## Determine the reactions at beam, Mechanical Engineering

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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.

Solution

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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