Beam Load Calculator
Find the maximum bending moment and support reactions for a simply supported beam carrying a uniformly distributed load (UDL). Enter the load per metre and the span, and the calculator returns the peak bending moment at midspan and the reaction at each support.
Formula
For simply supported beam with UDL: Mmax = wL²/8, Reaction = wL/2
- w is the uniformly distributed load in kN per metre, L is the span between supports in metres.
- Maximum bending moment for a UDL on a simply supported beam is Mmax = wL²/8, occurring at midspan.
- Each support carries half the total load, so the reaction at each end is wL/2.
- Total load on the beam is w × L; the two reactions add up to this total.
- This covers a single simply supported span with a uniform load — point loads or fixed ends use different formulas.
8 kN/m over a 5 m span
Inputs
- Uniform Load w (kN/m): 8
- Span L (m): 5
Mmax = (8 × 5²) / 8 = 25 kN·m at midspan. Reaction at each support = (8 × 5) / 2 = 20 kN.
Frequently asked questions
What does this calculator give me?
The maximum bending moment and the reaction at each support for a simply supported beam under a uniformly distributed load.
What is a uniformly distributed load?
A load spread evenly along the beam, measured in force per unit length (kN/m) — for example, the self-weight of a slab resting on the beam.
Why is the maximum moment wL²/8?
For a simply supported beam with a uniform load, the bending moment is largest at midspan and works out to wL²/8 from statics.
How big is each support reaction?
The total load wL is shared equally between the two supports, so each reaction is wL/2.