Structural Analysis Tool (2D)

What it solves

This is a free online 2D structural analysis calculator for frames and trusses. You define nodes, members, supports and loads, and the solver returns the support reactions, the axial force, shear and bending moment in every member, the nodal displacements, and the shear and bending moment diagrams along each member. It runs entirely in your browser - no install, no login, no upload.

It handles both structure types because they are the same solver with different member releases: a truss member carries axial force only, while a frame member also carries shear and moment. You can mix them in one model, which is what a real roof truss on moment-resisting columns actually is.

Frames versus trusses, and why the distinction matters

In a truss every joint is a pin, so members carry pure axial force and the shape is stable only if it is properly triangulated. In a frame the joints are rigid, so members carry moment as well and the frame resists lateral load by bending rather than by triangulation.

Modelling a frame as a truss will usually leave it a mechanism - the solver cannot find a solution because the structure has no way to resist the load. Modelling a truss as a frame is not an error but changes the answer: rigid joints attract secondary bending moments that a pin-jointed idealisation does not show. For a conventional truss those secondary moments are small and usually ignored, which is why the pin idealisation survives.

Reading the results

The solver reports member end forces with a consistent sign convention: axial tension positive, sagging moment positive. A truss member showing negative axial force is in compression, and that is the one to check for buckling - a tension member of the same size is almost always fine, while a compression member of the same size may not be.

Zero-force members appear naturally in the output rather than needing to be identified by inspection. They are a real feature of many truss layouts, not an error - a member with no force under one load case may be essential under another, and removing it can turn a stable truss into a mechanism.

Checking that the answer is right

Three checks catch nearly every modelling error, and all three take seconds. First, do the support reactions sum to the applied load, in both directions? If they do not, a load or a support is wrong. Second, is the deflected shape plausible - does it move the way you would expect if you pushed the structure by hand? Third, for a determinate structure, does a hand calculation of one member agree?

A solver will happily return a confident, precisely-formatted answer for a model with a support in the wrong place or a load in the wrong direction. Those errors produce plausible-looking output rather than obvious failures, which is why the equilibrium check is worth doing every time rather than only when something looks odd.

Formula reference

Stiffness relation

$\mathbf{K}\,\mathbf{u} = \mathbf{F}$

Truss member axial stiffness

$k = \dfrac{EA}{L}$

Frame member flexural stiffness

$k = \dfrac{EI}{L}$

Member axial force

$N = \dfrac{EA}{L}\,(u_2 - u_1)$

Degrees of freedom, 2D frame node

$u_{x,}\;u_{y,}\;\theta_z$

Static determinacy, plane truss

$m + r = 2j$

Shear-moment relationship

$V = \dfrac{dM}{dx}$

Assumptions and limits

The analysis is linear-elastic first-order: material stays elastic, displacements are small, and equilibrium is formed on the undeformed geometry. Second-order (P-delta) effects are not included, so a slender sway frame where they matter needs either an amplified-sway-moment method or a proper second-order analysis.

Members are prismatic with constant EA and EI, and the solver assumes they are laterally restrained. It reports member forces - it does not check members against any design code, so lateral-torsional buckling, flexural buckling, cross-section classification and every resistance check remain to be done separately in EN 1993 or your code of choice.

Buckling is not analysed at all, which matters most for compression members: a solver result showing a member comfortably within its squash load says nothing about whether it will buckle first. Support settlement, thermal effects, construction sequence, dynamics and material nonlinearity are outside the scope.

FAQ