Truss — Forces in Structure

System

Truss

Span

Depth

Panels

Forces

Single point load (slide it!) Deflected shape (exaggerated)

Wind direction

Wind H / W

Context: wind speed

A total load W is split over the loaded nodes; every member force reads as a multiple of W. Blue = compression, red = tension; thickness scales with force. Hover any member for its number. Slide the point load along the span and watch the diagonals change sign.

Array into a bay (3D model)

Trusses1

Spacing4.0 m

Purlins & bottom ties End cross-bracing

Display (3D model)

Member size60 mm

Show nodes

Import / Export

OBJ writes member centrelines as a line model — open it in Rhino / CAD to detail the connections. CSV lists every member with its length and force. PNG saves the current view. Import reads a relax-net.json handoff from the Relax form-finder (Relax's "Send to Truss" also lands here automatically for 15 minutes).

Sources & method

What is actually solved. The truss is solved by the linear-elastic direct stiffness method for pin-jointed members with uniform axial stiffness (EA = 1): assemble K, apply a unit total load W over the loaded nodes, pin the left bearing, roller the right (space frames: pinned corner columns or perimeter walls, solved with 3 dof per node), solve K·u = f by Gaussian elimination, and read each member's axial force. For a statically determinate truss this is exactly the method of joints from any statics text; for indeterminate ones it distributes force by (equal) stiffness. A near-singular K is reported honestly as a mechanism — try Vierendeel, or the "verticals only" web in Custom.

Determinacy count. The readout compares members + reactions (m + r) with the equilibrium equations (2 per joint in 2D, 3 in 3D) — Maxwell's rule. The count is necessary, not sufficient: the solver's pivot check has the final say.

Deflected shape comes from the same solve. With EA = 1 its shape is right but its scale is arbitrary, so it is drawn exaggerated to a fixed fraction of the span — read it as "where it sags and how", never as millimetres. The buckling watch ranks compressed members by |C|·L² (Euler capacity falls with 1/L²) and flags the worst — a risk ranking, not a capacity check.

Wind load case. Wind enters as a total horizontal force H expressed as a fraction of the gravity load W (the H/W slider), split equally over the top-chord nodes and solved by the same direct-stiffness method; load cases combine by superposition (the solve is linear). The solver is dimensionless (EA = 1, W = 1) and a planar truss has no compass orientation or cladding area, so a real speed→force conversion is impossible here — the V (m/s) box only computes the stagnation pressure q = ½·ρ_air·V² ≈ 0.613·V² Pa for physical context, and you choose the ratio. The reversed members count compares the active case against a gravity-only solve of the same structure — wind's real danger is turning slender ties into struts.

Imported nets (from Relax). The Relax form-finder can send its settled geometry here ("Send to Truss"): nodes are projected to their best-fit vertical plane (the out-of-plane RMS is reported, never hidden), coincident nodes merge, and Relax anchors become full pin supports — so an imported arch shows its horizontal thrust in the reactions. Only geometry and supports cross the bridge; Relax edge tensions are solver-unit estimates and are not imported as forces. A bare chain imports as a mechanism — correctly: a pin-jointed chain has no stiffness sideways. Import it as a chord profile instead: the curve becomes a chord of a Custom truss (arch → top chord over a flat deck, hanging chain → fish-belly bottom chord), you pick the web, and it stands.

Not solved: member sizing, buckling capacity, self-weight, connection design, load sharing between arrayed trusses (purlins are drawn, not solved), deflection limits, code checks. Span-to-depth is compared against preliminary-design rules of thumb (planar trusses ≈ 1:8–1:12, space frames ≈ 1:15–1:25). A learning + layout tool — a licensed structural engineer must analyse and size any real truss.

Sources. Method of joints / direct stiffness: Hibbeler, R.C., Structural Analysis, Pearson — pearson.com. Span-to-depth rules of thumb: Allen, E. & Iano, J., The Architect's Studio Companion, Wiley — wiley.com. Truss typologies and how each form carries load: Truss.