GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper

Question : 40 of 65

Marks: +1, -0

Consider a prismatic straight beam of length

{L}=π {m}

, pinned at two ends as shown in the figure. The beam has a square cross-section of side

p=6 {mm}

. The Young's modulus

{E}=200 {GPa}

, and the coefficient of thermal expansion

{a}=3 × 10^{-6} {K}^{-1}

. The minimum temperature rise required to cause Euler buckling of the beam is ___________K.

Solution:

According to the given condition

R_{t h}=R_{\;\text "buckling "\;}

α ∆ T E A=\;{π^{2} E I}/{L^{2}}

⇒ 3 × 10^{-6} × ∆ T × 36 × 10^{-6}=\;{π^{2} × {1}/{12} ×(6 × 10^{-3})^{4}}/{π^{2}}

⇒ ∆ T=1 K

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