A 2D thin plate with modulus of elasticity, 𝐸 = 1.0 N/m 2 , and Poisson’s ratio, 𝜇 = 0.5, is in plane stress condition. The displacement field in the plate is given by 𝑢 = 𝐶𝑥 2 𝑦 and 𝑣 = 0, where 𝑢 and 𝑣 are displacements (in m) along the 𝑋 and 𝑌 directions, respectively, and 𝐶 is a constant (in m −2 ). The distances x and y along X and Y, respectively, are in m. The stress in the 𝑋 direction is 𝜎 𝑋𝑋 = 40𝑥𝑦 N/m 2 , and the shear stress is 𝜏 𝑋𝑌 = 𝛼𝑥 2 N/m 2 . What is the value of 𝛼 (in N/m 4 , in integer)? ________

GATE 2023 Civil Engineering PYQ — Strength of Materials or Solid Mechanics

GATE 2023Set 2PYQNATanswer pendingexplanationmedium

Strength of Materials or Solid Mechanics · Stress-Strain-CE

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Drill mode: plane stress · 4/9

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Recurring concept

Stress-Strain-CE has appeared in GATE Civil Engineering 27 times across 17 years (2015, 2016, 2017, 2022, 2023, ...).