Solid: Enter the boundary of one filled polygon, including concave shapes. The last vertex connects automatically to the first. Area properties use signed polygon integration. Cutouts and multiple regions are not supported.

Thin-walled: First define points with “Add points”, then use “Connect points” to select two endpoints for each wall. Set each wall thickness in the connections table or click its edge in the sketch. Only explicit connections contribute material; unused points do not. Branches and separate walls are supported. Closed loops enclose empty space.

The thin-wall approximation uses dA = tᵢ ds on each wall, so A = ΣtᵢLᵢ. Centroid and moments are integrated along each straight segment. Thickness must be small relative to wall lengths. Terms of order t³, corner overlaps and fillets are neglected; an isolated straight wall can therefore have a zero principal moment in this approximation.

All coordinates and thicknesses are in mm. Walls may meet at shared endpoints. Split crossing walls into segments joined at a common point; overlaps and crossings without shared endpoints are rejected. The calculation uses wall midlines. “Show Thickness” adds bands at the entered thickness and labels each segment; this display does not change the calculation.

The shear center M is calculated for connected thin-walled profiles, including branches and closed cells, assuming a homogeneous material with constant shear modulus. Two unit shear loads and zero twist determine its coordinates in the sketch axes. Solid polygons, disconnected walls and collinear wall midlines are not supported for this calculation.

Stress analysis: Available for connected thin-wall profiles with a nonzero inertia determinant. All listed loads act simultaneously. On the positive z cut face: N is tensile, Vₓ/Vᵧ point along x/y, and moments follow the right-hand rule. Mₓ = ∫yσ dA and Mᵧ = −∫xσ dA. Force coordinates are absolute sketch coordinates; applied moment couples do not depend on their application point. Eccentric N contributes bending; eccentric V contributes torque about the shear center.

Manual section resultants: Enter the bimoment B directly, in N·mm². B is defined with the normalized sectorial coordinate ω by σw = Bω/Iω. Mz is the total torque; the optional warping torque Tω = dB/dz separates Tsv = Mz − Tω. A value of B alone does not determine Tω. Use Beam Analysis to calculate both from member loads and restraints.

Jt combines cell circulation with ΣLt³/3 for local strip torsion. Shear flow q integrates stress across thickness; local strip torsion has zero net flow. Total τ and von Mises use the more highly stressed wall face, with σVM = √(σ² + 3τ²). Normal stress is approximated as constant across wall thickness. Local corner, load-introduction and end effects are omitted; extrema are sampled, not a strength or buckling verification.

Reference: SCI P385 — Design of Steel Beams in Torsion.

Iₓ = ∫(y − ȳ)² dA, Iᵧ = ∫(x − x̄)² dA and Iₓᵧ = ∫(x − x̄)(y − ȳ) dA refer to centroidal axes. Principal values are the extrema of the second moment under axis rotation. J = Iₓ + Iᵧ is the polar area moment, not the torsion constant.

Add a load and calculate to show stress distributions.