GATE Mechanical Engineering (ME) 2018 Shift 1 Solved Paper

Question : 49 of 65

Marks: +1, -0

A simply supported beam of width

100 {mm}

, height

200 {mm}

and length

4 {m}

is carrying a uniformly distributed load of intensity

10 {kN} {/} {m}

. The maximum bending stress (in MPa) in the beam is ____________ (correct to one decimal place)

Solution:

Maximum bending moment will be at centre
Maximum B.M.M

=\;{w L^{2}}/{8}=\;{10 × 16}/{8}=20 {kNm}

(L=4)

Maximum Bending Stress

σ_{\max }=\;{M}/{I} y_{\max }=\;{20 × 10^{3}}/{(\;{0.1 × 0.2^{3}}/{12})} × 0.1

=30 × 10^{6} {N} {/} {m}^{2}=30 {MPa}

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