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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 −120×10−6σxx=30 MPa,σyy=50 MPa E=2×1011 N/m2=2×105N/mm2 =2×105 MPa Poisson ratio, μ=0.3 σzz=0 ∴ϵzz=σzzE−μ(σxx+σyy)E =−0.3(30+50)2×105 =−120×10−6

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