Calculate beam reactions and maximum bending moment for simply supported beams with point loads or uniformly distributed loads (UDL). Essential for structural engineers and civil engineers.
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Beam Reaction Formulas
Point Load at Centre: Ra = Rb = W/2 | Max BM = WL/4
UDL over full span: Ra = Rb = wL/2 | Max BM = wL²/8
Point Load at distance a from left: Ra = W×b/L | Rb = W×a/L (b = L − a)
10 kN point load at centre, 6m span: Ra = Rb = 10/2 = 5 kN each Max BM = 10×6/4 = 15 kNm
Frequently Asked Questions
A simply supported beam rests on two supports — one pinned and one roller — allowing rotation at the ends but no vertical movement. It is the most common beam configuration in structural design.
A point load acts at a single specific location on the beam, while a UDL (Uniformly Distributed Load) acts evenly across the entire length or a portion of the beam, such as the weight of a slab on a beam.