Problem 406 Cantilever Truss - Method of Joints

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Problem 406
The cantilever truss in Fig. P-406 is hinged at D and E. Find the force in each member.

Solution 406

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At Joint A
$\Sigma F_V = 0$

$F_{AB}\sin 30^\circ = 1000$

$F_{AB} = 2000 \, \text{N}$ tension

$\Sigma F_H = 0$

$F_{AC} = F_{AB}\cos 30^\circ$

$F_{AC} = 2000\cos 30^\circ$

$F_{AC} = 1732.05 \, \text{N}$ compression

At Joint B
$\Sigma F_y = 0$

$F_{BC} = 1000\cos 30^\circ$

$F_{BC} = 866.02 \, \text{N}$ compression

$\Sigma F_x = 0$

$F_{BD} = 1000\sin 30^\circ + 2000$

$F_{BD} = 2500 \, \text{N}$ tension

At Joint C
$\Sigma F_V = 0$

$F_{CD}\sin 60^\circ = 866.02\sin 60^\circ + 1000$

$F_{CD} = 2020.72 \, \text{N}$ tension

$\Sigma F_H = 0$

$F_{CE} = F_{CD}\cos 60^\circ + 866.02\cos 60^\circ + 1732.05$

$F_{CE} = 2020.72\cos 60^\circ + 866.02\cos 60^\circ + 1732.05$

$F_{CE} = 3175.42 \, \text{N}$ compression

Summary
AB = 2000 N tension
AC = 1732.05 N compression
BC = 866.02 N compression
BD = 2500 N tension
CD = 2020.72 N tension
CE = 3175.42 N compression

‹ Problem 405 | Method of Joints up Problem 407 Cantilever Truss - Method of Joints ›

Submitted by Romel Verterra on February 4, 2013 - 6:12am

3467 reads

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Problem 406 Cantilever Truss - Method of Joints

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Engineering Mechanics

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