What the page does Every solver reports how far to trust the answer: a determinacy verdict, equilibrium residuals, a condition number and, for beams, a bending and deflection check. Presets cover a hand-check triangle and simply supported, cantilever, fixed–fixed, multi-span, overhanging and hinged beams.
How to use it 01 Pick a side. Plane truss or Continuous beam; every preset loads an editable example. 02 Enter a truss. Nodes: x y restraint (xy, y, x or -); members: from to area in mm² from node 1; loads: node Fx Fy in kN, x right and y up (downward negative). 03 Enter a beam. Set length, material and section (IPE/HEA/HEB or custom I, W, A); supports: position kind (simple, fixed, free, guided, hinge); loads: point, moment, udl, linear, positive downward. 04 Read the checks first. The determinacy card says determinate, indeterminate to degree n, or n constraint(s) short; a failed solve returns E_SINGULAR naming the mechanism. Worked examples All readouts are exact.
Triangular truss preset
Readout
Input
3 bars, 1000 mm², E = 210 GPa; node 3 Fy = −10 kN
Max nodal displacement
0.1486 mm @ node 3
Max axial force
6.009 kN @ A–C
Member forces
A–B 3.333 kN tension; A–C and B–C −6.009 kN compression
Reactions A / B
Ry 5 kN / Ry 5 kN
Hand check: reactions P/2 = 5 kN, chord PL/(4h) = 3.333 kN, diagonals 5√13/3 = 6.009 kN.
Simply supported beam preset
Readout
Input
L = 6 m, IPE 300, E = 210 GPa, udl 20 kN/m
Reactions at 0 m / 6 m
60 kN / 60 kN
Max deflection
20.09 mm @ 3 m
Max moment
90 kN·m @ 3 m
Max shear
60 kN at either end — the card reads −60 kN @ 6 m
Utilisation
107.7 % — Strength NOT OK ; deflection 20.09 / 24 mm OK
Closed forms: δ = 5wL⁴/(384EI) = 20.09 mm, M = wL²/8 = 90 kN·m; σ = 168.8 MPa against f_y/γ = 156.7 MPa.
The mechanism preset is the trap. Four bars and four reaction components satisfy m + r = 2j = 8 and the card says determinate, yet the solve returns E_SINGULAR : the square can shear freely, so counting is necessary, not sufficient. Add the diagonal and it solves.
Where the numbers come from Truss bars carry axial force only; assembling their EA/L stiffnesses through the direction cosines yields displacements, bar forces and reactions. A determinate truss follows from statics regardless of EA; an indeterminate one splits load by relative EA.
The beam follows linear-elastic Euler–Bernoulli theory; reaction unknowns are counted against two equilibrium equations plus one condition per internal hinge, any surplus split by EI. Maxima sit at zeros of the derivative polynomials — hence the peak at exactly 90 kN·m @ 3 m.
Limits and what it does not do
One linear-elastic pass. Small deflections, prismatic members, nodal truss loads and span loads only; yielding, plasticity, second-order effects and dynamics are outside the model. No stability or connection design. Buckling, fatigue, connections and torsion are not checked; the beam check covers bending stress and deflection only. Section properties and material data live in the engineering handbook , a wider set of solvers in the engineering lab , and intermediate arithmetic in the scientific calculator . Reading the signs
Loads point down, reactions point up. Loads enter positive downward; reactions print positive upward, reaction moments counter-clockwise. The shear diagram carries −60 kN @ 6 m and its mirror +60 kN @ 0 m — one 60 kN peak read from both ends. Moments are sagging-positive, deflection positive downward, rotation positive clockwise.Self-weight is not added. Member and beam mass never enters the load.Steel-table properties follow the nominal outline. The root radius is ignored, so I, W and mass run a few percent below rolled-section tables. Where it fits Hand-checking a textbook truss The triangular preset reproduces method-of-joints numbers: 5 kN reactions, 3.333 kN chord, 6.009 kN diagonals, node 3 dropping 0.1486 mm.
Sizing a floor beam Start from a span, a UDL and a profile, then switch section or safety factor until utilisation drops below 100%. The default 6 m span at 20 kN/m reads 107.7% on an IPE 300.
Continuous and hinged beams The two-span preset gives 45 / 150 / 45 kN reactions and a hogging −90 kN·m ; the Gerber preset places a hinge where the moment is zero.
Questions Why does a truss with the right member count get called a mechanism? The count guarantees determinacy only for a stable configuration: a four-bar square satisfies it yet can shear without stretching a bar, so equilibrium has no unique solution and the solver reports E_SINGULAR.
Privacy All input and calculation run inside your browser and are never uploaded; this page records no user input.
References
Wikipedia, Truss — the m + r = 2j condition, necessary but not sufficient, and relative-stiffness force distribution. en.wikipedia.org （访问日期：2026-10-01）
Wikipedia, Direct stiffness method — member stiffness relations, assembly and restrained-DOF boundary conditions. en.wikipedia.org （访问日期：2026-10-01）
Wikipedia, Deflection (engineering) — δ = 5qL⁴/(384EI) and the small-deflection assumptions. en.wikipedia.org （访问日期：2026-10-01）
Wikipedia, Shear and moment diagram — the sagging-positive moment convention and dM/dx = Q. en.wikipedia.org （访问日期：2026-10-01）
Wikipedia, I-beam — IPE profiles per EN 10365 and designation by nominal height. en.wikipedia.org （访问日期：2026-10-01）
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Reviewed by CalcX Editorial Team
Updated 2026-10-01