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Civil FE · Mechanics of Materials · Problem 14 of 20Written by an engineer

A simply supported beam spans 6 m and carries a single 20 kN point load at midspan. Neglecting self-weight, the maximum bending moment in the beam is most nearly:

P = 20 kNL = 6 m
A. 15 kN·mB. 30 kN·m ✓C. 60 kN·mD. 120 kN·m

Worked solution

1. By symmetry each reaction is R = P/2 = 10 kN.

2. Shear is constant at 10 kN from the support to midspan, so the moment grows linearly to its peak under the load.

3. Mmax = R · L/2 = 10 kN × 3 m = 30 kN·m.

Handbook check: PL/4 = 20 × 6 / 4 = 30 kN·m.

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