Cold-Formed Steel (CFS), also known as Light Gauge Steel (LGS), experiences various buckling modes, including local, global, and distortional buckling, with the interaction between these modes often playing a critical role in the failure of light gauge steel members. To accurately predict the strength of cold-formed steel members, engineers must identify the most critical buckling mode for a given cross-section. While several design methods exist to determine buckling modes, global cold-formed steel standards primarily use the Effective Width Method (EWM) and the Direct Strength Method (DSM), both of which are widely recognized for their effectiveness in predicting the strength of cold-formed steel members.
Cold-Formed Steel Design: Effective Width Method
The Effective Width Method (EWM) is one of the oldest and most widely used design methods in the cold-formed steel industry. This method treats cold-formed steel sections as individual plate elements with varying end restraint conditions. Depending on the boundary conditions and loading patterns, these individual elements may deform from their original positions, leading to different buckling modes within the section. The buckling mode and corresponding stresses depend on several factors, which include the following:
- Boundary conditions of the individual elements within the section,
- Magnitude and type of applied load (e.g., compression, tension, bending),
- Shape of the section,
- Presence of stiffeners in the individual elements,
- Effective length of the section,
- Stress gradient within the section, and
- Location and size of holes within the section.
The strength prediction for cold-formed steel sections, considering the factors listed above, follows a series of well-defined steps. These steps are detailed in established standards such as:
- AS/NZS 4600:2018 Cold-formed steel structures
- AISI S100-16 North American Specification for the Design of Cold-Formed Steel Structural Members and
- BS EN 1993-1-3:2024 Eurocode 3 – Design of steel structures Part 1-3: Cold formed members and sheeting”.
The following sections summarize the steps outlined in these standards for using the Effective Width Method.
Strength determination using EWM
The first step involves calculating the geometric section properties of the given cross-section using fundamental principles of mechanics. These properties are derived from geometric inputs, including depth, breadth, thickness, bending radius, Young’s modulus, and shear modulus. The computed section properties include the following:
- Cross-sectional area,
- Moments of inertia about principal axes,
- Section moduli about principal axes,
- Centroid location,
- Radii of gyration, and
- Torsional warping constant.
Next, the width of individual plate elements within the cross-section is reduced based on the aforementioned factors. The effective width of each element is determined by considering the compressive forces acting on it. These compressive forces may exhibit either a uniform distribution or a gradient, depending on the loading conditions and structural actions applied to the member.
The figure below illustrates the varying stress gradients acting on individual plate elements within the cross-section.
After determining the geometric properties and effective widths of the section, the next step involves computing the effective stresses within its elements. These stresses depend on the applied load and the section’s symmetry. Cold-formed steel profiles are manufactured with various geometric symmetries, including monosymmetric, doubly symmetric, point-symmetric, and unsymmetric configurations. Based on the symmetry of the section, the process uses specific governing equations for different design actions to determine the capacity of the cold-formed steel section. These design actions include the following:
- Compression,
- Tension,
- Shear,
- Bending,
- Web crippling, and
- Combined actions.
The image on the left illustrates cold-formed steel sections with various geometric symmetries, while the image on the right depicts the effective widths and stress distributions under different design actions.
Scottsdale and Knudson by Scottsdale KFS, KFD and KFE family of roll forming machines can produce cold-formed steel sections of all geometric symmetry.
After determining the nominal strengths of the cold-formed steel sections based on their effective width, stress distribution, geometric symmetry, and element holes, the analysis factors the nominal capacities by considering the respective effective lengths of the member. The process then compares these factored strengths against the load demand to evaluate the design adequacy ratio of the member.
Cold-Formed Steel Design: Direct Strength Method
The Direct Strength Method (DSM) offers a modern and efficient approach to designing cold-formed steel members by addressing local, distortional, and global buckling behavior. Unlike the traditional Effective Width Method, which analyzes cross-sectional elements individually, DSM evaluates the entire member as a unified system. This method uses elastic buckling solutions from finite strip analysis and strength curves to provide more accurate and streamlined analyses, particularly for thin-walled members with complex cross-sections and stiffeners. Additionally, DSM accounts for the effects of holes in sections and restraints about various axes along the elements when determining strengths.
Researchers developed DSM by building on foundational studies in distortional buckling, and the cold-formed steel community has since integrated it into design standards such as AS/NZS 4600 and AISI S100. The method predicts buckling behavior by applying elastic local buckling stress and design curves, simplifying calculations for intricate geometries. Due to its efficiency and reliability, DSM has become a preferred method for modern structural applications in cold-formed steel design.
Finite Strip Method and Direct Strength Method (DSM)
The Direct Strength Method (DSM) uses elastic buckling solutions derived from the Finite Strip Method (FSM) to address local, flange-distortional, and overall buckling in cold-formed steel members. Local buckling involves plate flexure within the section, typically occurring at short half-wavelengths with a significant post-buckling reserve. Flange-distortional buckling involves membrane bending of stiffeners and edge stiffeners, occurring at intermediate half-wavelengths with moderate post-buckling reserve. Overall buckling entails global translation or torsional-flexural modes of the cross-section, occurring at longer half-wavelengths with minimal post-buckling reserve. DSM bases strength predictions on elastic buckling stresses, incorporating simplified assumptions and adjustments, such as those in AS/NZS 4600 and AISI S100, to account for boundary conditions and section-specific interactions. These approaches streamline complex calculations, ensuring reliable strength predictions for any cold-formed steel section.
Strength Determination Using DSM
To determine strength using the Direct Strength Method (DSM), the geometry of the cold-formed steel section is first defined. This geometry is input into finite strip analysis software to determine the corresponding buckling modes, buckling factors, and buckling moments. The analysis requires additional inputs, such as the steel grade, yield strength, and ultimate tensile strength, to calculate the buckling load factors. The results are presented as load factor versus half-wavelength curves, and the minima for local, distortional, and global buckling factors are identified to determine the strengths.
The extracted load factors are applied to the design equations specified in standards such as AS/NZS 4600 and AISI S100 to calculate the nominal capacity of the section for various actions, including compression, tension, bending, shear, and combined actions. After determining the nominal capacities, capacity reduction factors are applied to establish the section strength. Finally, this strength is combined with the effective lengths of the members to determine the member capacities of the cold-formed steel section under consideration.
Image below shows a cold-formed steel lipped channel section from Scottsdale’s steel framing machine showing various buckling modes and load factor versus member half-wavelength curve.
Key Differences between EWM and DSM
Both design methods are popular and widely used in the engineering community for designing cold-formed steel structures. Design standards, such as AS/NZS 4600 and AISI S100, acknowledge and include these methods. However, these methods differ significantly in how they determine capacities. Therefore, designers must carefully choose the appropriate method. The key differences between these methods are summarized below.
Effective Width Method (EWM)
- Uses an element-based approach, analyzing individual plate elements (e.g., flanges, webs) separately.
- Relies on empirical formulas to calculate the effective width of each element based on its slenderness ratio.
- More labor-intensive and requires iterative calculations for each element, making it suitable for hand calculations but cumbersome for complex geometries.
- Well-suited for simple, traditional cross-sections like C-sections or Z-sections. Complex shapes can become more tedious and cumbersome.
- Can be conservative, as it does not fully account for interactions between different buckling modes or post-buckling strength.
- Included in older versions of the design codes (e.g., AISI Specification) and is still widely used in practice around the globe.
Direct Strength Method (DSM)
- Uses a member-based approach, analyzing the entire cross-section as a whole.
- Uses the elastic buckling stresses (local, distortional, and global) of the entire member and applies strength curves to predict capacity.
- Computationally efficient and fast, relying on software (e.g., finite strip analysis) to determine elastic buckling stresses, simplifying the design process.
- More versatile and can handle complex cross-sections, such as those with stiffeners, perforations, or irregular shapes.
- Generally, more accurate, as it explicitly considers interactions between local, distortional, and global buckling and better captures post-buckling behavior.
- Included in modern design codes (e.g., AISI S100-16) and is gaining popularity due to its simplicity and accuracy. Some codes such as Eurocode doesn’t support it officially.
Which Cold-Formed Steel Design Method Should I Follow?
The choice between the Effective Width Method (EWM) and the Direct Strength Method (DSM) depends on the complexity of the design, the tools available, and the design code being followed. For simple cross-sections, such as traditional C-sections or Z-sections, and when working with older design codes or performing manual calculations, EWM is preferable. EWM works well for straightforward geometries and manual calculations, as it focuses on analyzing individual plate elements like flanges and webs. However, EWM can become labor-intensive for complex shapes and may not fully account for interactions between different buckling modes or post-buckling behavior, potentially leading to conservative designs. While some external software applications support EWM, they often limit the types of sections that can be analyzed.
For complex geometries, such as sections with stiffeners, perforations, or irregular shapes, DSM is the better choice. DSM handles complex cross-sections more effectively and provides greater accuracy by analyzing the entire cross-section and explicitly considering interactions between local, distortional, and global buckling modes. Software tools like finite strip analysis (e.g., CUFSM, ScotStruct, and CFS by RSG) can determine elastic buckling stresses, and DSM simplifies the design process once these values are obtained. Modern design codes like AISI S100-16 increasingly recommend DSM because it captures post-buckling strength and works well for non-standard cross-sections. When access to the necessary software is available and modern codes are followed, DSM typically serves as the more effective option for most designs.
Optimizing Cold-Formed Steel Usage in Your Next Project
The Direct Strength Method (DSM) generally offers slightly better steel optimization compared to the Effective Width Method (EWM). DSM effectively captures post-buckling strength and accounts for interactions between local, distortional, and global buckling modes, making it particularly suitable for complex or non-standard cross-sections. On the other hand, EWM, while dependable for simple geometries, often yields slightly conservative results, potentially leading to over-designed members. Engineers should carefully evaluate these differences when designing structural elements for a project.
Efficient detailing also significantly influences steel optimization, as cladding spans frequently dictate stud, truss, or joist spacing. Aligning structural elements with these practical constraints can sometimes outweigh the minor advantages of DSM. Designers must pay close attention to these factors throughout the design process to ensure material efficiency and adherence to project requirements.
The Scottsdale suite of software tools, ScotSteel and ScotStruct, includes functionalities to design cold-formed steel members using both the Effective Width Method (EWM) and the Direct Strength Method (DSM), offering users maximum flexibility in the design process. Contact us to learn more about how our software suite can assist in designing your next project.
