👋 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 Circular Hollow Section (CHS) 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 CHS steel section.

Steel Section
	Type	CHS
	Standard	355.6x8.0
	Diameter, d	356mm
	Thickness, t	8.0mm

🔢 Calculation Steps

*Below is using Eurocode symbol to calculate.

Cross-sectional Area ^ⓘ
$A$	=	$(d^2 - (d - 2 \times t)^2) \times \pi$
	=	$((356mm)^2 - (356mm - 2 \times 8mm)^2) \times \pi$
	=	$8736 mm$

Second Moment of area (major axis) ^ⓘ
$I_{y}$	=	$(d^4 - (d - 2 \times t)^4) \times \pi$
	=	$((356mm)^4 - (356mm - 2 \times 8mm)^4) \times \pi$
	=	$13200 cm^4$

Second Moment of area (minor axis) ^ⓘ
$I_{z}$	=	$((d)^4 - (d - 2 \times t)^4) \times \pi$
	=	$((356mm)^4 - (356mm - 2 \times 8mm)^4) \times \pi$
	=	$13200 cm^4$

Elastic Section Modulus (major axis) ^ⓘ
$W_{el,y}$	=	$\frac{I_{y}}{d / 2}$
	=	$\frac{13200cm^4}{356mm / 2}$
	=	$742 cm^3$

Elastic Section Modulus (minor axis) ^ⓘ
$W_{el,z}$	=	$\frac{I_{z}}{d / 2}$
	=	$\frac{13200 cm^4}{356mm / 2}$
	=	$742 cm^3$

Plastic Section Modulus (major axis) ^ⓘ
$W_{pl,y}$	=	$\frac{d^3 - (d - 2 \times t)^3}{6}$
	=	$\frac{(356mm)^3 - (356mm - 2 \times 8mm)^3}{6}$
	=	$967 cm^3$

Plastic Section Modulus (minor axis) ^ⓘ
$W_{pl,z}$	=	$\frac{d^3 - (d - 2 \times t)^3}{6}$
	=	$\frac{(356mm)^3 - (356mm - 2 \times 8mm)^3}{6}$
	=	$967 cm^3$

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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.