Structural Analysis: Plane Trusses and Continuous Beams

The page runs two solvers side by side: a plane truss and a continuous beam. The truss side returns reactions, axial forces, stresses, elongations and a deformed-shape overlay; the beam side returns reaction, shear, moment, rotation and deflection diagrams. Both update as you type and run entirely in the browser.

Updated 2026-10-01Reviewed by CalcX Editorial Team5 sources4 min read

How to use it

Pick a side.Plane truss or Continuous beam; every preset loads an editable example.
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).
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.
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.

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）