Tests to Collapse of Simple Structures and Comparison with Existing Codified Procedures

The results of tests on fifteen four-column frame specimens subjected to progressive unidirectional ground shaking up to collapse are analyzed. Test structure performance is compared with proposed limits for minimizing P-∆ effects in highway bridge piers. The stability factor is found to have a strong relation to the relative structural performance in this regard. Specimens with θ less than 0.25 satisfied the proposed criteria for at least a portion of their respective test schedule. The limit is violated prior to the final test in which complete specimen collapse occurs. Finally, a series of shake table tests are compared with an analytical model using two methods. Introduction The arbitrary lateral drift limits prescribed by modern design codes to limit non-structural damage also indirectly ensure that structural performance is minimally affected by the effect of gravity on the lateral force resistance of structures (a.k.a. P-∆ effect). However, as conventional drift limits are progressively eliminated and replaced by other performance-based limits, inelastic behavior is relied upon to a greater extent in the dissipation of seismic input energy. Therefore, accurate quantification of the destabilizing effect of gravity is becoming more significant for structural design. As a result, it may be desirable to investigate the behavior of those structures in order to enhance our understanding of the condition ultimately leading to their collapse, and to ensure public safety during extreme events. While many experimental studies and theoretical damage models support these calculated values, it remains that few experimental studies have pushed the shake table tests up to collapse. A recently published report (Vian and Bruneau 2001) discusses a program of shake-table testing of simple frames through collapse. This series of tests provide well-documented data, freely available on the world wide web, which may be used to develop or validate algorithms capable of modeling the inelastic behavior of steel frames up to collapse. Fifteen specimens having various properties were tested in an attempt to identify some of the general parameters responsible for trends in behavior of Single-Degree-of-Freedom (SDOF) structures to collapse under earthquake loading. Ph.D. Candidate, Dept. of CSEE, University at Buffalo, Amherst, NY 14260. Deputy Director, MCEER, Professor, Dept. of CSEE, University at Buffalo, Amherst, NY 14260. In this paper, some basic concepts of P-∆ behavior are summarized, allowing for comparison with the recorded results of the above-mentioned testing program. This is followed by a preliminary investigation of behavioral trends observed from the shake table results. In particular, peak responses are compared with limits proposed by others to minimize P-∆ effects in bridge piers. Finally, experimental results are compared with those obtained using a simple analytical model, to illustrate use of the generated experimental data for to develop or calibrate models of inelastic behavior to collapse. Progressive bilinear dynamic analyses are performed and compared with shake table test results. A basic, bilinear model is used for illustration purposes, and some observations are made with respect to the effect of damping estimates, on analysis results, and a few other issues. P-∆ Behavior Some concepts for characterizing P-∆ effects in inelastic SDOF structures under lateral load are described below, along with an overall view of the fundamental structural behavior. Fig. 1a shows a column from a single bay, single story structure, with an infinitely stiff beam, thereby resulting in a lateral stiffness of the column, ignoring P-∆, of Ko = 12EI / L. A bilinear, SDOF model is shown in Fig. 1b. Elastic-perfectly plastic structural response (neglecting P-∆) is shown, as well as the response modified by the influence of P-∆. MacRae, Priestley and Tao (1993) provided a summary of additional concepts on P-∆ effects on simple structures during earthquakes. K2 = -θ Ko Vyp’ Vyp = Vyo (1 θ) Displacement La te ra l F or ce