How do I find the reactions of a simply supported beam with a point load?
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The question
A 6 m simply supported beam has a 12 kN point load 2 m from the left support. I need the support reactions and the maximum bending moment, and I keep getting the reactions the wrong way round.
Short answer
Take moments about one support to find the other reaction, then use vertical equilibrium for the second. Here the right reaction is 4 kN, the left is 8 kN, and the maximum bending moment is 16 kNm directly under the load.
Full expert answer
Structural engineering tutor
MEng Civil Engineering, CEng
Getting the reactions reversed usually means taking moments about the wrong point or using the wrong lever arm. Label the left support A and the right support B, and write every step down.
Step 1: moments about A
Taking clockwise as positive, the load produces 12 kN × 2 m = 24 kNm about A. The reaction at B acts upwards at 6 m, producing an anticlockwise moment of R_B × 6. For equilibrium these balance, so R_B = 24 / 6 = 4 kN.
Step 2: vertical equilibrium
Upward forces equal downward forces: R_A + R_B = 12 kN, so R_A = 8 kN. The larger reaction is at the support nearer the load, which is a useful sense check every time.
Step 3: maximum bending moment
For a single point load, the maximum moment occurs under the load. From the left, M = R_A × 2 = 8 × 2 = 16 kNm. Checking from the right gives R_B × 4 = 16 kNm, which confirms it.
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