2D Frame & Beam FEA Calculator — the guide

The calculator analyses beams, columns, braced frames, portal and gable frames and trusses — anything made of straight members in one plane — under static loading, and reports reactions, axial force, shear, bending moment, deflections and elastic stresses, per load case, per combination and as envelopes. It re-solves continuously as you edit: there is no Solve button and no mesh to manage.

Every result on screen is free and needs no account. The one thing that asks you to sign in — also free — is downloading the PDF report. Models are accepted up to 600 nodes, 900 members and 600 loads per case; a frame of ordinary size solves in well under a second, and the largest accepted models in a few seconds. The tool performs the analysis and compares it against limits you supply — it contains no design-code resistances, which is a deliberate boundary the methodology explains.

1. Open a template. The gallery offers 14 complete models — beams, portals, trusses, a two-storey frame, a crane runway and more. Pick Simply supported beam. It loads already solved, and the identity on its card (δ = 5wL⁴/384EI) is asserted against the engine on every build, so the starting point is known-good.
2. Change the span. In the tables panel under the canvas, edit node B's x coordinate from 6000 to 8000. The model re-solves as you commit the cell — watch the moment diagram grow.
3. Change the load. Step to Loads in the left rail and edit the UDL intensity, or add a point load partway along. Downward is negative F_y — the direction picker handles the sign for you.
4. Set your limits. Enter the deflection span ratio and stress allowables you design to. These are yours: the tool suggests nothing and checks against exactly what you type.
5. Read the verification panel first. Stable, equilibrium residual near 10⁻¹⁶, mesh study near zero — then trust the diagrams. Section 10 shows what each row means.
6. View the report. The toolbar's report button assembles the analysis basis, model tables, diagrams, envelopes and the verification record — the same numbers you saw on screen, from the same solver.

With the draw tool (key D), click to place nodes and chain members between them; Escape ends a chain. Clicking an existing member splits it at that point, so the new node is genuinely connected rather than sitting on top; the loads on that member are carried across the cut, so splitting changes the mesh and nothing else. The select tool (V) moves nodes, marquee-selects, and nudges with the arrow keys. Every action lands in one undo history — Ctrl+Z takes back anything.

The tables under the canvas are a spreadsheet view of the same model: nodes, members, sections, materials, supports and loads. Cells edit in place, and a block copied from Excel pastes from the focused cell, appending rows as needed. A cell that cannot be read is reported on its own row and left unchanged — nothing is guessed into the model, and a blank line in the middle of a paste does not shift the rows after it.

Three ways to get a cross-section, in decreasing order of convenience. The catalogue holds standard profiles — IPE, HEA, HEB, HEM, UB, UC, W shapes, SHS, RHS and CHS — stored as nominal dimensions and derived to properties through the same first-principles code as everything else, fillets included; the methodology shows the derivation and the measured accuracy. An outline section is the same machinery applied to dimensions you type: rectangle, I-section, RHS or CHS. And a custom section takes raw properties — A, I, and optionally the shear and fibre values — for anything else.

Edit any derived number by hand and the section becomes custom: the outline is dropped rather than left to disagree with the numbers. Leave an optional property out and the stresses that need it are reported as not available rather than computed from a guess — a section with only A and I still solves and still reports deflections and all internal actions.

Combined normal stress is the one that depends on what the member is doing, not only on what the section states. Without a fibre distance there is no M y/I to report, so a member carrying only axial force is still checked in full — for a truss chord, N/A is not a fragment of the normal stress, it is all of it. A member that also bends is left out of that check entirely and named, and no pass verdict is issued for the model until it has a fibre distance: publishing the axial part alone there would print a small number, and a pass, for a beam whose real stress nobody had computed.

The material picker offers typical elastic constants for steels, stainless, aluminium, concrete and timber — starting points, not a code source, and the report prints whichever values were actually used. For isotropic materials you may leave G blank and it follows from E and ν.

Concrete values are short-term uncracked moduli. For a cracked or long-term stiffness, enter your own reduced E — the tool will not adjust it for you, because that adjustment is a design decision.

Supports come as presets — fixed, pinned, roller in either direction — plus fully custom per-direction restraint, elastic springs, an inclined (skewed) support at any angle, and imposed settlement. Restrained directions are eliminated from the system exactly, not approximated with stiff springs, which is why reactions are exact equilibrium quantities; the methodology explains both mechanisms. Settlements are typed in global coordinates exactly as labelled, whatever the support's skew.

Releases live on member ends: moment (the pin of a truss or three-pin frame), axial, or shear. A released action is condensed out of the element exactly — see the condensation section — and releasing the same action at both ends of one member is refused, because it would disconnect the member. On the canvas, a joint where every framing member is pinned collapses to a single hinge ring; ends released at a mixed joint keep their own markers, because there which member is pinned is the information.

The load tool (L) places loads by clicking; the Loads step edits every value. The vocabulary: nodal forces and moments; member point forces and moments at any position along a member; distributed loads that can vary linearly and cover part of a span; uniform temperature change and through-depth gradient; support settlement; and self weight computed from each member's own density and area.

Group loads into cases, then combine cases with factors — 1.35 G + 1.50 Q and its siblings. Under linear analysis a combination is exactly the factored sum of its cases, so combinations cost nothing and you can afford as many design situations as the code asks for. Mark each combination strength, serviceability or both; the stress checks read the strength set and the deflection check the serviceability set. A combination with no factors, or whose factors all point at empty cases, is excluded from the design situations and says so.

The results dock plots N, V, M and δ for the selected member, per design situation, with the peaks marked at their exact positions — peaks are located analytically, not read off plot points, so the 5L/8 of a propped cantilever is reported as 5L/8. Hovering reads values at solver stations; clicking pins a value so it stays annotated while you edit. The tables tab lists reactions, end forces and peaks per member, and the envelope view reports the worst value at every position with the combination that caused it named beside it.

One convention to internalise before reading any diagram: the plots are signed ordinates, positive up — a sagging moment reads positive and is drawn above the axis, which is not the tension-face drafting habit. The full sign convention is the legend on the inputs panel, and the methodology walks through it with the figure that prevents the classic misreading.

The equilibrium residual deserves special trust: the applied loads are re-integrated from the load definitions, independently of the fixed-end forces used to solve, so agreement tests the load processing as well as the solution — the solver is not marking its own homework. And the panel never renders an unmeasured quantity as a zero: a skipped mesh study reads not evaluated, with the reason. Diagnostics appear alongside: errors that stopped the solve, warnings about meaning (crossing members, truncated loads, inert springs), and notes such as the automatic constraint of pin-joint rotations in a truss.

The solver itself carries a standing record beyond your model: the verification record solves every registered benchmark when you open the page and prints the analytical value beside the computed one with the measured error. It is code verification — evidence the equations are solved correctly — not validation against physical tests, and not a claim about your particular model.

The report assembles what a checker needs in one document: the analysis basis with the sign convention and assumptions, the full model and loading tables, reactions with the equilibrium check, the diagrams per design situation, envelopes with governing combinations, the stress and deflection checks against your limits, the verification record, and the scope statement. Viewing it is free; downloading the PDF asks for a free sign-in. Screen and PDF are produced by the same pure engine, so they cannot disagree about a number.

On very large models the per-situation diagram pages are omitted to keep the document usable — the tables and envelopes remain complete. The limits are stated honestly in the methodology's known-limitations list.

The entire model lives in the page URL — geometry, sections, materials, supports, loads, combinations and your limits. Copy link, send it, and the recipient opens exactly what you built, no account needed. The URL updates as you edit, so your browser history is also a crude version history.

Two pointer behaviours worth knowing: a mouse wheel zooms while a trackpad two-finger scroll pans (the tool tells the two apart, and Ctrl+scroll or pinch always zooms), and drags use pointer capture on the canvas itself, so a drag survives the re-renders that editing causes.

“The structure is unstable: node … can move”

The model is a mechanism and the message names the free node and direction. Usual causes, in order: a missing support direction (two rollers holding nothing horizontally); two members that cross without sharing a node and only look connected — redraw through a shared node, see section 4; or over-released ends, where a chain of pins leaves a joint free to spin or a member free to slide. The solver constrains a pin-joint rotation automatically only when nothing loads it, so a moment applied at a fully pinned joint is refused instead.

The deflection is enormous

Almost always units or properties: an E entered in GPa where MPa was meant, a section area or inertia three orders too small, a span in metres typed as millimetres. Check the conditioning row too — a pivot ratio far above 10¹² usually means one member is accidentally a noodle. If the deflection is genuinely large, the tool will also tell you the first-order assumption itself is strained.

A moment diagram is unexpectedly zero

Look for a moment release you forgot — a pinned end carries no moment by definition — or a load that landed on a different member than intended. A load placed beyond its member's end is refused with an error naming the position, precisely so it cannot silently migrate to a support and zero out the span moment.

A stress check says “not available”

The section in use is missing the property that stress needs — fibre distances for bending, Q/t or a shear area for shear. Generate the section from an outline and every property is derived; or type the missing value. Nothing is assumed in the meantime, deliberately: a zero here once meant a passing check on an overstressed beam, and that path is closed. Where a member that bends has no fibre distance, the combined-stress check names it, states the stress it can prove that member exceeds, and withholds the verdict for the whole model rather than reporting the peak of the members it could reach as though it were the peak.

The mesh study says “not evaluated”

Your model is above 600 free degrees of freedom, where re-solving everything subdivided would cost far more than the analysis itself. This is disclosure, not failure: the diagrams are mesh-independent by construction — the methodology explains why — and the record states that no figure was measured rather than showing a zero nobody computed.

• Coordinates and sign conventions — the signed-ordinate plotting rule and the legend the workspace renders.
• The element — the stiffness matrix, and when the Timoshenko setting matters, with the measured curve.
• Loads and fixed-end forces — why the load handling generalises to partial trapezoids without a table of cases.
• Recovery — why one element per member is exact, and the review story behind the shear term's sign.
• The verification record — the five measurements behind the panel in section 10.
• Known limitations — the honest list, from the adversarial review.
• The verification record page — every benchmark solved live, with the measured error.