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For the rigid jointed frame subjected to temp variation as in fig. Determine total deflection at 'c'.Assume α=12×106/c depth of members as 600mm.Neglect effect of axial force

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Subject: Structural Analysis II

Topic: Deflection of Statically Determinate Structures

Difficulty: Medium / High

1 Answer
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To find vertical difflection at 'c' apply dummy force of 1kN=p. vertically towards down

Axial force ˉ(N) and bending moment ˉ(M) diagram Applying C.O.E_

mA=0enter image description here

1×4MA=0

MA=4kN.m

Fy=0(+ve)

VA1=0

VA=1kN

Fx=0(+Ve)

Fx=0    HA=0 enter image description here

consider part AB_:

enter image description here

consider part BC_:

enter image description here

Deflection at C[neglecting axial force]_

For member at AB_

Δt=3010=20c    ˉA=3×4=12m2    h=0.6m

For member at BC_

Δt=4020=20c    h=0.6m    A=12×4×4=8m2

Pjdj=αt[Δth.A]

1c=12×106[200.6×(12)+200.6(8)]

c=12×106(425.33)

c=0.3500

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