06_PlateTheory_04_LateralLoads

06_PlateTheory_04_LateralLoads - Section 6.4 6.4...

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Section 6.4 Solid Mechanics Part II Kelly 144 6.4 Equilibrium and Lateral Loading In this section, lateral loads are considered and these lead to shearing forces y x V V , , in the plate. 6.4.1 The Governing Differential Equation for Lateral Loads In general, a plate will at any location be subjected to a lateral pressure q , bending moments xy y x M M M , , and out-of-plane shear forces x V and y V ; q is the normal pressure on the upper surface of the plate: + = = = 2 / ), , ( 2 / , 0 ) , ( h z y x q h z y x zz σ (6.4.1) These quantities are related to each other through force equilibrium. Force Equilibrium Consider a differential plate element with one corner at ) 0 , 0 ( ) , ( = y x , Fig. 6.4.1, subjected to moments, pressure and shear force. Taking force equilibrium in the vertical direction (neglecting a possible small variation in q , since this will only introduce higher order terms): 0 = Δ Δ Δ Δ + Δ + Δ Δ + Δ + = y x q y x x V V y V x y y V V x V F x x x y y y z (6.4.2) Fig. 6.4.1: a plate element subjected to moments, pressure and shear forces Eqn. 6.4.2 gives the vertical equilibrium equation q y V x V y x = + (6.4.3) y x () y y M y Δ + q ( ) y y V y Δ + () y y M xy Δ + () x x M x Δ + ( ) x x V x Δ + () x x M xy Δ +
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Section 6.4 Solid Mechanics Part II Kelly 145 Next, taking moments about the x axis: () () () () 0 2 / 2 / 2 / = Δ Δ Δ + Δ Δ + Δ + Δ Δ + + Δ Δ + Δ + Δ Δ Δ + + Δ Δ Δ + Δ = y
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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.

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06_PlateTheory_04_LateralLoads - Section 6.4 6.4...

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