The GATE Grind

GATE 2018 CE (CE1) – Question 14

Solid Mechanics · Column buckling · 1 mark · Multiple choice

A column of height h and rectangular section a×2a has buckling load P. If its section becomes 0.5a×3a and height 1.5h, its buckling load becomes ______.

  1. P/12
  2. P/4
  3. P/2
  4. 3P/4

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) P/12

Explanation

Euler buckling load scales as $I_{\min}/h^2$ for unchanged material and end restraints. Initially $I=2a(a^3)/12=a^4/6$. After redesign $I=3a(0.5a)^3/12=a^4/32$. The inertia ratio is 3/16 and height-square ratio 9/4, so load ratio is $(3/16)/(9/4)=1/12$ (A).