Quiz 4 solution

Quiz 4 solution - Quiz 4 solution An aluminum [E = 10,600...

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Quiz 4 – solution An aluminum [ E = 10,600 ksi; G = 4,000 ksi] plate is subjected to biaxial stress (Fig. P13.56). The normal stress in the x direction is known to be twice as large as the normal stress in the y direction. If the strain gage measures a normal strain of +560  in the indicated direction, determine (a) the magnitudes of the normal stresses x and y acting on the plate. (b) the in-plane principal strains, p 1 and p 2 (c) the maximum in-plane shear strain max in the plate. Fig. P13.56 Solution Derive an expression for from Eq. (13.18): 1 2(1 ) 2 EE G G   Determine Poisson’s ratio from this expression: 10,600 ksi 1 1 0.325 2 2(4,000 ksi) E G     (a) A strain transformation equation [Eq. (13.3)] 22 cos sin sin cos n x y xy can be written for the normal strain in the direction of strain gage: 560 με cos (40 ) sin (40 ) sin(40 )cos(40 ) x y xy     Note that the shear strain xy is related to the shear stress xy by Eq. (13.22): 1 xy xy G  Since xy = 0, the shear strain
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Quiz 4 solution - Quiz 4 solution An aluminum [E = 10,600...

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