# 06_PlateTheory_04_LateralLoads - Section 6.4 6.4...

This preview shows pages 1–3. Sign up to view the full content.

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 +

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
This is the end of the preview. Sign up to access the rest of the document.