Ministry of Transports, Constructions and Tourism

National Center for
Seismic Risk Reduction

266 Pantelimon Str., sector 2, Bucharest, Romania
Tel./Fax: + (40-21)- 2551667

Study on seismic design characteristics
of existing buildings in Bucharest, Romania

Authors:
Tudor POSTELNICU
Basarab CHESCA
Radu VACAREANU
Viorel POPA
Eugen LOZINCA
Dragos COTOFANA
Bogdan STEFANESCUMARCH 2004

STUDY ON SEISMIC DESIGN CHARACTERISTICS
OF EXISTING BUILDINGS IN BUCHAREST, ROMANIA
1. Introduction............................................................................................................................3
2. Evolution of the base shear coefficient..................................................................................3
2.1. CODE P13 – 63 ..............................................................................................................3
2.1.1. Seismic horizontal load............................................................................................3
2.1.2. Coefficients used to determine the seismic coefficient............................................3
2.1.3. Building design seismicity factors ...........................................................................4
2.2. CODE P13 – 70 ..............................................................................................................8
2.2.1. The determination of the horizontal seismic loads ..................................................82.3. CODE P100 – 78 ..........................................................................................................122.3.1. General equations for establishing the horizontal seismic forces..........................122.3.2. Establishing the horizontal seismic forces for the current types of buildings .......142.4. CODE P100 – 81 ..........................................................................................................16
2.4.1. General relations for establishing the seismic horizontal forces acting on a
structure............................................................................................................................16
2.4.2. Calculation of the horizontal seismic forces for current buildings structures .......19
2.5. CODE P100 – 92 ..........................................................................................................20
2.5.1. Basic relations for horizontal seismic loads computation for structures ...............20
2.6. Conclusions: .................................................................................................................25
2.6.1. Capacity Curves for Representative Building Types in Bucharest........................25
3. Evolution of the reinforced concrete design codes ..............................................................32
3.1. German Recommendations (1950) ...............................................................................32
3.1.1. Reinforced concrete beam subjected to pure bending: Generalities [2] ................32
3.1.2. Reinforced concrete beam subjected to pure bending: dimensioning ...................33
3.1.3. Reinforced concrete columns subjected to bending with axial force: Generalities..........................................................................................................................................34
3.1.4. Shear stresses: ........................................................................................................38
3.2. STAS 1546-50 [3].........................................................................................................40
3.2.1. The computation of the rectangular section elements under pure bending: ..........41
3.2.2. The computation to shear force of the concrete beams: ........................................423.2.3. Computation of the eccentric compressed members: ............................................423.3. STAS 10107-0/90 [4]....................................................................................................43
4. The evolution of the masonry structures design codes ........................................................52
5. Short description of the attached buildings plans: ...............................................................57
5.1. Reinforced concrete structures......................................................................................57
5.1.1. RC moment resisting frame structure built in 1963: RC S1 ..................................57
5.1.2. RC moment resisting frame structure RC S2.........................................................57
5.2. Masonry structures........................................................................................................57
5.2.1. Masonry structure - M S1 ......................................................................................57
5.2.2. Masonry structure - M S2 ......................................................................................59

Study on seismic design characteristics of existing buildings in Bucharest, Romania

21. INTRODUCTION
In order to start any retrofitting programme for a peculiar country it isimportant to understand the peculiarities of the building and the codes of practicethat were used during the design process. It is obviously that the codes werechanged along the history and that the building differs according to the design
period. This study contains the evolution of the base shear coefficient, the mostimportant factor in seismic design, the evolution of the reinforced concrete codes ofpractice and the evolution of the masonry structures codes of practice.
Because the information is nothing without examples, we attached to thisstudy the planes of four building built under different codes of practice and built ofdifferent material such us reinforced concrete or masonry.

2. EVOLUTION OF THE BASE SHEAR COEFFICIENT
Along the last half-century in Romania there were in force several codes forearthquake resistant design of buildings that contained different formula for thecomputation of the base shear force and for the computation of the base shear
coefficient. This chapter contains a short description of the formulas involved in theseismic design according to each code of practice.

2.1. CODE P13 – 63
2.1.1. Seismic horizontal load
The total seismic horizontal loading acting on a building (the base shear) can be
determined by the following eq.:

S = cQ

where:„c” is the seismic coefficient:c = K s βεψthat should be greater than 0.02.

2.1.2. Coefficients used to determine the seismic coefficient
1. K s is a coefficient which accounts for the design seismic factor. Can be
determined from the following table:
Table 1: The values of Ks according to building design seismic factor
Building design seismic
factor

Ks

7

0.025

8

0.050

9

0.100

Study on seismic design characteristics of existing buildings in Bucharest, Romania

32.1.3. Building design seismicity factors
The design seismicity factor should be established based on:-site seismicity factor-

importance of the building

The site seismicity factor can be determined from the Romania seismic map given by
STAS 36840-63 “Seismic intensity factors”.
The design seismicity factor can be determined using the following table, based on
the site seismic intensity factor and the building importance class.
Table 2: Classification of buildings according to importance class and the design seismicity factor
Importanceclass

Definition

The design seismicity factor
determined for a site seismicity factor
of:
7*

8

9

I

Monumental buildings, highimportance buildings

8

9

9

II

All buildings except classes I, III,IV, V

7

8

9

III

Single level industrial buildings,
energetic facilities of local interest,
etc.

7

7

8

IV

Single level buildings used for
housing, administrative orcommercial purposes.

7

7

8

V

Facilities which don't present any
hazard to human life in case ofcollapse,7782. β is the dynamic coefficient. It can be determined based on the vibration periodof the associated single degree of freedom system and the soil condition, as follows:*-

for soils with the maximum allowable stress σ ≥ 2kg / cm 2 , β0.9≤ 3 (figure 1)
determined by the following eq.: 0.6 ≤ β =T-for soils with de maximum allowable stress σ < 2kg / cm 2 , β can be
determined using the previous equation multiplied with 1.25. However itshould be limited to the value of 3 ( β ≤ 3 ).

-for very soft and humid soils β can be determined by the same eq.
multiplying with 1.5. However it should be limited to the value of 3 ( β ≤ 3 ).

can beBucharest had a site seimicity factor of 7 (MSK-64 intensity scale was used.)

Study on seismic design characteristics of existing buildings in Bucharest, Romania

4

β
3.0

β=

0.9
T

0.6
0.3

T

1.5

Figure 1: Amplification spectra

Observations:If available, mIcrozonation maps should be used to determine the soil category for a
specific site.
3. ε is a coefficient that makes the equivalence between the single degree of
freedom system and the real multi-degree one. It can be determined as follows:

Qk

Level nSn

Level k

Sk

un

uk

Figure 2: Distribution of seismic force
2

2

⎡ n
⎤
⎡ n
⎤
Q
u
⎢∑ k k ⎥⎢∑ Qk χ k ⎥= n⎣1 n ⎦ε= n⎣ 1 n ⎦where:
⎡
⎤⎡
⎡
⎤⎡
2⎤
2⎤
⎢∑ Qk ⎥ ⎢∑ Qk uk ⎥ ⎢∑ Qk ⎥ ⎢∑ Qk χ k ⎥
⎣1
⎦⎣ 1
⎦ ⎣1
⎦⎣ 1
⎦
- uk is the horizontal displacement of the structure at level k in the direction of
the seismic forces, for the considered vibration mode.

uk
is the ratio between the structural displacement at level k and theunstructural displacement at top- χk =

Study on seismic design characteristics of existing buildings in Bucharest, Romania

54. ψ is a coefficient that accounts for the structural and material types . It introduces
the influence of friction damping and can be determined as follows:- For reinforced concrete moment resisting frames and for reinforced concrete
frames pinned at top ψ = 1.2 ;- For very tall, flexible buildings such as independent chimneys, elevated watertanks, antennas: ψ = 1.5- For all other buildings ψ = 1.0n

The total gravity load Q = ∑ Qk is computed based on the gravity load at each “k”
1

floor Qk ” Floor loads can be determined by multiplying the standard gravity loads
with the following coefficients.
Table 3: Load combination for seismic design
No.

Load type

Loadingcoefficient

1

Permanent loads

1.0

2

Snow load

0.83Temporary loadsa) For tanks,
elevators

warehouses

or

1.0

b) For residential, administrative or
office buildings

0.8c) For industrial buildings

0.8

Observations:
For all other cases the loading coefficients should be taken 0.8.
n

The total seismic load is S = ∑ S k . It represents the sum of the seismic loads at each1

floor “k”, namely S k . S k can be determined as follows:- the total seismic load is distributed to each floor using the following eq.:QχQu
Sk = S n k k = S n k k∑ Qk uk ∑ Qk χ k1

1- or, S k can be directly determined by:

S k = ck Qkwhere:

ck = K s βψη kand,Study on seismic design characteristics of existing buildings in Bucharest, Romania

6nη k = uk

n

∑Q u

k

∑Q u

2
k

k

1
n

k

= χk

1

∑Q χ

k

∑Q χ

2
k

k

1
n

k

,

1

n

∑Q η

ε is related with η k by: ε = 1

k

k

Q

The total seismic load should be greater than:n

S = ∑ S k ≥ 0.02Q .
1

Observations:
For current buildings the seismic loads can be computed based only on the building
fundamental mode of vibration.
For tall buildings, such as chimneys, elevated water tanks, towers or antennas,
multistory buildings with more than 10 stories or all other buildings with ε <0.6
(previously defined), the seismic loads should be determined based on the first threevibration modes. In these cases the sectional efforts should be computed
independently for each vibration mode and then they should be superimposed using:N = N a2 + 0.5( N b2 + N c2 ) where

N a , N b and N c are the sectional efforts associated to each consideredvibration mode; N a is the biggest value of all three.

Study on seismic design characteristics of existing buildings in Bucharest, Romania

72.2. CODE P13 – 70
2.2.1. The determination of the horizontal seismic loads
The seismic horizontal loads that act on the building structure at the k level,
corresponding to the vibration mode r, are determined using the equation:

S k = k s β rψη kr ⋅ Qk
1) k s is the coefficient which takes into account the influence of the site seismicity
and the importance of the building. The values of this coefficient are presented in thetable bellow. The k s coefficient represents the ratio between the seismic design
acceleration and gravitational acceleration.
The seismic design acceleration depends on the seismic intensity defined for the site
(STAS 2923) and also on the importance of the building.
The classification of the buildings in importance classes takes into account the socialand economic importance of the building.
Table 4: The values of the ks coefficient according to importance class and seismic intensity
Importanceclass

Buildings types

ks
6

7†

8

9

I

Very important buildings: monumentalbuildings, museums, buildings that should
remain functional in case of earthquake(hospitals, administrative buildings, etc.),buildings which are very important for thenational economy.

0.03

0.05

0.08

0.12

II

All the buildings except those from theimportance classes I, III, IV.

--

0.03

0.05

0.08

III

Buildings with one story: residential,administrative and commercial buildings
which are not so important. Industrial
buildings with one story. Agriculturalbuildings.

--

0.02

0.03

0.05

IV

Buildings with small importance: buildings
used like shelters in agriculture andtemporary buildings.

--

--

--

0.03

2) β r is the coefficient which introduces the influences of the natural vibration periodof the building Tr and the foundation soil:- for normal soil conditions: β r =

†

0.8
Tr

Bucharest had a site seimicity factor of 7 (MSK-64 intensity scale was used.)

Study on seismic design characteristics of existing buildings in Bucharest, Romania

80.6 ≤ β r ≤ 2.0 , with Tr measured in seconds;-

for hard soil the values of the coefficient β r given in the preceding paragraphshould be reduced by 20% except for the masonry and precast reinforced
concrete structures.

-

For clay soils and in case of high underground water level the coefficient β rshould be increased by 50% without exceeding the limit value β r = 2.5 .

βr
2.0

β=

0.8
Tr

0.6
0.4

1.33

Tr (sec)

Figure 3: Amplification spectra

Observations:
The effect of the foundation rocking on the calculation of the natural vibration period
will be determined:-

For buildings with shear walls the surface inside the exterior foundation
should be consider as the foundation surface. For buildings with reinforced
concrete should be taken into account the surfaces of the insulated
foundations under the columns.

-

The settlement coefficient for the foundation rocking expressed in daN/cm3 is

σ at, σ at represents the allowable stress forB
the foundation soil (daN/cm3) and B represents the horizontal dimension of
the foundation in the vibration direction determined considering theinformation from the preceding paragraph.
limited to minimum value: Cθ ≥ 503) ψ is the coefficient which introduces the influences of the damping properties andthe ductility of the structure.
Table 5: The values of ψ coefficient according to structure type
Structure typeψ

RC frame structures

1.0

RC walls structures

1.2

Masonry structures

1.3

Very flexible structures

1.8

Elevated water tanks

2.0

Study on seismic design characteristics of existing buildings in Bucharest, Romania

9For all other types of structures that cannot be found in the table the value of thecoefficient will beψ = 0.2 .
4) η kr is the coefficient which introduces the influence of the vibration mode and isdetermined by:
n

∑Q u

jr

∑Q u

2
jr

j

η kr = ukr jn=1

j

j =1

ukr is the eigenvalue for the degree of freedom (k) for the modal shape of thevibration mode (r).
Level n

unI

unII
unIII

Level k

Qk

ukI

unII
unIII

Figure 4: First three vibration modes

5) Qk is the resultant load equal to the sum of the gravitational loads for level kwhich are determined using the code permanent and temporary loads. The
temporary loads should be multiplied by a coefficient equal with 0.8.

Observations:
The seismic horizontal loads S kI , corresponding to the first (fundamental) vibrationmode, should be determined tacking into account the equation:n

S I = ∑ S kI ≥ 0.02Q
k =1

S I is the base shear corresponding to the first vibration mode and Q is the resultant
force of the gravitational loads used in the determination of the seismic loads:nQ = ∑ Qk
k =1

Study on seismic design characteristics of existing buildings in Bucharest, Romania

10The base shear force corresponding to the vibration mode r can be determined using
the equation:
S r = cr Q

cr = k s β rψε r

ε r is the equivalence coefficient
2

n
⎡n
⎤
Q jη jr⎢∑ Q j u jr ⎥
∑
j =1
j =1
⎣
⎦
=
ε= n
Q
⎡
⎤⎡ n
⎤
2
⎢∑ Q j ⎥ ⎢∑ Q j u jr ⎥⎣ j =1 ⎦ ⎣ j =1⎦

Skr is the seismic horizontal load for level k

S kr = S r

Qk ukr
n

∑Q u
j

j =1

j

It is allowed to determine the seismic horizontal loads for current structural types
tacking into account only the fundamental vibration mode.
The horizontal seismic loads for high structures with the natural period greater then
1.0 s or total height grater then 40m should be calculated tacking into account thecontribution of the first three vibration modes. The stresses should be establishedseparately for each vibration mode (r) and the total stress N in one section will be
determined using the equation:
N=

3

∑N
r =1

2
r

N r is the stress in the considered section corresponding to the vibration mode (r).

Study on seismic design characteristics of existing buildings in Bucharest, Romania

112.3. CODE P100 – 78
2.3.1. General equations for establishing the horizontal seismic forces
The horizontal seismic forces that act on the structure should be determined for each
vibration mode. The forces at the kth floor (on the direction of the degree of freedom),corresponding to the rth vibration mode, are established with the relation:

S kr = ckr Gk;

where:

ckr = k s β rψη kr1) ckr is the seismic coefficient for the kth floor in the rth vibration mode;2) k s is the seismic coefficient corresponding to the attributed rank of seismic
protection of the construction. It represents the ratio between the maximum groundacceleration (that corresponds to the construction’s rank of seismic protection) andthe acceleration of gravity. The values of k s are given in the table below.
Table 6: The values of Ks according to the rank of seismic protection
The values of the coefficient Ks
The rank of seismic protectionof the construction

6

6½

7

7½

8‡

8½

9

Ks

0.07

0.09

0.12

0.16

0.20

0.26

0.32

3) β r is the dynamic coefficient that corresponds to the rth vibration mode. It depends
on the period of vibration Tr (for the considered vibration mode) and the nature of
the foundation ground as follows:-

foundation grounds with normal rigidity: β r =3, ( Tr in seconds) and limitedTr

between 0.75 ≤ β r ≤ 2.0 ;‡-for rigid foundation grounds: rocky lands, layers of stable deposits of sand,coarse gravel or high consistency clays (Tertiary layers or older) etc., thevalues of the β r should be reduced with 20%, but respecting the above given
limits;-for foundation grounds with reduced rigidity: layers of reduced consistency
clay (the consistency index I c < 0.5 with or without insertions of sand or othernon-cohesive formations, sand in refined state, (ramming rank D < 0.33 ),loess with high humidity ( w > 20% ) or for sandy or clayish land with high levelof underground water (depth < 5 m), the values of β r should be increased by
30%, but without exceeding the limit value β r = 2.5 .

Bucharest had a rank of seismic protection equal to 8 (MSK-64 intensity scale was used.)

Study on seismic design characteristics of existing buildings in Bucharest, Romania

124) ψ is the reduction coefficient of the seismic effects and it takes into account thestructural ductility, the stresses redistribution capacity, the contribution of strength
reserve not considered in the analysis (especially from the interaction with nonstructural elements) and the vibration damping effects. The values of ψ coefficientare given in the table below.
Table 7: The values of ψ coefficientNo.

Construction type and constructive system

Coefficient1

Buildings with a rigid structure (masonry or reinforced concrete cast-inplace or prefabricated shear walls) or a semi–rigid structure (shear walls
interacting with frames):- up to 5 stories (including the ground level) and the total height lessor equal to 15 m
- higher than 5 stories and the total height over 15 m

0.30
0.25

Multi-story frame buildings:- with one span
- with more spans

0.25
0.20

Industrial one-story plants and other related constructions:- with one span
- with more spans

0.20
0.15

4

Silos and other special constructions with a rigid structure

0.25

5

Very flexible tall constructions like chimneys and independent towers

0.35

6

Elevated water tanks

0.35

2

3

ψ

Remarks:
1. The values of the ψ coefficient for the multi-story frame buildings are
established considering that the ductility conditions for the structuralelements are fulfilled.
2. For steel structures, the ψ values from the table should be reduced with20%.
5) η kr is the coefficient of distribution of seismic forces corresponding to kth floor in
the rth vibration mode and it can be obtained with the following relation:
n

∑G u

kr

∑G u

2
kr

η kr = ukr 1n

k

k

;

where:

1

ukr is the component of the rth eigenvector corresponding to kth degree of freedom orin other words is the component of the rth shape mode at the kth floor. The shapemodes are obtained according to dynamics of structures.

Study on seismic design characteristics of existing buildings in Bucharest, Romania

13

Level n

unI

unII
unIII

ukI

Level k

Gk

unII
unIII

r =1

r =2

r =3

Figure 5: First three vibration modes

6) Gk represents the resultant of gravity loads at the kth floor.
7) The resultant of horizontal seismic forces (the base shear force) can be calculated
either by summing all the level seismic forces S kr , or directly with the relation:

S r = K s ⋅ β r ⋅ψ ⋅ ε r ⋅ G;

where:nG = ∑ Gk, and

1

ε r is the coefficient of equivalence between the real system (with “n” degrees of
freedom) and a system with a single degree of freedom corresponding to the rth
vibration mode. It is determined with the equation:
2

n
⎡ n
⎤
G
u
∑
k
kr
∑1 Gkη kr
⎢
⎥
1
⎣
⎦
ε= n
=
G
⎡
⎤⎡ n
2 ⎤
⎢∑ Gk ⎥ ⎢∑ Gk ukr ⎥
⎣1
⎦⎣ 1
⎦

Remarks:
The efforts in the structural elements are separately calculated for each vibration
mode. Usually, it is enough to consider only the first three oscillation modes. The
total design effort “N” in a section of a structural element is obtained with the relation:
N=

3

∑N

2
r

;

where:

1

N r is the effort in the considered section corresponding to the rth vibration mode.

2.3.2. Establishing the horizontal seismic forces for the current types ofbuildings
The current types of buildings are those constructions that have a fundamental
vibration period less than 1.5 sec., as for example: multi-story residential and sociocultural buildings with less than 10 stories and a maximum height above the ground
Study on seismic design characteristics of existing buildings in Bucharest, Romania14

of 30 m; industrial and agricultural one-story halls and multi-story industrial
constructions with at most 6 stories and a maximum height of 25 m above theground. The resultant S of horizontal seismic forces is determined, considering thefundamental vibration mode, with the expression:
S = c ⋅G;

where:

c = K s ⋅ β ⋅ψ ⋅ ε is called global seismic coefficient (of the base shear force); thecoefficients β and ε correspond to the fundamental vibration mode.
It is admitted to directly determine the horizontal seismic forces using the global
seismic coefficients given the following table.
Table 8: Global seismic coefficientNo.

Construction type and constructive system

1

Buildings with a rigid structure (masonry or
reinforced
concrete
cast-in-placeorprefabricated shear walls) or a semi–rigid
structure (shear walls interacting with frames):- up to 5 stories (including the groundlevel) and the total height less or equal
to 15 m- higher than 5 stories and the totalheight over 15 m

2

3

β

ε

ψ

c / k s = βεψ

2

0.75

0.30

0.45

2

0.75

0.25

0.38

Multi-story frame buildings:-

with one span

2

0.80

0.25

0.40

-

with more spans

2

0.80

0.20

0.32

2

1.00

0.20

0.40

2

1.00

0.15

0.30

Industrial one-story plants and other related
constructions:-with one span-with more spans

The resultant S of the horizontal seismic forces is distributed on the construction
height with the relation:Gu
Gh
Sk = S n k k ≈ S n k k∑ Gk uk ∑ Gk hk
1;

where:

1

S k is the horizontal seismic force at the kth level (floor). The fundamental shapemode of the structure is approximated through a linear variation.

Study on seismic design characteristics of existing buildings in Bucharest, Romania

15

Sn
un

Level nLevel k

Gk

uk

uk

Sk
hk
hk

Figure 6: Linear approximation of the fundamental vibration mode

2.4. CODE P100 – 81
2.4.1. General relations for establishing the seismic horizontal forces acting ona structure
The seismic horizontal forces that act on a building are established for eacheigenmode. The force that acts at the level k (on the direction of the degree of
freedom) in the rth eigenmode is calculated with the relation:

S kr = ckr Gk

where:

ckr = k s β rψη kr where:1) ckr is the seismic coefficient for level k and for the rth eigenmode;2) k s seismic intensity coefficient corresponding to the seismic protection level. It
means the ratio between the peak ground acceleration of the seismic motion
corresponding to the seismic zone where the building is situated and the gravity
acceleration. The values for k s are given in the next table.
Table 9: Values for the Ks coefficient
Values for the Ks coefficient
Seismic protection level of thebuilding

6

6

1
2

7

7

1
2

8§

8

1
2

9

Ks

0.07

0.09

0.12

0.16

0.20

0.26

0.32

3) β r dynamic amplification coefficient in the rth eigenmode of the building. It is
calculated depending on the vibration period of the structure Tr (for the consideredeigenmode) and on the nature of the ground type as follows:§

Bucharest had a 8 seismic protection level (MSK-64 intensity scale was used.)

Study on seismic design characteristics of existing buildings in Bucharest, Romania

16

3, obeying the requirement
Tr0.75 ≤ β r ≤ 2.0 , where Tr is measured in seconds;

βr =

-

ground type with normal stiffness,-for stiff ground: rock, deposits of very dense sand, gravel or very stiff clay
(tertiary layers or older) etc., the values of the coefficient β r are reduced by
20%, obeying the previous inequality;-

for ground with reduced stiffness: deposits of layers of low consistency clay(the consistency index I c < 0.5 ) with or without intrusions of sand or othercohesionless soils, loose sand (density index D < 0.33 ), high-humidity loess( w > 20% ), as well as in the case of ground with high level of the undergroundwater (depth < 5 m), the values of the coefficient β r are increased by 30%,
but it must be less than β r = 2.5 .

4) ψ is the coefficient for reduction of seismic effects taking into account thestructural ductility, the stress re-distribution capacity, the contribution of strength
reserve not considered in the analysis from the co-operation among of the structurewith non-structural elements and the vibration damping effects. The values of the ψ
coefficient are given in the next table.
Table 10: The values of the ψ coefficient
No.

Type of building and structural system

1

Buildings with rigid structure (masonry structural walls or reinforced
concrete structural walls, monolithically cast-in-situ or precast) or with semi
– rigid one (structural walls co-operating with frames):
-

2

3

4

up to ground floor + 4 floors ( ≤ 5 floors) and having the totalheight less than 15 m
more than ground floor + 4 floors (> 5 floors) and having the totalheight superior to 15 m

Coefficient

ψ

0.30
0.25

Multi-story buildings with frame structure:-having a single span

0.25

-

having more spans

0.20

Single story industrial buildings and other hall-type buildings:-

having a single span

0.20

-

having more spans

0.15

Silos, including the ones with cells supported on columns and otherspecial constructions with rigid structure

0.25

5

Very flexible tall constructions like chimneys, independent towers

0.35

6

Water tanks

0.35

Study on seismic design characteristics of existing buildings in Bucharest, Romania

17Remarks:
1. The values of the ψ coefficient for multi-storey buildings with frame structure areestablished considering that the structure fulfills the requirements for ductile
behavior.
2. For steel structures, the values of ψ given in the table are reduced by 20%.
3. For the constructions at point 5 and 6 the values of the ψ coefficient are given
considering that the provisions of present-day codes apply, according to which in thespecial combinations that contain the seismic action, the wind load is consideredwith a reduced intensity.
5) η kr is the coefficient that describes the distribution of the seismic force at the level„k” in the „r” eigenmode, which is determined with the next relation:
n

∑G u

kr

∑G u

2
kr

η kr = ukr kn=1
k =1

k

k

where

ukr is the component of the (r) modal shape on the (k) degree of freedom. The modal
shapes are determined by means of the methods of dynamics of structures.
6) The resultant of the horizontal seismic forces (the base shear force) can becalculated either by summation of the level horizontal seismic forces S kr , or directlywith the relation:

S r = K s ⋅ β r ⋅ψ ⋅ ε r ⋅ G

where:nG = ∑ Gk , and the coefficient of equivalence ε r between the actual system and the1

one with a single degree of freedom corresponding to the r vibration mode iscalculated with the relation:
2

n
⎡ n
⎤
G
u
Gkη kr∑⎢∑ k kr ⎥
k =1
⎣
⎦
k =1
ε= n
=
G
⎡
⎤⎡ n
2 ⎤
⎢∑ Gk ⎥ ⎢∑ Gk ukr ⎥⎣ k =1 ⎦ ⎣ k =1⎦

Remarks:
The efforts in the structure are determined separately for each vibration mode r.
Usually, taking into account the first three vibration modes is sufficient. The total
design effort N in a cross-section of an element of the structure is calculated with therelation:

Study on seismic design characteristics of existing buildings in Bucharest, Romania

18

N=

3

∑ N where2r1

N r is the effort in the considered cross-section corresponding to the r vibration
mode.

2.4.2. Calculation of the horizontal seismic forces for current buildings
structures
By current type structures one can understand those structures whose fundamental
natural period is less than 1.5s, that is multi-storey buildings for dwelling or for sociocultural purposes, having less than 9 floors and the height less than 30m above theground, industrial halls and agricultural ones with a single storey and multi-story
industrial buildings up to 6 floors and with the maximum height of 25m above theearth.
The resultant S of the horizontal seismic forces is calculated, considering thefundamental eigenmode, with the relation:
S = c ⋅G

where:

c = K s ⋅ β ⋅ψ ⋅ ε is called global seismic coefficient (of the base shear force); β and εcoefficients correspond to the fundamental eigenmode.
The simplified calculation of the horizontal seismic forces is accepted, by means of
the values given in the next table for the global seismic coefficient c.
Table 11: Global seismic coefficient
No.

Type of building and structural system

1

Buildings with rigid structure (masonry
structural walls or reinforced concrete
structural walls, monolithically cast-in-situ or
precast) or with semi – rigid one (structural
walls co-operating with frames):

2

3

-

up to ground floor + 4 floors ( ≤ 5floors) and having the total heightless than 15 m-

more than ground floor + 4 floors (>5 floors) and having the total heightsuperior to 15 m

β

ε

ψ

c / k s = βεψ

2

0.75

0.30

0.45

2

0.75

0.25

0.38

Multi-story buildings with frame structure:-having a single span

2

0.80

0.25

0.40

-

having more spans

2

0.80

0.20

0.32

2

1.00

0.20

0.40

2

1.00

0.15

0.30

Single story industrial buildings and otherhall-type buildings:-

having a single span-

having more spans

Study on seismic design characteristics of existing buildings in Bucharest, Romania

19

The distribution of the resultant S of the horizontal seismic forces on the height of thebuilding is calculated with the relation:Gu
Gh
Sk = S n k k ≈ S n k k∑ Gk uk ∑ Gk hk
1

where:

1

S k is the horizontal seismic force at the k floor. The fundamental mode shape isapproximated by an inclined straight line.

2.5. CODE P100 – 92
2.5.1. Basic relations for horizontal seismic loads computation for structures
The relations further provided will be used in determining the equivalent static loads,
used in engineering analysis, required by the common design method. These loads
take into account, in a simplified and implicit way, the effects of dynamic behavior
and post-elastic deformation phenomena.
The horizontal seismic loads, acting on a structure, are determined for each naturalmode of vibration. If the natural vibrations occur in one plane, the resultant ofhorizontal seismic loads (base shear force), corresponding to the ground motion
direction and to the „r”-th vibration mode, is determined using further relations:where: cr = α ⋅ k s ⋅ β r ⋅ψ ⋅ ε r where:S r = cr G1) cr is the overall seismic coefficient, corresponding to the „r”-th vibration mode;2) G resultant of gravity loads for the whole building;3) α importance coefficient of the building according to the classes of importance.
This factor differentiates the protection level of the building depending on theimportance classes. Based on the performance criteria the buildings are splitted into
four performance classes.
Table 12: Classes of importance for buildings
Classes of importance
I

II

III

IV

1.4

1.2

1.0

0.8

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Table 13: Classification of buildings according to importance classes

Class IClass IIClass IIIClass IV

Buildings of vital social importance, whose functionality during and
immediately after earthquakes should be fully granted:-

hospitals ambulance services, fire-stations;-administration buildings of great importance in organizing the emergency
post-earthquake activity;-communication buildings of national or country level importance;-

power plants belonging to the national system-buildings hosting museums of national importance.

Very important buildings requiring a limitation of damage, keeping in viewits potential consequences:-other health protection buildings;-

schools, crèches, kinder
handicapped, old people;-

high occupancy buildings: sports and performance halls, churches,
important shopping centers;-buildings sheltering special artistic, historic, scientific values;-

industrial buildings and plants where fire or toxic gases leakage may
occur;-

industrial buildings with equipment of high economic importance;-

stores for highly necessary products to be used in case of emergency.

gardens,boarding-housesforchildren

Normal importance buildings (not falling into classes I, II, or IV)-

residential buildings, hotels, boarding-houses (except those in class II)-

common industrial and agrozootechnical buildings.

Reduced importance buildings-

agrozootechnical structures of reduced importance (e.g. greenhouses,
various single story buildings for animal and poultry breeding. a.s.o.);-one or two story residential buildings;-

other civil and industrial buildings sheltering goods of low importance andreduced staff.

Remarks:
The above classification of the buildings on the importance classes is not the sameas that provided by STAS 10100/75.
The types of buildings that are not explicitly mentioned in the table, will fall into thefour classes, based on a technical argumentation provided by the design theme;
In certain cases, some components of the buildings, including installations andequipment, may fall into different classes of importance than the other parts of thebuildings
The decision on the classes of importance the buildings fall into, will be made by theowner, who will be advised by the technical authorities in charge.

Study on seismic design characteristics of existing buildings in Bucharest, Romania

214) The “ks” coefficient represents the ratio between the peak ground acceleration of
the seismic motion (with an average recurrence period of about 50 years),corresponding to the seismic zone, and the gravity acceleration. The “ks” coefficientare supplied in the next table, according to the seismic zones described on the code
map.
Table 14: The ks coefficient

Seismic zone

ks

A

0.32

B

0.25

**

C

0.20

D

0.16

E

0.12

F

0.08

5) The amplification factor (“βr”) is determined according to the natural oscillation
periods (“Tr”) of the building and to the local seismic conditions, characterized bycorner periods (“Tc”) using the following relations:

β r = 2.5

forTr ≤ Tc

β r = 2.5 − (Tr − Tc ) ≥ 1 for

Tr > Tc

βr

Tc=1.5 sec

2.5

Tc=1.0 sec
Tc=0.7 sec

1.0

0.7

1.0

1.5

2.2

2.5

3.0

Tr(sec)Figure 7: Amplification spectra

6) The coefficient of reduction of seismic forces (“y”) due to the structural ductility, tothe redistribution of the efforts and to the damping effects is provided in the following
table:**

Bucharest belongs to seismic zone C.

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Table 15: The values of ψ coefficient according to structural type

ψ coefficient

Structure type
A. Reinforced concrete structures
1 Multistory frame structures:- with infill walls designed as structural members............................

0.25- the infill walls are not considered structural members...................

0.20

2 Industrial halls and other one story structures:- with stiff beam-columns joints........................................................

0.15- with hinged joints............................................................................

0.20

3 Buildings with structural walls................................................................

0.25

4 Structures made of walls, columns and flat-slabs (no beams)..............

0.30

6 Elevated tanks.......................................................................................

0.35

7 Silos:.....................................................................................................

0.25

B. Masonry structures
1 Structures made of masonry structural walls with reinforced concreteboundary elements (spandrel beams and columns:................................
2 Structures with plain masonry structural walls.....................................

0.25
0.30

Remarks:
7) The equivalence coefficient between the real system and the system with one
dynamic degree of freedom for the vibration mode „r”, „ ε r ” is determined using thefollowing relation;⎡ n⎤⎢∑ Gk u kr ⎥⎦ε = ⎣ k =12

where:nG ∑ Gk u
k =1

2
kr

- ukr the „r”-th eigenvector component corresponding to the „k”-th freedom degree;n- Gk the resultant of gravity loads at ‚k” level G = ∑ Gk ;k =1

The „ukr” eigenvectors, as well as the „Tr” natural periods will be determined using
structural dynamics methods.
8) The seismic load, acting at the „k”-th level on the DOF direction, corresponding tothe „r”-th vibration mode, is determined using the following relation:

S kr = ckr Gk

where:

Study on seismic design characteristics of existing buildings in Bucharest, Romania

23

- S kr is the seismic load acting at the level „k” on the direction of the „r”-th dynamic
degree of freedom.
- ckr = αk s β rψη kr where:
n

∑G u

kr

∑G u

2
kr

η kr = ukr kn=1
k =1

k

k

Remark:The values S kr may be obtained by the distribution of the resultant (base shear force)„ S r ”of the seismic loads by the relation

S kr = S r

Gk ukr
n

∑G u
k

k =1

kr

9) The internal forces, displacements, a.s.o., are calculated separately for eachnatural vibration mode. If the oscillations analysis can be made independently, it isusually sufficient to take into account the first three natural vibration modes.
For the case of spectral analysis of the vertical plane vibrations, the overall stress(„N”) at a certain member section is determined using the relation:
N=

3

∑N

2
r

where

1

N r is the section force, corresponding to vibration mode „r”.

Remark:For crane-bridge working inside a one-story building braced in the longitudinal
direction by ductile frames, special measures will be applied for an eventual bracing
system collapse. Therefore, the structure without bracing system will be designed fora seismic coefficient over than 0.3k s ≥ 0.05 .
The designed energy dissipating mechanism has to induce plastic deformations at
the columns bottom, as well as under the covering beams; the structure should be
stiffened by bracings placed above the covering beams.

Study on seismic design characteristics of existing buildings in Bucharest, Romania

24

2.6. Conclusions:2.6.1. Capacity Curves for Representative Building Types in Bucharest
2.6.1.1. Description of Model Building Types

Table 16 lists the model building types most widely used in Bucharest.
Table 16: Model Building Types
HEIGHT
No.

Label

1
2
3
4
5
6

RC1L
RC1M
RC1H
RC2L
RC2M
RC2H

Description

Concrete Moment Frame

Concrete Shear Walls

Range
Name
Stories
Low-Rise
1-3
Mid-Rise
4-7
High-Rise
8+
Low-Rise
1-3
Mid-Rise
4-7
High-Rise
8+

Typical
Stories Meters
2
5.7
6
17.1
10
28.5
2
5.7
6
17.1
10
28.5

2.6.1.2. Capacity Curves
A building capacity curve (also known as a push-over curve) is a plot of a building’s
lateral load resistance as a function of a characteristic lateral displacement (i.e., aforce-deflection plot). It is derived from a plot of static-equivalent base shear versus
building (e.g., roof) displacement. In order to facilitate direct comparison withearthquake demand (i.e. overlaying the capacity curve with a response spectrum),the force (base shear) axis is converted to spectral acceleration and thedisplacement axis is converted to spectral displacement.
The building capacity curves developed are based on engineering design
parameters and judgment. Three control points that define model building capacity
describe each curve:• Design Capacity• Yield Capacity• Ultimate Capacity
Design capacity represents the nominal building strength required by current model
seismic code provisions or an estimate of the nominal strength for buildings notdesigned for earthquake loads.
Yield capacity represents the true lateral strength of the building considering
redundancies in design, conservatism in code requirements and true (rather than
nominal) strength of materials. Ultimate capacity represents the maximum strengthof the building when the global structural system has reached a fully plastic state.
Ultimate capacity implicitly accounts for loss of strength due to shear failure of brittle
elements. Typically, buildings are assumed capable of deforming beyond theirultimate point without loss of stability, but their structural system provides noadditional resistance to lateral earthquake force.
Up to the yield point, the building capacity curve is assumed to be linear withstiffness based on an estimate of the true period of the building. The true period is

Study on seismic design characteristics of existing buildings in Bucharest, Romania

25

typically longer than the code-specified period of the building due to flexing of
diaphragms of short, stiff buildings, flexural cracking of elements of concrete andmasonry structures, flexibility of foundations and other factors observed to affectbuilding stiffness. From the yield point to the ultimate point, the capacity curvetransitions in slope from an essentially elastic state to a fully plastic state. The
capacity curve is assumed to remain plastic past the ultimate point. An example
building capacity curve is shown in Figure 8.

Sa

Ultimate
Capacity

Au

Ay

Yield
CapacityAd

DesignCapacity

Dd

Dy

Du

Sd

Figure 8: Example of Building Capacity Curve

The building capacity curves are constructed based on estimates of engineering
properties that affect the design, yield and ultimate capacities of each model building
type. These properties are defined by the following parameters, Figure 8:
Cs
Te
α1
α2
γ
λ
µ

design strength coefficient (fraction of building’s weight),
true “elastic” fundamental-mode period of building (seconds),
fraction of building weight effective in pushover mode,
fraction of building height at location of pushover mode displacement,“overstrength” factor relating “true” yield strength to design strength,“overstrength” factor relating ultimate strength to yield strength, and“ductility” factor relating ultimate displacement to λ times the yielddisplacement (i.e., assumed point of significant yielding of thestructure)

The design strength, Cs is based on the lateral-force design requirements of seismic
codes. These requirements are a function of the building’s seismic zone locationand other factors including type of lateral-force-resisting system and building period.

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26

2.6.1.3. Major developments in four generations of seismic codes
Pre-code period (prior to 1941/45):
1941 Draft Instructions• Development of first national seismic
1945 Instructions
code after the 1940 earthquake: lateralseismic force was 5% of building

Low-code period (1963-1977):
P13-63

P13-70••Control period of response spectra TC=0.3 s
Maximum dynamic amplification DAF = max SA/PGA = 3
SA - structure absolute acceleration response spectra.

•••

Control period of response spectra TC=0.4 s
Max. dynamic amplification DAF = 2
Some ductility rules for RC frames.

Moderate-code period (1978 - 1990):
P100-78 • Development of the first seismic code based on the uniqueP100-81•••strong ground motion recorded in soft soil of Bucharest
during March 4, 1977 event: PGA = 0.2g and the long
predominant period of ground vibration was Tp =1.6s.
Control period of response spectra TC=1.5 s
Maximum dynamic amplification DAF = 2
Ductility rules for RC shear wall & frame structures.

Moderate to High-code period (1990-present):
P100-90 • Control period of response spectra TC=1.5 s
P100-92 • Maximum dynamic amplification DAF = 2.5• Advanced ductility rules for RC shear wall and frame
structures and for steel structures.
It is emphasized that after the 1977 event, new ductility rules for RC structures were
imported from US practice and incorporated into Romanian seismic codes, P100.
According to the EUROCODE 8 requirements the rules were significantly improved
after 1989.
Table 17 summarizes design capacity for each building type and design level.
Building period, Te, push-over mode parameters α1 and α2, the ratio of yield to design
strength, γ, and the ratio of ultimate to yield strength, λ, are assumed to be
independent of design level. Values of these parameters are summarized in Table
18&Table 19 for each building type. Values of the “ductility” factor, µ, are given in
Table 20 for each building type and design level. The values are given only formedium and high-rise RC buildings considered to be representative for Bucharest.

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Table 17: Code Building Capacity Parameters - Design Strength (Cs)
Building Seismic Design Level (Percentage of Building Weight)
Type
RC1M
RC1H
RC2M
RC2H

1941-1962 1963-1969 1970-1977 1978-1989 1990-2002
5
5
5
5

3.21
2.25
7.71
4.15

3.4
2.4
7.2
4.4

8
8
10
10

10
10
12.5
12.5

Table 18: Code Building Capacity Parameters - Period (Te), Pushover Mode

Response Factors (α1, α2) and Overstrength Ratios (γ, λ) - 1941-1977
Building Height to Period, Te
Type

Roof (m)

(Sec)

RC1M
RC1H
RC2M
RC2H

17.1
28.5
17.1
28.5

0.7
1
0.4
0.7

Modal Factors

Overstrength Ratios

Weight, α1 Height, α2
0.85
0.75
0.9
0.8

0.6
0.6
0.7
0.7

Yield, γ

Ultimate, λ

1.4
1.4
1.4
1.4

1.5
1.5
1.5
1.5

Table 19: Code Building Capacity Parameters - Period (Te), Pushover Mode

Response Factors (α1, α2) and Overstrength Ratios (γ, λ) - 1978-2002
Building Height to Period, Te
Type

Roof (m)

(Sec)

RC1M
RC1H
RC2M
RC2H

17.1
28.5
17.1
28.5

0.6
0.85
0.35
0.6

Modal Factors

Overstrength Ratios

Weight, α1 Height, α2
0.85
0.75
0.9
0.8

0.6
0.6
0.7
0.7

Yield, γ

Ultimate, λ

1.5
1.5
1.5
1.5

2
2
2
2

Table 20: Code Building Capacity Parameter - Ductility (µ)
Building Seismic Design Level (Percentage of Building Weight)
Type
RC1M
RC1H
RC2M
RC2H

1941-1962 1963-1969 1970-1977 1978-1989 1990-2002
2
2
2
2

3
3
3
3

3
3
3
3

5
5
4
4

5
5
4
4

Building capacity curves are assumed to have a range of possible properties that are
lognormal distributed. Capacity curves described by the values of parameters given
in Table 17, Table 18 Table 19and Table 20 represent median (best) estimates ofbuilding capacity.
Table 21, Table 22, Table 23, Table 24 and Table 25 summarize yield capacity andultimate capacity control points.
Study on seismic design characteristics of existing buildings in Bucharest, Romania

28

Table 21: Code Building Capacity Curves - 1941-1962
Building
Type
RC1M
RC1H
RC2M
RC2H

Yield Capacity
Point
Dy (cm)Ay (g)
1.00
2.32
0.31
1.07

0.082
0.093
0.078
0.088

Ultimate Capacity
Point
Du (cm)Au (g)
3.01
6.96
0.93
3.20

0.124
0.140
0.117
0.131

Table 22: Code Building Capacity Curves - 1963-1969
Building
Type
RC1M
RC1H
RC2M
RC2H

Yield Capacity
Point
Dy (cm)Ay (g)
0.64
1.04
0.48
0.88

0.053
0.042
0.120
0.073

Ultimate Capacity
Point
Du (cm)Au (g)
2.90
4.70
2.15
3.98

0.079
0.063
0.180
0.109

Table 23: Code Building Capacity Curves - 1970-1977
Building
Type
RC1M
RC1H
RC2M
RC2H

Yield Capacity
Point
Dy (cm)Ay (g)
0.68
1.11
0.45
0.94

0.056
0.045
0.112
0.077

Ultimate Capacity
Point
Du (cm)Au (g)
3.07
5.01
2.00
4.22

0.084
0.067
0.168
0.116

Table 24: Code Building Capacity Curves - 1978-1989
Building
Type
RC1M
RC1H
RC2M
RC2H

Yield Capacity
Point
Dy (cm)Ay (g)
1.26
2.87
0.51
1.68

0.141
0.160
0.167
0.188

Ultimate Capacity
Point
Du (cm)Au (g)
12.63
28.73
4.06
13.42

0.282
0.320
0.333
0.375

Table 25: Code Building Capacity Curves - 1990-2002
Building
Type
RC1M
RC1H
RC2M
RC2H

Yield Capacity
Point
Dy (cm)Ay (g)
1.58
3.59
0.63
2.10

0.176
0.200
0.208
0.234

Ultimate Capacity
Point
Du (cm)Au (g)
15.79
35.91
5.07
16.77

0.353
0.400
0.417
0.469

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29

The values of yielding and ultimate displacement and acceleration given in Table 21
to Table 25 are represented in Figure 9, Figure 10, Figure 11 and Figure 12 forbuilding types RC1H and RC2H.

4.0
3.5

RC1H
RC2H

3.0

Dy , cm

2.5
2.0
1.5
1.0
0.5
0.0
1941-1962

1963-19691970-1977

1978-1989

1989-2002

Seismic code period
Figure 9: Yielding displacement according to seismic code period

40
RC1H

35

RC2H

30

Du , cm

25
20
15
10
5
0
1941-1962

1963-19691970-1977

1978-1989

1989-2002

Seismic code period
Figure 10: Ultimate displacement according to seismic code period

Study on seismic design characteristics of existing buildings in Bucharest, Romania

30

0.25
RC1H
RC2H
0.20

Ay , 'g

0.15

0.10

0.05

0.00
1941-1962

1963-19691970-1977

1978-1989

1989-2002

Seismic code period
Figure 11: Yielding acceleration according to seismic code period

0.50
0.45

RC1H
RC2H

0.40
0.35
Au , 'g

0.30
0.25
0.20
0.15
0.10
0.05
0.00
1941-1962

1963-19691970-1977

1978-1989

1989-2002

Seismic code period
Figure 12: Ultimate acceleration according to seismic code period

Study on seismic design characteristics of existing buildings in Bucharest, Romania31

3. EVOLUTION OF THE REINFORCED CONCRETE DESIGN CODES
3.1. German Recommendations (1950)
The design codes for reinforced concrete structures appeared in Romania
since 1932. These recommendations were not enforced as design codes but
designers used them as technical regulations. The first rules that were used in
Romania were translated from the German book “Beton Kalender”. The most known
translation belongs to the professor M. D. Hangan (1932)[1].
The principles of the method are presented in the following paragraphs.
3.1.1. Reinforced concrete beam subjected to pure bending: Generalities [2]Under small loads the beam is in the behavior stage 1, defined by the fact that wholeconcrete section is active in taken the exterior efforts. The concrete from the tension
zone take the great part of the tension stresses. The tension reinforcement is as
small acted as the width of the beam increases. The greatest tension stresses in theconcrete are smaller than the concrete tensile ultimate stresses, leading to no cracks
in the beam.
As the exterior loads on the beam are raising, the tensile stresses in the concrete
are greater than the concrete ultimate tensile stress and cracks appears in the regionof the largest bending moment. The cracks are perpendicular to the direction ofprincipal stress. The beam is in behavior stage II meaning that the tensile stresses
are taken by the tension reinforcement while the tension concrete zone haspractically no static influence on the behavior of the beam.
The further increasing in the exterior loads leads to reaching of the ultimate strain in
the tensile reinforcement and then to beam failure.
In the behavior stage I the neutral axis is in the lowest position while in the behavior
stage III the neutral axis is in upper position.
The computation models generally used are assuming the behavior stage II – withcracked tension concrete zone and are based on the following simplified
assumptions:a) the plane section remain plane after the bendingb) Hook’s low “the stresses are proportional to strains” is applied to steel as well as
to concrete from compressed zone. The elasticity modules used are:⎧ E a = 2100000kg / cm 2⎪2
⎨ Eb = 140000kg / cm
⎪n = E / E = 15.
ab⎩c) The tension stresses are taken only by the tension reinforcement. The tensilezone of the concrete is considered as not-subjected to stresses and the concrete
situated under the neutral axis is considered as unsolicited.

Study on seismic design characteristics of existing buildings in Bucharest, Romania

32

Figure 13: Simple reinforced concrete section

In order to establish the stresses the following equations are used (see Figure 13):
From hypothesis a and b it results:

1⋅ σ a : σ b = (h − x ) : xnσ a = nσ b⋅ ⋅1
⋅ σ 'a : σ b = ( x − h ') : x
n

h−x
x

σ 'a = nσ b⋅ ⋅x = h⋅

x − h'xnσ b= αhnσ b + σ a

If we denote by Cb the sum of all the compression stresses in the concrete,
Ca the sum of the compression stresses of the steel reinforcement the resultant of
Cb and Ca is C. Let’s denote by T the sum of all tensile stresses in thereinforcement. In order to have an equilibrium in the section we can write:
Cb+Ca-T=0 or C=T
The forces C and T represents the force couple with internal level arm z. This
couple should be in equilibrium with the exterior bending moment M: so
M=Cz=Tz
The above equations are sufficient to determine the stresses σ b , σ a andσ 'a when the external bending moment M and beam dimensions are known.
3.1.2. Reinforced concrete beam subjected to pure bending: dimensioning
We will consider only the case of the rectangular shape beam.

Figure 14: Simple reinforced concrete section

Study on seismic design characteristics of existing buildings in Bucharest, Romania33

If we choose the stresses σ b and σ a the neutral axis position results from theequation x = αh . The internal level arm (for triangular distribution of compression
stresses) of the interior forces is:1
z = h − ⋅ x = β ⋅h,3and the sum of the compression stresses:

Cb =

1
ασ
⋅ σ b xbo = bo h ⋅ b22

The sum of the tensile stresses is: T = Ω ao ⋅ σ a
Because Cb =T we get: Ω ao =

2σ a
bo h
where k =kασ bFrom the moment equation we can obtain:

Mo =Effective height is h = r

bo h 2
r2

ασ b

⋅ βh

or

where r 2 =2

M o = Cb ⋅ z = bo h ⋅

2

αβσ b

Mo
bo

3.1.3. Reinforced concrete columns subjected to bending with axial force:
Generalities
Lets consider the case of an exterior axial force N acting in the axis of the column
and a bending moment Mm with respect to the same column axis. We can replace
the two efforts by only one exterior force N applied eccentrically at the distanceem=Mm:N. em is considered from the column axis to the compressed zone of thesection if it is compression and to the tension zone of the section if it is a tensile
force. The eccentrically force N with the eccentricity em should be in equilibrium withthe resultant of the interior forces Ri, so N should be equally and opposite sign to Ri.
If consider the values of Mm and N we can have to distinct casesa) if N is a compression or tension force, the whole section will be acting in the
behavior stage 1 with the whole section compressed so that there will be no cracks.
If the exterior force N is N is a tension force the active section will be only the part in
between the two reinforcement layers. Because Ωa and Ω’a are tensioned, N should
remain in equilibrium with the two tension forces.
This method can be applied as long as em ≤c
. The concrete is in the behavior stage
2

II.
In the German codes of practice translated into Romanian the computation of thecolumns subjected to bending with axial force in case I is made by the aid of thetables.
Study on seismic design characteristics of existing buildings in Bucharest, Romania

34

Let’s consider the case of a concrete column subjected to bending and axial force
with small eccentricity.

Figure 15: Concrete section subjected bending and axial force with small eccentricityb=is the width of the concrete sectiond=is the height of the concrete sectionΩa=αbd- is the tension reinforcement in cm2Ω’a=α’bd- is the compressed reinforcement in cm2ΩI=bd(1+15α+15 α’)= bd:γ is the ideal concrete section in cm2

Wo=bd2:δo is the resistance modulus for σoWu=bd2:δo is the resistance modulus for σuem=the eccentricity of the axial forsm=βd=the displacement of the gravity center from the middle section

In order to compute the extreme fiber stresses, σo and σu we have to compute first
the quantities:

ψ o = γ − βδ o ψ u = γ + βδ u γ =1
1 + 15α + 15α 'and we obtain for the case of asymmetric reinforcement.

σo = −N ⎛eδ ⎞⎜ψ o + m o ⎟
bd ⎝
d ⎠

σu = −N ⎛eδ ⎞⎜ψ u − m u ⎟
bd ⎝
d ⎠

or in the case of symmetrical reinforcement:

σ o respective σ u = −N ⎛eδ⎞⎜ψ ± m ⎟ .
bd ⎝
d ⎠

1
The above equations should be used only when σ u ≤ − σ o . The maximum value of2
the eccentricity for this limit case is emax=εd.
The asymmetric reinforcement pattern is recommended if the resultant of the exterior
forces is always acting on the same side of the section. For economy reasons it isStudy on seismic design characteristics of existing buildings in Bucharest, Romania

35

recommended to use a 0.3% reinforcement ratio for the tension side so that
α=0.003.
The symmetric reinforcement (Ω’a=Ωa) if the resultant of the exterior forces may fallon one side or the other side of the section.

b) The case of the column subjected to axial force and bending moment with great
eccentricity.
em = M m : N
This case is applicable when the exterior longitudinal forces is acting outside thecentral core of the section, for compressed rectangular sections when em ≥ εd (εgiven in tables with values between 0.310 and 0.448 depending on the reinforcementcpercentage) and when ε ≥ for tensioned rectangular sections:2
Sign rule:the bending moments are taken without sign
the axial force N is positive when it is a compression force

the axial force N is negative when it is tension force, so thatem and eu will be positive for compression and negative for tension.
The position of the axial force will be in the compressed zone for thecompression exterior effort and in tensioned zone for the tensile exterior effort.

em = M m : N

eu = em + u

The equilibrium equations:

Ca + Cb − T − N = 0
Neu + Ca c − Cbυ = 0
We will call “replacement bending moment” the always-positive bending
moment of the exterior force N with respect to the tension zone reinforcement.

M u = Neu = N (em + u ) = M m + N u
M u = Ca c + Cbυ
We can observe that the compressed zone of member subjected to bending
and axial compression behaves like it is subjected to pure bending with a bending
moment equal to Mu. The general dimensioning method for members subjected toaxial compression with great eccentricity em is to consider the member under purebending, to compute the reinforcement area and the to reduce the reinforcement
amount with N : σ a so that the tensile reinforcement will be:Ω a = Ω au −N

σaAccording to the previous equation we have to reduce the reinforcement
amount for compression case and to increase it for tension case, according to thesign of the exterior force N.

Study on seismic design characteristics of existing buildings in Bucharest, Romania

36c) the case of the rectangular section used totally.
We choose the width bo and the stresses σb and σa and we are interested in theeffective height h and reinforcement amount Ωa.
Because in the expression for Mu the effective height it should be introduced byapproximation with h = r M u : bo . Usually Mu should be modified and then the valueof h is recalculated and the reinforcement area determined by the formula:Ωa =bo h N−. The coefficients k and r are given in tables.
k σad) Rectangular section, simple reinforced partially used:
We choose the dimensions bo, h and steel stress and we are interested in thecompression strength and steel reinforcement amount.

Figure 16: Rectangular section, single reinforced partially used

If M u < (bo h 2 : r 2 ) the compression stress cannot be fully used, so we have to findr 2 = bo h 2 : M u and then choose from tables σb and k corresponding to r2 in order tobh N.
apply the equation Ω a = o −k σae) Double reinforced rectangular section:
We choose the dimensions bo, g, c and allowable stresses σb and σa and we areinterested in the reinforcement amount Ωa and Ω’a.

Figure 17: Double reinforced rectangular section

Study on seismic design characteristics of existing buildings in Bucharest, Romania

37

Usually the whole allowable stresses σb and σa are used. The compressedb h2
reinforcement is needed only when M u > o 2 . In order to solve the problem werhave to find in table the values for k, r2, and σa’ corresponding to σb and σa.
The unbalanced bending moment:b h2∆M = M u − o 2r

The tension reinforcement amount:Ωa =The compressed reinforcement amount: Ω'a =bo h ∆M N+−kcσ a σ a
∆M
.
cσ 'a

3.1.4. Shear stresses:
In any beam subjected to bending will appear, in the plane of neutral axis and inplanes parallel to it sliding (shear) stresses. If we consider a prism like in the next
figure for the horizontal plane as for the vertical plane there is force aτ o . The
resultant of these forces has the value aτ o 2 and the direction of the 45o. The
inclined stresses should be taken into account for the sliding assurance, without
concrete aid, by means of stirrups or bent-up bars or both.

Figure 18: Principal stresses

Dimensioning of the reinforcement for shear efforts:
The inclined tension T45 is the resultant of the tensions in the 45o inclined surfacesof total length s = a ⋅ cos 45o . Because σ s = τ o we have:

T45 = sboσ s = a ⋅ cos 450 boτ o .
The sliding stress is: H = aboτ o so T45 = H ⋅ cos 45o .
The relation between the reinforcement area and the shear force is:

T45

σa

=

H cos 45oσa

= Ω a 45 + Ω s ⋅ cos 45

Study on seismic design characteristics of existing buildings in Bucharest, Romania38H = 2σ a Ω a 45 + σ a Ω s = L45 + Ls

Figure 19: Shear force decomposition

The bent-up bars undertake the L45 force of the sliding total force while theother part is taken by the stirrups (Ls).
In order to simplify the computation in the Romanian version of the German
recommendations there are some tables.

L45 = 1.414σ a ⋅ Ω a 45
LS = σ a Ω S = 2 fσ a
The bent-up bars undertake on the length ν the following efforts:
The bending moment:∆M 45 = L45 ⋅ z

The shear force:

V45 =The shear stress:

τ 45 =

L45 ⋅ z

υ

L45
boυ

And the stirrups with two braces, with a spacing equal to e and area 2f on the lengthν.

The bending moment:∆M s = Ls ⋅ z

The shear force:Vs =Ls ⋅ zυLs
2 fσ a=boυ
bo e
The distribution of the stirrups and bent-up bars should be made in such a way thatthey undertake in any position along the beam the same efforts.

The shear stress:τs =Study on seismic design characteristics of existing buildings in Bucharest, Romania

39

Figure 20: Reinforcement detailing provision

3.2. STAS 1546-50 [3]The first Romanian reinforced concrete design standard appeared in 1950. It was
influenced by the Russian standards and in Romanian is known as a standard with“unique safety coefficient”. It contained the characteristics of the material used,(concrete and steel), basic computation principles with the unique safety coefficients,
constructive provisions and computation methods.
The concrete was characterized by the concrete mark that was the mean
compression strength in kg/cm2 of concrete cubes with edge of 20cm at the age of
28 days.
Table 26: The design values for different concrete
CONCRETE MARKACTION
90

110

140

170

200

250

300

400

500

600

Axial
compression

72

88

108

125

145

175

200

260

310

350

Axial tension

10

11

13

15

17

20

23

27

31

35

Compression
by bending

90

110

135

155

180

220

250

325

390

440

The steel-yielding limit:
For tensioned or compressed reinforcement made of OL38:……2850 kg/cm2
For tensioned or compressed reinforcement made of OL52:……3500 kg/cm2.
Basic design rules:
The values for safety coefficients used are given in the following table:

Study on seismic design characteristics of existing buildings in Bucharest, Romania

40

Table 27: The values for safety coefficients
FAILURE MODES

LOADS

Qu
Qg

The concrete reach thecompression allowable stress or
the reinforcement reach theyielding limit
Columns,archessupports

Other elements

The concrete
reach its
tensileallowable
stressesc
Fundamental
loads

<2

Fundamental
and accidental
loads

<2

Fundamental
accidental andextraordinary
loads

c1

2,0
2,2

1,8
2,0

2,2
2,4

>2

1,8
2,0

1,6
1,8

2,0
2,2

any

1,6

1,5

1,8

>2

3.2.1. The computation of the rectangular section elements under purebending:

Figure 21: Simple rectangular section under pure bendingx⎞⎛cM = Ribx⎜ h − ⎟2⎠⎝Af σ c = Ribx
with the limitation of the height of the compressed zonex ≤ 0.5ho
and of the maximum reinforcement percentage:µ ≤ 0.5Ri

σcStudy on seismic design characteristics of existing buildings in Bucharest, Romania

41

3.2.2. The computation to shear force of the concrete beams:
In the case of the beams, no matter the computation results if there is nocompressed reinforcement, we have to provide stirrups at the maximum spacing ¾ h
or 50 cm (h-beam height). For the case of the beams with compressed reinforcement
taken into consideration in the computation process, the maximum stirrups spacing
will be 15 times the compressed reinforcement diameter. The stirrups will be closed
and we have to provide supplementary reinforcement so that at least one from two
reinforcement bars to be in the stirrups corner.
The shear stress of the stirrups can be computed by the formula:σ etr . =Aeσ c nabc

Ae - stirrup brace arean - number of stirrup braces (sections)a - stirrup spacingb - beam width or web width for T shape beam.

Figure 22: Computation to shear force

3.2.3. Computation of the eccentric compressed members:
According to Romanian standard from 1950 we may have two cases:
Case I of eccentric compression:x ≤ 0.55hox⎞⎛cNe = Ribx⎜ ho − ⎟ + A' f σ c (h − a')2⎠⎝cN = Ribx − ( A f − A' f )σ cwith the restriction x ≥ 2a 'Study on seismic design characteristics of existing buildings in Bucharest, Romania

42Figure 23: Eccentric compressed reinforced concrete member

Case IIx ≥ 0.55ho
cNe = 0.5 R pr bho2 + A' f σ c (ho − a ')cNe' = 0.5 R pr bh'o2 + A f σ c (ho − a )3.3. STAS 10107-0/90 [4]The actual code of practice for reinforced concrete is in force since 1990. Before thisit was another version (P8000) with few minor differences. The main difference in
STAS 10107-90 is the fact that it deals with concrete class and no with concrete
mark. The mark is the medium strength of the concrete while the class is thestrength with an non-exceedance probability of 5%.
Table 28: Concrete characteristics according to concrete classConcrete
class

Bc7.
5

Bc10

Bc15

Bc20

Bc25

Bc30

Bc35

Bc40

Bc40

Bc50

Tensilestrength(N/mm2)

0.50

0.60

0.80

0.95

1.10

1.25

1.35

1.45

1.65

1.85

Designstrength(N/mm2)

4.7

6.5

9.5

12.5

15.0

18.0

20.5

22.5

26.5

31.5

14

21

24

27

30

32.5

34.5

36

38

40

Elasticity
modulus(kN/mm2)

Study on seismic design characteristics of existing buildings in Bucharest, Romania

43

Table 29: Reinforcement characteristics according to steel type
Steel Type

Diameter (mm)Design strength (N/mm2)

PC60

6….40

350

6….28

300

32…40

290

6….40

210

PC52
OB37

The main requirements for reinforced concrete columns detailing are:For longitudinal reinforcement:•

For efficient confinement in end regions, column bars should be reasonably
closely spaced around the periphery. Bars should not be farther apart than
200mm center to center;•

Minimum bar diameters – 12mm for PC60 or PC52;•

Maximal recommended diameters – 28mm;•

Minimum distance between bar - 50mm;•

Maximum distance between bars axes – 250mm;•

4 cornered bars reinforcement is admitted just for columns with b ≤ 350mm•

Reinforcement ratio should be less than 2.5%.

For transversal reinforcement:•

Maximum distance between stirrups ae = 15d ≤ 200mm (d – is the minimal
diameter of longitudinal reinforcement•

Maximum distances between stirrups along the height of the column on the hinge⎧ae ≤ 6d⎪region should be considered ⎨ae ≤ h5⎪⎩ae ≥ 100mm•

lp The height of hinge region should be considered the maximum value between⎧l ≥ H column
6⎪p⎪⎨l p ≥ h⎪⎪⎩l p ≥ 600mm•

Minimal diameter of stirrups is considered 1 from the maximal diameter of
4longitudinal reinforcement but no less than 8mm.

A short time after the apparition of the standard a guide book [8] was publishedhaving the same authors as the standard. This book is very used in common design
because it has algorithms for every important problems that may appear.

Study on seismic design characteristics of existing buildings in Bucharest, Romania

44

The most important algorithms are inserted below with the following notations:
b
h
Aa
Aa’
Ae
ae
Rc
Ra
Rt
Mcap
N

section width
section heighttensioned reinforcement area
compressed reinforcement area
stirrup brace reinforcement area
stirrups spacing
concrete compressive design strength
reinforcement design strength
concrete tensile design strength
section capable bending moment
axial force in column

Q

shear force in beam/column.

Study on seismic design characteristics of existing buildings in Bucharest, Romania

45

1.Compute the distance “a" between therebar center and section edge

2. ho = h − a

3. p =

Aa100(%)bho

4. ξ =

p Ra⋅
100 Rc⎧0.60 _ forOB37
5. ξ b = ⎨⎩0.55 _ forPC 52, PC 60

6.
ξ ≤ ξbNO⎧0.42 _ forOB37
9. mb = ⎨⎩0.40 _ forPC 52, PC 60

7. Compute⎛ ξ⎞
m = ξ ⎜1 − ⎟⎝ 2⎠

10. M cap = mb bho2 Rc(8)
8. M cap= mbho2 Rc

NO11.
p ≤ 0.1%

YES

13.
p ≥ 0.05%
12.The value of Mcap isthat computed at point 8

YES

No rebarconsidered.

(8 )M cap = 0.85M cap

Figure 24: Computation of the capable bending moment for a simple reinforced concrete section under purebending. We know b,h,Aa,Rc,Ra and we are interested in Mcap

Study on seismic design characteristics of existing buildings in Bucharest, Romania46

1. Compute the distance “a” between therebar center and section edge
3. ho = h − a2.
Is the section in a
potential plastic zone?

YES
4. ξ =

NOxN=
ho bho Rc⎧0.60 _ forOB37
5. ξ = ⎨⎩0.55 _ forPC 52, PC 60

NO6.
ξ ≤ ξb ?

YES
NO
8.

7.The concrete section is
insufficientfortheductility conditionξ ≤ 0.40 ?

9.The transversal reinforcement percentage
and the plastic potential zone length aremajored according to code provisions.

YES

10.Compute:
A R a
N
n=
;α= a a;bhRc
bh Rc h11.Extract m from guidetable no. 9.

12. M c = mbh 2 Rc

13. ea =h≥ 20mm30

14. M cap = M c − Nea
Figure 25: Computation of the bending capacity for a column section with eccentricity. We knowb,h,Rc,Ra,N,Aa=Aa’ and we are interested in Mcap

Study on seismic design characteristics of existing buildings in Bucharest, Romania

47

1.Compute the distance„a” between the rebar
center and section edge

2. ho = h − a

3. Q =YESQ
bho RtNO

4. For beams: Q ≤ 0,50 ?
For slabs:

Q ≤ 0.75 ?
6. Is the section
in a plastic
potential zone ?

5. For beams it is notnecessary
thecomputation of the 7. Q ≤ 1 ?
stirrups. There are
used
only
the
constructive
provisions. For slabs
there is no need oftransversal
YES
reinforcement

NO

3−Q
2

8. m s =9. Rt (red ) = m s Rt

10. Q =

Q
bho m s Rt
11. Q ≤ 4 ?

12.

YES

NO

25. Increase the member crosssection so that Q ≤ 4 ?

Study on seismic design characteristics of existing buildings in Bucharest, Romania48

7.
12. p =

13. p e =14.

Aa ( m )
bho

11.

100%

2

Rt (red )100%
3 .2 p R a
Q

100 p Rt (red )
si
=
⋅
ho
pe
0 .8 R as
15. i ≤ 2.5 ?
ho

YES

⎛
p⎞
⎜Q −
⎟50 Rt (red )
⎜
⎟
2
.
5
⎠
17. p e = ⎝Ra(corresponding to s i ho = 2.5 )NO

16. pe computed at
13 is good
18. p e ≥ 0.1% ?

NO
YES
19.Consider
p e = 0.1%

20.Choose
Ae or ae ?

Choose ae

Choose Ae

21.

100ne Aeae ≤pe b
22.Establishae ≤ ae (max) considering
constructive provisions

23.Chooseae ≤ ae (max) considering
constructive provisions

24. Ae ≥a e pe b
100ne

Figure 26: Computation of the stirrups for an element without axial force: We know b,h,Rt,Ra,Q,Aa and weare interested in Ae, ae.

Study on seismic design characteristics of existing buildings in Bucharest, Romania

49

1.Compute the distance„a” between the rebar
center and section edge

2. ho = h − a

3.Compute the shear force corresponding to the failure
mechanism, considering the capable bending moment at
each column end or only at one end and at the other end thecorresponding bending moment

4.Compute 1.5Qs and

YESNO

6. Q ≤

Qs

ψ

ψ
NO

Q ≥ 1.5Qs ?
YES?

8. Consider Q = 1.5Q s
9. n =

7.Consider Q =

Qs

N
bhRc

Qs

ψ

10. R ' t = Rt (1 + 0,5n )11. Q =

YES

13.

Q
bho Rt12. Q ≤ 0,50 ?

NO

14.

Study on seismic design characteristics of existing buildings in Bucharest, Romania

50

1.

12

YES
13.There is noneedtocomputestirrups. Thereareusedconstructive
provisions

15. p =

16. p e =

17.

YES
19.

si
≤ 2 .5 ?
ho

Aa ( m )bho

14. Q ≤ 2

NO100%

32. Increase themembercross
section or theconcrete class sothat Q ≤ 2

2

R't
100%
3 .2 p R a
Q

100 p R ' tsi=ho
p e 0 .8 R al
18. o ≥ 2,5 ?
ho

NO

20.

NO
YES

22.Pe computed at 16
is good

21.
⎛
p⎞
⎜Q −
⎟50
⎜
⎟
2
.
5
⎝
⎠
pe =
Ra

(corresponding tos i / ho = 2.5 )s i lo
≤ ?
ho ho

NO

23.

YES

⎛
p ⎞
⎜Q −
⎟50 Rt
⎜
⎟
l
h
/
o
o ⎠
⎝
pe =
Ra
corresponding tosi / ho = lo / ho

24.Establishtheminimumtransversal
reinforcement
percentage according to codeii
25. pe (21,22,23) ≥ pe (min 24) ?

YES

NO

27.Choose
Ae or ae ?

26.Consider pe = pe (min 24)
Choose Ae

100ne Ae
28. ae ≤pe b
29.Establish ae ≤ ae (max) considering
constructive provisions

Choose ae

30.Chooseae ≤ ae (max) considering
constructive provisions

31. Ae ≥ae pe b100ne

Figure 27: Computation of the stirrups for an element with axial force: We know b,h,Rt,Ra,N,Q,Aa and we areinterested in Ae, ae.
Study on seismic design characteristics of existing buildings in Bucharest, Romania

51

4. THE EVOLUTION OF THE MASONRY STRUCTURES DESIGN CODESThe only recommendations that existed before 1975 were in the form of a table withthe masonry wall thickness for different types buildings, assumption based on a
maximum allowable soil pressure of 2.5kg/cm2.
Table 30: Masonry wall width according to storey and other considerations [5]Interiorwalls
with
openings
supporting
floor beams

High
wall
without
openings but supporting
floor beams

Staircase walls

Exteriorwalls
with
openings
supporting
floor beams

Interiorwalls
with
openings
supporting
floor beams

High
wall
without
openings but supporting
floor beams

Staircase walls

Basement
Ground floor
1st story
2nd story
3rd story
4th story
Attic

INDUSTRIAL BUILDINGS

Exteriorwalls
with
openings
supporting
floor beams

STOREY NAMERESIDENTIAL BUILDINGS

0.84
0.70
0.56
0.56
0.42
0.42
0.42

0.56
0.56
0.42
0.42
0.42
0.42

0.70
0.56
0.56
0.42
0.42
0.42
0.28

0.42
0.42
0.42
0.28
0.28
0.28
0.28

0.98
0.84
0.70
0.56
0.56
0.42
0.42

0.70
0.56
0.56
0.42
0.42
0.42

0.84
0.70
0.56
0.56
0.42
0.42
0.28

0.56
0.42
0.42
0.42
0.28
0.28
0.28

The actual code of practice for masonry structure design is in force from 1985 [7]andis a revision of the code published in 1975[6].
The assumptions for the computations are:•

The floors are considered infinitely rigid in order to be able to consider the loads
redistribution, after an element or other elements have reach the ultimate bearing
capacity and works in post elastic range.

•

By load redistribution the elements with strength reserves are also loaded•

The differences between the real behavior and design behavior are corrected bya working conditions coefficient•

The immersed reinforced concrete elements works together with masonry andalso affects its strength by a working condition mz=0.85 base of the materials
different stiffness.

•

For walls with openings for doors and windows the favorable spandrel effect istaken into account supposing the section with zero bending moment due tohorizontal loads in the middle of the spandrel.

Study on seismic design characteristics of existing buildings in Bucharest, Romania

52Modeling:
Each element out of the spatial structure is considered a vertical cantilever, fixed at
the bottom, load with horizontal forces, and connected at each floor.
The plane dimensions of the structural masonry walls are established on eachprincipal dimension, taking into consideration the active width for T and L section
flange.
The horizontal connection can be pinned connection (for slabs without spandrelbeam) ar fixed connection for spandrel beam.
The basic relation:
The computation for capacity design of the structure is made with the aid of thefollowing formula:
k= j

i =t

k =n

i =1

η ∑ sk ≤ m∑ Tcij

where:

Sk

horizontal seismic force al story k;

Tcijminimum shear force capacity of structural wall I at story j; (min(TCM, Tcf, Tcp))

ηload coefficient that takes into account the torsion effectmworking condition coefficient according to the following tablennumber of storiest

total number of structural walls on the design considered direction
Table 31: The values of the working coefficient m

SEISMIC ACTIONSLAB TYPE

RATIO

B( width)
L(length)m COEFFICIENT

Longitudinal
direction

Cast in place, precast

B≤L

0,8

Transversal
direction

Cast in place, or
equivalently precast> 0,200,8Panels connected,
overcast in place strips≤ 0,200,8Precast panels made ofnarrow strips≤ 0,20

0,65

0.25

0,67

0,30

0,68

0,35

0,70

0,40

0,72

0,45

0,73

0,50

0,75

The shear capacity for eccentric compression for masonry structural walls without
considering the spandrel beam effect is:

Study on seismic design characteristics of existing buildings in Bucharest, Romania53•For simple masonry:

TCM =
TCM

M c Neo 1.25RSc
=
=
Z
Z
Z

shear capacity of the masonry structural wall “i” at story k.

MCbending capacity of the structural masonry structural wall at the consideredstoryNmaximum axial load for the masonry structural wall at the considered storyZvertical distance from the design section to the application point of thehorizontal seismic force above considered story
Rmasonry compression strengthScstatic moment of the compressed zone with respect to the axis that cross thesection centroid.

Sc = Ac eo
Ac =•For confined masonry with concrete columns

TCM =
Rb

N
1,25 R

Mc 1= (Rb Sb + RS z − NYN ) where:ZZ

concrete compressive strengthSbstatic moment of the concrete compressed zone with respect to the centroidof tensioned reinforcementSz

the same, for the compressed masonry

distance between the centroid of the tensioned reinforcement to the axis that
YN
passes through the application point of the gravity force N.

Ac = Az + Ab
Az =N + Aa Ra − Ab Rb; S z = AzYz ; Sb = AbYb
R

The shear capacity considering sliding of the masonry in horizontal joints iscomputed with the aid of the following formula:•

For rectangular sections with simple masonry:
If eo =TCM N 1b⋅l
(R f + 0.7 fσ o )≤ l then Tef =N
1.5
6

If eo =

0.7 fNTCM N 1> l then Tef =where:
N
6
1.5

b⋅l

wall section area

Rfshear design masonry strength

Study on seismic design characteristics of existing buildings in Bucharest, Romania54

ffriction coefficientσomean compression stress σ o =•NAFor rectangular sections with reinforced masonry:
Tef = 0,5 f ( N + Aa Ra ) + (∑ Aai − Aa )Ra where:

Aai sum of the vertical bars area from all the columns in the considered wall
Aa sum of the vertical bars area from the tensioned side column
R a reinforcement design strength
The computation is done considering the both cases, reinforced and simple
masonry and from these cases the biggest value should be considered.
The shear capacity of the structural masonry wall considering tensile stresses in the
wall:

•

For rectangular sections with simple masonry

Tcp =Rp ⋅ b ⋅ lµi

1 + 0,8Φ

σoRp

R p the design tensile strength of the masonry obtained by multiplying thestandard value with a coefficient m = 1.2 when it is subjected to seismic action

Φ the multiplying coefficient that depends on relative eccentricity l / eo .
Table 32: The values of Φ according to relative eccentricity

RELATIVE ECCENTRICITY

l
eo

Φ

≥6

6≥

1
⎛ l
⎞
− 1⎟⎟
2⎜⎜
⎝ 4eo
⎠

l
≥4
eo
≤4

where

•

0

l
N
=
eo TCP ⋅ Z

For reinforced masonry when the tensile stress is taken by the masonry wall wehave to replace the mean axial stress σ o with the formula:σo =Nand µi with
Rb
Az +
Ab
R

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55

µi =

Sid
⋅ li where Sid and I id are the characteristics
I idof the equivalent masonry section.

•

For reinforced masonry when the tensile stresses are not taken by the masonrywall because it is cracked and the whole tensile stress should be taken by thegirder beam reinforcement and joint reinforcement the formulas are:For girder beam and joint reinforcement:

TCP =2 Aac Raµi⋅li
> TCP for simple masonry.
het

For column reinforcement:
TCP =2∑ Aas Ra liµi∑l> TCP for simple masonry where:1

Aac
the reinforcement area from girder beam designed to undertake only seismic
action and the total reinforcement area from masonry joints.

∑ A the reinforcement area from column from the interior of the wall (not end
ascolumn reinforcement)∑lisum of the afferent walls length corresponding to column

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56

5. SHORT DESCRIPTION OF THE ATTACHED BUILDINGS PLANS:
5.1. Reinforced concrete structures
5.1.1. RC moment resisting frame structure built in 1963: RC S1This building was efected in the year 1963 in Constanta. This building has been
considered because at the design time there were no differences in design forbuildings build in different regions. The only rule used for designing to earthquake
action was to consider a base shear coefficient equal to 0.05. The destination of thebuilding was a hospital and nowadays it is still functioning as a hospital. The
Romanian engineers are trying at this moment to retrofit this building. The mostimportant problem that can be seen if you analyze the plans is that of the shortanchorage length and the good point for this building is the regular shape of it. The
masonry partition walls are anchored using 6 mm diameter reinforcement.
5.1.2. RC moment resisting frame structure RC S2This building was designed in the year 2000 according to the provisions of the
Romanian seismic code of practice P100/92 and Romanian reinforced concrete
design standard 10107/0-90. At the ground floor the building can be enclosed by arectangle with dimensions 17,20x14,20. The elevation of the building is made of six
levels, namely basement, ground floor and other four stories. The story height issituated in between 2,775 to 4,75 with the most common value of 3,15m. The spaceplanning of the building allows it to be used as a first destination as office andapartment building.
The structural system is made of reinforced concrete frames, on the two orthogonal
directions. The partition walls were not considered as structural walls. The slabs andthe stairs are made of cast in place reinforced concrete.
The foundation system is made of a reinforced mat foundation and of shallow
continuous foundation under basement extension. The mat foundation is cast inplace over a layer of 15 cm thickness of compacted gravel and of 10 cm of plain
concrete slab. The basement walls are made of cast in place reinforced concrete.
The allowable soil pressure given in the geotechnical study has the values of 250kPa
for short action loads.
The exterior (closure) walls 25cm width are made of bricks with vertical holes ofwhile the interior (partition) walls has 12.5 or 25 cm width.
The designer guaranties the maximum story drift of 3.5%o.

5.2. Masonry structures
5.2.1. Masonry structure - M S1
The building is the headquarter of the Ministry of Agriculture. It was built in between
1884 and 1887. It is a great building with great spans and higher story heights. The
plane shape is a U-shape, one of the side wing extending behind the central zone.

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57

The plane dimensions of these zones are of 47.00x17.80m for central zone,
50.00x13.00m for one wing and 65.00x16.00 for the other wing.
The height regime is basement, ground floor, two stories and attic. The different
story heights that varies from 3.50m at the basement to5.5m (maximum story height)
for the ground floor.
The structural system is made of masonry structural walls, with floor made of steel
beams and masonry domes or concrete at inferior profile flange and ribbon-iron ties.

Figure 28: View of the main façade of the M S1 building, “Central” wing

Figure 29: View of the main façade of the M S1 building, “Slaninc” wing

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Figure 30: View of the main façade of the M S1 building, “Bratianu” wing

5.2.2. Masonry structure - M S2This building will be built this year in Bucharest. It is a residential one family building
and it is design according to the actual codes of practice. The elevation of thebuilding is made of four stories, namely partial basement, ground floor and twostories. The plans that we provide you are not the final plans because it might be few
minor changes because of the architectural solution. The partition walls andenclosure walls are connected with the main structural elements according to codeprovisions. The story height is around 3 meters. The slabs are made of reinforced
concrete. The basement walls are made of cast in place reinforced concrete. The
foundation system is made of continuous foundation under partial basement andunder ground floor walls.
Because the designer does not want to take chances, and because the Romanian
masonry structures design codes is in force since 1985 when the capacity design
was not well known, the design choose to increase the column section so that it
becomes a strong column, weak beam system.
ACKNOWLEDGMENTS:
The authors are greatly indebt to Mr. Eng. Mircea MIRONESCU for providing them theplans for building M S1 and to Ms. Eng Serban ALTENLIU for providing the plans for thebuilding RC2.

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Figure 31: Rendered image of the M S2 building (main façade)Figure 32: Rendered image of the M S2 building (side view)

Study on seismic design characteristics of existing buildings in Bucharest, Romania

60References:
1. Hangan M.D. German Commission for reinforced concrete recommendations, (inRomanian translated from German by Hangan M.D.)
2. Niculescu C., Workbook for reinforced concrete, translated in Romanian from
Beton-Kalender, AGIR 1947
3. STAS 1546-50, Civil and Industrial Buildings. Design of reinforced concreteelements. Provisions. (in Romanian)
4. STAS 1017/0-90, Civil and Industrial Buildings. Design and detailing of concrete,
reinforced concrete and prestressed concrete structural members (in Romanian)
5. Asquini V.,Technical indicators for buildings, Ed. Cartea Romaneasca 1938, (inRomanian)
6. P2-75 Code of practice for the detailing and design of masonry structures (inRomanian)
7. P2-85 Code of practice for the detailing and design of masonry structures (inRomanian)
8. Agent R., Dumitrescu D., Postelnicu T., Guide for the design of the structural
reinforced concrete elements, (in Romanian), Editura Tehnica 1992

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