Comparative Study of Pushover Analysis on RCC Structures

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 non-linear 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 zone-V 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, ATC-40, Performance Point.

1. 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 non-linear time history analysis which is at this time is considered overly complex as it requires accurate acceleration data of previous earthquake data. Available simplified non-linear 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 ATC-40 guidelines. The objective of this study is to emphasize the use of non-linear static procedure in general and focus on the capacity spectrum method as per ATC-40.

2. 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 non-linear static pushover method

   .

   4 @ 4m

   4@4m

   4 @ 3m

   8@ 3m

   12@ 3m

   Fig1. Plan of 4, 8 12 storey Elevation

3. METHODOLOGY

   1. 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

   2. 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 low-rise

   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.

   NON-LINEAR STATIC ANALYSIS

   Available simplified nonlinear analysis methods referred to as non-linear static analysis procedures such as Capacity Spectrum method (ATC-40), displacement co-efficient 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 figure-2 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

   1. 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 ATC-40 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

4. 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	4-storey		8-storey		12-storey
   		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	2.08E-16	0.904633	1.79E-20	1.353848	0
   Mode	4	0.4227	1.04E-16	0.508243	4.08E-16	0.555972	1.3E-16
   Mode	5	0.3257	0.00334	0.362795	0.000284	0.497833	0.03005
   Mode	6	0.3257	2.43E-05	0.362795	0.000174	0.497833	0.07231
   Mode	7	0.2572	1.36E-16	0.331378	0.09111	0.451185	2.3E-15
   Mode	8	0.2294	4.77E-15	0.331378	0.004808	0.379983	8.3E-05
   Mode	9	0.2112	0.00367	0.302836	1.38E-16	0.379983	1.5E-05
   Mode	10	0.2112	0.08203	0.282369	6.31E-14	0.377693	1.6E-17
   Mode	11	0.203	6.56E-05	0.272649	3.09E-16	0.301559	6.5E-06
   Mode	12	0.203	4.02E-05	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 4-storey

   Intersection of Capacity Curve and Demand Spectrum-Performance 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 ATC-40 procedure-4 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)
     2.70E-05	0
     0.085896	3838.31
     0.101658	4434.98

     Force displacement relationship

     Intersection of Capacity curve and Pushover curve-Performance point

     0.05

     0.04

     0.03

     Base shear

     vs roof displacemen t

     6000

     4000

     2000

     0

     0.00E+00 1.00E-01 2.00E-01

     Roof displacement,m

     Sa

     Base shear kN

     Table 4. Base Shear Vs Roof displacement for 8-storey

     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 ATC-40 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 12-storey

   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 Curve-Performance Point

   0.8

   0.6

   0.4

   0.2

   0

   Sa

   Table7. Summary of Capacity and Demand curve of 8 storey as per ATC-40 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.

5. CONCLUSIONS

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

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

2. 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.

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

4. 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.

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

6. 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.

7. 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.

8. 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.

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

6 REFERENCES

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

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

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

4. IS 1893-2002 (Part I) Indian Standard Criteria for Earthquake Resistant Design of Structures (New Delhi, 2002)

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

6. IS 456:2000 Plain and Reinforced Concrete – Code of Practice-Indian Standards

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

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

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

10. G. P. Cimellaro, A.M.-ASCE-Bidirectional Pushover Analysis of Irregular Structures