800 1000

Fig. 6 Assumed time historyof temperature

explosions due to jet fuel was assumed to dislodge the thermal insulation in the WTC incident.
Therefore, reduction curves [8] were adopted for the elastic modulus and the yield strength of raw
steel due to the elevated temperatures as shown in Fig. 5. It was found that the elastic modulus of thecolumns with no thermal insulation reduced to 60 % of its original value, and the yield strength
reduced to 10 % of its original strength at 700 degrees Celsius, which is a typical temperature in a fire.
The temperature of the beam elements in the ranges indicated in Fig. 4 was assumed to have increased
to 700 degrees Celsius in seven minutes as shown in Fig. 6. In addition, a time increment control wasapplied to enable continuous calculation from static to dynamic phenomena. The analysis required
approximately eight hours of simulation time using a personal computer (CPU: 2.93 GHz Xeon).
Figures 7 and 8 show the collapse modes of the tower exposed to each fire pattern when themember joint strength ratio CM was set to 0.3 and the axial force ratio in the columns of the 1st floor
was set to 0.33 with the regular-strength outrigger truss system (structural strength similar to thebeams on the 1st floor) placed on the roof. The colors of the elements indicate the fy values in Eq. 2. In
all of the cases, total collapse was inevitable, and the results clearly show the effect of the weakness ofthe member joints compared to the fully rigid joints and the effect of the strength reduction due to theelevated temperatures. As shown in the figures, the collision of the upper structure with the lower
structure created shock waves that propagated through the columns and moved faster than the falling
motion of the upper structure. The shock waves destroyed the member joints as they moved towards

Performance, Protection and Strengthening of Structures under Extreme
Loading

500 s

527 s

529 s

537 s

445 s

550 s

Fig. 7 Collapse mode (CM = 0.3, axial force ratio= 0.33, fire pattern A)
1600
1400

1600

1000

800
600
400
200
0.2

0.3

0.4

800
600
400
200
0

0.5

Axial force ratio

0

1

1.5

(a) Fire pattern A
Collapse initiation time [s]

1200
1000
800
600
400
200
0.3

0.4

1000
800
600
400
200
0

0.5

1

1.5

2

(a) Fire pattern A

1400
1200

CM = 0.1
CM = 0.2
CM = 0.3
CM = 0.4
CM = 0.5

1800

CM = 0.1
CM = 0.2
CM = 0.3
CM = 0.4
CM = 0.5
CM = 0.6

1600

1000
800
600
400

1600
1400
1200
1000
800
600
400
200

200
0

0.5

2000

1800

1400

0.2

1200

(a) Fire pattern A

without outrigger truss systemwith outrigger truss system

1600

1400

Member strength ratio of outrigger truss

2000

1800

1600

0

2

Member strength ratio of outrigger truss

2000

Collapse initiation time [s]0.5CM = 0.1
CM = 0.2
CM = 0.3
CM = 0.4

1800

CM = 0.1
CM = 0.2
CM = 0.3
CM = 0.4
CM = 0.5
CM = 0.6

1200

1000

465 s

2000

1800
1400

1200

450 s

Fig. 8 Collapse mode (CM = 0.3, axial force ratio= 0.33, fire pattern B)
Collapse initiation time [s]without outrigger truss systemwith outrigger truss system

Collapse initiation time [s]Collapse initiation time [s]

1800

0

449 s

2000

2000

0

447 s

Collapse initiation time [s]

348

0

0.5

1

1.5

2

0

0

0.5

1

1.5

2

Axial force ratio

Member strength ratio of outrigger truss

Member strength ratio of outrigger truss(b) Fire pattern B(b) Fire pattern B(b) Fire pattern B

Fig. 9 Collapse initiation timevs. the axial force ratio

Fig. 10 Influence of structuralparameters on thecollapse initiation time
(axial force ratio= 0.33)

Fig. 11 Influence of structuralparameters on the collapse
initiation time
(axial force ratio= 0.19)

the ground level. The fire patterns did not appear to affect the overall collapse behavior; however, theslant angles at the collapse initiation phase were different, and the collapse initiation time was shorter
if the fire pattern was asymmetrical. The collapse initiation time depends on the strength and thenumber of outrigger trusses that support the load paths near the structural deficiencies. Figure 9 shows
the relationship between the collapse initiation time and the axial force ratio. The collapse initiation
time was not affected by the presence of the outrigger truss system if the axial force ratio was larger.
However, the effect of the outrigger truss system on the collapse initiation time increased in all of thecases if the axial force ratio had small values. Therefore, the influence of the structural parameters on
the collapse initiation time were investigated and compared in two different cases: (1) axial force
ratio=0.33 (floor load: 10.0 kN/m2) where the difference of collapse initiation times was smaller and(2) axial force ratio=0.19 (floor load: 5.0 kN/m2) where the difference was larger. Figure 10 shows theresults for the former case. The results without plots are the cases in which the tower model did notApplied Mechanics and Materials Vol. 82

349

collapse throughout the entire calculation time. Although the greater strength of the outrigger trusses
and the member joints slightly increased the collapse initiation time for fire pattern A, it did notappear to significantly affect the collapse initiation time if the fire pattern became asymmetrical as infire pattern B. In particular, each of the cases, except for the case where CM =0.1, exhibited a constantcollapse initiation time of around 450 s when fire pattern B was applied (Fig. 10(b)). Figure 11 shows
the results for the latter case when the floor loads were smaller. The collapse initiation time appears to
be largely affected by the presence of the outrigger truss system. However, the member strength of theoutrigger truss is not the most significant parameter. In this case, the member joint strength ratio CM is
the most significant parameter. For example, the collapse initiation time with CM =0.2 under fire
pattern A varies approximately 80 s between the models with and without the outrigger truss system,
while the collapse initiation time with CM =0.3 increases for about 600 s if the system is present.
These results confirmed that the collapse initiation times can be significantly affected by themember joint strength ratio, particularly if the axial force ratio is small (floor loads are low), under thecondition that the fire pattern is nearly symmetrical and the load paths to and from the outrigger truss
system are sufficiently protected.
Conclusion
The numerical results of this paper indicate that the collapse initiation time of a high-rise towerwith an outrigger truss system depends on fire patterns. The outrigger truss system delays the time
until collapse initiation in the models with a smaller axial force ratio, a member joint strength ratio of
0.3 or greater and for symmetrical fire patterns.
We plan to perform further investigations using full-scale, fire-induced collapse analyses of the
WTC towers.
References[1] D. Isobe and Z. Sasaki: Aircraft Impact Analyses of the World Trade Center Towers, CD-ROM
Proceedings of the 1st International Workshop on Performance, Protection, and Strengtheningof Structures under Extreme Loading (PROTECT2007), (2007), Whistler, Canada.
[2] D. Isobe, H. Yokota and L. T. T. Thanh: Fire-Induced Progressive Collapse Analyses ofHigh-Rise Towers, CD-ROM Proceedings of the 2nd International Workshop on Performance,
Protection, and Strengthening of Structures under Extreme Loading (PROTECT2009), (2009),
Hayama, Japan.
[3] K.M. Lynn and D. Isobe: in Int. J. for Numerical Methods in Engineering, Vol. 69, No. 12, (2007),
pp.2538-2563.
[4] W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery: Numerical recipes in
FORTRAN: The art of scientific computing, New York: Cambridge University Press, (1992).
[5] ASCE/FEMA, World Trade Center Building Performance Study: Data Collection, Preliminary
Observation and Recommendations, (2002).
[6] T. Hirashima, N. Hamada, F. Ozaki, T. Ave and H. Uesugi: in J. Struct. Constr. Eng., AIJ, Vol.
621, (2007), pp. 175-180, in Japanese.
[7] Y. Toi and D. Isobe: in Int. J. for Num. Methods in Engineering, Vol. 36, (1993), pp.2323-2339.
[8] NIST NCSTAR 1: Federal Building and Fire Safety Investigation of the World Trade Center
Disaster: Final Report on the Collapse of the World Trade Center Towers, National Institute ofStandards and Technology (NIST), (2005).

Performance, Protection and Strengthening of Structures under Extreme Loading
doi:10.4028/www.scientific.net/AMM.82
Effects of Outrigger Truss Systems on Collapse Initiation Times of High-Rise Towers
Exposed to Fire
doi:10.4028/www.scientific.net/AMM.82.344