Use this beam calculator to analyse a simply supported beam under a uniformly distributed load (UDL). It calculates reactions, shear force, bending moment, and beam deflection at any position along the span. This tool is ideal for structural engineers, mechanical engineers, and students performing beam calculations quickly and accurately, with results available in both metric and imperial units.
This beam calculator supports both metric and imperial units and allows mixed unit inputs without requiring manual conversion. You can enter values in different unit systems using the dropdown selectors, and the calculator will automatically handle all conversions, ensuring accurate and efficient results.
The following example demonstrates how to calculate reactions, shear force, bending moment, and deflection for a simply supported beam with a uniformly distributed load.
For a simply supported beam with a uniformly distributed load, the reactions at both supports are equal:
Reaction at each support = (w × L) / 2
= (50 × 5) / 2 = 125 N
The maximum bending moment occurs at the centre of the beam:
M = (w × L²) / 8
= (50 × 5²) / 8 = (50 × 25) / 8 = 156.25 Nm
The maximum deflection for a simply supported beam with a UDL occurs at midspan:
δ = (5 × w × L⁴) / (384 × E × I)
= (5 × 50 × 5⁴) / (384 × 200 × 109 × 8.0 × 10-6)
= (5 × 50 × 625) / (384 × 200 × 109 × 8.0 × 10-6)
≈ 0.00254 m (2.54 mm)
A uniformly distributed load (UDL) is a load that is spread evenly along the length of a beam. It is usually expressed as force per unit length (e.g. N/m or lb/ft) and is commonly used to represent loads such as weight, pressure, or evenly distributed materials.
This calculator determines support reactions, shear force, bending moment, and beam deflection for a simply supported beam with a uniformly distributed load. Results can be calculated at any point along the beam.
The calculator supports both metric and imperial units. You can input values such as length, force, and material properties in your preferred unit system, and the results will be displayed accordingly.
Beam deflection is the amount a beam bends or displaces under load. It depends on factors such as the applied load, beam length, material properties, and the moment of inertia of the beam section.
Beam deflection is influenced by the magnitude of the load, the span length, the material's Young’s modulus (stiffness), and the moment of inertia of the beam cross-section. Increasing stiffness or reducing load and span will reduce deflection.