Question

Calculate the support reactions for the beam shown in fig.

Answer 1

Since Beam is overhang. At point A hinge support and point D Roller support is acting. First change UDL and UVL in to point load. As shown in, let ∑H & ∑V is the sum of horizontal and vertical component of the Resultant forces, the supported beam is in equilibrium, hence resultant force is zero. Convert UDL and UVL in point load and draw the FBD of the beam as shown in fig,

∑H = 0;

R_AH = 30 cos 45° 

R_AH = 21.21K N

∑V = 0;

R_AV –50 – 30 sin 450 + R_DV – 27 = 0

R_AV + R_DV = 98.21 KN .......(i)

Now taking moment about point ‘A’ 

– R_DV × 7 + 50 × 2.5 + 40 + 30 sin 450 × 5 + 27 × 9 = 0

R_DV = 73.4 KN

Putting the value of R_DV in equation (i)

R_AV = 24.7KN.