Nonlinear Pushover Analysis of Steel Frame Structure

Nonlinear Pushover Analysis of Steel Frame Structure Dahal, Purna P., Graduate Student Southern Illinois University, Carbondale

Abstract: The applicability of the SAP2000 software for the nonlinear pushover analysis is documented. The two story steel frame structure is modeled for moderate earthquake. Different stages of deformation followed by hinges formation is studied for the prediction of post yielding behavior using pushover analysis tool included in the software. Damage in the structure is identified by plastic hinges at different level of safety definition from FEMA-356 and ATC 40. Frame performance for the lateral load is interpreted with family of capacity-demand curves.

 Keywords: Nonlinear Analysis, pushover analysis, hinges, steel frame structures, Introduction: Linear elastic analysis of the structural member is based on stresses up to yield stress. Material is considered as perfectly elastic before yielding. Equation of equilibrium is written on the undeformed configuration which seems to be limited approach of the analysis procedure. To improve this inadequacy, a concept of nonlinear analysis is introduced. Nonlinear analysis considers the deformed geometry and nonlinear behavior of the material. The load resisting behavior is significantly affected when nonlinearities included in the analysis [6]. Nonlinear analysis involves with huge iteration process. Since material stiffness will be reduced in each increment loading, the analysis is performed for secant stiffness of the member. This method of analysis in the seismic design is used for (a) to assess and design seismic retrofit solutions for existing structure (b) design new structure that employ structural materials, systems, or other features that do not conform to current building code requirements (c) assess the performance of structure for specific requirements [7]. The main purpose of present study is to perform nonlinear analysis using commercial nonlinear finite element software SAP2000 [8] and to

investigate the failure behavior of steel frame for the quake load. The failure behavior will be used in performance based design of structure. The nonlinear static analysis is carried out for the general loading on two story steel frame and lateral seismic load is applied to perform pushover analysis at specified displacement. The various pushover curve, load-deformation curve are presented. Methodology: Frame structure is loaded first with general loading and then pushover load is applied monotonically at its deformed configuration of general loading. 2 nd story (from Joint 3 indicated in figure 1) displacement is monitored up to 12 inches. Lateral allowable story drift is taken from table12.12-1, ASCE7-10[2] as 6.48 inches defined by following expression. ∆ =0.02h,

h = story height form ground label

After yielding, plastic hinges will form at different location indicating the risk of occupant as shown in the figure 4. The performance point is calculated from the guideline defined in FEMA-356 and ATC-40.

as a guideline for practicing engineer. ATC-40 [1], FEMA-356 [4], FEMA-273 [5] are well known available document to perform pushover analysis. In SAP2000, hinge will be added at the each stage when the structure yielded to the prescribed level defined in FEMA-356 and ATC 40. The performance of the structure is determined by hinges formation. Various types of plastic hinges: uncoupled/coupled moment, torsion, axial force and shear hinges are available. In this study, uncouple moment hinges are presented.

Modeling: Joint 3

M2 n

2  Story 12 ft

M1

st

1  Story 15ft

24ft

24ft

Figure 1- Steel frame Structure (A992Fy50) Table 1: Section and Loading Properties of 2-Story Steel Frame

Story

Columns

Beams

1 2

W14x90 W14x90

W24x62 W12x26

Lump masses (kips2 sec  /in) 0.1941 0.5156

Effective Loading for Beam 0.2kip/ft 0.1kip/ft

In SAP2000, material nonlinearity can be define from its stress strain relationship (figure 2).

Fig 3: Expected Capacity Curve of the frame element

0.6 0.4    )    2   n    i    /   s   p    i    K    (-0.3   s   s   e   r    t    S

0.2 0 -0.1

-0.2

0.1

0.3

-0.4 -0.6 Strain(in/in)

Figure 2 – Stress relationship for Steel A992Fy50 Pushover Analysis: To identify the nonlinear response for the seismic hazard assessment of the structure, a nonlinear static analysis called pushover analysis has been carried out. Many researches were done [3] for the performance study of structure and the outcome of the research are documented

Figure 4 – Risk indicator curve The lateral force is applied at the deformed state of the general loading from point A. No hinges will formed before point B where structure will shows linear behavior and after that one or more hinges will start to form. Software will shows hinges with following remarkable indication:  Immediate Occupancy (IO)  – yielding of steel, significant cracking of concrete and nonstructural damage will arises

 Life Safety (LS)  - damage of structural and nonstructural components will starts. We have to make essential circulation routes accessible to minimize risk of injury and causality for this stage. Collapse Prevention (CP) – This point ensure a small risk of partial or complete building collapse by limiting structural deformations and forces to the onset of significant strength and stiffness degradation.

Point C is the indication of ultimate capacity of the structure and Point D indicate residual strength for the structure. Complete failure will occur at point E. The capacity and demand curve is plotted for the seismic coefficient Ca and Cv as 0.7 considering moderate earthquake zone. Figure 6 – Base Shear Vs Roof Displacement (Joint 3) Curve

Result: The capacity-demand curve is plotted as shown in figure 5. The behavior of the structure is observed with unique indicator until the failure occurs.

The frame is pushed well into inelastic range. The demand curve meets capacity curve at 5.1 in displacement of joint 3 with base shear 260.7 kips (step 3-4).

Performance Point

Capacity Curve

Step-1 Demand Curve

Figure 5 – Capacity/Demand Spectrum

Step -2

Step – 3

Step -7

Step -4

Step-8 (collapse of 1  story column)

st

Figure 6 – Plastic Hinges formation steps 1-8 Conclusion and Discussion:

Step – 5

Pushover analysis is very useful tool to identify the behavior of structure to the incremental loading. The frame structure modeled for the seismic coefficient 0.7 defined in ATC40 can perform well. Permanent hinges starts to form at roof displacement 10.72 inches which is far more than allowable lateral drift as per ASCE 7. Present study concludes that: a.

The Nonlinear analysis is essential to observe the behavior of structure. b. Nonlinear pushover analysis feature available in SAP2000 software can be used to predict post yielding mechanism in of the structure.

Step 6

Since the aim of the study is to identify applicability of the SAP2000 software for nonlinear pushover analysis for frame structure, further research is needed to find usefulness of the software for nonlinear analysis of solid structure like shear wall, dam foundation etc.

References: 1) Applied Technology Council, ATC-40, Seismic evaluation and retrofit of concrete Buildings, California, 1996; Vols. 1 and 2. 2) ASCE 7-2010, Minimum Design Loads for Buildings and Other Structures. 3) Chopra, A.K., and Goel, R.K. (2002). “A Modal Pushover Analysis Procedure for Estimating Seismic Demands for Buildings”. Earthquake Engineering and Structural Dynamics, Vol.31, pp. 561582. 4) Federal Emergency Federal Agency, FEMA-356. Prestandard and Commentary for Seismic Rehabilitation of Buildings. Washington DC, 2000.

5) Federal Emergency Federal Agency, FEMA-273. NEHRP Guidelines for the Seismic Rehabilitation of Buildings, Washington DC, 1997. 6) Kassimali, A. and Badiey, M. (1984) Nonlinear behavior and stability of latticed Domes under combined loading. 7) Nonlinear Structural Analysis for Seismic Design, NEHRP Seismic Design Technical Brief No. 4-2010 8) SAP 2000, Ver. 14.0.0, integrated finite element analysis and design of structures reference manual. Berkeley (CA, USA): Computers and Structures INC.