Response Spectrum Analysis of Reinforced Concrete Buildings

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O R I G I N A L C O N TR I B U T I O N

Response Spectrum Analysis of Reinforced Concrete Buildings

N. R. Chandak

Received: 22 March 2012/ Accepted: 4 July 2012 / Published online: 29 August 2012 The Institution of Engineers (India) 2012

Abstract In this work, a parametric study on reinforced

concrete (RC) structural walls and moment resisting framesbuilding representative of structural types using response

spectrum method is carried out. Here, the design spectra

recommended by Indian Standard Code [1] and two other

well known codes (Uniform Building Code, Euro Code 8)

have been considered for comparison. The main objective of

this study is to investigate the differences caused by the use

of different codes in the dynamic analysis of multistoried

RC building. Three different floor plans that are symmetric

(SB), monosymmetric (MB), and unsymmetric (UB) with

torsional irregularity are taken as sample buildings. To

evaluate the seismic response of the buildings, elastic

analysis was performed by using response spectrum methodusing the computer program SAP2000. Periods, base shears,

lateral displacement and interstory drift, torque located at

code defined ground type are comparatively presented. It is

observed from the comparative study that the base shear

using IS code is higher in all the three buildings, when

compared to that of with other codes.

Keywords Response spectrum analysis IS1893 Euro code UBC Elastic analysis

NotationsAh Design horizontal acceleration spectrum valueS ag

Spectral acceleration coefficient

T Time in sec

R Response reduction factor

Ca, Cv Soil modified ground motion parametersS Soil factor

g Damping correction factor, its reference value is

g = 1 for 5 % viscous damping

W Seismic weight of building

Introduction

Earthquake codes are periodically revised and updated

depending on the improvements in the representation of ground motions, soils, and structures. Moreover, these

revisions have been made more frequently in recent years.

The Indian Standard Code [1] was also revised in 2001 and

has been in effect since 2002. This improvement was done

followed to destructive earthquake occurred in Bhuj

(Gujarat State, India) on 26th January, 2001 which resulted

in more than 19,000 recorded death and 1,66,000 injuries.

Preliminary indications are that 600,000 people were left

homeless, with 48,000 houses destroyed and an additional

844,000 damaged. The Indian State Department estimates

that the earthquake affected, directly or indirectly, 15.9

million people, nearly 50 % of the population of Gujarat.More than 20,000 cattle were reported killed. Government

estimates place direct economic losses at $1.3 billion,

although more recent estimates indicate losses may exceed

$5 billion. A number of separate teams from different

bodies conducted damage surveys and reported some

conclusions as briefly summarized below.

Early reports stressed that quality of construction were

poor and that there were many structural mistakes and

deficiencies due to the non-compliance with the earthquake

N. R. Chandak (&), Associate Member

Department of Civil Engineering, G.H. Raisoni Institute of Engineering & Management, Jalgaon 425002,Maharashtra, Indiae-mail: [email protected]

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J. Inst. Eng. India Ser. A (May–July 2012) 93(2):121–128

DOI 10.1007/s40030-012-0012-9



code. It was concluded that the nature of the strong-motion

was also a major contribution factor to the level of damage.

Under the light of observations and lessons from the

2001 earthquake and past earthquakes, many studies have

been carried out up to now and number of improvements

are made [1]. The influence of local ground conditions on

the seismic action is considered depending on the ground

types descried in the various codes considered in thepresent study. That is why the emphasis has been given on

the differences caused by the use of spectra given in IS

Code and other well known codes such as UBC and EC8 in

the seismic analysis of sample buildings.

The effect of ground types defined in the codes on the

seismic response of buildings was also investigated for

different building configurations and different supporting

soils. Base shear and interstory drift for considered ground

types and buildings are compared to reveal the differences.

Investigations have been performed earlier on the structural

responses of three typical Perth structures, a masonry

house, a low-rise building (reinforced concrete frame), and

a high-rise building (reinforced concrete frame with core

wall), on various rock and soil sites to earthquake ground

motions of different return periods using numerical

dynamic analysis [2].

Elastic, Inelastic Response and Design Spectra

Various seismological and geophysical parameters affectthe shape of response spectra. The researchers have pre-

sented and discussed the effects of earthquake magnitude,

source-to-site distance, site classification, and style-of

faulting on the strong-motion accelerograms and conse-

quently response spectra [3, 4]. As known, the damping

ratio and structural vibration period are other parameters

affecting the response spectra. The earthquake induced

ground shaking is generally represented in the form of

acceleration response spectra or displacement response

spectra. Acceleration response spectra in all current seismic

codes, the earthquake actions are represented in the form of

a spectrum of absolute acceleration. But code accelerationspectra tend to be conservative at longer periods with the

result that the long-period ordinates of the displacement

spectra are unnecessarily high [5]. Figure 1 shows typical

shape of elastic design spectra.

A typical shape of horizontal elastic design spectrum has

been given in Fig. 1, where T shows the periods of struc-

ture, SeA and SeB show the ordinate values at points A and

B of the elastic design spectra, TB and TC show the lower

and the upper limits of the period of the constant spectral

acceleration branch, and TD shows the value defining the

beginning of the constant displacement response range of

the spectrum.The ordinates of elastic design spectra Se and inelastic

design spectra Sd for the reference return period defined by

the earthquake codes can be determined using the expres-

sions given in Table 1. Figure 2 shows the normalized

elastic design spectra drawn for ground types described in

Period (s)

S

p e c t r a l a c c e l e r a t i o n

SeB

e

S A

B C

D

E

eA

S

TB CT TD T

Constant

accelerationConstant

velocityConstant

displacement

Fig. 1 Typical shape of elastic design spectra

Table 1 Ordinates of elastic and inelastic design spectra (Se and Sd ) for IS, UBC and EC8

Code T TB TB T TC T TC

IS* For hard soil

S ag ¼

1 þ 15T 0:00 T 0:10

2:50 0:10 T 0:401:00

T 0:40 T 4:00

8<:

For medium soil

S ag ¼

1 þ 15T 0:00 T 0:10

2:50 0:10 T 0:551:36

T 0:55 T 4:00

8<:

For soft soil

S ag ¼

1 þ 15T 0:00 T 0:10

2:50 0:10 T 0:6701:67

T 0:67 T 4:00

8<:

S d Rg

¼1 þ 15T 0:00 T 0:10

2:50 0:10 T 0:401:00

T 0:40 T 4:00

8<:

S d Rg

¼1 þ 15T 0:00 T 0:10

2:50 0:10 T 0:551:36

T 0:55 T 4:00

8<:

S d Rg

¼1 þ 15T 0:00 T 0:10

2:50 0:10 T 0:6701:67

T 0:67 T 4:00

8<:

UBC Se ¼ ½Ca þ ð1:5 Ca TÞ= TB g Se ¼ 2:5 Ca g Se ¼ Cv= T g

Sd ¼ ½Ca þ ð1:5 Ca TÞ= TB ggI=R Sd ¼ 2:5 Ca ggI=R Sd ¼ Cv= T ggI=R

EC8 Se ¼ ag S ½1 þ ðT =TBÞðg2:5 1Þ Sd ¼ 2:5=q ag S TC T TD ! Se ¼ 2:5ag S g TC =T ½

Sd ¼ ag S ½2=3 þ ðT =TBÞð2:5=q 2=3Þ TC T TD ! Sd ¼ ð2:5=qÞ:ag S TC =T ½

*IS code refers Se as Sa

122 J. Inst. Eng. India Ser. A (May–July 2012) 93(2):121–128

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IS code, UBC code, and EC 8 code. Same inelastic design

spectra can also be drawn for ground types described in IS

code, UBC code, and EC 8 code [6, 7]

The concept of dividing the elastic response spectra by a

single factor to arrive at the inelastic design spectra is a

practical one and has been adopted by most earthquake

codes. The factor used for reducing the elastic response

spectrum is called response reduction factor (R) in IS code,

behavior factor (q) in EC8, R coefficient in the UBC.

Earthquake codes describe different behavior factors.

The values of the maximum allowable behavior factor aretaken considering the type of structural system, regularity

in elevation and prevailing failure mode in the system with

wall in IS as well as in EC8.

Structural Data

Sample buildings described herein were selected as typical

six story reinforced concrete buildings. The buildings have

three different floor plans that are symmetric (SB),

monosymmetric (MB), and unsymmetric (UB). Six build-

ings are considered and they are henceforth referred to as;6-SB, 6-MB, 6-UB. The plan dimensions of buildings,

typical at all floors, are 22.7 m by 13.75 m, with a story

height of 3 m as shown in Fig. 3. The structural systems of

the buildings are selected as structural systems consisting

of structural walls and moment resisting frames in both

directions. It is assumed that the structural systems have

nominal ductility level. Seismic load reduction factor

(R) for special moment resisting frame is taken as 5

[referring Table 7 of IS 1983 (Part I)-2002].

Columns, beams, structural walls, and slabs are sized

considering the requirements given in IS code. The

dimensions of columns and structural walls for x and ydirections, the thickness of slabs, the width and height of

beams are given in Table 2. As seen from this table, the

cross-sections of columns have been changed after the 3rd

story for 6-story building. Flexural rigidities for longitu-

dinal and transverse directions are different for each

building. Total moments of inertia of vertical structural

elements can be determined using dimensions given in

Table 2 for x and y directions. It should be noted that

Fig. 3 Floor plan for six story building

Fig. 2 Elastic design spectra drawn for ground types described in IS,UBC, and EC8. (a) Response Spectra for different soils for 5 %damping (IS). (b) Elastic design spectra for UBC. (c) Elastic designspectra for EC8 (g were taken to be 1.0)

J. Inst. Eng. India Ser. A (May–July 2012) 93(2):121–128 123

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values used for rigidities are gross values and they are not

reduced to consider cracking. According to IS, torsional

irregularity occurs in buildings when floor diaphragms are

rigid in their own plane in relation to the vertical structural

elements that resist the lateral forces. Torsional irregularity

to be considered to exist when the maximum story drift,

computed with design eccentricity, at one end of the

structures transverse to an axis is more than 1.2 times theaverage of story drifts at the two ends of the structure. No

other structural irregularities occurred for sample

buildings.

Finite Element Modeling of Buildings and Analysis

Results

To evaluate the seismic response of the buildings, elastic

analyses were performed by the response spectrum method

using the computer program SAP2000 [8]. The seismic

analyses of the buildings are carried out separately in thelongitudinal and the transverse directions. However, seis-

mic responses only for x direction are comparatively pre-

sented with graphs and tables in this work for the sake of

brevity. Floor plan of six story building is shown in Fig. 3.

Sample finite element models of the six story buildings are

shown in Fig. 4. Degrees of freedom at the base nodes are

fixed, for other nodes are left free. Therefore, there is no

finite element model for subsoil to consider soil–structure

interaction. Columns and beams are modeled with frame

elements, slabs and structural walls are modeled with shellelements. Slabs also have been considered as a rigid dia-

phragm in each story level. The masses of infill walls are

also taken into account in the model. In the analysis,

Young’s modulus and unit weight of concrete are taken to

be 28,000 MPa and 25 kN/m3, respectively. The damping

ratio is assumed as 5 % in all modes. The reference peak

ground acceleration is taken to be 0.4 g that is recom-

mended in IS code and seismic zone 4 in UBC. Thus, it is

assumed that the buildings are sited in high seismicity

Fig. 4 The view of three-dimensional finite element models of sixstory building

Table 2 Dimensions of structural members for building considered for analysis

Buildings Structural members Six story buildings

1–3 stories 4–6 stories

bx (mm) by (mm) bx (mm) by (mm)

Symmetric buildings (6-SB) C1 600 600 500 500

C2 900 900 700 700W1, W2, W3, W4, W5 250 1,750 250 1,750

W3 3,000 250 3,000 250

Mono-symmetric buildings (6-MB) C1 600 600 500 500

C2 900 900 700 700

W1, W2 1,750 250 1,750 250

W3 3,000 250 3,000 250

W4, W5 250 1,750 250 1,750

Unsymmetric buildings (6-UB) C1 600 600 500 500

C2 900 900 700 700

W1 250 1750 250 1,750

W2, W3 3,000 250 3,000 250

W4, W5 250 1750 250 1,750Thickness of slab S 150

Beam size B 250 9 500


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zone. Seismic analysis of the buildings accounting for the

influence of the local ground conditions is carried out with

the help of the design spectra given in Fig. 2 for IS, UBC,

and EC 8.

Base Shear for the Analyzed Buildings

The base shear expressions defined in the codes are given

in Table 3. The base shears of the buildings were acquiredfrom seismic analysis using the design spectra corre-

sponding to 5 % critical damping and considering fixed

base condition. Seismic analysis of buildings were carried

out for three ground types defined in IS, out of five ground

types in UBC and in EC8 three ground types only con-

sidered which are similar to the ground type mentioned in

IS code for comparison. Therefore, nine ground types in

total are considered for the site. Figure 5 present the base

shears and maximum differences obtained for six story

buildings.

As seen from Fig. 5, IS code gives maximum base shear

for similar ground type defined in UBC and EC8.

Periods for the Analyzed Buildings

The mode numbers taken into account for six story build-

ings are 10. The first seven modes with periods and partic-

ipating mass ratios for the buildings are presented in

Table 4. As seen from this table, the fundamental periods

are in the range between 0.548 and 0.071 s. In the first mode

the 6-SB, vibrate dominantly in the x direction; whereas

6-MB and 6-UB vibrate in the y direction. The third mode

takes place as torsional modes for all buildings considered.

Base Shear for 6-SB Buildings

IS code gives maximum base shear for ground type III as

shown in Fig. 5a and maximum difference reaches to 24 %

between III and I. UBC gives maximum base shear for SD,

the maximum difference reached to 34 % between SD and

SA. Similarly EC 8 gives maximum base shear for ground

type E and maximum difference reaches to 31 % between

E and A.

Base Shear for 6-MB Buildings


shown in Fig. 5b and maximum difference reaches to 15 %

between III and I. UBC gives maximum base shear for SD,

the maximum difference reached to 63 % between SD and

III

III

SA A

SD EDSC

0

1000

2000

3000

4000

5000

Ground type

B a s e s h e a r ,

k N

B a s e s h e a r ,

k N

B a s e

s h e a r ,

k N

IS 1893 UBC-94 EC-8(b)

I

II

III

SA A

D

E

SC

SD

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

Ground type

IS 1893 UBC-94 EC-8(c)

I II

III

SA

SC

A

SD

D

E

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Ground type

IS 1893 UBC-94 EC-8(a)

Fig. 5 Base shear for 6-story buildings considering nine grounds typedefined in the codes. (a) For 6-SB building. (b) For 6-MB building.(c) For 6-UB building

Table 3 Base shear defined in the IS, UBC, and EC8 codes

Codes Base shear

IS V B ¼ Ah W , which is given by Z IS n2 Rg

UBCV s ¼ S d ðT Þ ¼

w

g

0:11C ac1:w

0:8 ZN vc1

R :wð for zone 4Þ

8><>:

2:5C ac1

R W V s

T ¼ minðT a ; 1:3T e ÞForzone 4

EC8 F b ¼ S d T ð Þ wg k where k ¼ 0:85 if T i 2T i or k ¼ 1:00 otherwise


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SA. Similarly, EC 8 gives maximum base shear for ground

type E and maximum difference reaches to 47 % between

E and A.

Base Shear for 6-UB Buildings


shown in Fig. 5c and maximum difference reaches to 26 %

between III and I. UBC gives maximum base shear for

ground type SD, the maximum difference reached to 31 %

between SD and SA. Similarly, EC 8 gives maximum base

shear for ground type E and maximum difference reaches

to 38 % between E and A.

Lateral Displacements and Interstory Drifts

for the Analyzed Buildings

Minimum lateral displacement were estimated for all the

buildings with ground types SA 13 mm for 6-SB, 12 mm

for 6-MB, and 14 mm for 6-UB in UBC. IS code gives the

maximum, and UBC gives the minimum lateral displace-

ment values for the buildings. Figure 6 present drifts esti-

mated from seismic analysis of the 6-story building. As per

IS code, the maximum value of story drifts within a story,

shall not exceed 0.004 times the story height (i.e.,

0.004 9 3 = 0.012 m). As seen from the Fig. 6 the sample

building taken for study satisfies the condition defined in

the IS code.

All maximum and minimum displacement values

determined for each code are given in Table 5. As seen

from this table, the smallest difference between maximum

and minimum displacement values for the 6-story building

are obtained as to be 37 % between ground type III and I in

IS, 50 % between SD and SA in UBC and 45 % between E

and A in EC8.

The largest difference between maximum and minimum

displacement values for the 6-story building is obtained as

to be 80 % between E and A in EC8.

Torsional Response for 6-SB Buildings

IS code gives maximum torque for ground type III as shown

in Fig. 7a and maximum difference reaches to 8 % between

(a)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

6.5

1 2 3 4 5 6

Story

I

II

III

SA

SD

SC

A

E

D

(b)

0

0.5

1

1.5

2

2.5

3

3.5

4

1 2 3 4 5 6

(c)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

1 2 3 4 5 6

Story

Story

D r i f t ( 1 0 -

3 m

)

D r i f t ( 1 0 -

3 m

)

D r i f t ( 1 0 -

3 m

)

Fig. 6 Drift for six story buildings considering nine ground typesdefined in the codes. (a) Story drift for 6-UB building. (b) Story driftfor 6-MB building. (c) Story drift for 6-UB building

Table 4 First seven periods (s) and modal properties of three dif-ferent buildings

Buildings Modalproperties

Horizontal modes for the buildings

x-direction y-direction Torsionalmode

6-SB Mode, period 1st, 0.548 2nd, 0.450 3rd, 0.363

4th, 0.172 5th, 0.126 7th, 0.0906th, 0.108

Mass ratio 1st—0.767 2nd—0.000 3rd—0.000

4th—0.050 5th—0.000 7th—0.000

6th—0.050

6-MB Mode, period 2nd, 0.428 1st, 0.480 3rd, 0.384

6th, 0.115 4th, 0.148 5th, 0.120

7th, 0.104

Mass ratio 2nd—0.718 1st—0.000 3rd—0.010

6th—0.000 4th—0.000 5th—0.050

7th—0.073

6-UB Mode, period 2nd, 0.416 1st, 0.474 3rd, 0.362

5th, 0.115 4th, 0.142 6th, 0.100

7th, 0.071

Mass ratio 2nd—0.008 1st—0.719 3rd—0.020

5th—0.005 4th—0.1268 6th—0.070

7th—0.0524


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III and I. UBC gives maximum torque for SC, the maximum

difference reached to 27 % between SC and SA. Similarly

EC 8 gives maximum torque for ground type D and maxi-

mum difference reaches to 25 % between D and A.

Torsional Response for 6-MB Buildings

IS code gives maximum torque for ground type III as shownin Fig. 7b and maximum difference reaches to 7 % between

III and II. UBC gives maximum torque for SC, the maxi-

mum difference reached to 3 % between SC and SA.

Similarly, EC 8 gives maximum torque for ground type D

and maximum difference reaches to 10 % between D and A.

Torsional Response for 6-UB Buildings

IS code gives maximum torque for ground type III as shown

in Fig. 7c and maximum difference reaches to 4 % between

III and I. UBC gives maximum torque for SD, the maximum

difference reached to 10 % between SC and SD. SimilarlyEC 8 gives maximum torque for ground type D and maxi-

mum difference reaches to 10 % between D and E.

Conclusions

From the parametric study on reinforced concrete build-

ings, the following conclusions are drawn as:

• IS code depict the higher values of base shear for

similar ground types defined in the other codes which

may lead to overestimate the overturning moment and

could results in heavier structural members in the

building.

• For the buildings, IS code gives the maximum and UBC

gives the minimum displacement values.

• In case of torsional response, IS code gives maximum

and UBC, EC8 gives minimum values.

• In most cases, the estimated drifts for structural compo-

nents subjected to earthquake force satisfied the drift

demand (as per IS Code) for immediate occupancy level,

indicatingthat the structural responses are mainly elastic.

0

10

20

30

40

50

60

70

Ground type

(b) IS 1893 UBC-94 EC-8

III

III

SA SD SC A D E

0

10

20

30

40

50

60

Ground type

T o r q u e , k - N m

T

o r q u e ,

k - N m

T o r q u e ,

k - N m

(c)

III III

SA SD SC A DE

IS 1893 UBC-94 EC-8

0

10

20

30

40

50

60

70

80

Ground type

(a) IS 1893 UBC-94 EC-8

III

III

SA

SD SC

A

DE

Fig. 7 Torsional response for 6-story buildings considering nineground types defined in the codes. (a) For 6-SB building. (b) For6-MB building. (c) For 6-UB building

Table 5 Maximum and minimum displacement obtained for the three different buildings

Buildings IS-1893 (Part-I) UBC-94 EC-8

Min. Max. Min. Max. Min. Max.

6-SB Displacement 18 mm 29 mm 13 mm 21 mm 15 mm 27 mm

Ground type I III SA SD A E

6-MB Displacement 19 mm 26 mm 12 mm 18 mm 13 mm 20 mm

Ground type I III SA SD A D

6-UB Displacement 21 mm 32 mm 14 mm 21 mm 20 mm 29 mm

Ground type I III SA SD A E


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Acknowledgments The author is grateful to Raisoni Group of Institutions, Nagpur, India for publishing this research work.

References

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4. J.J. Bommer, A.B. Acevedo, The use of real earthquake acceler-ograms as input to dynamic analysis. J. Earthquake Eng. 8, 43–91(2004)

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Response Spectrum Analysis of Reinforced Concrete Buildings

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