Determine the reactions at bea:

A cantilever AB, 1.8 m long is fixed at A and carries uniformly distributed load of 20 kN/m over its entire length and a point load of 30 kN at the free end. Determine the reactions at A.

Solution

 Let the reaction components at A be H_A, V_A and M_A as illustrated in Figure. Let us replace the uniformly distributed load of 20 kN/m by a single force of 20 × 1.8 = 36 kN acting at the centre of AB, i.e. at 0.9 m from A. There is no horizontal force acting on the beam.

∑ F_x = 0                                           ∴ H _A = 0

∑ F_y = 0

∴ V_A  - (20 × 1.8) - 30 = 0

∴ V_A  = 36 + 30

= 66 kN

Taking moments at A, we get :

∑ M _A = 0

∴ - M _A + (20 × 1.8) (0.9) + 30 × 1.8 = 0

∴ M _A = 32.4 + 54

= 86.4 kN - m

Thus, the reaction at A consists of a vertical force acting upwards having magnitude 66 kN, and anticlockwise moment of 86.4 kN-m.