The direct strength method in cold-formed steel design

Why cold-formed steel demands explicit buckling analysis

Brooks Smith opened by drawing a contrast with hot-rolled steel design, where engineers classify sections as compact, non-compact, or slender and apply rules accordingly. In cold-formed steel, Brooks noted, every section must be treated as slender. The walls are thin enough that buckling governs in practically every case, and the design method has to reflect that directly.

Because of this, AS/NZS 4600 explicitly separates three distinct buckling modes rather than collapsing them into a single slenderness check. Local buckling occurs when the corners of the cross section stay fixed and only the flat plate elements between corners deform, typically at half wavelengths of around 100 to 250 millimeters. Distortional buckling allows some corners to move: the canonical example is a C section where the flange tip and its stiffener lip rotate inward, occurring at half wavelengths in the range of 400 to 800 millimeters. Global buckling translates or rotates the entire cross section as a rigid unit and corresponds to lateral-torsional buckling in hot-rolled terminology, starting at half wavelengths above roughly 1.5 meters.

The Effective Width Method, which AS/NZS 4600 also supports, accounts for buckling by treating each plate element as if it were shorter than it really is. Each plate is analyzed independently, and the more stiffeners a section has, the more separate calculations are needed. For a standard C or Z section this is manageable, but for complex proprietary sections used in Australian construction, such as Quiet Studs or Whisper Wall profiles with multiple web stiffeners and intermediate lips, the plate-by-plate approach becomes unwieldy. The Direct Strength Method analyses the entire cross section as a single unit, meaning the calculation effort is the same regardless of how complex the section geometry is. Brooks noted the capacity improvement is typically up to around ten percent, not transformative, but the consistency and flexibility of the method are the stronger practical arguments for using it.

The Finite Strip Method and the signature curve

The mechanism that makes DSM work is the Finite Strip Method, which AS/NZS 4600 refers to as rational analysis. Brooks explained that unlike Finite Element Analysis, which meshes a volume into small triangles or rectangles, the Finite Strip Method uses strips that span the full length of the member. Each strip is analyzed independently at a series of half wavelengths, starting from a short value such as 25 millimeters and stepping up through progressively longer values. A separate analysis is run at each half wavelength, and the results are assembled into a signature curve: a plot of half wavelength on the horizontal axis against a load factor representing how susceptible the section is to buckling at that wavelength.

The signature curve typically shows two local minima. The first, at the shorter half wavelength, identifies local buckling. The second identifies distortional buckling. Global buckling does not appear as a minimum but is read off the curve at the point corresponding to the actual unbraced length of the member. When only one minimum appears, Brooks advised that it is always safe to assume both local and distortional buckling occur at that location rather than trying to determine which mode it represents.

Two main software options perform Finite Strip Analysis. CUFSM was developed by Johns Hopkins University, is free, and is extremely powerful, but Brooks described its interface as designed by researchers who were not thinking about day-to-day design use. Thinwall was developed at the University of Sydney, is a paid product, and has a more accessible interface. Calcs.com uses a Python port of CUFSM running in the background, with automated extraction of the critical buckling parameters.

The standard Finite Strip approach can produce ambiguous results when the minima are not sharply defined. To resolve this, the constrained Finite Strip Method runs three separate analyses: the full unconstrained signature curve, a local-only analysis with all corners locked so that only inter-corner plate bending can occur, and a distortional analysis with global buckling suppressed. The clear minimum of the local-only curve gives the local critical buckling load, and the minimum of the distortional-constrained curve gives the distortional critical load. Brooks noted that the local-only minimum will always be unambiguous because locking the corners forces the analysis into a single clean mode.

The DSM section of AS/NZS 4600 is almost verbatim copied from the US standard AISI S100, differing mainly in unit systems. Brooks recommended keeping a copy of the AISI S100 commentary, which is freely available, because its explanations of the theory and intent behind the equations are more detailed than what appears in the Australian standard text.

Applying the DSM design equations

Once the critical buckling loads for local, distortional, and global modes have been established from the Finite Strip analysis, the design equations in AS/NZS 4600 are straightforward. For each mode, the engineer calculates a slenderness parameter lambda by taking the square root of the yield moment or yield load divided by the critical buckling load for that mode. If lambda is below a threshold, the section reaches full yield capacity. If it exceeds the threshold, a weighted average between yield and the critical buckling load gives the capacity for that mode. The final member capacity is the minimum of the three mode capacities, multiplied by the capacity factor: 0.9 for bending and 0.85 for compression.

For standard C and Z sections, global buckling can be calculated analytically using the torsional and lateral buckling stress parameters FOY and FOZ rather than reading off the signature curve. This is what Calcs.com does for those section types. For complex proprietary sections where the analytical equations do not apply, a full Finite Strip analysis is required for the global buckling step. In Calcs.com these complex sections take a couple of extra seconds to compute because the FSM runs in the background, but the calculation remains essentially automatic from the engineer's perspective.

One detail Brooks flagged as easy to overlook is the bending-shear interaction check. The moment term in that interaction equation is M sub s, the local buckling capacity without any global buckling consideration, not the full member capacity M sub v. She explained that because shear capacity is governed by local plate behaviour, the moment term needs to be compatible, using only the local mode. To calculate M sub s, the lambda expression uses the yield moment rather than the global critical load in the denominator.

For members carrying combined bending and axial load, the pure bending and pure axial capacities are calculated separately through the same DSM framework and then combined using a single interaction equation. Inelastic reserve capacity is an optional enhancement that allows a small amount of localized yielding in corners or tips of the cross section, provided the member is not welded. Brooks noted this gives a marginal capacity increase and most engineers will not use it in routine design.

Deflection checks use an effective second moment of area derived from the DSM capacity equations with the actual service moment substituted for the yield moment. This produces a nonlinear deflection response: as service moment increases, buckling effects on stiffness increase, and deflection grows faster than proportionally. Brooks noted this is unlike most materials and can catch engineers off guard if they are expecting a linear relationship between load and deflection.

Cold-formed steel design in Calcs.com

Brooks demonstrated the workflow starting from the cold-formed steel beam calculator. For a standard C section floor joist with default loads, the Member Selector evaluates every section in the database and shows pass or fail with utilization, allowing rapid selection of the most efficient size. The global buckling calculation uses the analytical FOY and FOZ equations, and every step is expandable to show the individual equations in use.

Calcs.com has integrated Standards Australia, so clicking on an equation reference in the calculation, such as clause 7.2.2.1, opens that clause from AS/NZS 4600 in a sidebar panel. Cross-references within the standard are also clickable, allowing engineers to navigate between clauses directly within the calculator. Brooks showed clicking through from the member capacity clause to the local buckling sub-clause and reading the equation and conditions directly from the standard text.

For complex proprietary sections, Brooks opened a Quiet Stud calculator. Because the section geometry is not a standard C or Z, the global buckling calculation runs a full Finite Strip analysis in the background rather than using the analytical equations. This adds a couple of seconds to the calculation time. Brooks showed the signature curve displayed in the calculator and pointed out that the FSM-derived global buckling value feeds directly into the capacity check.

The custom thin-walled section properties calculator provides a full front-end to the CUFSM engine for arbitrary cross sections. An engineer can input any geometry, and the calculator runs the full signature curve and constrained FSM analyses, automatically extracting the critical local and distortional buckling parameters. Brooks demonstrated a case where reducing section thickness produced an unusually large distortional buckling half wavelength of 1,500 millimeters, well outside the typical 400 to 800 millimeter range. The calculator flagged this with a warning and displayed the signature curve so the engineer could inspect the result visually and confirm whether it was reasonable.

For shear capacity of complex sections, Brooks recommended summing the total vertical web areas and then applying the shear buckling calculation only over the largest contiguous web length, because buckling can only develop over an uninterrupted plate. This gives a conservative but practical estimate without requiring a separate DSM shear analysis of each web segment.

Portal frame design using cold-formed steel sections is supported through Calcs.com's Portal Frame Analysis calculator. Engineers design individual CFS members using the beam or column calculators, then link those calculations to the portal frame model to pull in the section properties. Doubled back-to-back or boxed sections were not yet supported in the calculator at the time of the session, but Brooks confirmed that was on the development roadmap.