# 250 Reaction at the supports of cantilever truss

**Problem 250**

The cantilever truss shown in Fig. P-250 carries a vertical load of 10.8 kN. The truss is supported by bearing at A and B which exert the forces A_{v}, A_{h}, and B_{h}. The four forces shown constitute two couples which must have opposite moment effects to prevent movement of the truss. Determine the magnitude of the supporting forces.

**Solution 250**

$A_v = 10.8 \, \text{ kN}$

The given load and A_{V} produce a counterclockwise couple

$C = 1.8(10.8)$

$C = 19.44 \, \text{ kN}\cdot\text{m counterclockwise}$

$\Sigma F_H = 0$

$B_h = A_h$

Since B_{h} = A_{h}, the two are clockwise couple.

$C_{counterclockwise} = C_{clockwise}$

$19.44 = 1.2B_h$

$B_h = 16.2 \, \text{ kN}$

Thus,

$A_h = 16.2 \, \text{ kN}$

Summary (answer)

$A_v = 10.8 \, \text{ kN upward}$

$A_h = 16.2 \, \text{ kN to the left}$

$B_h = 16.2 \, \text{ kN to the right}$