Question

Determine the resultant ‘R’ of the four forces transmitted to the gusset plane if θ = 45° as shown in fig.

Answer 1

First resolved all the forces in horizontal and vertical direction, Clearly note that the angle measured by x-axis,

∑H = 4000 cos 45° + 3000 cos 90°+1000 cos 0°+5000 cos 225°

= 292.8N ...(i) 

∑V = 4000 sin 45° + 3000 sin 90°+ 1000 sin 0°+5000 sin 225°

= 2292.8N ...(ii)

R² = R_H² + R_V²

R² = (292.8)² + (22923.8)²

R = 2311.5N

Let angle made by resultant is θ

tanθ = ∑V /∑H

= 2292.8/292.8

θ = 82.72º.