Steel Beam Calculator

A simply supported beam is one of the most common structural configurations in buildings, bridges, and industrial frameworks. When a uniformly distributed load — such as floor loading, self-weight, or snow load — is applied across the full span, the beam experiences bending and shear that vary along its length. The maximum bending moment occurs at mid-span, while the maximum shear forces occur at the two support reactions.

The three governing formulas are derived from classical Euler-Bernoulli beam theory. The maximum bending moment is M = wL²/8, where w is the load per unit length (N/m or kN/m) and L is the span. The maximum shear force at each support is V = wL/2, representing half the total applied load. The maximum deflection at mid-span is δ = 5wL⁴/(384EI), which depends not only on the load and span but also on the material stiffness E (Young's modulus) and the cross-sectional second moment of area I — both of which resist bending deformation. For structural steel, E is typically taken as 200 GPa (200,000 MPa) per standard codes including AISC and Eurocode 3.

In practice, engineers use these results to check that the selected beam section keeps bending stresses below the allowable limit (σ = M/Z, where Z is the section modulus), that shear stresses are acceptable, and that deflections satisfy serviceability criteria — commonly L/300 to L/360 for floor beams under live load. Universal Beam (UB) and Wide Flange (W-shape) sections are catalogued with their I values, making it straightforward to substitute into these formulas during preliminary design.

This calculator applies strictly to a simply supported beam with a full-span uniformly distributed load. It does not cover cantilever beams, fixed-end beams, continuous multi-span beams, or beams with point loads, partial UDLs, or combined loading scenarios — all of which have different bending moment and deflection expressions. The deflection formula assumes linear elastic (Hookean) behaviour throughout; it is not valid once the beam yields or buckles. Lateral-torsional buckling, which can govern design for deep, unrestrained beams, is not assessed here. The calculator also does not account for dynamic loads, fatigue, or load combinations required by building codes such as ASCE 7, Eurocode 1, or AS/NZS 1170. For final structural design, always consult a licensed structural engineer and verify results against the applicable design standard (AISC 360, Eurocode 3, or equivalent). Section properties (I values) should be obtained from certified section tables rather than estimated.