👋 Introduction

Section classification decides how much of a section's strength we are allowed to use in design, and it depends on the stress distribution the section is subject to — not just its geometry. In this article we classify the same I-section (457x191x67) under two stress states:

Pure bending — the web is in bending (compression on one side, tension on the other)
Pure compression — the web is in uniform compression

The flange is in compression in both cases, so its check is unchanged; but the web's limits tighten under uniform compression, which can push the same section into a lower class. As we'll see, this section is Class 1 (plastic) in bending but Class 4 (slender) in compression.

The concept behind this and its corresponding structural meaning can be found in another article: Classification of Steel Sections - I-Section, CHS, and RHS Explained.

ℹ️ Class Naming Difference between Eurocode 3, IS 800 and AISC

The classification concept is the same worldwide, but the class names and the limiting ratios differ slightly between codes:

Design Capability	Eurocode 3	IS 800	AISC 360
Plastic design (full hinge rotation)	Class 1	Plastic	Compact
Full plastic moment, limited rotation	Class 2	Compact	Compact
Elastic capacity (yield at extreme fibre)	Class 3	Semi-compact	Noncompact
Elastic with reduced (effective) section	Class 4	Slender	Slender

Note that the material factor ε also uses a different constant: EN 1993-1-1 uses ε = √(235/f_y), while IS 800 uses ε = √(250/f_y).

📐 Design Data

Below are the design information of the I-section (457x191x67), which we will check under both pure bending and pure compression.

Steel Section
	Type	I-section
	Standard	457x191x67
	Breadth, b	190mm
	Height, h	453mm
	Flange Thickness, t_f	12.7mm
	Web Thickness, t_w	8.5mm
	Root Radius, r	10mm

Material
Steel Grade		S355
Yield Strength, f_y		355 N/mm²

🔢 Calculation Steps

*Below is using Eurocode symbols and limits Table 5.2, EN 1993-1-1. For IS 800, use ε = √(250/f_y) and the limits in its Table 2.

Common checks (geometry & flange)

The flange outstand and web clear depth depend only on the section geometry, and the flange is in compression under both bending and compression — so these checks are the same for both stress states.

Material factor ^ⓘ
$\varepsilon$	=	$\sqrt{\frac{235}{f_y}}$
	=	$\sqrt{\frac{235}{355}} = \sqrt{0.662} = 0.81$
	=	$0.81$

Flange outstand width ^ⓘ
$c$	=	$\frac{b - t_w - 2 \times r}{2}$
	=	$\frac{190 - 8.5 - 2 \times 10}{2} = \frac{161.5}{2}$
	=	$\text{80.75 mm}$

Flange classification check (outstand in compression) ^ⓘ
$\frac{c}{t_f}$	=	$\frac{c}{t_f} \le 9\varepsilon \text{ (Class 1)} / 10\varepsilon \text{ (Class 2)} / 14\varepsilon \text{ (Class 3)}$
	=	$\frac{80.75}{12.7} = 6.36 \quad (9\varepsilon = 7.29)$
	=	$6.36 \le 7.29 \rightarrow \text{Class 1}$

Web clear depth ^ⓘ
$c_w$	=	$h - 2 \times t_f - 2 \times r$
	=	$453 - 2 \times 12.7 - 2 \times 10 = 453 - 25.4 - 20$
	=	$\text{407.6 mm}$

Under bending

Here the web is an internal element in bending, checked against the 72ε / 83ε / 124ε limits.

Web classification check — under bending (internal element in bending) ^ⓘ
$\frac{c_w}{t_w}$	=	$\frac{c_w}{t_w} \le 72\varepsilon \text{ (Class 1)} / 83\varepsilon \text{ (Class 2)} / 124\varepsilon \text{ (Class 3)}$
	=	$\frac{407.6}{8.5} = 47.95 \quad (72\varepsilon = 58.3)$
	=	$47.95 \le 58.3 \rightarrow \text{Class 1}$

Section class — under bending ^ⓘ
$\text{Section Class}$	=	$\text{Worst of flange and web classes}$
	=	$\text{worst(Class 1 flange, Class 1 web)}$
	=	$\text{Class 1 (Plastic)}$

Moment capacity to use — under bending ^ⓘ
$M_{Rd}$	=	$M_{pl,Rd} \text{ for Class 1/2, } M_{el,Rd} \text{ for Class 3}$
	=	$\text{Section is Class 1 (plastic)}$
	=	$M_{pl,Rd} = W_{pl,y} \cdot f_y / \gamma_{M0}$

Under compression

Here the web is an internal element in uniform compression, checked against the tighter 33ε / 38ε / 42ε limits.

Web classification check — under compression (internal element in compression) ^ⓘ
$\frac{c_w}{t_w}$	=	$\frac{c_w}{t_w} \le 33\varepsilon \text{ (Class 1)} / 38\varepsilon \text{ (Class 2)} / 42\varepsilon \text{ (Class 3)}$
	=	$\frac{407.6}{8.5} = 47.95 \quad (42\varepsilon = 34.0)$
	=	$47.95 > 34.0 \rightarrow \text{Class 4 (Slender)}$

Section class — under compression ^ⓘ
$\text{Section Class}$	=	$\text{Worst of flange and web classes}$
	=	$\text{worst(Class 1 flange, Class 4 web)}$
	=	$\text{Class 4 (Slender)}$

Compression capacity to use — under compression ^ⓘ
$N_{Rd}$	=	$A \cdot f_y / \gamma_{M0} \text{ (Class 1/2/3), } A_{eff} \cdot f_y / \gamma_{M0} \text{ (Class 4)}$
	=	$\text{Section is Class 4 (slender)}$
	=	$N_{Rd} = A_{eff} \cdot f_y / \gamma_{M0}$

💡 Key takeaway:

The same I-section is Class 1 (plastic) in bending but Class 4 (slender) in compression. Only the web's stress state changed — the geometry is identical. This is why section classification must always be checked against the actual stress distribution, not just the section shape.

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#steel design #work example #structural

CivilSimple Team

The CivilSimple Team writes practical engineering guides for the profession and the curious. All articles are reviewed for technical accuracy before publication.