Analyse a continuous beam over up to six spans with UDLs and point loads. Get reactions, support moments, span moments and deflection. Run it free in CalcTree.
Tell us what you need, or sign up and build it yourself in minutes.
Leave your email and we'll tell you when a template for it is ready:
Your request has been received. We will let you know when it is available.
Oops! Something went wrong while submitting the form.
About this Continuous Beam Calculator
This calculator runs an elastic analysis of a continuous beam over any number of supports up to six spans, with a different length and uniformly distributed load on each span, point loads anywhere, and pinned or fixed ends. It returns every reaction, the hogging moment over each support, the sagging maximum in each span with its position, the largest shear and the deflection against a span limit. It is for:
- Structural engineers sizing floor beams, purlins and bridge girders that run over several supports, who need the design envelope rather than a single-span approximation.
- Engineering students checking a moment distribution, three-moment or coefficient-table hand solution against an exact elastic analysis.
- Site and design managers who want a quick, checkable answer to how much a continuous beam gains over a run of simple spans.
More info on Continuous Beam Analysis
How the beam is modelled
Each span is a prismatic beam with the stiffness you enter, continuous over intermediate pin supports. The ends can be pinned or fixed. Loads are a uniformly distributed load per span and any number of point loads placed by span and distance from the start of that span. The analysis is linear elastic and uses PyCBA, a continuous beam analysis library, under the hood.
What the results show
The page lists the reaction at every support, the moment over every interior support, the sagging maximum in each span with the distance to it, the largest shear anywhere on the beam and the largest deflection with its position. The chart draws the shear force, bending moment and deflected shape over the full length so the sign changes and the governing locations are plain to see.
Pattern loading
A continuous beam carries its largest support moment with every span loaded and its largest span moment with alternate spans loaded. The page analyses one load arrangement at a time, so run the arrangements that govern each location and take the envelope, or use the code's simplified coefficients where the spans and loads qualify.
From analysis to design
The output moments and shears feed a member design check to the relevant steel, concrete or timber standard. For a concrete beam the hogging moment over the support sets the top reinforcement, and the code may allow a limited redistribution of that moment into the spans.
Common Calculation Errors to Avoid
- Treating each span as simply supported. A continuous beam has a hogging moment over each interior support and a smaller span moment than a simple span. Ignoring continuity misses the support moment entirely.
- Loading every span and calling it the envelope. Full loading gives the largest support moment but not the largest span moment. Alternate-span loading governs the spans.
- Forgetting that an unloaded end span can lift. With load on one span only, the far end reaction can be negative. A support that cannot hold the beam down changes the structure.
- Mixing units in the stiffness. The second moment of area and the modulus must be in consistent units for the deflection to come out right. The page carries units through, so enter them with the value.
Engineering templates
Common calculators
Design guides
FAQs
How many spans can the calculator handle?
Up to six spans, each with its own length and uniformly distributed load, plus point loads on any span.
Are the support moments the same as the coefficient tables?
Yes, for equal spans and uniform load the results match the standard coefficients: a two-span beam gives a support moment of one eighth of the span moment quantity and reactions of three eighths and five quarters. Unequal spans and mixed loads are solved exactly rather than by coefficient.
Can I model a fixed end?
Yes. Choose fixed at either or both ends and the analysis adds the end restraint moment.
Does the page apply pattern loading automatically?
No. It analyses the arrangement you enter. Run the arrangements that govern each location, usually all spans loaded for the support moments and alternate spans for the span moments, and take the envelope.
Why is one of the reactions negative?
A span loaded next to an unloaded span pushes the far end of the unloaded span upward. A negative reaction means that support must hold the beam down, which is worth checking at the connection.
Learn about the benefits of using CalcTree on engineering projects!