> ## Documentation Index
> Fetch the complete documentation index at: https://calcs.com/docs/llms.txt
> Use this file to discover all available pages before exploring further.
# Analyze a Thin-Walled Section: Properties and Buckling
> Run rapid buckling analysis of any thin-walled cross-section. A CUFSM port returns critical buckling parameters Mol, Mod, and Mo for the Direct Strength Method.
Perform rapid buckling analysis of any thin-walled cross-section. Default options make it easy to input the geometry for Cees, Zeds, or any arbitrary folding of sheet material. The analysis runs a port of CUFSM (Constrained and Unconstrained Finite Strip Method) in the background, to obtain critical buckling parameters Mol, Mod, and Mo for use in the Direct Strength Method of analysis for materials such as cold-formed steel and aluminum.
## Method & scope
| Property | Detail |
| -------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| Regions | United States, Australia & New Zealand, Canada, Europe |
| What it checks | Cross-section geometry, Warping and torsion constants, Finite Strip Method buckling analysis, Boundary conditions and GBT options, Material properties, Linking to design calculators |
#### Calculation method
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 fibers
* **Shear center** (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 normalized 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 analyzed (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 Generalized 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, aluminum, 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 utilization 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.
## How to use it
Open it from **Run calc** in the About this calculator panel above.
Work through the input sections from top to bottom. Click any input label to see its reference explanation, clause, conditions and assumptions. See [Checks, References, Conditions and Assumptions](/docs/running-calculations/checking-results/checks-references-conditions-assumptions).
Check the utilization of each governing check in the summary, then export a PDF report. See [Views and Export](/docs/running-calculations/exporting-reports/views-and-export).
## Common questions
The calculator runs a port of CUFSM (Constrained and Unconstrained Finite Strip Method) to determine elastic critical buckling loads for local, distortional, and global (lateral-torsional) buckling modes. These critical loads, Mol, Mod, and Mo, are the inputs required by the Direct Strength Method (DSM) as defined in AISI S100, AS/NZS 4600, and equivalent standards. The calculator itself does not apply load combinations or safety factors; it supplies the buckling parameters that a linked design calculator uses.
Section type (Cee, Zed, Hat, or Custom), wall thickness, cross-section geometry defined as a sequence of straight segments with turn angles and lengths, corner inner radius, material properties (E, Fy, Fu, Poisson's ratio, density), boundary conditions for the strip analysis (simply-supported or fixed), member length range for the signature curve, and number of eigenvalues to extract.
Traditional cross-section properties, area, second moments of area (Ixx, Iyy, Ixy), principal axis properties, section moduli, plastic section moduli, shear center coordinates, warping constant (Cw), and St Venant torsion constant (J). In addition, the Finite Strip Method analysis produces elastic critical buckling loads across a range of half-wavelengths, from which Mol, Mod, and Mo are extracted. A signature curve plot shows the critical load vs. half-wavelength relationship.
Yes. The custom input mode accepts any sequence of straight segments defined by turn angle and length, allowing you to model hats, tracks, lip-stiffened sections, sigma sections, or fully custom profiles built from folded sheet. The section geometry is drawn interactively and the strip mesh is generated automatically from the fold table.
Once you have run the cross-section analysis, use the typed-linking feature in the Calcs.com platform to connect this calculator to a CFS beam, column, or member design calculator in the same project. The design calculator reads Mol, Mod, and Mo directly, no manual copying of values. When you modify the section geometry here, the linked design check updates automatically.
## Next steps
Analyze any arbitrary cross-section for second moments of area, section moduli, and warping and torsion constants, then link it into design calculators.
Complete list of Calcs.com design calculators available for United States projects (AISC, ACI, NDS, ASCE 7, IBC, and related standards).
Design cold-formed steel beams to AISI S100-16(2020) w/S2-20 with the Direct Strength Method. Checks flexure, shear, web crippling and deflection.
Design cold-formed steel studs and columns to AISI S100-16(2020) w/S2-20 with the Direct Strength Method and separate effective lengths per axis.
Design cold-formed steel beams to AS/NZS 4600:2018 using the Direct Strength Method, with a built-in database of Australian CFS sections.
Design cold-formed steel members to AS/NZS 4600:2018 by the Direct Strength Method. Input analysis forces to check moment, shear, bearing, and combined actions.
Learn how to build a custom truss layout, define member types, create a custom cross-section, and link it into the Custom Truss Analysis calculator.
