Beam Diagram
Shear Force Diagram
Bending Moment Diagram
Deflection Curve
📊 Numerical Results
Whether you're a structural engineering student wrestling with your first simply supported beam problem, or a practicing engineer checking a quick floor joist design, a reliable bending moment and shear force calculator is one of the most useful tools you can have at your fingertips. This free online beam calculator gives you instant, accurate results for shear force diagrams (SFD), bending moment diagrams (BMD), deflection curves, and support reactions — all without leaving your browser.
Let's walk through what each result actually means, and why it matters.
"Students almost universally arrive with the same intuition — that a beam sitting on more supports must be safer. It's an understandable assumption, and it's also consistently wrong in ways that matter. It does add redundancy, yes — but it also introduces statically indeterminate behaviour that completely changes how loads are distributed. A two-span continuous beam doesn't just share the load evenly between three supports. The stiffness of the beam itself decides how much each support carries. When students can instantly compare a simply supported case against a continuous one using a tool like this, and actually see the moment diagram shift, the concept clicks in a way that a blackboard derivation rarely achieves."
Key takeaway: Use the calculator to compare determinate and indeterminate configurations side by side — the visual difference in bending moment diagrams is one of the most effective teaching tools available.
When a load is applied to a beam, the beam's cross-sections don't just bend — they also try to slide past one another. This sliding tendency is what engineers call shear force. The shear force at any point along the beam equals the net sum of all vertical forces acting to one side of that cross-section.
The Shear Force Diagram (SFD) plots this value along the entire span. At a pin or roller support, you'll see a sharp jump in the diagram — that's the reaction force kicking in. Under a uniformly distributed load (UDL), the shear force changes linearly because the load accumulates gradually. Under a concentrated point load, it jumps abruptly.
Why does this matter in practice? Because shear stress governs the design of certain beam types — particularly short, deep beams, timber members, and bolted or welded connections. A structural engineer checking a steel beam will always verify that the peak shear value doesn't exceed the web's shear capacity.
If shear force is about sliding, the bending moment is about rotating. At any cross-section, the bending moment equals the sum of all moments caused by forces on one side. It tells you how much the beam is being bent at that point.
The Bending Moment Diagram (BMD) is arguably the most important output of any beam analysis. The location of maximum bending moment is where your beam is under the highest stress — and therefore where failure is most likely. For a simply supported beam with a central point load, this peak occurs exactly at midspan. For a cantilever under a uniform load, the worst moment sits right at the fixed wall.
A critical concept here is the sign convention. Sagging moments — where the beam curves like a smile — are treated as positive. Hogging moments — where it curves like a frown, common near fixed supports or interior supports in continuous beams — are negative. This calculator lets you toggle between sagging-positive and hogging-positive conventions, which is especially helpful when matching results to your textbook or design code.
Points of contraflexure, where the bending moment passes through zero and changes sign, are equally important. These are natural hinge points in continuous structures and are often used to simplify construction detailing.
"This sounds trivial but it genuinely isn't. I've reviewed calculation packages from competent engineers who switched from British Standards to Eurocode mid-project and inadvertently flipped their hogging and sagging conventions without realising it. The downstream effect on reinforcement detailing — particularly where you're deciding which face of a concrete section to put tension steel — can be significant. The ability to toggle between sagging-positive and hogging-positive on the BMD is not just a cosmetic feature. It's a practical safeguard when you're matching output to a specific code or sharing results with a team working in a different convention."
Key takeaway: Always confirm which sign convention your design code requires before interpreting bending moment results, especially on mixed-team or cross-border projects.
Strength checks tell you whether a beam will survive. Deflection checks tell you whether it will actually behave acceptably in use. A beam that technically doesn't break under load but sags 40 mm under a tiled floor is still a design failure.
Deflection is calculated by integrating the bending moment diagram twice — a process rooted in the Euler-Bernoulli beam equation. The result depends not just on the loads and span, but critically on the beam's flexural rigidity (EI) — the product of the elastic modulus E and the second moment of area I. A stiffer material (high E) or a deeper section (high I) both reduce deflection significantly.
Common serviceability limits include L/360 for live loads under brittle finishes, L/250 for total load deflection per Eurocode, and L/480 for particularly sensitive installations. This calculator checks your result against whichever limit you select and flags an exceedance clearly.
"Most people's eyes go straight to the moment diagram — what surprises younger engineers is how often it's the deflection result that ultimately determines which section you walk away with. I've seen projects where the steel section passed every strength check comfortably, then failed serviceability because nobody properly accounted for long-term creep on top of the elastic deflection. Having a tool that immediately plots the deflection curve and flags L/360 or L/250 exceedances means that conversation happens at the design stage, not during site inspections. That's where it genuinely saves money."
Key takeaway: Always run your deflection check against the appropriate serviceability limit before finalising a section size — not as an afterthought.
A beam is statically determinate (DSI = 0) when its reactions can be found using equilibrium equations alone — sum of vertical forces equals zero, sum of moments equals zero. Simple spans with a pin and a roller are the classic example.
Add an interior support, or fix one end, and you've introduced more unknowns than equations. This is a statically indeterminate structure, and it requires more advanced analysis. This calculator automatically detects the degree of static indeterminacy and switches to the Direct Stiffness Method — a matrix-based approach used by professional finite element software — to solve for reactions precisely.
"The Steel, Concrete, and Timber presets for elastic modulus are useful for early-stage estimates, and I appreciate that they're there. But I always caution engineers — particularly less experienced ones — that real material behaviour is more nuanced. Concrete's effective modulus varies with age, loading duration, and mix design. Timber is orthotropic and highly moisture-sensitive. For preliminary sizing these presets are perfectly reasonable. For final design, always replace them with values drawn from your project-specific material specifications or the relevant code annex. The tool gives you the right framework — the engineer still needs to supply the right inputs."
Key takeaway: Treat built-in material presets as a starting point for early design iterations. Final calculations should always use project-specific, code-verified material properties.
Getting started takes less than a minute. Set your span length, choose your support conditions, and add loads using the Load Manager. Point loads, UDLs, trapezoidal loads, and applied moments are all supported. Define your section properties — or pick Steel, Concrete, or Timber from the material presets — and hit Analyse Beam. Results appear instantly, complete with interactive diagrams and a full set of step-by-step hand calculations you can copy or export to PDF for your project documentation.
Free beam analysis tool for engineers and students. Calculate support reactions, shear force diagrams, bending moments and deflection in seconds — SI and Imperial units supported.
Price: Free
Price Currency: $
Operating System: Single Page Application
Application Category: Calculator
