Continuous Beam Calculator

Analyze continuous beams with multiple spans. Calculates support reactions, shear force, bending moment diagrams, and mid-span deflections. Educational use only.

This page documents the scope, inputs, outputs, and computational approach of the Continuous Beam Calculator on steelcalculator.app. The interactive calculator is designed to run in your browser for speed, but this documentation is written so the page remains useful (and indexable) even if JavaScript is not executed.

What this tool is for

Fast screening of multi-span beam configurations during preliminary design.
Generating shear force and bending moment diagrams for beams continuous over two or more supports.
Understanding how span ratios, loading patterns, and support conditions affect internal forces.

What this tool is not for

It is not a replacement for a full structural analysis package with pattern loading, moving loads, or dynamic analysis.
It does not account for lateral-torsional buckling, local effects, or construction-stage loading.
It does not guarantee compliance with any specific standard.

Key concepts this page covers

three-moment equation (Clapeyron's theorem)
moment distribution for multi-span beams
pattern loading and critical load arrangements
support reactions and influence lines

Inputs and outputs

Typical inputs: number of spans, span lengths, support conditions (pinned, fixed, cantilever), distributed and point loads per span, section properties (E, I).

Typical outputs: support reactions, bending moment diagram, shear force diagram, maximum positive and negative moments, mid-span deflections, and the controlling span.

Computation approach

The solver uses the stiffness method (or equivalent three-moment equation formulation) to assemble the system of equations for unknown support moments, solve the system, then back-calculate reactions, shear, and moment at discrete points along each span. Deflections are computed by numerical integration of the M/EI diagram.

Verification workflow

Simple cases first: verify a two-span beam with equal spans and uniform load against published coefficient tables.
Equilibrium check: confirm that the sum of all support reactions equals the total applied load.
Moment continuity: at interior supports, the bending moment from the left span must equal the moment from the right span.
Sensitivity test: increasing a span length should increase the moment in that span and redistribute reactions.

Frequently Asked Questions

How does a continuous beam differ from simply supported spans? A continuous beam has moment continuity over interior supports, which redistributes bending moments between spans. This typically reduces the maximum positive (mid-span) moment compared to simply supported spans of the same length, but introduces negative (hogging) moments at the supports that must be designed for.

What is pattern loading and why does it matter? Pattern loading means applying live load only on selected spans to produce the worst-case effect at a particular location. For a continuous beam, loading alternate spans maximizes positive mid-span moment, while loading adjacent spans maximizes the negative support moment. Design codes require checking multiple pattern load arrangements to find the critical combination.

Can I use this for steel, concrete, and timber beams? The analysis is material-independent; it depends only on the elastic stiffness distribution (EI) along the beam. The results apply to any material as long as the beam behaves elastically and the section properties you enter are correct.

Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice, a design service, or a substitute for an independent review by a qualified structural engineer. Any calculations, outputs, examples, and workflows discussed here are simplified descriptions intended to support understanding and preliminary estimation.

All real-world structural design depends on project-specific factors (loads, combinations, stability, detailing, fabrication, erection, tolerances, site conditions, and the governing standard and project specification). You are responsible for verifying inputs, validating results with an independent method, checking constructability and code compliance, and obtaining professional sign-off where required.

The site operator provides the content "as is" and "as available" without warranties of any kind. To the maximum extent permitted by law, the operator disclaims liability for any loss or damage arising from the use of, or reliance on, this page or any linked tools.