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 RA.
Let rod is inclined at an angle of θ . The rod is in position of equilibrium.
ΣV = 0
RBcosθ - RCcosθ + 100cosθ = 0
RC - RB = 100 ...(i)
Taking moment about A:
ΣMA = 100 × 0.6 - RC × 0.4 + RB × 0.2 = 0
2RC - RB = 300 ...(ii)
Solving the equation (i) and (ii)
RC = 200 .......ANS
RB = 100 .......ANS
ΣH = 0
RA + RBsinθ - RCsinθ + 100sinθ = 0
RA + 100sinθ - 200sinθ +100sinθ = 0
RA = 0 .......ANS