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• W2464193996 abstract "The purpose of a progressive collapse analysis is to determine whether a structure remains stable when one or more members (usually columns or bearing wall panels) are suddenly removed. Progressive collapse analyses can be performed using linear or nonlinear methods of structural analysis. This paper is concerned mainly with nonlinear methods. This paper considers the following topics. • The basic concepts of progressive collapse analysis. • Linear vs. nonlinear analysis methods. • Static vs. dynamic analysis. • Modeling requirements for nonlinear analysis. • Special features that are needed for progressive collapse analysis. • Progressive collapse analysis vs. analysis for earthquake resistant design. • The Perform-Collapse computer program, as a practical tool for use in design. Introduction Progressive collapse occurs when the loss or failure of one member in a structure leads to loss or failure of other members, progressing through the structure and leading to partial or full collapse. Progressive collapse analysis is a design tool that can be used to assess whether progressive collapse is likely to occur. This paper is concerned only with the effects of sudden member removal, not with the causes It is important to keep the goal in mind. A collapse analysis is a merely a design tool. Its purpose is not to provide an exact simulation of structural collapse, but to provide the designer with useful information for assessing the performance of the structure and making reasonable decisions about its safety. The same is true of analyses for earthquake loads. The purpose is not exact simulation of the dynamic response of the structure (which is an impossible task), but a reasonable assessment of its performance. Behavior Following Sudden Removal of a Column The essential aspects of behavior following sudden removal of a column can be illustrated using the simple frame shown in Figure 1. Figure 1. Simple Frame to Illustrate Behavior Figure 1(a) shows the frame. When the frame is intact, column CF takes essentially all of the load P, and hence the force in the column is P. If the column is suddenly removed, its force is suddenly transferred to frame ABCDE, and the frame responds dynamically. Depending on its strength, the frame may remain essentially elastic, it may yield but not collapse, or it may collapse completely. Figure 1(b) shows an analysis model consisting of two bars, one to model the column CF and the second to model the frame ABCDE. A mass at the load point models the vertical inertia of frame ABCDE. Figure 1(c) shows the properties for the column and frame. The column is much stiffer than the frame, and the column is elastic whereas the frame can yield. The “correct” analysis sequence for sudden removal of the column is : (1) apply load P, then (2) suddenly remove the column CF and calculate the dynamic response. However, the following analysis sequence will give the same results : (1) remove the column CF, then (2) suddenly apply the load P. The results that are of most interest are as follows. (1) The maximum deflection at C. From this the following can be found. (2) If the frame remains elastic (or is to be designed to remain elastic), the maximum forces in the frame members. (3) If the frame is allowed to yield, the maximum deformations (e.g., plastic hinge rotations) in the frame members. To get the dynamic response it is necessary to perform a dynamic analysis. However, the maximum deflection at C can be calculated without doing a dynamic analysis, by considering energy balance. As the structure deflects, the load P loses potential energy, and the frame ABCDE gains strain energy (in the elastic case) or gains strain energy and dissipates inelastic energy (in the yielding case). When the loss of external potential energy equals the gain in internal energy, the maximum displacement is reached. Consider the case where the frame ABCDE has an elastic-perfectly-plastic relationship between load and deflection. For this case, Figure 2 shows the maximum deflections for three different frame strengths. Figure 2. Energy Balance for Elastic-Perfectly-Plastic Behavior In case (a) the frame ABCDE is very strong. In this case the maximum deflection is twice the deflection that would be obtained by applying the load statically. This deflection, and also the maximum forces in the frame members, can be calculated by performing a conventional linear analysis of the frame for a load equal to twice the actual load. In case (c) the frame ABCDE has a strength smaller than P. In this case it is not possible to reach an energy balance, and the frame collapses completely. In case (b) the frame ABCDE has a strength between P and 2P. The frame yields until an energy balance is reached, and the maximum deflection is larger than the elastic deflection in case (a). This deflection, and also the plastic hinge rotations in the frame members, can be calculated by performing a nonlinear analysis (in this case a very simple one) until an energy balance is reached. A relationship can be established between the frame strength and the displacement ductility ratio, μ , equal to the maximum displacement divided by the yield displacement. If the strength is 2P or larger, the structure remains elastic and μ is 1.0. if the strength is P, μ is infinite. For a strength aP, where a is between 1 and 2, μ is given by : ) 1 ( 2 − = a a μ (1) For example, for a strength of 1.09P (a = 1.09), μ = 6. This shows that the ductility demand can be reasonable even if the strength is only slightly larger than the gravity load. Equation (1) is for elastic-perfectly-plastic behavior. If the structure strain hardens after yield, the ductility demands are smaller. For example, Figure 3 shows the case where the yield strength of frame ABCDE is 1.0P but there is strain hardening. In this case the displacement ductility ratio is given by :" @default.
• W2464193996 created "2016-07-22" @default.
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• W2464193996 date "2004-01-01" @default.
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• W2464193996 title "PRESENTED AT LATBSDC, 2004. BADLY OUT-OF-DATE, BUT HAS SOME USEFUL MATERIAL, IN PARTICULAR THE NOTES ON ENERGY BALANCE. A MAJOR OMISSION IS DISCUSSION OF DAMPING (ASSUMES ZERO). COLLAPSE ANALYSIS MADE EASY (MORE OR LESS)" @default.
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