**Problem 406**

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

**Solution 406**

**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