This study is on progressive collapse analysis of a sample steel building using various procedures suggested by the General Service Administration and the Department of Defense. The progressive collapse was accommodated by removing columns as per above guidelines. The analysis methods considered were linear static, linear dynamic, non-linear static and nonlinear dynamic using SAP2000 structural simulation program. The analysis model was a 3D nine-storey steel moment resisting building. For linear analysis, rigid moment connections were used, while for nonlinear analysis pre-Northridge connections were used. The effect of an extreme event was incorporated by removing a column in the analysis model. The static analysis was performed on the model with a column removed subjected to static gravity loadings. The dynamic analysis employed a ramp function to simulate the dynamic effect of the removal of a column. For nonlinear analysis, material nonlinearity was incorporated using strength degrading nonlinear hinges of pre-Northridge connections as per FEMA 356. The paper documents the results of this analysis with comparison among methods. The potential for collapse and performance levels of the building were determined using the demand capacity ratio and the rotational limit obtained through the analysis. Figure 8. Defl ected shape of the frame and displacement history (cm) of Node 461 after Column 2796 was removed. Nonlinear static analysis procedureA load combination of 1.2DL + 0.5LL was applied to the structure, except that to bays adjacent to the removed columns a load combination of 2.4DL + LL was applied (per DoD). The beam-column connections were modelled using the strength degrading moment-rotation relationship as shown in Figure 9 per FEMA 356 (FEMA, 2000) for pre-Northridge Welded Unreinforced Flanges (WUF) connections.At fi rst, only one column was removed at a time per DoD guidelines similarly to linear analyses. However, there were no plastic hinges formed at the beam-column joints. To further study nonlinear responses of the structure, two columns were removed simultaneously, signifying an event even M θ θ y Mψ Figure 9. Force-deformation curve in FEMA 356.470

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Abstract. This article studies the free vibration of composite ring-stiffened cylindrical shells by the continuous element method (CEM). The dynamic stiffness matrix (DSM) of the studied structure has been constructed based on the analytical solutions of the governing equations of motion for composite cylindrical shells and annular plates. By applying the assembly procedure of the continuous elements method, natural frequencies and harmonic responses of composite ring-stiffened cylindrical shells are determined. In addition, the proposed model allows to exactly extract ring-stiffener vibration modes. Numerical examples confirm advantages of the proposed model: high precision solution even in medium and high frequencies, saving in calculating time and volume of data storage.

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