Question

Calculate the support reactions for the following. Fig,

Answer 1

First change UDL in to point load. 

Resolved all the forces in horizontal and vertical direction. Since roller at B (only one vertical reaction) and hinged at point A (one vertical and one horizontal reaction). 

Let reaction at hinged i.e., point B is RBH and RBV, and reaction at roller support i.e. point D is RDV Let ∑H & ∑V is the sum of horizontal and vertical component of the forces ,The supported beam is in equilibrium, hence

∑H = ∑V = 0

R_H = R_BH = 0

R_BH = 0 ........(i)

∑V = R_BV –50 –5 – R_DV = 0

R_BV + R_DV = 55 .......(ii)

Taking moment about point B

50 × 0.5 – R_BV × 0 – R_DV × 5 + 5 × 7 = 0

R_DV =12 KN

Putting the value of R_BV in equation (ii)

R_BV = 43KN

Hence R_BH = 0, R_DV = 12KN, R_BV = 43KN.