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Question

A cantilever beam PQ of uniform flexural rigidity (EI) is subjected to a concentrated moment M at R as shown in the figure


The deflection at the free end Q is

A
3ML24EI
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B
3ML28EI
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C
ML24EI
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D
ML26EI
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Solution

The correct option is B 3ML28EI
We know that

ΔQ=ΔQ1+ΔQ2...(1)
ΔQ1=ΔR=M(L/2)22EI=ML28EI...(2)
And ΔQ2=θR.(L2)
=M(L2)EI×(L2)
=ML24EI...(3)
From (1), (2) & (3) we can write
ΔQ=ML28EI+ML24EI
=(1+2)ML28EI
ΔQ=3ML28EI

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