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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.
Let the reaction components at A be HA, VA and MA 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.
∑ Fx = 0 ∴ H A = 0
∑ Fy = 0
∴ VA - (20 × 1.8) - 30 = 0
∴ VA = 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.
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