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Question

Flexibility matrix of the beam shown below is δ=13EI[2228]



If support B settles by ΔEIunits, what is the reaction at B

A
4Δ
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B
Δ
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C
2Δ
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D
8Δ
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Solution

The correct option is C 2Δ
Stiffness matrix [K] is inverse of flexibility matrix [δ]

[K]=[δ]1=(13EI)1[2228]1
=3EI[2/31/61/61/6]

We know [p] = [k][Δ]
[p1P2]=[K][Δ1Δ2]

[p1p2]=3EI[2/31/61/61/6]ΔEI0

Δ2= 0 as no displacement at 2
p1= reaction at 1 due to settlement at 1
p1=3EI×23×ΔEI
p1=2Δ

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