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GATE CE 2023 Set 2 — Question 56

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NAT+2 / -0HardElastic Constants & RelationsStress, Strain & BeamsStructural EngineeringHooke's Law

Structural Engineering → Stress, Strain & Beams → Elastic Constants & Relations

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Question

A 2D thin plate with modulus of elasticity, E=1.0 N/m2E = 1.0 \text{ N/m}^2, and Poisson’s ratio, μ=0.5\mu = 0.5, is in plane stress condition. The displacement field in the plate is given by u=Cx2yu = Cx^2y and v=0v = 0, where uu and vv are displacements (in m) along the XX and YY directions, respectively, and CC is a constant (in m−2\text{m}^{-2}). The distances xx and yy along XX and YY, respectively, are in m. The stress in the XX direction is σXX=40xy N/m2\sigma_{XX} = 40xy \text{ N/m}^2, and the shear stress is τXY=αx2 N/m2\tau_{XY} = \alpha x^2 \text{ N/m}^2. What is the value of α\alpha (in N/m4\text{N/m}^4, in integer)?
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