3D frame analysis

Space frames and space trusses by the direct stiffness method: displacements, support reactions, and axial force, shear, torsion and biaxial bending along every member — in a view you can turn, with the working shown.

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INPUTkN · m · Z up

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1 · Nodes x, y, z in m

2 · Members β = roll about the member axis, in degrees

3 · Loads + along the axis · moments by the right-hand rule

Results update as you type. Gravity is a negative load along global Z. A member's local z points up in the vertical plane through the member and local y is horizontal; with β = 0 an I-beam stands upright and carries gravity on its strong axis. For a vertical member local y is global Y. A member load along a global axis is per metre of member. A beam between two pinned supports can spin about its own axis: hinge both of its ends (○i ○j) or fix one support.

VIEW drag the drawing to turn it

|M|MAX · MEMBER 519.46 kN·m

|N|MAX · MEMBER 222.61 kN

|T|MAX · MEMBER 80.00 kN·m

MAX |u| · NODE 53.90 mm

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HOW IT'S CALCULATED · WITH YOUR NUMBERS

Step by step, with your numbers

01
Equilibrium████ ██ ███████ · ██████ = ██.██
02
Reactions████ ██ ███████ · ██████ = ██.██
03
Shear force████ ██ ███████ · ██████ = ██.██
04
Bending moment████ ██ ███████ · ██████ = ██.██
05
Deflection████ ██ ███████ · ██████ = ██.██
06
Stress████ ██ ███████ · ██████ = ██.██

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Method: direct stiffness method, 12 × 12 Euler–Bernoulli space-frame element with St Venant torsion. Reference results: closed-form beam and truss solutions; rolled-section data to EN 10365.

ASSUMPTIONS & LIMITS

Linear-elastic, first-order (small displacements): no P-Δ, no buckling, no lateral-torsional buckling.
Euler–Bernoulli members: shear deformation ignored; members prismatic between nodes; loads act through the shear centre.
Torsion is St Venant torsion only (GJ/L). Warping restraint is ignored — for open sections such as I-beams the real torsional stiffness can be higher and the warping stresses are not found.
The torsion constant of the rolled I-sections is computed from their dimensions, fillets included; hollow sections are computed with sharp corners.
Hinges are ideal ball joints (no moment, no torque); supports are rigid.
Member loads act over the full member (UDL) or at a point; a load along a global axis is per unit member length, not per unit of plan length.
Stresses and code checks are not included — use the member forces with a design check.

DISCLAIMER · For education and preliminary sizing only. Results must be reviewed by a qualified engineer before use in design.

BEYOND FIRST ORDER

P-Δ, buckling, warping torsion, dynamics and connections — we run the full structural model.

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