STRUCTURE magazine April 2006 24 Dynamic Model of Progressive Collapse Progressive collapse analysis is carried out as threat independent by instantaneously removing one of several major load-bearing elements and analyzing the ability of the damaged structure to absorb the energy. Per GSA Progressive Collapse Guidelines (GSA, 2003), only one primary load bearing element needs to be removed at a time. A finite element model of the example structure with the assumed column loss scenario is shown below in Figure 1. Assumptions To simplify the analysis while illustrating the dynamic analysis procedure, the following assumptions are made: 1. The structure is modeled as two-dimensional. 2. Effects of large deflections are neglected. 3. Elastic-perfectly-plastic moment-rotation relationships are used 4. Equivalent structural damping of 5% is assumed throughout the analysis. 5. All beam-to-column connections are moment-resistant and are stronger than the beams, so plastic hinges will form in the body of the beam and not in the column or in the joint (strong column – weak beam principle). 6. All beams are adequately confined by shear reinforcement so that beams are not shear controlled. 7. Columns have adequate strength to resist additional load redistribution due to the loss of the primary column. D Y N A M I C A N A L Y S I S P R O C E D U R E S F O R P R O G R E S S IV E C O L L A P S E Following the collapse of the World Trade Center towers in September 2001, there has been heightened interest among building owners and government entities in evaluating the progressive collapse potential of existing buildings, and in designing new buildings to resist this type of collapse. Although some technical literature addressing progressive collapse became available after the 1968 Ronan Point collapse in Britain, little research has been done in this area since the mid-1970’s. Recently, the General Services Administration and Department of Defense have issued updated guidelines for evaluating a building’s progressive collapse potential (GSA, 2003; DoD, 2005). However, both documents fall short of providing clear procedures for performing progressive collapse analysis using dynamic methodologies. Furthermore, both documents seem to discourage the use of nonlinear dynamic analysis procedures due to their perceived complexity. Progressive collapse is an inherently dynamic event, and an analysis should be modeled as such when assessing a structure’s vulnerability to progressive collapse. Typical static analysis procedures mandated by the General Services Administration (GSA, 2003) or Department of Defense (DoD, 2005) attempt to capture dynamic behavior through a dynamic amplification factor applied to the load (usually a factor of 2). This can be shown to be not only unconservative, but unnecessary, as dynamic analysis procedures are just as simple and straightforward to implement as static analysis. This article demonstrates the use of commercially available finite element structural analysis software to perform dynamic analysis for progressive collapse determination using SAP 2000. The procedures presented can be implemented using any finite element program capable of nonlinear dynamic analysis. Progressive Collapse Phenomenon Progressive collapse occurs when the sudden loss of a critical load-bearing element initiates a chain reaction of structural element failures, eventually resulting in partial or full collapse of the structure. The cause of the initiating damage to the primary load-bearing element is un- important; the resulting sudden changes to the building’s geometry and load-path are what matter. This means that the analysis is threat independent. Both GSA and DoD guidelines incorporate a threat independent approach to progressive collapse analysis. Progressive collapse is a dynamic event involving vibra- tions of building elements and resulting in internal dy- namic forces, such as inertia and damping, whose energy may or may not be absorbed by the structure. Progressive collapse is also inherently a non-linear event in which structural elements are stressed beyond their elastic limit to failure. By Elizabeth Agnew, M.S. and Shalva Marjanishvili, Ph.D., P.E. Figure 1: Finite element model of example structure S T R U C T U R E ® magazine Copyright