GATE Civil Engineering (CE) 2018 Shift 1 Solved Paper

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Question : 55 of 65

Marks: +1, -0

The figure shows a simply supported beam PQ of uniform flexural rigidity EI carrying two moments

{M}

and

2 {M}

The slope at P will be

0
ML/(9EI)
ML(6EI)
ML/(3EI)

Solution:

Now

\;\; R_{1}+R_{2}=\;{1}/{2} × \;{L}/{3} × \;{M}/{E I}=\;{M L}/{6 E I}

Σ M_{Q}=0

R_{1} L \;\; -\;{1}/{2} × \;{L}/{3} × \;{M}/{E I}(\;{2 L}/{3}+\;{L}/{9})-\;{1}/{2} × \;{L}/{3} × \;{M}/{E I}(\;{L}/{3}+\;{L}/{9})

+\;{1}/{2} × \;{L}/{3} × \;{M}/{E I} × \;{2 L}/{9}=0

R_{1}= \;\; \;{7 M L}/{54 E I}+\;{4 M L}/{54 E I}-\;{M L}/{27 E I}=\;{M L}/{6 E I}

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