Keywords: load increment method, pushover curve, limit point, Davidenko curve.

Pushover analysis involves certain approximations and simplifications such that some amount of variation is always expected to exist in seismic demand prediction of pushover analysis. In this paper, the innovative modal adaptive pushover procedure proposed by Gupta and Kunnath [1] is improved using a modified normal flow algorithm through an extensive comparative study involving different pushover methods, either single or multi mode, adaptive. The Newton-Raphson iterative algorithm is used along the flow path normal to the Davidenko curves with a modified convergence rate. Contrary to the previous arc-length methods, this algorithm which uses the Homotopy approach, is based upon new mathematical concepts. The stability points of pushover curves may be classified into limit points with snap-through and snap-back. Advanced incremental iterative methods have been developed based upon the arc-length approach [2,3]. In the current work, using the proposed method, the number of the iterations in the vicinity of the mentioned points decreases in addition to having the possibility of passing the post yield stiffness. Of equally noteworthy significance is perhaps the fact that the proposed adaptive pushover schemes are as simple to use as standard pushover methods. In order to evaluate the proposed method, a frame is analyzed using the algorithm presented and the results are compared with non-linear dynamic analysis (NDA) results and the pushover analysis followed DRAIN-2DX [4]. The total number of iterations used by the proposed method are significantly less than that of other methods. As a conclusion, the moment-resistance frames have highly non-linear behavior regarding the number of degrees of freedom and the level of load applied. Among the non-linear analysis methods simple iterative and incremental methods are weak in passing the limit points of the post-yield stiffness. In fact, they may fail in passing the limit points of the load and displacement. In the present method, based upon the mathematical concepts, the condition equation is transmitted to the normal flow path first, and then using the incremental iterative method, the stability path of the structure is followed in fewer steps. The method developed in this paper which uses the modified normal flow algorithm decreases the time and the cost for non-linear analysis of frames when compared with NDA results. In addition the method developed has the ability of passing beyond the pushover curve.

1

B. Gupta, S.K. Kunnath, "Adaptive spectra-based pushover procedure for seismic evaluation of structures", Earthquake Spectra, 16(2), 367-391, 2000. doi:10.1193/1.1586117

2

D.A. Pecknold, J. Ghaboussi, T.J. Healey, "Snap-through and bifurcation in a sample structure", Journal of Engineering Mechanics, ASCE, 111(7), 909-922, 1985. doi:10.1061/(ASCE)0733-9399(1985)111:7(909)

3

F. Fujii, E. Ramm, "Computational bifurcation theory: path-tracing, pinpointing and path-switching", Engineering Structures, 19(5), 385-392, 1997. doi:10.1016/S0141-0296(96)00094-6

4

G.H. Powell, V. Prakash, S. Campbell, "DRAIN-2DX Base Program Description and User Guide - Element Description and User Guide for Elements TYPE01, TYPE02, TYPE04, TYPE06, TYPE09, TYPE15", Version 1.10, Report No. UCB/SEMM-93/18, Structural Engineering Mechanics and Materials, University of California at Berkeley, December, 1993.

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