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Question

# Find the rotation at B for the frame shown below.

A
57EI clockwise
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B
57EI anticlockwise
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C
47EI clockwise
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D
47EI anticlockwise
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Solution

## The correct option is D 47EI anticlockwise¯¯¯¯¯¯MAB=¯¯¯¯¯¯MBA=0 ¯¯¯¯¯¯MBC=Mb(3a−l)l2=5×2×(3×3−5)25=+1.6 kNm MBC=¯¯¯¯¯¯MBC+2EIθBLBC(2θB+θC−3ΔL) θC=0;Δ=0 MBC=¯¯¯¯¯¯MBC+4EIθBL (using slope deflection equation for span BC) =1.6+4EIθB5=1.6+0.8EIθB Using slope deflection equation for span AB, MBA=¯¯¯¯¯¯MBA+2E(2I)LAB(2θB+θA−3ΔL) MBA=4EI×2θB4(Δ=0;θA=0) =2EIθB At joint B, MBA+MBC=0 ⇒1.6+0.8EIθB+2EIθB=0 ⇒2.8EIθB=−1.6 ⇒θB=−47EI Negative sign shows that rotation is in anticlockwise direction.

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