ISET GOLDEN JUBILEE SYMPOSIUM Indian Society of Earthquake Technology Department of Earthquake Engineering Building IIT Roorkee, Roorkee October 20-21, 2012

Paper No. D002

APPLICATION OF PUSHOVER ANALYSIS METHODS FOR BUILDING STRUCTURES A. Kiran1, G. Ghosh2 and Y. K.Gupta3 1

M. Tech. Student, Motilal Nehru National Institute of Technology, Allahabad,U.P., India, [email protected]

2

3

Assistant Professor, Motilal Nehru National Institute of Technology, Allahabad, U.P., India, [email protected]

Associate Professor, Motilal Nehru National Institute of Technology, Allahabad, U.P., India, [email protected]

ABSTRACT To have a reliable estimate of the performance of a structure, sophisticated analytical tools are necessary. Nonlinear dynamic analysis is the most accurate method available for the analysis of structures subjected to earthquake excitation. Nonlinear static (Pushover) Analysis is also an attractive choice because of its simplicity and ability to identify component and system-level deformation demands with accuracy comparable to dynamic analysis. Many methods have evolved, over the years, for pushover analysis of structures. People have a lot of doubt about which one of those will be the most preferred pushover method for the analysis of structures. To fulfill that objective, in the present study, a comparison has been made between the results of the pushover analysis with the dynamic timehistory analysis, with a view to find out the most preferred pushover method. The existing pushover analysis methods as per the literatures and codes have been considered in the study. For the analysis purpose, two types of building structures have been considered. It has been observed that in most of the cases, pushover analysis results are conservative as compared to the time history results. It has been observed that in most of the cases ELM method of FEMA 440 gives good result in comprasion to time history analysis. Keywords: Pushover, Building, time history analysis

INTRODUCTION To make a decision on the safety, adequacy or to asses the real behavior of the structures, sophisticated analytical methods are needed. Non linear Static (Pushover) Analysis has become a popular method during the last few decades for the seismic assessment of structure. Never the less, the main advantage of the same is to make the computational cost lower as compared to nonlinear dynamic time history analysis. Simplified Nonlinear Static (Pushover) procedures for buildings have been presented in the ATC-40 and FEMA273, 356, 440 to determine the displacement demand imposed on a building expected to deform inelastically. The Pushover procedures presented in these documents are based on the methodology developed by Freeman et al. (1975) and Freeman (1978). Capacity Spectrum Method of ATC-40 has been modified in FEMA-440 and stated as Equivalent Linearization Method (ELM). Displacement Coefficient Method (DCM) of FEMA-273 has also been enhanced to Displacement Modification Method (DMM) in FEMA-440. Many methods of pushover analaysis are available, over the years. However, there exists a conflict of ideas about which one of those will be the most preferred method for the nonlinear static analysis of structures. To fulfill that purpose, the present studies are focoused on following objectives:

    

To develop a complete comprehensive model of the Symmetric and Asymmetric Building Structures To design the buildings as per IS codal provisions To determine the response of the symmetrical and asymmetrical building structures by nonlinear (static) pushover analysis for five different earthquake ground motions To compare the results of Pushover Analysis with the Nonlinear Dynamic Time History Analysis To determine the most effective pushover methods for the building structures

BUILDINGS CONSIDERED FOR THE STUDY For the study purpose, two building structures have been considered. First one is a symmetrical building which is having 5 bays (with each bay of 4 m) in longitudinal as well as transverse directions. The height of the building (5 story) is 17.5 m with each storey height of 3.5m. The second one is a asymmetrical building (Fig.1) structure which can be divided into two parts. In one part, the building is having 2 bays in the shorter direction and 3 bay in the longer direction upto 3 stroey height. In another part, the building is having 2 bays in the shorter direction and 5 bays in the longer direction upto 5 storey height. The length of bay is 4 m in the shorter direction and 5 m in the longer direction. The height of each storey is 3.5 m. The site of the building is considered to be within Seismic Zone IV of Indian Seismic Zoning (IS: 1893-2002, Part 1).

z y

x

Fig. 1 Asymmetrical Building

MODELLING AND ANALYSIS Nonlinearity has been considered in all the elements of the building. Plastic hinges at bottom and top of each element have been assigned to model the nonlinear properties. For the analysis purpose, both the Nonlinear Dynamic (NLTHA) and Static (Pushover) Analysis have been performed and results have been compared. In case of pushover analysis, Equivalent Linearization Method (ELM) and Displacement Modification Method (DMM) as per FEMA 440 have been considered. Also, five different lateral load distributions have been considered in the Pushover Analysis. SEISMIC LOADING CONSIDERED Site specific response spectra (Fig. 2) for the Maximum Considered Earthquake (MCE) have been considered for the study. Five ground acceleration time histories (Fig. 3), recorded for different earthquakes, world over, for different source and site conditions have been scaled in frequency domain, preserving their phase information (Kumar 2004), to make them compatible with the design response spectra for MCE loading condition.

0.9 0.8

MCE

0.7

DBE

0.6 0.5

Sa/g

0.4 0.3 0.2 0.1 0 0

0.5

1

1.5

2

2.5

3

3.5

4

Time Period (sec)

0

20

30

40

0.6 0.3 0 -0.3 -0.6 -0.9

Kobe 0

10

20

Northridge

0

10

20 Tim e (sec)

30

0.35 0.24 0.13 0.02 -0.09 -0.2

40

30

40

50

Tim e (sec)

Time (sec)

Accl. (g)

0.6 0.4 0.2 0 -0.2 -0.4

10

Accl. (g)

Elcentro

0.7 0.45 0.2 -0.05 -0.3 -0.55

Accl. (g)

0.35 0.21 0.07 -0.07 -0.21 -0.35

Accl. (g)

Accl. (g)

Fig. 2 Site specific design response spectra for 5% damping

Lom a Prieta 0

10

20 Tim e (sec)

30

40

San Fernando

0

10

20

30

Tim e (sec)

Fig. 3 Ground motion time histories considered for the study

RESULTS AND DISCUSSIONS Two buildings (one symmetrical and the other one asymmetrical) have been designed as according to the Indian Standard Code (IS: 1893 (2002) Part 1). Both the pushover as well as time history analyses have been performed for the buildings and the results are compared. Two types of pushover analyses viz. ELM and DMM, as per FEMA 440, are considered. In case of pushover analysis, five different pattern of lateral load distributions are considered viz. uniform load, modal load, uniform acceleration, parabolic load and triangular load.

Dynamic Characteristics Table 1 shows the dynamic characteristics of the symmetrical building. The modal participating mass ratio for the first mode is in the range of 80% - 85%. So it is expected that initial modes will contribute more to the response and effect of torsion will be negligible.

Table 1 Dynamic characteristics of the symmetrical building Longitudinal Direction Fundamental time Modal period mass ratio (sec) 0.66

(%) 83

Transverse Direction Fundamental Modal time period mass ratio (sec) 0.65

(%) 82

Table 2 shows the dynamic characteristics of the aymmetrical building. Since the mass participating factor in asymmetrical building is not more than 80% and also participation exists for both long. X/Trans. Y as well as Rotation about Z directions i.e. torsion exists. So, it can not be predicted that which mode will contribute to the response. But the effect of torsion will be there on the response of building.

Mode

Period (sec)

Table 2 Dynamic characteristics of the asymmetrical building Modal mass ratio Longitudinal X

Transverse Y

Vertical Z

Rotation about X

Rotation about Y

Rotation about Z

1

0.582336

0.00502

0.70855

5.365E-10

0.54989

0.00341

0.58428

2

0.509616

0.48915

0.03593

7.13E-08

0.02365

0.30752

0.00011

3

0.450189

0.29107

0.0209

2.246E-07

0.0113

0.16375

0.22234

Parametric Study The responses of the building have been determined for both the DBE and MCE loading conditions and compared with pushover analysis results. Two parameters are considered for the study viz. maxm. displcement and maxm. base shear. Tables 3 and 4 show the responses of the symmetrical building for DBE and MCE loading conditions. It has been observed that in case of DBE and MCE loading, the maximum displacement and maximum base shear of the structure by Equivalent Linearization Method (ELM) with modal pattern of loads is closer with the time history results.

Table 3 Response of the symmetrical building structure in DBE loading condition Load Pattern Pushover Methods Maxm. Displ. (m) Maxm. Base Shear (kN)

Modal ELM DMM

Uniform Load ELM DMM

Triangular ELM DMM

Parabolic ELM DMM

Uniform Accl. ELM DMM

Time History

0.028

0.018

0.013

0.009

0.010

0.007

0.017

0.012

0.024

0.016

0.027

712

510

1226

844

1224

801

1075

821

833

601

750

Table 4 Response of the symmetrical building structure in MCE loading condition Load Pattern Pushover Methods Maxm. Displ. (m) Maxm. Base Shear (kN)

Modal ELM DMM

Uniform Load ELM DMM

Triangular ELM DMM

Parabolic ELM DMM

Uniform Accl. ELM DMM

Time History

0.058

0.038

0.026

0.018

0.021

0.014

0.035

0.023

0.050

0.034

0.050

1424

950

2370

1720

2449

1663

1910

1429

1600

1053

1450

Tables 5, 6, 7 and 8 show the responses of the asymmetrical building for DBE and MCE loading conditions.

In Longitudinal Direction In case of DBE and MCE loadings, the maximum. Displacement of the structure by Equivalent Linearization Method (ELM) with modal, parabolic and uniform pattern of loads is 83% closer with the time history results. The maximum Base shear of the structure by ELM with modal pattern is 23% lower than the time history results. With the other pattern of loads, the values are 40% to 45 % higher than the time history results. Whereas, by using DMM method with all the load pattern other than modal pattern, the maximum Base shear of the structure are closer with the time history results.

In Transverse Direction In case of DBE and MCE loadings, the maximum. Displacement of the structure by ELM and DMM with uniform and parabolic pattern of loads is closer with the time history results whereas by using other pattern of loads the values are on the conservative side. The maximum Base shear of the structure is 47% higher than the time history results, for all the methods with various distributions of loads.

Table 5 Response of the unsymmetrical building structure for DBE loading in longitudinal direction Load Pattern Pushover Methods Maxm. Displ. (m) Maxm. Base Shear (kN)

Modal ELM DMM

Uniform Load ELM DMM

Triangular ELM DMM

Parabolic ELM DMM

Uniform Accl. ELM DMM

Time History

0.020

0.012

0.015

0.007

0.012

0.005

0.020

0.010

0.023

0.014

0.026

415

482

1031

514

1008

468

933

471

878

521

542

Table 6 Response of the unsymmetrical building structure for MCE loading in longitudinal direction Load Pattern Pushover Methods Maxm. Displ. (m) Maxm. Base Shear (kN)

Modal ELM DMM

Uniform Load ELM DMM

Triangular ELM DMM

Parabolic ELM DMM

Uniform Accl. ELM DMM

Time History

0.039

0.023

0.030

0.015

0.023

0.012

0.04

0.02

0.046

0.027

0.046

1005

1100

2062

1069

2016

998

1866

953

1703

1024

1124

Table 7 Response of the unsymmetrical building structure for DBE loading in transverse direction Load Pattern Pushover Methods Maxm. Displ. (m) Maxm. Base Shear (kN)

Modal ELM DMM

Uniform Load ELM DMM

Triangular ELM DMM

Parabolic ELM DMM

Uniform Accl. ELM DMM

Time History

0.015

0.020

0.010

0.006

0.008

0.007

0.014

0.009

0.014

0.016

0.013

470

396

450

670

1060

556

1025

622

723

507

390

Table 8 Response of the unsymmetrical building structure for MCE loading in transverse direction Load Pattern Pushover Methods Maxm. Displ. (m) Maxm. Base Shear (kN)

Modal ELM DMM

Uniform Load ELM DMM

Triangular ELM DMM

Parabolic ELM DMM

Uniform Accl. ELM DMM

Time History

0.030

0.039

0.020

0.013

0.015

0.015

0.028

0.017

0.029

0.031

0.028

915

754

960

1396

2120

1170

2050

1268

1318

1007

805

CONCLUSIONS In the present study, the response of the symmetrical and asymmetrical building structures has been determined by the Nonlinear static (Pushover) analysis and Nonlinear dynamic time history analysis and the results from both the methods have been compared. Five different types of ground motions compatible to the MCE and DBE response spectrums have been considered. The main conclusions of the study are as follows:  A carefully performed pushover analysis can provide insight into structural aspects that control the performance of the structure during a severe earthquake. In most of the cases, the results of the pushover analysis are on the conservative side, as compared with the time history results.  In case of symmetrical building, the ELM method with modal pattern of loads is quite better as compared with the other pattern of loads. DMM can also be used but ELM is quite accurate.  In case of asymmetrical building, both ELM as well as DMM gives good results for few cases, but in most of the cases, the pushover results are quite higher than the time history results. REFERENCES 1. 2. 3. 4.

Applied Technology Council (1996). ‘Seismic Evaluation and Retrofit of Concrete Buildings’, ATC-40, Redwood City, Calif. Federal Emergency Management Agency (1997). ‘Nehrp Guidelines for the Seismic Rehabilitation of Buildings’, FEMA-273, Washington, D.C. Federal Emergency Management Agency (2000). ‘Prestandard and Commentary for the Seismic Rehabilitation of Buildings’, FEMA-356, Washington, D.C. Federal Emergency Management Agency (2005). ‘Improvement of Nonlinear Static Seismic Analysis Procedures’, FEMA-440, Washington, D.C.

5.

6. 7. 8.

Freeman, S. A., Nicoletti, J. P., and Tyrell, J. V. (1975). ‘Evaluation of Existing Buildings for Seismic Risk: A Case Study of Puget Sound Naval Shipyard, Bremerton,Washington’, Proceedings of US National Conference on Earthquake Engineers, EERI, Berkeley, California. Freeman, S. A. (1978). ‘Prediction of Response of Concrete Buildings to Severe Earthquake Motion’, Douglas McHenry International Symposium on Concrete and Concrete Structures, SP-55, ACI, 589-605. IS: 1893-Part 1 (2002). Criteria for earthquake resistant design of structures-General provisions and buildings. Bureau of Indian Standards, New Delhi. Kumar, A. (2004). ‘Software for Generation of Spectrum Compatible Time History’, Proceedings of 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada, August, paper no. 2096.