---
title: "Classification of steel sections by buckling"
subject: "Design of Steel and Timber Structure"
chapter: 1
key: "semester_6/design_of_steel_and_timber_structure:classify-steel-local-buckling"
source: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/classify-steel-local-buckling
site: BCT Engineering
---

# Classification of steel sections by buckling

Design of Steel and Timber Structure · Chapter 1: Steel Structures and their Analysis and Design

- Asked in: 2080 Chaitra, 4 marks; 2073 Bhadra, 4 marks (asked 2 times)
- Video: [Steel Design - Section Classification and Local Buckling - SD424](https://www.youtube.com/watch?v=l8-0hPLjuPw) — FireSUN
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/classify-steel-local-buckling
- Whole chapter: https://www.bctengineer.com/md/semester_6/design_of_steel_and_timber_structure/chapter-1

## Question

Classify and describe steel sections according to their local buckling behaviour.

## Short answer

IS 800:2007 classifies sections as plastic (Class 1), compact (2), semi-compact (3) or slender (4) using width-to-thickness ratios and ε=√(250/fy). Plastic sections allow full plastic rotation; compact reach Mp with limited rotation; semi-compact only elastic yield at extreme fiber; slender buckle before yield, needing effective section.

## Answer

IS 800:2007 (cl. 3.7, Table 2) classifies cross-sections by how their plate elements (flanges, web) behave under local buckling, using the width-to-thickness ratios $b/t_f$ and $d/t_w$ and $\varepsilon=\sqrt{250/f_y}$.

| Class | Name | Behaviour | Plastic hinge / rotation capacity |
|---|---|---|---|
| 1 | Plastic | Can form a plastic hinge and rotate enough for plastic redistribution of moment | Full plastic moment $M_p$, high rotation |
| 2 | Compact | Can reach $M_p$ but local buckling limits rotation | $M_p$, limited rotation |
| 3 | Semi-compact | Extreme fibre reaches $f_y$, but local buckling prevents the plastic moment | Elastic moment $M_y = Z_e f_y$ |
| 4 | Slender | Local buckling occurs before the yield stress is reached in the extreme fibre | Less than $M_y$; effective section used |

Typical limits (rolled I-section, outstand flange $b/t_f$): Class 1 $\le 9.4\varepsilon$, Class 2 $\le 10.5\varepsilon$, Class 3 $\le 15.7\varepsilon$. For the web of an I-section in bending (neutral axis at mid-depth): $d/t_w \le 84\varepsilon$ (plastic), $105\varepsilon$ (compact), $126\varepsilon$ (semi-compact).

Design use: Class 1 and 2 sections use the plastic section modulus $Z_p$ (with $\beta_b=1.0$); Class 3 uses the elastic modulus $Z_e$; Class 4 uses effective properties after deducting the buckled width.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How does a Class 1 (plastic) section differ from a Class 2 (compact) section?
   A. Class 1 never reaches Mp
   B. Class 1 reaches Mp with high rotation capacity, Class 2 reaches Mp but with limited rotation
   C. Class 2 can form a full mechanism, Class 1 cannot
   D. Class 1 has slender flanges
   Answer: B. Both reach Mp, but only Class 1 has enough rotation for plastic redistribution; local buckling limits rotation in Class 2. (Key point: Plastic vs compact)

2. What happens in a Class 3 (semi-compact) section?
   A. Local buckling occurs before yield at the extreme fibre
   B. A full plastic hinge forms
   C. The extreme fibre reaches fy but local buckling prevents the plastic moment
   D. It carries Mp with limited rotation
   Answer: C. Class 3 sections reach yield in the extreme fibre only, so the moment capacity is the elastic moment My = Ze fy. (Key point: Semi-compact behaviour)

3. Which section properties are used for design of Class 1/2, Class 3 and Class 4 sections respectively?
   A. Ze, Zp, effective
   B. Zp, Ze, effective properties
   C. Zp, effective, Ze
   D. Ze, Ze, Zp
   Answer: B. Class 1 and 2 use plastic modulus Zp, Class 3 uses elastic modulus Ze, and Class 4 uses effective properties after deducting the buckled width. (Key point: Section modulus used)

## Related in Design of Steel and Timber Structure

- [Buckling behaviour of columns](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abuckling-behaviour-of-column) — Design of Steel and Timber Structure, chapter 6
- [Structural steel and its classification](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Astructural-steel-classification) — Design of Steel and Timber Structure, chapter 1
- [Grade and classification of structural steel](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Agrade-classification-structural-steel) — Design of Steel and Timber Structure, chapter 1
- [Lateral-torsional buckling; flange curtailment](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Altb-curtailment-plate-girder) — Design of Steel and Timber Structure, chapter 7
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