KIC000109

# KIC000109 - Direct DlsplacemuJt M thud Introduction The...

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Direct DlsplacemuJt M thud The direct displacement method is another technique that can be used to analyze indeterminate structures. This method can be generalized and is commonly used in structural analysis software. In this method, all degrees of freedom of a structure are restrained, i.e. "locked", and the member fixed end forces are calculated due to any applied loads on the member. As in moment distribution, each degree of freedom is then independently released, i.e."un- locked", and the member end forces are determined due to an application of a unit displacement that corresponds to each degree of freedom. This displacement can either be a rotation or a translation. The actual member end forces are then calculated by satisfying equilibrium conditions at each of the degrees of freedom. The steps required to complete an analysis based on the direct displacement method are illustrated in the following simplified example: Given a structure: 1---- l---+------ l--------' A i) Determine the kinematic degree of indeterminacy, i.e, the number of degrees of freedom. The kinematic degree of freedom is the number of independent joint displacements (rotations and translations). This sample problem has two degrees of kinematic indeterminacy since the structure can undergo rotations at both joints Band C. X. ,,,. A + However, the moment at Joint C is determinate. However, since the moment at C is zero, modified stiffness can be utilized for member BC. Modified stiffness is used by not including the rotation at C as an unknown reaction. This reduces the kinematic indeterminacy

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KIC000109 - Direct DlsplacemuJt M thud Introduction The...

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