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Question

A plate in equilibrium is subjected to uniform stresses along its edges with magnitude σxx=30 MPa and σyy=50 MPa as shown in figure.

The Young's modulus of the material is 2×1011 N/m2 and the Poisson's ratio is 0.3. If σzz is negligibly small and assumed to be zero, then the strain ϵzz is

A
120×106
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B
60×106
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C
0.0
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D
120×106
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Solution

The correct option is A 120×106
σxx=30 MPa,σyy=50 MPa
E=2×1011 N/m2=2×105N/mm2
=2×105 MPa
Poisson ratio, μ=0.3
σzz=0
ϵzz=σzzEμ(σxx+σyy)E
=0.3(30+50)2×105
=120×106

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