Analyze the frame shown in fig for the forces in values members. All the members may be assumed to have the same $\frac{L}{AE}$ value.

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written 7.3 years ago by

teamques10 ★ 70k

• modified 3.9 years ago

Subject :- Structural Analysis II

Title :- Analysis of Indeterminate truss

Difficulty :- Hard

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structural analysis

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1 Answer

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written 7.3 years ago by

teamques10 ★ 70k

1) Degree of redundancy :-

$D_{se}$ (Degree of external redundancy) = R-3 = 3-3 = 0

$D_{si}$ (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 :-

Σ$M_c$ = 0 (+ve) = 54 - $V_B$4 = 0

$V_B$ = 5KN

Σ$F_y$ = 0 (+ve) = $V_C$-5+5 = 0

$V_C$ = 0

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Joint A :-

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4) K-Analysis :-

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Table :-

Member	P	K	PK	$K^{2}$	F=P+$R_K$
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
			Σ$P_K$ = 3.55	Σ$K^2$ = 4.016

R = -[$\frac{ΣP_k}{ΣK^2}$] = -$\frac{(3.55)}{4.016}$ = -0.88

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