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Simply supported beam reactions calculator.

Calculate support reactions, maximum shear, and the governing positive bending moment for a full-span UDL plus an off-centre point load.

read the result

Start with equilibrium, then find the critical section.

The reactions come from vertical-force and moment equilibrium. The shear changes linearly under the UDL and jumps at the point load; the maximum positive moment is found from the key load positions and any zero-shear point within a load segment.

Governing equations

For span L, UDL w, point load P at distance a from the left support: RA = wL/2 + P(L - a)/L and RB = wL + P - RA. In a segment after the point load, M(x) = RAx - wx2/2 - P(x - a).

Keep it as a load-case screen.

  • Both supports are idealised as simple supports and all loads are vertical and downward.
  • Self-weight, load factors, support settlement, stiffness, lateral stability, shear resistance, and deflection limits are not checked.
  • Use the result to frame a load path and then complete the applicable member, connection, and code checks.