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.