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Unformatted text preview: Section 6.3 Solid Mechanics Part II Kelly 139 6.3 Plates subjected to Pure Bending and Twisting 6.3.1 Pure Bending of an Elastic Plate Consider a plate subjected to bending moments 1 M M x = and 2 M M y = , with no other loading, as shown in Fig. 6.3.1. Figure 6.3.1: A plate under Pure Bending From equilibrium considerations, these moments act at all points within the plate they are constant throughout the plate. Thus, from the momentcurvature equations 6.2.31, one has the set of coupled partial differential equations y x w x w y w D M y w x w D M = + = + = 2 2 2 2 2 2 2 2 2 2 1 , , (6.3.1) Solving for the derivatives, , ) 1 ( , ) 1 ( 2 2 1 2 2 2 2 2 1 2 2 = = = y x w D M M y w D M M x w (6.3.2) Integrating the first two equations twice gives 1 ) ( ) ( ) 1 ( 2 1 ), ( ) ( ) 1 ( 2 1 2 1 2 2 1 2 2 1 2 2 2 1 x g y x g y D M M w y f x y f x D M M w + + = + + = (6.3.3) and integrating the third shows that two of these four unknown functions are constants: B x g A y f y F y w x G x w = = = = ) ( , ) ( ) ( ), ( 1 1 (6.3.4) 1 this analysis is similar to that used to evaluate displacements in plane elastostatic problems, 1.2.4 this analysis is similar to that used to evaluate displacements in plane elastostatic problems, 1....
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This note was uploaded on 01/20/2012 for the course ENGINEERIN 2 taught by Professor Staff during the Fall '11 term at Auckland.
 Fall '11
 Staff

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