What load conditions does this calculator cover?

This calculator handles a uniform distributed load (UDL) applied across the full span of a simply-supported beam. Point loads, partial UDLs, cantilevers, and continuous beams are not covered and require separate analysis.

How are the support reactions calculated?

For a simply-supported beam with a full-span UDL (w) and span (L), each support carries exactly half the total load: R = wL/2. The beam is symmetric so both reactions are equal.

Where does the maximum bending moment occur?

For a uniform load on a simply-supported beam the maximum bending moment occurs at mid-span and equals M_max = wL²/8. This is the critical design moment for bending strength checks.

How is mid-span deflection calculated?

Mid-span deflection is computed using the standard formula δ = 5wL⁴/(384EI). This is the elastic deflection at the centre of the span. It requires the modulus of elasticity (E) and moment of inertia (I) of the beam cross-section.

What units should I use for E and I?

In Imperial mode enter E in ksi (kips per square inch) and I in in⁴. Common values: steel A992 E = 29,000 ksi; Douglas Fir (No. 2) E ≈ 1,600 ksi. In Metric mode enter E in GPa and I in cm⁴. Steel E = 200 GPa; concrete E ≈ 25–30 GPa.

What is an acceptable deflection limit?

Most building codes limit live-load deflection to L/360 for floor beams (to prevent cracking of brittle finishes) and L/240 for roof beams. Total (dead + live) deflection limits are often L/240. Compare the calculated δ to these ratios manually after running the tool.

Beam Load Calculator

Name: Beam Load Calculator
Availability: InStock
Author: Nham Vu

Calculate support reactions, maximum bending moment, shear force, and mid-span deflection for a simply-supported beam under a uniform distributed load.

Beam Parameters

Span Length (L) — ft

Uniform Load (w) — kips/ft

Modulus of Elasticity (E) — ksi

Steel ≈ 29,000 ksi | Wood ≈ 1,600 ksi

Moment of Inertia (I) — in⁴

See beam tables for I values of standard sections.

Results

Enter beam parameters and click Calculate.

Beam Diagram

Summary

Calculate support reactions, maximum bending moment, shear force, and mid-span deflection for a simply-supported beam under a uniform distributed load.

How it works

Select your preferred unit system: Imperial (kips, ft, in) or Metric (kN, m, cm).
Enter the clear span length of the beam between supports.
Enter the uniform distributed load intensity (load per unit length).
Enter the modulus of elasticity (E) for your beam material.
Enter the moment of inertia (I) of the beam cross-section.
Click Calculate to get reactions, maximum moment, maximum shear, and mid-span deflection.

Use cases

Sizing floor beams and joists during early schematic design.
Verifying that an existing beam can carry an added uniform floor or roof load.
Quick hand-check of structural software output for simply-supported members.
Estimating mid-span deflection to check serviceability and code limits (L/360, L/240).
Comparing steel, wood, and concrete beams by swapping E and I values.
Educational reference for structural engineering students learning beam theory.
Pre-screening beam sizes before running a full FEM analysis.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu