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Analyze the frame shown in fig for the forces in values members. All the members may be assumed to have the same LAE value.

Subject :- Structural Analysis II

Title :- Analysis of Indeterminate truss

Difficulty :- Hard

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1 Answer
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1) Degree of redundancy :-

Dse (Degree of external redundancy) = R-3 = 3-3 = 0

Dsi (Degree of internal redundancy) = M-[2j-3] = 6-[2(4)-3] = 6-[8-3] = 6-5 = 1

Total = 0+1 =1

2) Let AD be the redundant :-

Remove member AD

3) P-Analysis :-

ΣMc = 0 (+ve) = 54 - VB4 = 0

VB = 5KN

ΣFy = 0 (+ve) = VC-5+5 = 0

VC = 0

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Joint A :-

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4) K-Analysis :-

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Table :-

Member P K PK K2 F=P+RK
AB 0 -0.71 0 0.504 0.62
AC 0 -0.71 0 0.504 0.62
AD 0 1 0 1 -0.88
BD -5 -0.71 3.55 0.504 -4.37
BC 0 1 0 1 -0.88
CD 0 -0.71 0 0.504 0.62
ΣPK = 3.55 ΣK2 = 4.016

R = -[ΣPkΣK2] = -(3.55)4.016 = -0.88

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