Most standard steel structural shapes these days are designed to prevent local buckling, as it’s a tricky little check that’s easy to miss, and these shapes are known as compact. Compact shapes don’t need to be checked for local buckling effects.
But several legacy shapes do still exist in the steel manual that are either noncompact or slender, and steel designers specifying their own built-up beams can easily stumble into troubled waters as well.
How can you tell if a steel shape is compact, and what happens if they aren’t?
Video Option
Check out my YouTube video on this topic for more info / if you prefer that format!
What is Local Buckling?
You’ve probably heard of “lateral-torsional buckling” or “Euler column buckling”, which are both kinds of global buckling phenomena, where the entire section kicks out to the side or twists, resulting in a loss of load-carrying capacity prior to material failure. This kind of buckling is usually countered with bracing, to prevent the unwanted lateral movement of the member.
In structural sections, there are two types of instability failures: global buckling and local buckling. Just like with global buckling, local buckling results in the loss of capacity prematurely, but local buckling isn’t something that can be fixed with bracing.
In local buckling, elements of the overall cross-section, such as a single flange or web portion, crumple under compression due to their slenderness. These local element slenderness ratios are typically based on simple dimensions, like comparing the flange thickness and width.
With flange-local buckling, the flanges ripple or kink in on themselves, locally turning the section into a weaker shape.
Web-local buckling (also called web crippling) can be even more catastrophic, as most efficient structural shapes rely on having heavy flanges flung far out away from the neutral axis. If the web collapses, the flanges lose their separation, and most of the strength and stiffness of the shape rapidly degrades.
How are Steel Cross Sections Classified?
Steel shapes are classified as either compact, noncompact, or slender, depending on when they’re expected to experience local buckling. The equations for predicting local buckling all hinge on the width-to-thickness ratios of the cross-section, and this ratio is given the symbol λ.
Most modern shapes in the AISC Steel Construction Manual are designed to be compact, so as to alleviate the worries of local buckling, but there are still a few noncompact w-shapes in there, as well as a few slender sections in the other shapes.
To check if a section is compact, calculate the width-to-thickness ratio λ per AISC Specification Table B4.1b (for members subjected to flexure), and compare to λ.p and λ.r from the same table.
- If λ is less than λ.p for all elements subjected to compression in the shape, then the shape is compact.
- If λ is between λ.p and λ.r for any element of the section, and no section is less than λ.r, then the shape is noncompact.
- If λ for any element is less than λ.r, then the shape is slender.
Compact Steel Sections
Steel shapes are classified as compact if they are able to reach their full plastic moments before experiencing any local buckling effects. In this case, local buckling effects can be totally ignored for ordinary design, as we already need to prevent the section from forming plastic hinges in most cases.
Some consideration of local buckling may still be needed for extreme limit-states designs that push past the plastic moment.
Noncompact Steel Sections
If a steel shape is classified as noncompact, then some consideration may have to be given to local buckling effects. These shapes are expected to experience local buckling prior to the development of the full plastic moment, but after the onset of first yielding.
In any design that limits stresses to elastic design stresses (designs based on the elastic section modulus, S, rather than the plastic section modulus, Z) we can totally ignore local buckling. However, most designers these days do allow steel sections to use their plastic moment, so keep in mind the limitations of local buckling in these designs.
Slender Steel Sections
Local buckling will govern the allowable stress or nominal moment for these sections, as local buckling is expected to occur prior to the first material yielding under bending.
This is often the case in certain built-up sections, and in other materials, like cold-formed steel and custom aluminum extrusions used in facade framing.
How to Incorporate Local Buckling Strength in Noncompact and Slender Cross-Sections
Chapter F of the Specification contains different equations for flexural design.
Doubly-Symmetric I-Shaped Members, for example, are governed for design by the following sections:
- F2. Doubly-Symmetric Compact I-Shaped Members and Channels Bent About Their Major Axis
- F3. Doubly Symmetric I-Shaped Members with Compact Webs and Noncompact or Slender Flanges Bent About Their Major Axis
- F4. Other I-Shaped Members With Compact or Noncompact Webs Bent About Their Major Axis
- F5. Doubly Symmetric and Singly Symmetric I-Shaped Members With Slender Webs Bent About Their Major Axis
Summary
As you can see, the classification of steel cross-sections governs which equations to use for design, but the Steel Construction Manual has made it so easy to use the design aids in the front of the book that many engineers forget to ever flip to the full Specification at the back.
That’s usually fine, but if you’re going to engineer based off the tables alone, make absolutely sure you read all the footnotes!
The super-convenient Table 3-2 “W-Shapes – Selection by Z.x” has any shape that’s noncompact or slender marked with footnote “f”, which should be your clue to either account for local buckling effects, or just pick a different, compact section.
Don’t forget to swing by PPI2Pass for all your FE, PE, and SE prep needs!