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GATE 2019 ME (ME2) – Question 41

Mechanics of Materials · Deflection of beams · 2 marks · Multiple choice

The prismatic straight elastic cantilever shown has triangular transverse load, q at the fixed end and zero at the free end. With length L, Young’s modulus E and area moment I, find maximum deflection magnitude.

Diagram for GATE 2019 ME (ME2) question 41
  1. $qL^4/(15EI)$
  2. $qL^4/(30EI)$
  3. $qL^4/(10EI)$
  4. $qL^4/(60EI)$

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Show answer and explanation

Correct answer: (B) $qL^4/(30EI)$

Explanation

At distance x from the fixed end,the moment is $M(x)=-q(L-x)^3/(6L)$. Virtual work with a unit tip load gives $\delta=q\int_0^L(L-x)^4dx/(6LEI)=qL^4/(30EI)$. Maximum displacement occurs at the free end. **Answer:B**.