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GATE 2018 CE (CE1) – Question 37

Solid Mechanics · Simple bending theory, flexural and shear stresses, shear centre · 2 marks · Multiple choice

A 2 m steel cantilever with square section 0.1 m × 0.1 m carries a vertical free-end load producing 5 mm tip displacement. Given $E=2\times10^{11}$ N/m², maximum fixed-end bending stress is ______.

  1. 20.0 MPa
  2. 37.5 MPa
  3. 60.0 MPa
  4. 75.0 MPa

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Correct answer: (B) 37.5 MPa

Explanation

For a tip-loaded cantilever, $\delta=PL^3/(3EI)$ and $\sigma=PLc/I$. Eliminate P/I: $\sigma=3E\delta c/L^2=3(2\times10^{11})(0.005)(0.05)/2^2=37.5$ MPa (B).