16.21 techniques for structual analysis

# 16.21 techniques for structual analysis - 16.21 Techniques...

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16.21 Techniques of Structural Analysis and Design Spring 2005 Unit #1 Ra´ul Radovitzky February 2, 2005 In this course we are going to focus on energy and variational methods for structural analysis. To understand the overall approach we start by con- trasting it with the alternative vector mechanics approach: Example of Vector mechanics formulation: Consider a simply supported beam subjected to a uniformly-distributed load q 0 , (see Fig. 1 ). To analyze the equilibrium of the beam we consider the free body diagram of an element of length Δ x as shown in the ±gure and apply Newton’s second law: F y = 0 : V q 0 Δ x ( V + Δ V ) = 0 (1) Δ x M B = 0 : V Δ x M + ( M + Δ M ) + ( q 0 Δ x ) = 0 (2) 2 Dividing by Δ x and taking the limit Δ x 0: dV = (3) dx q 0 dM = V (4) dx 1

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± ² x L q0 z x dx M+dM M V V+dV q0 A B A B Figure 1: Equilibrium of a simply supported beam Eliminating V , we obtain: d 2 M + q 0 = 0 (5) dx 2 Recall from Uni±ed Engineering or 16.20 (we’ll
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## This note was uploaded on 11/07/2011 for the course AERO 16.21 taught by Professor Dffs during the Fall '10 term at MIT.

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16.21 techniques for structual analysis - 16.21 Techniques...

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