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prob_15_01_04

# prob_15_01_04 - Problem 15.1-4 Given An isotropic thin...

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Problem 15.1-4 Given: An isotropic thin rectangular plate has dimension a parallel to the x axis and dimension b parallel to the y axis. The x -parallel edges are simply supported; the y -parallel edges are free. Uniform downward pressure p is applied to the upper surface. What are the principal stresses at the middle of the lower surface? What is the lateral deflection at the center of the plate. Solution: a b Free edge x y When bending occurs making a cylindrical surface, then the plate acts like a beam with a uniform distributed load. A simply supported beam with a uniform distributed load has the following deflection formula: w 5q L 4 384 E I = We can adapt this to the plate using: qp 1 () = distributed load per unit width EI D = Et 3 12 1 ν 2  = q b/2 qb/2 V M y Lb = Thus: w 60 q b 4 1 ν 2 384 E t 3 = Using a free body diagram, the maximum moment in a simply supported beam at the center is

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prob_15_01_04 - Problem 15.1-4 Given An isotropic thin...

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