Custom Thin-Walled Section Properties

How it calculates

The Custom Thin-Walled Section Properties calculator performs two classes of computation: classical thin-walled beam theory for cross-section properties, and a Finite Strip Method (FSM) buckling analysis using a port of the CUFSM algorithm. Together these supply every parameter needed for a Direct Strength Method member design.

Cross-section geometry

The section is defined as a sequence of straight plate segments. Each segment is described by a turn angle (measured from the previous segment direction), a length, a corner inner radius, and a number of discretisation elements at each corner. Cee, Zed, and Hat modes pre-populate the segment table from standard parametric dimensions; the Custom mode accepts an arbitrary fold sequence.

From the geometry, the calculator assembles the mid-line coordinates of each plate element and computes the gross cross-section properties using the thin-wall assumption (thickness is small relative to plate width):

• Area A = sum of element areas (t × element length)
• Centroid from first moments of area
• Second moments Ixx, Iyy, Ixy about centroidal axes
• Principal axes orientation angle and principal second moments I1, I2
• Section moduli Sx, Sy (elastic) to the extreme fibres
• Shear centre (xo, yo) from integration of shear flow around the cross-section under unit transverse loads

Warping and torsion constants

The warping constant Cw is calculated by integrating the normalised warping function around the mid-line. The St Venant torsion constant is:

J = sum(b_i × t³) / 3

summed over all plate elements. These constants govern torsional and lateral-torsional stiffness and are direct inputs to global buckling calculations.

Finite Strip Method buckling analysis

The CUFSM finite strip formulation divides each plate element into strip elements and assembles a geometric stiffness matrix Kg and an elastic stiffness matrix Ke. At each trial half-wavelength, an eigenvalue problem is solved for the lowest eigenvalues. The result at each half-wavelength is the elastic critical load multiplier, plotted as a signature curve.

Critical loads are read from the signature curve as follows:

• Local buckling Mol - the first local minimum on the signature curve, at a short half-wavelength where individual plate elements buckle within the member length
• Distortional buckling Mod - the second local minimum at an intermediate half-wavelength where the stiffened element (e.g. lip of a Cee section) rotates relative to the web
• Global (lateral-torsional) buckling Mo - the load at the long-wavelength plateau where the full cross-section displaces as a rigid body

The number of half-wavelengths analysed (default 30) and the number of extracted eigenvalues (default 10) can be adjusted for accuracy vs. speed.

Boundary conditions and GBT options

By default the analysis uses simply-supported boundary conditions, consistent with the Direct Strength Method assumptions in AISI S100 and AS/NZS 4600. Fixed boundary conditions can be selected where appropriate. The Generalised Beam Theory (GBT) constraint parameters control which deformation modes are included: global, distortional, local, and other modes can be included or excluded to isolate specific buckling families for research or verification purposes.

Material properties

Material inputs include elastic modulus E, yield strength Fy, ultimate strength Fu, Poisson's ratio (default 0.3 for steel), mass density, and thermal expansion coefficient. The calculator supports cold-formed steel, aluminium, and other thin-walled metallic materials. The strip analysis is purely elastic, so material strength is not applied here - it enters only in the linked design calculator.

Linking to design calculators

The three buckling parameters Mol, Mod, and Mo are written to the calculator output in the active unit system. When a CFS design calculator in the same Calcs.com project is typed-linked to this section calculator, it reads these values directly. The utilisation check in the design calculator is expressed as:

utilization = demand / capacity ≤ 1.0

where capacity is computed from Mol, Mod, and Mo via the DSM equations in the applicable standard (AISI S100, AS/NZS 4600, or equivalent). Modify the section geometry in this calculator and all linked design checks update automatically.