A simply supported beam of span 6 m carries a uniformly distributed load of 20 kN/m over its full length. Find the support reactions, the maximum shear force and the maximum bending moment, and say where the maximum moment occurs.
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Worked answer. Total load W = w × L = 20 × 6 = 120 kN, shared equally by symmetry.
- Reactions R_A = R_B = 60 kN.
- Maximum shear force = 60 kN, at the supports (it falls linearly to zero at midspan).
- Maximum bending moment M = wL²/8 = 20 × 6² / 8 = 90 kN·m, at midspan, where the shear force is zero.
Check from first principles: at x = 3 m, M = 60 × 3 − 20 × 3 × 1.5 = 180 − 90 = 90 kN·m.
Original UniCircle question. Last reviewed 21 Oct 2026.