Keywords: earthquake engineering, pushover analysis, structural optimization, performance-based design, steel structural design, earthquake damage assessment.

Since FEMA-273 [1] adopted pushover analysis procedure as a major tool to evaluate the seismic demands, interest in developing new pushover analysis technique is escalating among researchers. Hasan, Xu and Grierson [2] proposed a pushover analysis method by introducing 'fictitious plastic-hinge connections' at both ends of beam-column elements. Non-dimensional 'plasticity-factors' for plastic-hinge connections were introduced to monitor the progressive plastification (stiffness degradation) of building frame members under increasing lateral loads. Chopra and Goel [3] introduced modal pushover analysis procedure, which was regarded as an important development in extending the capability of pushover analysis technique to building frameworks having significant higher mode response. Modal pushover analysis accounts for several vibration mode effects to predict the seismic demands imposed on building frameworks by earthquake hazards. However, the application of modal pushover analysis for performance-based seismic design requires considerable computational effort since the iterative synthesis process involves many re-analyses of the structure. For practical use in engineering offices, the optimal performance-based seismic design of steel building frameworks requires a computational algorithm that efficiently integrates the modal pushover analysis together with a design optimization (or automation) methodology [4].

The paper identifies the characteristics for the so-called advanced pushover analysis procedure to be used for the design of steel building frameworks under seismic loading. The characteristics are: 1) this analysis can capture the behavior associated with beam, column, and beam-column strength limit states with sufficient accuracy such that the method alone suffices as a verification of the adequacy with respect to these limit states; 2) this analysis can evaluate structural responses under earthquake loading with sufficient accuracy such that the method alone suffices as a tool for seismic design. The first characteristic is realized by considering various member limit states such as local buckling, overall buckling (lateral-torsional buckling strength limit will be introduced in the future study) in the nonlinear finite element model. The second characteristic is realized by using modal pushover analysis concept. A spectrum-based modal pushover analysis procedure is proposed to evaluate structural seismic demands for this study.

Then, the paper presents a performance-based design optimization model for steel building frameworks subject to multi-level earthquake loadings. Least structural weight and minimum earthquake damage are taken as the design criteria. The damage-mitigating objective can be stated as pursuing a uniform ductility demand in all stories. The damage function to be minimized is defined as,

where: is the number of building stories; and are the drift of story and the roof drift at the performance level, respectively; is the vertical distance from the base of the building to story ; and is the height of the building. In fact, defines the coefficient of variation of the lateral plastic deflection distribution, since and represent story-drift ratio and mean-drift ratio, respectively. By definition, the value of is equal to zero for a perfectly uniform inter-story drift distribution.

An optimality criteria algorithm is applied to solve the design optimization problem to find member sizes for which structure weight and earthquake damage are minimized and appropriate structural behavior is ensured at multiple performance levels. A 9-story steel building framework is illustrated using the proposed design procedure.

1

Federal Emergency Management Agency (FEMA-273), "NEHRP Guideline for the Seismic Rehabilitation of Buildings", Building Seismic Safety Council, Washington DC, 1997.

2

Hasan, R., Xu, L., Grierson, D.E., "Pushover Analysis for performance-Based Seismic Design", Journal of Computers and Structures, 80, 2483-2493, 2002. doi:10.1016/S0045-7949(02)00212-2

3

Chopra, A.K., Goel, R.K., "A modal pushover analysis procedure for estimating seismic demands for buildings", Earthquake Engineering and Structural Dynamics, 31, 561-582, 2002. doi:10.1002/eqe.144

4

Gong, Y., "Performance-Based Design of Steel Building Frameworks Under Seismic Loading", Ph.D. Thesis, University of Waterloo, Ontario, Canada, 2003.

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