The ship’s plate in Problem 3.3 is subjected to plane strain (ϵzz = ϵzx = ϵzy = 0). If σxx = σ1 = 500 MPa and ϵxx = 2ϵyy, determine the magnitude of σyy = σ2 and σzz = σ3, assuming linearly elastic conditions.
Problem 3.3
A square plate in the side of a ship with 800-mm sides parallel to the x and y axes has a uniform thickness h = 10 mm and is made of an isotropic steel (E = 200 GPa and ν = 0.29). The plate is subjected to a unifom1 state of stress. If σzz = σzx = σzy = 0 (plane stress), σxx = σ1 = 500 MPa, and ϵyy = 0 for the plate, determine σyy = σ2and the final dimensions of the plate, assuming linearly elastic conditions.
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