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Reaction at B for Two Point Loads

Mediumbeam reactionsequilibriummoments
A simply supported beam spans 8 m from pin A to roller B. Two downward point loads act at 2 m and 6 m from A: 12 kN and 20 kN, respectively. Neglect beam self-weight. What is the vertical reaction at B?
  1. A14 kN
  2. B18 kN
  3. C20 kN
  4. D32 kN
Show solution

Answer: B. 18 kN

Take moments about A: RB(8) = 12(2) + 20(6) = 144 kN·m, so RB = 144/8 = 18 kN upward. Check vertical equilibrium: RA = 12 + 20 − 18 = 14 kN, and 14 + 18 = 32 kN total load. Therefore RB = 18 kN upward.
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