Question

A beam 8m long is hinged at A and supported on rollers over a smooth surface inclined at 300 to the horizontal at B. The beam is loaded as shown in fig. Determine the support reaction.

Answer 1

F.B.D. is as shown in fig,

∑H = 0

R_AH ⋅ + 8 cos 45° – R_Bsin 30° = 0 

0.5R_B – R_AH ⋅ = 5.66 ...(i) 

∑V = 0

R_AV –10 – 8 cos 45° – 10 + R_B cos 30° = 0

R_AV + 0.866 RB = 25.66

Taking moment about point A:

∑M_A = 10 × 2 + 8 cos 45° × 4 + 10 × 7 – R_B cos 30° × 8= 0

R_B = 16.3KN

From equation (ii)

R_AV = 11.5KN

From equation (1)

R_AH = 2.5KN.