Simply supported, center point load
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About this case
How to analyze a simply supported beam with a center point load
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The classic textbook case: reactions R = P/2 at each support, maximum moment M = PL/4 at midspan, maximum deflection δ = PL³/(48EI) at midspan. Shear is constant at P/2 between the support and the load, then jumps to −P/2.
What to watch for with center point loads
Real loads are rarely exactly at midspan. Drag the load off-center and watch the reactions shift (R_A = P·b/L, R_B = P·a/L) and the maximum moment move to the load point (M_max = P·a·b/L). The deflection curve becomes asymmetric — the maximum is no longer at midspan.
If you have multiple point loads, superposition applies: add the moments and deflections from each load. The calculator does this automatically when you add multiple loads, so you don't need to do the math by hand.
Related calculators
Compare with the simply supported UDL case (wL²/8 vs PL/4 for the same total load: a center point load gives 2× the moment of a UDL with the same total load). For steel beams, start with the steel beam calculator and pick a W-shape from the library.