👋 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. For an RHS (Rectangular Hollow Section), that means two checks — the compression flange (top and bottom walls) and the web (side walls) — and the worst class governs. Because an RHS is a closed box section, both walls are internal elements. The flange is in compression under both bending and compression, so its check is unchanged; but the web's limits tighten under uniform compression (from 72ε in bending to 33ε in compression). In this article we classify the same RHS (250x150x12.5) under both pure bending and pure 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 RHS (250x150x12.5), which we will check under both pure bending and pure compression.

Steel Section
	Type	RHS
	Standard	250x150x12.5
	Breadth, b	150mm
	Height, h	250mm
	Thickness, t	12.5mm
	Corner Radius, r	25mm

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 flat width and web clear depth depend only on the section geometry, and the flange is an internal element 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 flat width (internal element) ^ⓘ
$c$	=	$b - 2 \times t - 2 \times r$
	=	$150 - 2 \times 12.5 - 2 \times 25 = 150 - 25 - 50$
	=	$\text{75 mm}$

Flange classification check (internal element in compression) ^ⓘ
$\frac{c}{t}$	=	$\frac{c}{t} \le 33\varepsilon \text{ (Class 1)} / 38\varepsilon \text{ (Class 2)} / 42\varepsilon \text{ (Class 3)}$
	=	$\frac{75}{12.5} = 6.0 \quad (33\varepsilon = 26.7)$
	=	$6.0 \le 26.7 \rightarrow \text{Class 1}$

Web clear depth ^ⓘ
$c_w$	=	$h - 2 \times t - 2 \times r$
	=	$250 - 2 \times 12.5 - 2 \times 25 = 250 - 25 - 50$
	=	$\text{175 mm}$

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) ^ⓘ
$\frac{c_w}{t}$	=	$\frac{c_w}{t} \le 72\varepsilon \text{ (Class 1)} / 83\varepsilon \text{ (Class 2)} / 124\varepsilon \text{ (Class 3)}$
	=	$\frac{175}{12.5} = 14.0 \quad (72\varepsilon = 58.3)$
	=	$14.0 \le 58.3 \rightarrow \text{Class 1}$

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) ^ⓘ
$\frac{c_w}{t}$	=	$\frac{c_w}{t} \le 33\varepsilon \text{ (Class 1)} / 38\varepsilon \text{ (Class 2)} / 42\varepsilon \text{ (Class 3)}$
	=	$\frac{175}{12.5} = 14.0 \quad (33\varepsilon = 26.7)$
	=	$14.0 \le 26.7 \rightarrow \text{Class 1}$

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

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

💡 Key takeaway:

The web's limit tightens from 72ε (58.3) in bending to 33ε (26.7) in compression, but this stocky RHS web (c_w/t = 14.0) stays Class 1 in both — so the section class is unchanged (Class 1). A thinner-walled RHS could drop a class under compression, just as the I-section did (Class 1 → Class 4).

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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.