Beam Load Calculator

This beam load calculator works out the support reactions, the maximum shear force and the maximum bending moment for a simply supported beam, the starting point for checking whether a beam is strong enough for the load it carries. It handles the two most common cases together: a uniformly distributed load spread evenly along the span, such as the self-weight of a floor or the pressure of a roof, plus a single point load applied at the centre, such as a post or a piece of plant. Enter the span between the supports, the intensity of the distributed load in kilonewtons per metre and the size of the central point load in kilonewtons, and the calculator adds the loads, splits them equally between the two supports because the arrangement is symmetric, and returns the reaction at each end, the peak shear and the peak bending moment at midspan. The bending moment is the number designers care about most, because it drives the size and grade of timber, steel or concrete you need. This tool gives the load effects only: turning them into a member size also needs the material strength and the section properties, so treat the result as a first check and have any structural element confirmed by a chartered engineer.

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m
kN/m
kN
20 kN·m
maximum bending moment at midspan
Reaction each end15 kN
Maximum shear15 kN
Total load30 kN

A 4 m simply supported beam carrying 5 kN/m plus a central 10 kN point load has 15 kN reactions at each support, a peak shear of 15 kN and a maximum bending moment of 20 kN·m at midspan.

Assumes a simply supported beam, a uniform load over the full span and a point load at the centre. Load effects only: sizing the beam also needs material strength and section properties. Have structural work confirmed by an engineer.

How it works

Because both loads are symmetric about the centre, each support carries half the total load. The total load is the distributed load times the span, plus the point load. The reaction at each end is half of that total, and the maximum shear force at the supports equals that reaction. The maximum bending moment occurs at midspan and is the sum of two standard results: the uniform load contributes w times the span squared, divided by 8, and the central point load contributes the point load times the span, divided by 4.

Worked example

A 4 m beam carries a distributed load of 5 kN per metre and a 10 kN point load at the centre. The distributed load totals 5 times 4, which is 20 kN, and adding the 10 kN point load gives 30 kN total. Each support reaction is half of that, 15 kN, and the maximum shear is also 15 kN. The bending moment is 5 times 4 squared, divided by 8, which is 10, plus 10 times 4, divided by 4, which is another 10, giving a maximum bending moment of 20 kN·m at midspan.

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Frequently asked questions

How do I find the reactions on a simply supported beam?

For a symmetric load each support carries half the total load. A 4 m beam with 5 kN per metre over its length (20 kN) plus a central 10 kN point load (30 kN total) gives 15 kN at each end.

How is the maximum bending moment calculated?

For a simply supported beam the uniform load contributes w L squared over 8 and a central point load contributes P L over 4, both peaking at midspan. Here that is 10 plus 10, so 20 kN metres.

Does this include the beam's own weight?

No. Add the beam's self-weight to the uniform load if it is significant. This tool gives reactions, shear and moment only; sizing the beam also needs the material strength and section properties.