Structural Steel Design / module 5
Steel sections and cross-section classification
Why a thin plate gives way before the steel it is made of ever reaches yield — and why a section does not have a class until you say what it is carrying.
What you will understand
- Explain why a compression plate can buckle below the yield stress
- Say why an internal element is far better off than an outstand, and by how much
- Compute plate slenderness and relate it to the class limits it stands in for
- Classify a section under a stated action, plate by plate
- Explain why a higher steel grade makes local buckling MORE likely
- State what each class permits, and what a Class 4 section loses
Lessons
Why a plate buckles before the steel yields
A section is not a solid shape. It is an assembly of thin plates, and a thin plate in compression has its own opinion about how much stress it will take.
The four classes, and what a section is allowed to do
Classification is not a property of a section. It is a property of a section carrying a particular thing, and the same beam can be Class 1 in bending and Class 4 in compression.
Module summary
- Plate buckling depends on E and geometry, and not at all on fy
- σcr goes with (t/b)², so thickness is the strong lever and width the weak one
- An internal element is restrained on both edges; an outstand on one — about nine times better
- λ̄p = √(fy/σcr) is the ratio the class limits stand in for
- The limits are CALIBRATED boundaries, not the slenderness at which a plate buckles
- ε = √(235/fy) is where grade enters — higher grade, tighter limits
- A section takes the WORST class of any of its plates
- A section has no class until you say what it carries: bending and compression differ
Teaching basis and review status
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesCheck your understanding
Practice
A plate 400 mm wide and 15 mm thick is an internal element in uniform compression. What is σcr, in N/mm²? Take π²E/[12(1−ν²)] = 189 800 and kσ = 4.0.
Practice
What is ε for S460 steel?
Practice
A web has c/t = 55 and is in S275 (ε = 0.924). The Class 3 limit for an internal element in COMPRESSION is 42ε. Does it pass? Give the limit.
Practice
A plate has λ̄p = 1.20 and is in uniform compression (ψ = 1). What is the effective-width factor ρ?
Practice
By what factor is an internal element's critical stress greater than an outstand's, all else equal?
Practice
An I section in major-axis bending has a shape factor of 1.13. If it is downgraded from Class 2 to Class 3, by what percentage does its bending resistance fall?