GATE 2016 ME (ME3) – Question 43
A square plate of dimension L × L is subjected to a uniform pressure load p = 250 MPa on its edges as shown in the figure. Assume plane stress conditions. The Young’s modulus E = 200 GPa. The deformed shape is a square of dimension 𝐿−2 𝛿. If 𝐿= 2 m and 𝛿= 0.001 m, the Poisson’s ratio of the plate material is __________
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Correct answer: 0.18 to 0.22
Explanation
The measured strain in either loaded direction is−2δ/L=−0.001. Plane-stress Hooke’s law gives ε=(−p+νp)/E=−250(1−ν)/200000. Equating strains gives1−ν=0.8, hence **ν=0.20**. The transverse compression reduces the net contraction through Poisson coupling.