Seismic Behaviour and Pushover Analysis of Steel Frames

 

Dr. S. Elavenil1, Vijayakumar2

1Professor in Civil, School of Building Sciences,

V.I.T University (Chennai Campus), Vandalur, Chennai. Tamilnadu  India

2S.R.M. University, Chennai Tamilnadu, India

*Corresponding Author: s_elavenil@yahoo.com

 

ABSTRACT:

The research concentrates on a computer based push-over analysis technique for performance-based design of steel building frame works subjected to earthquake loading. Through the use of a plasticity-factor  that measures  the degree of plasticisation, the standard elastic and geometric stiffness matrices for frame elements (beams, columns, etc.) are progressively modified to account for nonlinear elastic–plastic behaviour under constant gravity loads and incrementally increasing lateral loads. The proposed analysis technique is illustrated for two steel frameworks of solid and hollow member properties .This investigation studies aim to analyse the comparison between hollow and solid frames. The technique is based on the conventional displacement method of elastic analysis. The analytical procedure developed is to estimate the inelastic deformations of beams, columns and connections are validated by incorporating the same in pushover analysis. Based on the analysis results it is observed that inelastic displacement of the structure is within the collapse prevention level.

 

KEY WORDS: Seismic Performance, Pushover, Non-linear, performance levels, Steel frame, Capacity Curves.

 

INTRODUCTION:

Pushover analysis is a static, nonlinear procedure in which the magnitude of the structural loading is incrementally increased in accordance with a certain predefined pattern. With the increase in the magnitude of the loading, weak links and failure modes of the structure are found. The loading is monotonic with the effects of the cyclic behaviour and load reversals being estimated by using a modified monotonic force-deformation criteria and with damping approximations. Static pushover analysis is an attempt by the structural engineering profession to evaluate the real strength of the structure and it promises to be a useful and effective tool for performance based design.

 

Pushover Analysis:

Pushover analysis is a performance based analysis. According to ATC 40, there are two key elements of a performance-based design procedure - demand and capacity. Demand is the representation of earthquake ground motion or shaking that the building is subjected to.

 

In nonlinear static analysis procedures, demand is represented by an estimation of the displacements or deformations that the structure is expected to undergo. Capacity are a representation of the structure’s ability to resist the seismic demand. The performance is dependent on the manner that the capacity is able to handle the demand. In other words, the structure must have the capacity to resist demands of the earthquake such that the performance of the structure is compatible with the objectives of the design.

 

Pushover analysis is an approximate analysis method in which the structure is subjected to monotonically increasing lateral forces with an invariant height-wise distribution until a target displacement is reached. Pushover analysis consists of a series of sequential elastic analysis, superimposed to approximate a force-displacement curve of the overall structure.

 

A two or three dimensional model which includes bilinear or trilinear load-deformation diagrams of all lateral force resisting elements is first created and gravity loads are applied initially. A predefined lateral load pattern which is distributed along the building height is then applied. The lateral forces are increased until some members yield. The structural model is modified to account for the reduced stiffness of yielded members and lateral forces are again increased until additional members yield. The process is continued until a control displacement at the top of building reaches a certain level of deformation or structure becomes unstable. The roof displacement is plotted with base shear to get the global capacity curve.

 

Figure: 1. Design capacity curve

 

Modelling:

The STAAD Pro V8i software is utilized to create 2D model and carry out the Pushover analysis. The buildings are modelled as a series of stories from 5 to 40 with same bay width and storey height. The study is performed for applied lateral load to find base shear and the displacement. The buildings adopted consist of reinforced concrete. The frames are assumed to be firmly fixed at the bottom and the soil–structure interaction is neglected. The input parameters for the model geometry for both solid and hollow sections are given in Table.1

 

Table 1: Input parameters for both sections

Number of stories

Type of  frame

Bay  width

Height of each storey

5

2D-Frame

6m

3m

10

2D-Frame

6m

3m

15

2D-Frame

6m

3m

20

2D-Frame

6m

3m

25

2D-Frame

6m

3m

30

2D-Frame

6m

3m

35

2D-Frame

6m

3m

40

2D-Frame

6m

3m

 

Material properties for both Solid and Hollow sections:

Figure-2 shows the cross section of the solid and hollow sections

Youngs modulus of material (E)     = 2.05x108 kN/m2

Poissons ratio (nu)                           = 0.3

Density                                           = 76.8195kN/m3

Thermal expansion                        = 1.2x10-5

Critical damping                              = 0.03

 

Fig. 2 Cross section of both Solid and Hollow sections

 

Pushover Analysis Methodology:

Figure 3 shows the pushover methodology for both solid and hollow section. In this chart describes the pushover steps and details over the pushover analysis.

Figure 3 : Pushover analysis methodology

 

RESULTS AND DISCUSSION:

The capacity curve obtained through the pushover analysis is shown in Figure 4,5,6,7,8,9,10. The difference in results is due to difference in the applied lateral force and its estimation. In this paper, the lateral forces has been estimated by using seismic coefficient method as per IS: 1893-2002. The zone is considered as zone V with medium soil. The analysis carried out by representing the proposed inelastic member behaviour with semi-rigid connection will resemble the most practical case. The sequence of hinge formation observed during the analysis is shown in Figure 11. At the end of interaction severe hinges are observed in first floor beams and ground floor columns and which gives an insight in structural behaviour and understanding. It may be concluded that under a severe earthquake the first floor beams and ground floor columns retrofit may not meet all the structural requirements of the life safety level. Table 2 shows the inelastic response displacements of the frame. It is observed that inelastic displacement of the structure is within collapse prevention.

 

Figure 4 : Capacity curve for 5-storey 2-D frame

 

Figure 5 : Capacity curve for 10-storey 2-D frame

 

Figure 6 : Capacity curve for 15-storey 2-D frame

 

Figure 7 : Capacity curve for 20-storey 2-D frame

 

Figure 8 : Capacity curve for 25-storey 2-D frame

 

Figure 9 : Capacity curve for 30-storey 2-D frame

 

Figure 10 : Capacity curve for 35-storey 2-D frame

 

 

Figure 11: Formation of plastic hinges-5 storey

Level : <=IO         , Colour : Green

Level : <=IO-LS   , Colour : Blue

Level : <=LS-CP  , Colour : Magenta

Level : <=CP        , Colour : Red.

 

 

Table 2 : Results of Displacement, Base shear and Performance Level

Models

Storey level

Displacement in mm

Base shear in kN

Performance level

Solid section

5-storey

496.869

1211.879

IO - LS

10-storey

501.037

1127.953

IO - LS

15-storey

500.328

511.839

IO - CP

20-storey

502.833

369.625

P*

25-storey

508.349

404.824

P*

30-storey

533.106

328.047

P*

35-storey

570.086

323.151

P*

Hollow section-1

5-storey

413.315

2690

IO

10-storey

500.140

2304.661

IO

15-storey

502.681

1469.171

P*

20-storey

503.392

1014.527

P*

25-storey

511.116

753.338

P*

30-storey

540.131

601.590

P*

Hollow section-2

5-storey

388.734

3037.833

LS - CP

10-storey

500.134

2513.278

IO - LS

15-storey

500.459

1642.466

P*

20-storey

504.837

1138.995

P*

25-storey

510.418

840.159

P*

30-storey

518.374

644.675

P*

Hollow section-3

5-storey

370.616

3279.376

LS - CP

10-storey

500.549

2648.393

IO - LS

15-storey

501.966

1784.332

P*

20-storey

501.785

1123.604

P*

25-storey

503.858

896.065

P*

30-storey

511.216

687.266

P*

 

Hollow section-4

5-storey

352.962

3507.017

IO - LS

10-storey

500.507

2770.105

IO - LS

15-storey

500.742

1888.673

P*

20-storey

505.462

1305.431

P*

25-storey

504.152

949.701

P*

30-storey

511.017

728.511

P*

35-storey

545.327

605.834

P*

Note: Performance levels are as follows,

IO-Immediate Occupancy,

LS- Life Safety,

CP- Collapse Prevention,

C-Collapse,

P*- Performance point beyond collapse.

 

The displacement and the base shear are shown in Figure12 and 13. Effect of lateral displacement for 5-storey 2-D frame with hollow section provides 16.73% reduction when compared with the solid sections. Base shear values for 5-storey 2-D frame with hollow section when compared with  solid section which is increased up to 54 %.

 

SS
 


Figure 12: Displacement for various stories

 

Figure 13: Base shear for various stories

 

CONCLUSIONS:

In this study, 2-D frames are modelled for both solid and hollow sections for various stories with constant bay width and storey height which was analysed by pushover analysis using STAAD.Pro.

·         When the number of storey decreases corresponding base shear increases and also number of storeys increases corresponding displacement increases.

·         It is found that the drift to height ratio is limited to 35 stories despite of increased base width.

·         The performances of all the solid and hollow section 2-D models lies in between life safety and collapse prevention. Formation of plastic hinges were maximum when the storey levels are minimum.

·         Comparing the results of solid and hollow sections base shear vs displacement curve indicates that the hollow section is far better than solid sections.

·         Effect of lateral displacement for 5-storey 2-D frame with hollow section provides 16.73% reduction when compared with the solid sections.

·         Base shear values for 5-storey 2-D frame with hollow section when compared with  solid section which is increased up to 54 %.

·         When storey level get increased pushover load steps get decreased, so the capacity curve become linear for some models corresponding to its storey level.

·         Self weight of both solid and hollow section clearly reveals that the hollow section is having maximum dead weight than solid sections. Comparatively 60% of self weight values get increased in hollow section than the solid section.

·         The seismic performance evaluation of a steel building frame is carried out by using pushover analysis accounted for user defined inelastic material behaviour and assigning inelastic effects to plastic hinges at member ends.

·         The analytical procedure developed to estimate the inelastic deformations of beams, columns and connections are validated by incorporating the same in pushover analysis. Based on the analysis results it is observed that inelastic displacement of the structure is within the collapse prevention level.

 

REFERENCES

1.     Anil K. Chopra, and Rakesh K. Goel,(2004) “A modal pushover analysis procedure to estimate seismic demands for unsymmetric-plan buildings” Earthquake engineering and structural dynamics  vol; 33:P. 903–927

2      Bülent AKBAŞ, Jay SHEN, F. İlknur KARA, Ülgen Mert Tuğsal,(2003) “Seismic behavior and pushover analyses in steel frames çelik çerçevelerin deprem  performanslari ve öteleme analizleri” Fifth National Conference on Earthquake Engineering, 26-30 May 2003, Istanbul, Turkey Paper No: AT-053

3.     D.K. Baros ,  S.A. Anagnostopoulos ,(  2008) “An overview of pushover      procedure for the analysis of building susceptible to torsional behaviour” The 14thWorld Conference on Earthquake Engineering October 12-17, Beijing, China.

4.     Cinitha A, Umesha P.K, Nagesh R . Iyer  “Evaluation of seismic performance of an existing steel building- pushover analysis approach” CSIR- Structural Engineering Research Centre, Taramani, Chennai.

5.     Elavenil.S,Nabin Raj.C,(2012) ‘Analytical study on Seismic Performance of Hybrid Structural System subjected to Earthquake’, International Journal of Modern Engineering Research (IJMER) Vol.2, No.4, pp-2358-2363

6.     R. Hasan, L. Xu, D.E. Grierson,( 2002) “Push-over analysis for performance-based seismic design” Computers and Structures , Vol.80,pp 2483–2493.

7.     T. Hasegawa ,and H. Kamura, (2008) “Seismic response prediction of steel frames utilizingplastic strain energy obtained from pushover analysis” The 14th World Conference on Earthquake Engineering October 12-17, Beijing, China

8      G.D.P.K. Seneviratna and Helmut Krawinkler, and (1988) “Pros and cons of a pushover analysis of seismic performance evaluation” Engineering Structures, Vol. 20, pp. 452-464,

9      Sigmund Multi A. Freeman, Kent. K. Sasaki, and Terrence F. Paret, (6th US national conference) “Mode pushover procedure( MMP)-A method to identify the effects of higher mode in a pushover analysis”

10.   L. Xn, and Y. Liu, (2005)  “Nonlinear Analysis of Inelastic Steel Frames” Advances in Steel Structures, Vol.1,pp.217-224

 

 

Received on 22.08.2014                                   Accepted on 20.09.2014       

©A&V Publications all right reserved

Research J. Engineering and Tech. 5(3): July-Sept. 2014 page 128-134