Determine the reaction at specific points:

A light rod AD can be supported by frictionless pegs at B and C and rests against frictionless wall at A as shown in the given figure . A force of 100N is applied at end D. Determine the reaction at points A, B and C.

Sol.: As roller supports at point B, C, so that the vertical reactions are there RB, RC. At point A rod is in the contact with wall that is wall give contact reaction to the rod say R_A.

Let rod is inclined at an angle of θ . The rod is in position of equilibrium.

ΣV = 0

R_Bcosθ   - R_Ccosθ   + 100cosθ = 0

R_C  - R_B = 100                                                                                                                                 ...(i)

Taking moment about A:

ΣM_A = 100 × 0.6 - R_C × 0.4 + R_B × 0.2 = 0

2R_C  - R_B = 300                                                                                                                                ...(ii)

Solving the equation (i) and (ii)

R_C = 200                                                                                         .......ANS

R_B = 100            .......ANS

ΣH = 0

R_A  + R_Bsinθ   - RCsinθ   + 100sinθ   = 0

R_A  + 100sinθ   - 200sinθ   +100sinθ   = 0

R_A = 0                                        .......ANS