Truss analysis by the method of joints: the force in every member
Choose a truss type, panels, angle and load, and the tool solves the force in every member by the method of joints. The result is a drawing and a 3D model you download as STL or 3MF.
Opens without an account 3 times a day. A free account removes the limit.
- 12 modesfrom member forces to printability
- 9 truss typesfrom Warren to space
- STL, 3MF and CSVthe model and the numbers
- Eurocode and profilescombinations and a section catalogue
What the truss analysis calculator shows
This truss analysis calculator from EduFacturing is a free online tool that solves the forces in a truss by the method of joints and shows them as a drawing and a 3D model. The colour of each member shows tension, compression or a negligible force (under 2% of the largest), and its thickness follows the force.
Besides the truss there are frame and beam, influence lines, Eurocode combinations, buckling, frequencies, deflection, collapse, temperature and settlement, optimisation, a print check and catalogue sections.
What it does: forces, buckling, printing
Solves a truss by the method of joints
Nine types: Warren, Pratt, Howe, K-truss, scissor, arch, dome, cantilever and space. From 2 to 12 panels and a load of 1 to 100 kN per joint. A mechanism or an indeterminate system is rejected with a message.
Shows the structure as a truss and as a frame
The general stiffness system also solves indeterminate frames, up to 6 storeys and 6 bays. Pinned joints give a truss, rigid joints give a frame.
Checks buckling, frequencies and deflection
Buckling by Euler or Johnson, natural frequencies and resonance, deflection checked against FL³/48EI, the failure order of the members, and forces from temperature and support settlement.
Gives a model to print and numbers
It optimises the lightest Warren truss, checks the member diameter and overhang for the nozzle and shows catalogue sections: IPE, HEA, HEB, HEM, UPN and L angles. STL and 3MF are one fused body, and the numbers download as CSV.
When you need it: statics, a check, a mock-up
A truss is the structure whose forces can still be checked by hand.
A statics course
A student changes the truss type and the load and sees how the forces change.
A preliminary check
An engineer estimates forces, buckling and deflection before the full calculation.
A model for a mock-up
A model maker prints a truss at a chosen scale and checks the members for printability.
Choosing a scheme
A designer compares Warren, Pratt, Howe and K-trusses by the largest tension and compression.
How a truss is solved by the method of joints
Every joint is in equilibrium: the sum of the forces along x and along y is zero. That gives two equations per joint, solved all at once.
Determinacy
For n joints, m members and r reactions there are 2n equations and m + r unknowns. It solves only when they are equal; otherwise it is a mechanism or indeterminate.
Solving
The system is solved by Gaussian elimination with partial pivoting. A positive force is tension, a negative one is compression, and a force below 10⁻⁶ N counts as zero.
Section and material
Members are a round tube with a diameter of 5 to 100 mm and a wall of 0.5 to 8 mm. The yield strength is 235 MPa, while E and density are set by sliders.
| Applies to | Formula | Meaning |
|---|---|---|
| Euler | P_cr = π²·E·I / (K·L)² | K from 0.5 to 2.1; for a short member Johnson applies |
| Johnson | P_cr = A·σ_y·(1 − σ_y·λ² / (4π²·E)) | for λ below λ_c = √(2π²·E / σ_y); λ = K·L / i |
| EN 1990 combination | w_Ed = γG·G + γQ·leading + Σ γQ·ψ0·accompanying | the leading action is Q, S or W; Q as accompanying has ψ0 = 1; the heaviest is taken |
Zero-force members stay, results are checked
Zero-force members are not removed
A member with no force under this load is marked, not deleted: under another load it may carry force.
Frequencies are those of the truss itself
Frequencies are those of the assembled truss, and the figure for a beam with this span sits beside them for comparison. Buckling gives the critical force of a single member and a multiplier for the whole truss.
Results are checked
An example from the tests: a 4 × 2 m triangular truss under 10 kN gives reactions of 5000 N each.
The tool does not replace a structural design. It does not calculate fatigue, local buckling of a thin wall, welds or a full 3D modal analysis, and the moving load is only for a simple beam. The space truss and the dome are a planar calculation.
The force mode needs a statically determinate truss. Deflection is that of a simple beam, not of the truss. The 3D deformation is exaggerated 40 times. Member radii in STL and 3MF follow the length and the force, not the diameter from the slider.
Questions about trusses: zero-force members, Eurocode
How to calculate truss forces?
By the method of joints: every joint is in equilibrium, so the forces along x and along y sum to zero. That gives two equations per joint, solved all at once.
What is a zero force member, and should I remove it?
A member with no force under this load; in 3D a member below 2% of the largest force is coloured this way. The tool marks it but does not remove it: under another load it may carry force.
How do you know if a truss is statically determinate?
Count n joints, m members and r reactions. The force mode solves only when the 2n equations equal the m + r unknowns. Otherwise it is a mechanism or indeterminate.
What is the difference between a truss and a frame?
A truss has pinned joints and its members carry only axial force. A frame has rigid joints, carries bending too and is statically indeterminate.
How are loads combined under the Eurocode?
Under EN 1990 in three cases, with Q, S or W leading. The accompanying snow and wind carry ψ0, 0.5 and 0.6 by default, and Q as an accompanying action enters with ψ0 = 1. The heaviest is taken.
How to 3D print a truss?
Download the STL or 3MF: one fused body (a boolean union of members and joints) at a chosen scale, 20 mm per metre by default. Print checks the member diameter against the nozzle and the overhang angle.
Do I need an account to solve a truss?
Without an account the tool opens 3 times a day, and with a free account there is no limit.
The trusses and beams tool is free. Pro opens the rest
Pro costs 15 EUR a month and opens 45 Pro tools.
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Solve your truss
Opens without an account 3 times a day. A free account removes the limit.