Limitation of irregular structure for seismic response

INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING

Volume 3, No 3, 2013

© Copyright by the authors - Licensee IPA- Under Creative Commons license 3.0

Research article ISSN 0976 – 4399

Received on January 2013 Published on March 2013 579

Limitation of irregular structure for seismic response Arun Solomon A

1, Hemalatha G

2

1- Post Graduate Student, School of Civil Engineering, Karunya University, Coimbatore

2- Associate Professor, School of Civil Engineering, Karunya University, Coimbatore

[email protected]

doi:10.6088/ijcser.201203013053

ABSTRACT

Structural engineer's greatest challenge in today’s scenario is constructing seismic resistant

structure. Uncertainties involved and behaviour studies are vital for all civil engineering

structures. To understand and find accurate result in provisions of drift, deflection and hinge

of structure under seismic force, non Linear Static Analysis is commonly employed and this

method of analysis is called Pushover Analysis. This method of analysis shows the base shear

carrying capacity of a structure and performance level of each component of structure under

various zones or different intensity of seismic force. The present study incorporates the non

linear behaviour of irregular structures. Because of the constraints some of the structures are

highly irregular as too long, and too tall. This study aims to identify the limitations of the too

long and too tall structures using the software SAP 2000.

Keyword: Inter storey drift, nonlinear static analysis, pushover curve, too long structure, too

tall structure.

1. Introduction

Modern construction demands the architect to plan the buildings which are irregular in plan

and elevation. The structural engineer on the other hand has the major responsibility to make

the structure safe against all external forces. When such irregular buildings are placed in a

high seismic zone, the structural engineer’s role becomes further challenging. So ideal and

clear understanding of the behaviour of irregular structures during earthquake is significant

for structural engineers. This paper is an effort to study the limits upto which these irregular

structures can be constructed for safety against seismic forces.

Increased length and enormous plan area of any structure or building will not perform well for

seismic force. General calculation of seismic force assumes that the ground moves as a rigid

mass over the bas of the building but this is a reasonable assumption only for a small area. In

addition to that, the ground is assumed to be elastic and the propagation of seismic waves is

not instantaneous. If different parts of the building are shaken, additional stresses are being

imposed and this effect increases with size. Thus buildings that are too long (Figure 1(a)) in

plan may be subjected to different earthquake movements simultaneously at the two ends,

leading to disastrous results.

In tall buildings with large height to base ratio (Figure 1(b)) (slenderness ratio >4), the

horizontal movement of the floors during ground shaking is large. For buildings with

slenderness ratio less than 4, the movement is reasonable. The more slender a building, the

worse the overturning effects of the earthquake. The axial column force due to overturning

moment in such buildings tends to become unmanageably large. Also, the compressive and

pull out forces acting on the foundation increase tremendously.

Limitation of irregular structure for seismic response

Arun Solomon A, Hemalatha G

International Journal of Civil and Structural Engineering 580

Volume 3 Issue 3 2013

Devesh P. Soni (2006) deals with Mass, Set-back, Stiffness, strength and Vertical Irregular

structures. It was concluded that the drift demand is increased for the tower portion of the set-

back structures, the effect of strength irregularity has been found to be larger than the effect of

stiffness irregularity. Rucha S. Banginwar (2012) explains the consequence of earthquake of

varies geometrical configuration by Response Spectrum Method. This study is based on the

damage of the building by the past earthquake and concluded that, displacement, storey drift,

storey shear has increased for large plan c configuration and irregular configuration of the

structure when compared to the regular structure. Zeynep Yesim Harmankaya (2012) studied

the failure of structures in Turkey by earthquake and concluded that there was a strong

relationship between architectural design and building resistance. Architects should

understand the dynamic behavior of the structure.

1.1 Objective

In tall buildings with large height-to-base size ratio (Figure 1(a)), the horizontal movement of

the floors during ground shaking is large. In short but very long buildings (Figure 1(b)), the

damaging effects during earthquake shaking are many. Analytical investigation carried out

using SAP 2000 to determine the limitation of the aspect ratio for too long and too tall

structure are presented in this paper.

Figure 1: Typical Too Long and Too Tall Structures

2. Analytical investigation

2.1 Pushover analysis

In SAP 2000, Non Linear Static Analysis can be performed called Push over analysis. In this

Pushover analysis FEMA 356 and ATC 40 graph will be obtained. FEMA 356 (Federal

Emergency Management Agency) gives the graph developed between base shear and

displacement. From this graph one may understand the damage level of structural and non

structural elements. ATC 40 (Applied Technology Council) gives the graph between spectral

acceleration and spectral displacement. This graph shows, the demand spectrum of a structure

and required capacity spectrum of structure, from this graph one may understand wheather

the structure meets the seismic demand or not. Pushover analysis is simplified approach for

nonlinear static procedure to evaluate seismic structural deformation and inter storey drift.

Force-Displacement relationship or capacity curve for a structure or element of structure shall

be determined from this analysis. This analysis uses the incremental static analysis.

In the pushover analysis, horizontal loads are applied to the structure with prescribed pattern

incrementally, that means it pushes the structure until collapse condition and simultaneously





it plots the applied shear force and coupled lateral displacement. The sequence of cracks

development, plastic hinge formation, yielding and failure of various structural elements are

recorded with respect to the horizontal load increment. The structural deficiencies are

recorded in a serious of iteration process, so that deficiencies are rectified in one iteration

after another. The progression of iteration of analysis and design continues until all the

elements of structure satisfy mandatory performance criteria. The performance criteria of

Pushover analysis are commonly shown in terms of spectral displacement amplitude of

respective floors of the structure.

Pushover analysis performs the approximate analysis on the basis of increasing lateral force

in different height of the structure until the predefined displacement is obtained. In SAP 2000

the model is created with proper support specification and gravity loads are applied as per the

codel provision with respect to the requirement of building. According to the past earthquake

data’s and as per the zonal requirement of the building, predefined lateral load is applied to

the structure. This predefined lateral force is successively augmented until some member of

structure gets yielded. Then the element of the yielded section of the structure is revised

according to reduced stiffness and lateral load is increased until the entire member gets

yielded. This process of iteration is continued until permissible displacement is attained at

roof floor. Finally, curve is plotted between roof displacement and base shear called global

capacity curve.

2.2 Elements of force-displacement curve

Figure 2 explains the characteristics of structure in terms of force-displacement. This is the

model graph obtained all for structures while analyzing in SAP2000. This graph shows the

nonlinear force-displacement characteristics of the structure. In the figure 2 the terms of IO,

LS and CP are explained in the figure 3.

Figure 2: Force-deformation for pushover hinge

Point A refers to the unloaded state of the structure, in this stage applied force is zero and its

coupled displacement is also zero. Ordinate B indicates yielding of any member of the

structure, in this stage mild and clear changes happens in force displacement graph. The

intersection C refers to deformation changing abruptly at which the structure begins to lose its

strength. The line falls from C showing the initial failure of element of structure.

Theoretically it is impossible to carry further lateral load analysis beyond the point C. The





ordinate D represents, the state of structure to resist further gravity loads. Beyond the point E,

the structure attains its maximum deformation, and the structure will not carry any more

loads.

Figure 3: Performance Chart of Structure

3. Modelling of structure

3.1 Description of buildings

The details of buildings modelled for analysis are displayed in table 1, table 2. For too long

structures and table 3 for too tall structures.

Table 1: Too long Type - I structure

Structure

No.

Length

M

Breadth

m

Height

m

No of bays

in Length

Direction

No of bays in

Breadth

Direction

No. of

storeys

L1 65 15 12 13 3 3

L2 70 15 12 14 3 3

L3 75 15 12 15 3 3

L4 80 15 12 16 3 3

L5 85 15 12 17 3 3





Table 2: Too long Type II Structure

Table 3: Too tall structure

Structure

No

Length

m

Breadth

m

Height

m

No of bays

in Length

Direction

No of bays in

Breadth

Direction

No. of

storeys

T10 15 15 80 3 3 20

T11 15 15 84 3 3 21

T12 15 15 88 3 3 22

T13 15 15 92 3 3 23

3.2 Materials and member properties

The basic material properties used are as follows:

Modulus of Elasticity of steel, Es = 21, 0000 Mpa

Modulus of Elasticity of concrete, EC = 22,360.68 MPa

Characteristic strength of concrete, fck = 25 MPa

Yield stress for steel, fy = 415 MPa

Poisson’s Ratio = 0.2

Co efficient of thermal expansion = 9.9 x 10-6

Concrete cube compressive strength = 27.579 MPa

Bending Yield Stress of Rein. = 413.685 MPa

Depth of Slab = 0.15m

Size of Beam = 0.3 x 0.75 m

Size of column

Too long structure = 0.5 x 0.5 m

Too tall structure = 0.7 x 0.7 m

The stress - strain relationship is followed as per IS 456:2000. The dimensions of the beams

and columns are designed as per the codel provisions.

3.3 Loading details

The following loads are applied in the models of the structure.

Self Weight : SW of the Beam, Column, and Slab

Dead Load : 2 kN /m2

Floor Finish : 0.2 kN/ m2

Live Load : 2 kN/ m2

Structure

No

Length

M

Breadth

m

Height

m

No of bays

in Length

Direction

No of bays in

Breadth

Direction

No. of

storeys

L6 130 25 12 26 5 3

L7 135 25 12 27 5 3

L8 140 25 12 28 5 3

L9 145 25 12 29 5 3





Lateral loads as specified in SAP 2000

3.4 Model of structure

Figure 4(a) and 4(b) shows the typical model of too long and too tall structure. The length,

breadth, height of the structure and the bay specifications are listed in the table 1 and 2. The

modeling and analysis is done using SAP 2000 software, then the push over curve and inter

storey limit has been obtained as the result of analysis.

Figure 4(a): Typical Too long Structure model (b): Typical too tall structures model

3.5 Typical analysis results

Figure 5 shows typical non linear static push over curve. The curve is plotted between

spectral acceleration and spectral displacement.

Figure 5: Typical non linear static pushover curve





In this graph green line indicates the capacity curve, the red line indicate demand spectrum

and the yellow line shows the push over curve. The right side of the push over graph indicates

the performance point. If the performance point is achieved, the structure meets the demand

to resist the lateral force and vice versa.

4. Analysis results

The structures mentioned in table 1 to 3 are modelled and analysed using SAP 2000 software

and the Pushover curve is obtained. Table 4 to 6 gives the analysis results.

Table 4 shows the results of too long type I structure. The performance point is obtained for

L1 to L4 structures and the performance point is not obtained for the L5 structure, That

means, the structure meets the seismic demand when the aspect ratio is (80/15)=5.33 and the

structure does not meet the seismic demand when the aspect ratio is (85/15)=5.66.

Table 5 explains the results of too long type II structure. The performance point is obtained

for L6 to L8 structures and the performance point is not obtained for the L9 structure. That

means, the structure meets the seismic demands when the aspect ratio is (140/25) =5.6 and

the structure does not meet the seismic demand when the aspect ratio is (145/25) =5.8.

Table 6 summarizes the results of too tall structure. The performance point is available for

structures numbers T10 to T12 and the performance point is not available for the T13

structure. That means, the structure meets the seismic demand when the aspect ratio is

(88/15) =5.86 and the structure does not meet the seismic demand when the aspect ratio is

(92/15) =6.13.

4.1 Check for storey drift limitation

4.1.1 Storey drifts

As per IS 1893 (Part I):2002 storey drift is defined as, the displacement of one level relative

to the other level above or below the floor under consideration Earthquake-induced

deformations may be quantified by the roof displacement ∆roof as well as the interstorey

displacement ∆i as shown in figure 5 Inter-storey drift ratio at the ith

floor can be defined as





where hi is the storey height.

Figure 5: Roof displacement and inter-storey displacement

Past earthquake demonstrates that the extent of damage to buildings is closely related to the

inter-storey drift demand. Excessive inter-storey drift could cause damage to both the

structural and non structural components. Collapse of buildings is often resulted from the

local concentration of deformation at a particular “weak storey”. So check of the inter storey

drift limit of structure is an important aspect.

4.2 Storey drift limitation

As per the IS 1893:2000 storey drift in any storey due to minimum specified design lateral

force with partial load factor of 1.0, shall not exceed 0.004 times the storey height.

4.3 Storey drift for too long Type I structure

As mentioned above, Displacement is arrived from the analysis results of SAP 2000 for too

long structure as described in the table 1. Then Storey drift is calculated, as the difference of

displacements of one storey with respect to the adjacent storey.

The maximum value of storey drift = 0.004 x 4 = 0.016

Storey Drift for L4 Structure = 0.0155

Storey Drift for L5 Structure = 0.0205

Hence the structure L5 exceeded the limiting value of storey drift when compared to the

structure L4. These results are explained in figure 6.

4.4 Storey drift for too tall structure

Displacement is arrived from the analysis results of SAP 2000 for too tall structures as

mentioned in the table 3. Then Storey drift is calculated, as the difference of displacements of

one storey with respect to the adjacent storey.

The maximum limited value of storey drift = 0.004 x 4 = 0.016

Storey Drift for T12 Structure = 0.01268





Storey Drift for T13 Structure = 0.01928

Therefore, the structure T13 exceeds the limiting value of storey drift when compared to the

structure T12. These results are explained in figure 7.

4.5 Maximum base shear

The maximum base shear of the too long structures and too tall structure are shown in table 7

and 8. Figure 8 shows the typical base shear, displacement curve arrived from the SAP 2000.

In the tables, the point C is the maximum base shear carrying capacity (refer section 2.2).

From the calculation of maximum base shear capacity the structure can be altered to resist the

lateral load carrying capacity according to the seismic vulnerability.

Figure 6: Comparison of Inter Storey Drift of Too Long Type I Structure

Figure 7: Comparison of Inter Storey Drift of Too Tall Structure





Figure 8: Typical Base Reaction-Displacement curve

Table 7: Elements of displacement- force of too long structure

Ele

men

ts

A

B

C

D

E

Dis

pla

cem

ent

Ba

se

Rea

ctio

n

Dis

pla

cem

ent

Ba

se

Rea

ctio

n

Dis

pla

cem

ent

Ba

se

Rea

ctio

n

Dis

pla

cem

ent

Ba

se

Rea

ctio

n

Dis

pla

cem

ent

Ba

se

Rea

ctio

n

Str

uct

ure

No

: L

4

0.0

14

62

87

.71

0.0

18

76

78

.48

0.0

28

10

772

.6

0.0

35

12

431

.2

0.0

4

13

507

.3

Str

uct

ure

No

: L

5

0.0

14

65

43

.16

0.0

18

80

07

.16

0.0

29

11

213

.4

0.0

36

12

973

0.0

41

14

210

.3





Table 8: Elements of force- displacement of too tall structure

Ele

men

ts

A

B

C

D

E

Dis

pla

cem

ent

Ba

se

Rea

ctio

n

Dis

pla

cem

ent

Ba

se

Rea

ctio

n

Dis

pla

cem

ent

Ba

se

Rea

ctio

n

Dis

pla

cem

ent

Ba

se

Rea

ctio

n

Dis

pla

cem

ent

Ba

se

Rea

ctio

n

Str

uct

ure

No

: T

12

0.0

82

48

33

.18

8

0.1

03

60

41

.46

9

0.1

65

96

63

.70

8

0.2

06

12

024

.712

0.3

3

15

590

.415

Str

uct

ure

No

: T

13

0.0

87

49

12

.15

4

0.1

09

61

39

.99

1

0.1

74

97

84

.74

6

0.2

17

12

096

.232

0.3

4

13

394

.871

5. Conclusions

From the investigation carried out, too long and too tall structures are modeled, loads are

applied and a pushover analysis was carried out. The results of the pushover curve and inter

storey drift are obtained to study the performance of the building.

5.1 Conclusion for Too Long Structures

From the investigation on the two types of too long structures the following results are

obtained. The aspect ratio of the building is

1. Type I Building aspect Ratio (85/15) = 5.66.

2. Type II Building aspect Ratio (145/25) = 5.8

Hence it may be concluded that in too long structures if one dimension of the structure

exceeds 5.6 times the other dimension, the structure does not meet the performance limit.

Hence these types of the structures should be avoided while constructing in earthquake prone

areas.

5.2 Conclusion for Too Tall Structures

From the investigation on too tall structure the following result is obtained. The aspect ratio

of the building is (92/15) = 6.13 > 5.6. Hence it may conclude that, a too tall structure does

not meet the performance limit if the structure’s aspect ratio exceeds 5.6 times the other

dimension

6. References

1. Devesh P. Soni and Bharat B. Mistry, (2006), Qualitative review of seismic response

of vertically irregular building frames, ISET Journal of Earthquake Technology,

Technical Note, 43(4), pp 121-132.





2. Zeynep Yesim Harmankaya and Asena Soyluk (2012), Architectural Design of

Irregular Buildings in Turkey, International Journal of Civil and Environmental

Engineering, 12(1), pp 42-48.

3. Kalkan and Kunnath (2009), Adaptive Modal Combination Procedure for Predicting

Seismic Response of Vertically Irregular Structural Systems, The 14th World

Conference on Earthquake Engineering.

4. Earthquake Tips, Learning Earthquake Design and Construction, IITK-bmtbc.

5. Dubey and Sangamnerkar, (2011), Seismic Behaviour of Assymetric RC Buildings,

International Journal of Advanced Engineering Technology, 2(4), pp 296-301.

6. Men Jinjie, Shi Qingxuan and Zhou Qi, (2008), Method Of Performance Based

Seismic Evaluation For Irregular Plane Reinforced Concrete Frame Structures, The

14th World Conference on Earthquake Engineering.

7. A.D’Ambrisi, M. De Stefano and S. Viti, (2008), Seismic performance of irregular 3d

RC frames, The 14th

World conference on earthquake engineering.

Limitation of irregular structure for seismic response

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