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GATE 2020 CE (CE2) – Question 17

Solid Mechanics · Simple bending theory, flexural and shear stresses, shear centre · 1 mark · Multiple choice

The weightless cantilever of span L carries tip force P and opposing tip couple PL as shown. Material is uniform and cross-section rectangular of constant width. From the flexure-critical perspective, which longitudinal profile is most economical?

Diagram for GATE 2020 CE (CE2) question 17
  1. Figure A
  2. Figure B
  3. Figure C
  4. Figure D

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Show answer and explanation

Correct answer: (C) Figure C

Explanation

At distance x from the root, the tip force produces moment P(L − x), opposing couple PL. Net magnitude is Px, increasing toward the tip. For constant width, section modulus is proportional to depth squared. Thus the economical profile increases in depth toward the free end: **C**.