 Open Access
 Total Downloads : 224
 Authors : Ashwini K. C, Dr. Y. M. Manjunath
 Paper ID : IJERTV6IS060075
 Volume & Issue : Volume 06, Issue 06 (June 2017)
 DOI : http://dx.doi.org/10.17577/IJERTV6IS060075
 Published (First Online): 02062017
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Comparative Study of Pushover Analysis on RCC Structures
Ashwini.K.C 1
1 PG Student, Department of Civil Engineering,
The National Institute of Engineering, Mysore, Karnataka, India
Dr. Y. M. Manjunatp
2Professor,
Department of Civil Engineering, The National Institute of Engineering, Mysore, Karnataka, India,
Abstract: Nowadays nonlinear static analysis is gaining its importance for structural design and seismic assessment of reinforced concrete members. Overall shape, size and geometry of the building determine the behaviour of a building during earthquakes. Progressive collapse refers to a phenomenon in which local damage in a primary structural element leads to total or partial structural system failure. The method can be used to study the behaviour of reinforced concrete structures including force redistribution. In this study, four, eight and twelve storied buildings are analysed and compared in seismic zoneV using Response Spectrum Method and Non linear static method (Pushover method). The base shear, roof displacements and various structural forces are tabulated and the performance point is determined using SAP2000 which gives information about the global behaviour of the structure.
Key words: Response Spectrum method, Pushover Analysis, ATC40, Performance Point.

INTRODUCTION
Non linear static procedure (pushover analysis) has been widely used for evaluating the performance of existing buildings and verifying the design of seismic retrofits. Various methods, both elastic (linear) and inelastic (non linear) are available for the analysis of existing concrete
buildings. Elastic analysis methods available include code static lateral force procedure, code dynamic lateral force procedure and elastic procedure using demand capacity ratios. The most basic inelastic analysis method is the complete nonlinear time history analysis which is at this time is considered overly complex as it requires accurate acceleration data of previous earthquake data. Available simplified nonlinear static analysis procedures include the capacity spectrum (CSM) that uses the intersection of the capacity (pushover) curve and a reduced response spectrum to estimate maximum displacement of the structure as per ATC40 guidelines. The objective of this study is to emphasize the use of nonlinear static procedure in general and focus on the capacity spectrum method as per ATC40.

DESCRIPTION OF THE WORK UNDER STUDY The RCC structures chosen for the study are 4, 8, 12 storeys of each storey height 3m subjected to earthquake forces in the form of site specific spectra. Different types of earthquake analysis carried out are equivalent static method, response spectra method and nonlinear static pushover method
.
4 @ 4m
4@4m
4 @ 3m
8@ 3m
12@ 3m
Fig1. Plan of 4, 8 12 storey Elevation

METHODOLOGY

Modelling of the structure
The RCC structures are modelled as three dimensional finite element using analysis software SAP2000. The structures considered are 4, 8 and 12 storeys of 4 bay
symmetric in both directions. The structures are analysed for equivalent static method, response spectrum method, pushover analysis.
Properties of the structures:
Grade of Concerte
M30
Grade of Steel
Fe 500
column size
350X350 mm
beam size
230X400 mm
Slab thickness
175 mm
Live Load
2kN/m2
Super dead load
1.5kN/m2
Project Site
Bongaigoan, Assam
Zone factor
0.36( very severe)
Importance factor (I)
1.5
Response reduction factor
(R)
5

Method of Analysis
Modal Analysis
Modal analysis is used to determine the dynamic properties of the structure such as amplitudes, frequency and mode shapes which depends on the overall mass and stiffness of a structure.
Equivalent Static Method
This method of analysis is based on the assumption that the fundamental mode of the building makes the most significant contribution to the base shear and the total building mass is considered as against the dynamic procedure. For this to be true, the building must be lowrise
and must not twist significantly when the ground moves. Seismic analysis of most structures is still carried out on the assumption that the lateral (horizontal) force is equivalent to the actual (dynamic) loading. This method requires less effort because, except for the fundamental period, the periods and shapes of higher natural modes of vibration are not required.
RESPONSE SPECTRUM METHOD
This is the most common linear dynamic method of analysis suitable for problems involving the structural design of new structures. Response spectrum analysis uses the vibration properties such as natural frequencies, natural modes, and modal damping ratios of the structure and the dynamic characteristics of the ground motion through its response spectrum. This is required in many building codes for all except for very simple or very complex structures. The response of a structure can be defined as a combination of many mode shapes. For each mode, a response is read from the design spectrum, based on the modal frequency and the modal mass, and they are then combined to provide an estimate of the total response of the structure. In this we have to calculate the magnitude of forces in all directions
i.e. X, Y & Z and then see the effects on the building. Combination methods include the following:

Absolute peak values are added together

Square root of the sum of the squares (SRSS)

Complete quadratic combination (CQC) a method that is an improvement on SRSS for closely spaced modes
This method doesnt hold good for too tall and irregular structure. In the present study, site specific spectrum is used instead of the design spectra specified in IS: 1893 2002 and the type used is SRSS method.
NONLINEAR STATIC ANALYSIS
Available simplified nonlinear analysis methods referred to as nonlinear static analysis procedures such as Capacity Spectrum method (ATC40), displacement coefficient method (FEMA 273) and secant method.
EVALUATION PROCEDURES
The basic principles of all non linear procedures are same
i.e they all use bilinear approximation of the pushover curve. In this static procedure, the properties of every multi degree of freedom (MDOF) structures is equated to corresponding single degree of freedom (SDOF) equivalents, and the expected maximum displacement is approximated using the response spectrum of relevant earthquake intensity .
ATC 40[1] – 1996 – Capacity Spectrum Method (CSM) This method is based on the equivalent linearization of a nonlinear system. The important assumption here is that inelastic displacement of a nonlinear SDF system will be approximately equal to the maximum elastic displacement of linear SDF system with natural time period and damping values greater than the initial values for those in nonlinear system. ATC 40 describes three procedures (A, B and C) for the CSM and the second one is used in this study
LOADS CONSIDERED:
Dead load: Self weight of the structure
Live load: 2N/m2 Superimposed dead load: 1.5kN/m2
Seismic loads: The structure shall be analysed for site specific design acceleration spectra instead that given in figure2 of IS: 1893 (Part1). The site specific acceleration spectra along with multiplying factors include the effect of the seismic environment of the site, the importance factor related to the structures and the response reduction factor. Hence, the design spectra do not require any further consideration of the zone factor (Z), the importance factor

and response reduction factor (R) as used in the IS: 1893(Part 1 and Part 4). Horizontal seismic acceleration spectral coefficients (in units of g)
3
Site Specific Acceleration Spectrum
2.5
2
1.5
1
Response Spectrum
5% damping
1
0.5
0
0
1
2 T(s) 3
4
5
Sa(g)
Fig 2. Site Specific Acceleration Spectrum
To convert acceleration spectra to ADRS format, following relation is used as per ATC40 guidelines. Hence spectral displacement is given by
=
Sd
3
ADRS Spectrum
2.5
2
1.5
1
demand spectra
0.5
0
0.5
0
0.5
1 Sd(m1.)5
2
2.5
Sa(g)
Fig 3. Acceleration Displacement Response Spectrum


RESULTS AND DISCUSSIONS
The RCC structures are analysed using SAP2000. The base shear, roof displacements of 4, 8 and 12 stories are obtained for response spectrum method, pushover analysis are plotted for purpose of comparison.
Analysis results
StepType
StepNum
4storey
8storey
12storey
Period, sec
UX
Period, sec
UX
Period, sec
UX
Mode
1
0.6203
0.84247
0.987095
0.66
1.495811
0.39754
Mode
2
0.6203
0.00576
0.987095
0.17
1.495811
0.41849
Mode
3
0.57
2.08E16
0.904633
1.79E20
1.353848
0
Mode
4
0.4227
1.04E16
0.508243
4.08E16
0.555972
1.3E16
Mode
5
0.3257
0.00334
0.362795
0.000284
0.497833
0.03005
Mode
6
0.3257
2.43E05
0.362795
0.000174
0.497833
0.07231
Mode
7
0.2572
1.36E16
0.331378
0.09111
0.451185
2.3E15
Mode
8
0.2294
4.77E15
0.331378
0.004808
0.379983
8.3E05
Mode
9
0.2112
0.00367
0.302836
1.38E16
0.379983
1.5E05
Mode
10
0.2112
0.08203
0.282369
6.31E14
0.377693
1.6E17
Mode
11
0.203
6.56E05
0.272649
3.09E16
0.301559
6.5E06
Mode
12
0.203
4.02E05
0.242599
0.002913
0.301559
0.00053
ESM
RSPM NSM
Base Shear kN
Table 1.Modal properties of the structures
Base Shear vs Storey level for 4 storey structure
800
600
400
200
0
Story4 Story3 Story2 Story1 Base
Storey level
Fig4. Base shear variation vs storey
Base Shear vs Storey level for 8 storey structure
800
600
400
ESM
200
RSPM
0
NSM
Storey level
Base Shear kN
Base Shear kN
Fig5. Base shear variation vs storey
Base Shear vs Storey level for 12 storey
structure
500
400
300
200
100
0
ESM
RSPM NSM
Storey level
FORCE
DISPLACEMENT RELATION
5000
4000
3000
2000
1000
0
0.02
Force Displacement Relationship
Story12
Story11 Story10 Story9 Story8 Story7 Story6 Story5 Story4 Story3 Story2 Story1
Base
Base Shear kN
Fig6. Base shear variation vs storey
Displacement
BaseForce
m
KN
0.031273
3113.707
0.042256
3925.926
0.044486
4029.447
0.045922
4077.245
0.045931
4042.097
0.04618
4050.352
0.04619
3929.134
0.047264
4006.019
0.047278
4006.645
Roof Displacement, m
0.06
0.04
0.02
0
Table 2. Base Shear Vs Roof displacement for 4storey
Intersection of Capacity Curve and Demand SpectrumPerformance Point
1
0.1
0.05
Sd,m
0
Capacity
Demand
0.5
0
Sa
Fig7. Capacity Demand Curve of 4 Storey
Step
Teff
Beff
SdCapacity
SaCapacity
SdDemand
SaDemand
Unitless
Sec
Unitless
m
Unitless
m
Unitless
0
0.463385
0.05
0
0
0.046043
0.863214
1
0.463385
0.05
0.027814
0.521452
0.046043
0.863214
2
0.492804
0.090066
0.038815
0.643407
0.041809
0.693048
3
0.501841
0.101939
0.041116
0.657235
0.041042
0.65604
4
0.50906
0.111674
0.042619
0.662064
0.040486
0.628929
5
0.531073
0.144463
0.045425
0.64838
0.038861
0.554678
6
0.532508
0.146056
0.045718
0.64905
0.038822
0.551136
Table 3. Summary of Capacity and Demand curve as per ATC40 procedure4 storey
Fig8. Plastic hinge formation corresponding to performance point

The performance point is 0.66m/s2 acceleration at 0.0404mdisplacement with 0.502sec effective time period which lies between 3rd and 4th step.

The highest plastic hinge in 4th and 5th step obtained is at life safety level.

Hence the structure is safe for the above specified base shear of 4027KN at roof displacement of 0.0404m

Therefore minor retrofitting may be required for few beams at lower storey level.
Displacement (m)
Base Force (KN)
2.70E05
0
0.085896
3838.31
0.101658
4434.98
Force displacement relationship
Intersection of Capacity curve and Pushover curvePerformance point
0.05
0.04
0.03
Base shear
vs roof displacemen t
6000
4000
2000
0
0.00E+00 1.00E01 2.00E01
Roof displacement,m
Sa
Base shear kN
Table 4. Base Shear Vs Roof displacement for 8storey
0 0.05 0.1 0.15
Sd, m
Capacity
Demand
0.02
0.01
0
Fig9. Capacity Demand Curve of 8 Storey
Step
Teff
Beff
SdCapacity
SaCapacity
SdDemand
SaDemand
Unitless
Sec
Unitless
m
Unitless
m
Unitless
0
0.902823
0.05
0
0
0.077706
0.043055
1
0.902823
0.05
0.05347166
0.026409349
0.088706
0.033055
2
0.902823
0.05
0.08862825
0.036364573
0.097706
0.023055
Table5. Summary of Capacity and Demand curve of 8 storey as per ATC40 procedure
Fig10. Plastic hinge formation corresponding to performance point

The performance point is 0.033m/s2 acceleration at 0.088m displacement with 0.903sec effective time period which lies between 1st and 2nd step.

The highest plastic hinge in 1st and 2nd step obtained has crossed little bit beyond collapse prevention level.

Hence the structure is subjected to failure of few peripheral beams and columns for the above specified base shear of 4434KN at roof displacement of 0.101m.

Therefore most the peripheral beams and columns need to be retrofitted for the revised forces.
Displacement
BaseForce
m
KN
0.000041
0
0.231246
6799.436
0.628941
17079.51
0.628948
17030.41
0.634539
17168.95
0.629408
16963.64
Force displacement relationship
20000
15000
10000 Base shear vs
5000 roof
0 displacement
0 0.5 1
Roof displacement,m
Base Shear V,kN
Table 6. Base Shear Vs Roof displacement for 12storey
Step
Teff
Beff
SdCapacity
SaCapacity
SdDemand
SaDemand
Unitless
Sec
Unitless
M
Unitless
M
Unitless
0
1.358341
0.05
0
0
0.134968
0.294477
1
1.358341
0.05
0.046145
0.100681
0.134968
0.294477
2
1.422072
0.065048
0.125691
0.250208
0.132074
0.262913
3
1.465308
0.071499
0.209953
0.393645
0.132668
0.248741
4
1.487736
0.070395
0.296875
0.53996
0.135271
0.246031
5
1.499725
0.068548
0.373917
0.669254
0.137345
0.245827
6
1.501421
0.069551
0.37396
0.66782
0.136962
0.244587
7
1.502028
0.069168
0.381217
0.680229
0.137222
0.244854
Demand
spectrum
Capacity spectrum
Intersection of Capacity Curve and Demand CurvePerformance Point
0.8
0.6
0.4
0.2
0
Sa
Table7. Summary of Capacity and Demand curve of 8 storey as per ATC40 procedure
Sd, m
0.6
0 0.2 0.4
Fig11. Capacity Demand Curve of 12 storey
Fig12. Plastic hinge formation corresponding to performance point

The performance point is 0.294m/s2 acceleration at 0.134m roof displacement with 1.358sec effective time period which lies between 1st and 2nd step.

The highest plastic hinge in 1st and 2nd step obtained is between Operational and Immediate occupancy zone. Hence there wont be localized collapse for this level of earthquake.

Hence the structure is safe for the above specified base shear of 16963KN at roof displacement of 0.629m.


CONCLUSIONS
The results have shown clear information about the evaluation methods which can be concluded as follows:

The base shear obtained from equivalent static and response spectrum is more than that of the pushover method of analysis.

In both 4 & 8 storey structures, performance point is figured in the non linear region. Therefore elastic method of assessment doesnt hold good for seismic evaluation of structures in severe ground motions.

The 4 storey structure is in life safety level after locating the performance point. Therefore damages may occur in the nonstructural members but serviceable.

In 8 storey structure, few hinges have crossed collapse prevention level i.e large damage to structural members, therefore its not serviceable and requires major retrofitting to structural elements.

The performance point in 12 storey structure is figured in the elastic region which shows more strength and stiffness towards lateral loading.

In 12 storeyed structure most of the plastic hinges generated are in Immediate occupancy level i.e less damage but serviceable. Hence no retrofitting is required.

From the results of pushover analysis, the weak links in the structure are identified and the performance level achieved by structure is known. This helps to find the retrofitting location to achieve the performance objective.

The above results have showed that intersection of demand curve with capacity curve near the elastic range, the structure has a good resistance and high safety against collapse.

Intersection of demand and capacity curve indicates that the properly detailed reinforced concrete frame building is adequate
6 REFERENCES

Applied Technology Council, ATC 40: Seismic Evaluation and Retrofit of Concrete Buildings (USA,1996).

Feeral Emergency Management Agency, FEMA 356: Pre standard and Commentary for the Seismic Rehabilitation of Buildings (Washington, 2000).

Federal Emergency Management Agency, FEMA 440: Improvement of Nonlinear Static Seismic Analysis Procedures (Washington, 2005).

IS 18932002 (Part I) Indian Standard Criteria for Earthquake Resistant Design of Structures (New Delhi, 2002)

Graham H Powell – Performance Based Design using Nonlinear Analysis – seminar notes – (Computers and Structures, Inc., 2006)

IS 456:2000 Plain and Reinforced Concrete – Code of PracticeIndian Standards

SAP 2000, V 14.0, Computers and Structures, Inc. Berkeley, California, USA.

Helmut Krawinkler, Professor Stanford University Stanford, California Pushover Analysis: Why, How, When, and When not to use it

Hiroshi Kuramoto and Kazuyuki Matsumoto MODE ADAPTIVE PUSHOVER ANALYSIS FOR MULTI STORY RC BUILDINGS

G. P. Cimellaro, A.M.ASCEBidirectional Pushover Analysis of Irregular Structures