👋 Introduction

Steel Properties is one of the first essential design in most of the steel design, as no matter structural analysis or capacity design, the steel properties is the major parameter to compute. While there's steel section properties table available, it's also always a good idea to understand how every value comes from. This article aims to demonstrate the steps involved in calculating the Area, Second Moment of Inertia, Elastic Modulus and Plastic Modulus of a Rectangular Hollow Section (RHS) through worked numerical examples.

The concept behind this and its corresponding structural meaning can be found in another article: 4 Steel Section Properties Every Steel Designer Should Know.

ℹ️ Symbols Difference between Eurocode and AISC

Please note that this is first principle logic about the section properties, so it can be applied to all codes of standard worldwide. However, symbols may be a bit different. Below is a table showing the symbol difference between eurocode and AISC:

Item	Eurocode	AISC
Area	A	A
Second Moment of Area(Major)	$I_{y}$	$I_{x}$
Second Moment of Area(Minor)	$I_{z}$	$I_{y}$
Elastic Section Modulus(Major)	$W_{el,y}$	$S_{x}$
Elastic Section Modulus(Minor)	$W_{el,z}$	$S_{y}$
Plastic Section Modulus(Major)	$W_{pl,y}$	$Z_{x}$
Plastic Section Modulus(Minor)	$W_{pl,z}$	$Z_{y}$

📐 Design Data

Below are the design information of the RHS steel section.

Steel Section
	Type	RHS
	Standard	250x150x12.5
	Breath, b	150mm
	Height, h	250mm
	Thickness, t	12.5mm

Radius
External Radius, r_ext	= 3 x t =	38mm
Internal Radius, r_in	= 2 x t =	25mm

🔢 Calculation Steps

*Below is using Eurocode symbol to calculate.

Cross-sectional Area ^ⓘ
$A$	=	$b \times h - (b - 2 \times t)\times(h - 2 \times t)$
		$- 4 \times ((r_{ext})^{2} - \frac{\pi \times (r_{ext})^{2}}{4}) + 4 \times ((r_{in})^2 - \frac{\pi \times (r_{in})^2}{4})$
	=	$150mm \times 250mm - (150 - 2 \times 12.5mm)\times(250mm - 2 \times 12.5mm)$
		$- 4 \times ((38mm)^{2} - \frac{\pi \times (38mm)^{2}}{4}) + 4 \times ((25mm)^2 - \frac{\pi \times (25mm)^2}{4})$
	=	$8704 mm^4$

Second Moment of Area (major axis) ^ⓘ
$I_{y}$	=	$\frac{b \times (h)^3}{12} - \frac{(b-2 \times t) \times (h-2 \times t)^3}{12}$
	=	$\frac{150mm \times (250mm)^3}{12} - \frac{(150mm - 2 \times 12.5mm) \times (250mm - 2 \times 12.5)^3}{12}$
	=	$6633 cm^4$

Second Moment of Area (minor axis) ^ⓘ
$I_{z}$	=	$\frac{h \times (b)^3}{12} - \frac{(h-2 \times t) \times (b-2 \times t)^3}{12}$
	=	$\frac{250mm \times (150mm)^3}{12} - \frac{(250mm -2 \times 12.5mm) \times (150mm -2 \times 12.5mm)^3}{12}$
	=	$3002 cm^4$

Elastic Section Modulus (major axis) ^ⓘ
$W_{el,y}$	=	$\frac{I_{y}}{h / 2}$
	=	$\frac{6633 cm^4}{250mm / 2}$
	=	$531 cm^3$

Elastic Section Modulus (minor axis) ^ⓘ
$W_{el,z}$	=	$\frac{I_{z}}{b / 2}$
	=	$\frac{3002 cm^4}{150mm / 2}$
	=	$400 cm^3$

Plastic Section Modulus (major axis) ^ⓘ
$W_{pl,y}$	=	$\frac{b \times h^2 - (b-2 \times t) \times (h-2 \times t)^2}{4}$
	=	$\frac{150mm \times 250mm^2 - (150mm-2 \times 12.5) \times (250mm -2 \times 12.5mm)^2}{4}$
	=	$678 cm^3$

Plastic Section Modulus (minor axis) ^ⓘ
$W_{pl,z}$	=	$\frac{h \times b^2 - (h-2 \times t) \times (b-2 \times t)^2}{4}$
	=	$\frac{250mm \times (150mm)^2 - (250mm -2 \times 12.5mm) \times (150mm -2 \times 12.5mm)^2}{4}$
	=	$477 cm^3$

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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.