**SEO keyword:** beam bending moment calculator
**Meta description:** Understand wL²/8 and wL/2 for a simply supported beam with a full-span uniform load.
The loading assumptions come first
A beam calculator cannot choose the correct equation without knowing support conditions and the location of applied loads. The familiar formulas below apply to a simply supported beam with a uniform load acting over its entire span.
Maximum bending moment
For a full-span uniformly distributed load w in kN/m over span L in metres, the maximum sagging bending moment is M = wL²/8 in kN·m. For w = 8 kN/m and L = 5 m, M = 25 kN·m.
Support shear force
For the same beam, the reaction at each support is V = wL/2. With w = 8 kN/m and L = 5 m, each reaction is 20 kN. These values are actions, not verified member capacities.
When these equations do not apply
Continuous beams, cantilevers, point loads away from midspan, partial-span loading and moment connections require different analyses. Design also requires load combinations, material resistance, stability, deflection and detailing checks.
Calculate preliminary beam actions
MzStructCalc provides separate preliminary bending moment and shear calculators. Use them as arithmetic aids after verifying the structural model.
**Explore the calculators:** Open the MzStructCalc structural calculators directory.
*Engineering note: These tools provide preliminary calculations, not code-compliant structural designs. Obtain independent professional verification before construction.*