❓ Why Steel Section Properties Matter

Before designing structural steel, it helps to understand the following section properties and how each one affects a member's capacity and performance — so a better section can be selected.

This article covers briefly the essential properties to know, what they mean physically, and how they influence structural behavior.

1️⃣ Cross-sectional area, A

Cross sectional area is the section area of the steel member. It can be computed by simple geometry.

Common symbol in eurocode:

Eurocode2 AISC

Section	Equation
Rectangle	$A = bh$
Circle	$A = \pi r^2$
I / H-section	$A = 2bt_f + (h-2t_f)t_w$
RHS	$A = bh-(b-2t)(h-2t)$
CHS	$A = \frac{\pi}{4}(D^2-d^2)$

The Area will directly affecting:

🛡️ Tension/Compression Capacity

The relationship of A and axial capacity:

$N = f_y \cdot A$

A larger area means more axial capacity — more material to carry tension or compression before yielding.

⚖️ Mass

The relationship of A and self-weight:

$m = \rho \cdot A \cdot L$

Mass is directly proportional to area — a bigger cross-section means more steel, and more weight to support.

💰 Cost

The relationship of A and material cost:

$Cost \propto m \propto A$

Since steel is typically priced by weight, a larger area generally means a higher material cost.

2️⃣ Second Moment of area, I

The second moment of area, (also called moment of inertia), measures a section's resistance to bending and its stiffness. It is a geometrical property of an area which reflects how its points are distributed with regard to an axis (y or z).

Second Moment Area

\begin{aligned}I = \int y^{2} dA\end{aligned}

Core Underlying Equation

The Symbols of Second moment of area are a bit different across eurcodoe and AISC:

Item	Eurocode	AISC
Second Moment of Area(Major)	$I_{y}$	$I_{x}$
Second Moment of Area(Minor)	$I_{z}$	$I_{y}$

General Calculation of Second Moment of area of different shapes:

Section	Equation
Rectangle	$I = \frac{bh^3}{12}$
Circle	$I = \frac{\pi r^4}{4}$
I / H-section	$I = 2\left[\frac{bt_f^3}{12}+bt_f\left(\frac{h-t_f}{2}\right)^2\right]+\frac{t_w(h-2t_f)^3}{12}$
RHS	$I = \frac{bh^3-(b-2t)(h-2t)^3}{12}$
CHS	$I = \frac{\pi}{64}(D^4-d^4)$

The Second Moment of Area will directly affecting:

🛡️ Bending Stiffness

This bending stiffness is: EI.
A larger I means a stiffer section — it resists bending more for the same material.

〰️ Deflection

The relationship of I and deflection, δ :

$\delta \propto \frac{1}{EI}$

Deflection is inversely related to I — doubling I roughly halves the deflection under the same load.

3️⃣ Elastic Section Modulus, S, W_el

The elastic section modulus relates the moment of inertia to the distance from the neutral axis to the extreme fiber of the section. The stress in section is experiencing linear distribution, as shown below.

Second Moment Area

\begin{aligned} W_{el,y} = \frac{I}{y_{max}}\end{aligned}

Core Underlying Equation

The Symbols of Elastic Section Modulus are a bit different across eurcodoe and AISC:

Item	Eurocode	AISC
Elastic Section Modulus(Major)	$W_{el,y}$	$S_{x}$
Elastic Section Modulus(Minor)	$W_{el,z}$	$S_{y}$

General Calculation of Elastic Section Modulus of different shapes:

Section	Equation
General	$W_{el} = \frac{I}{y_{max}}$
Rectangle	$W_{el} = \frac{bh^2}{6}$
Circle	$W_{el} = \frac{\pi r^3}{4}$
I / H-section	$W_{el} = \frac{I}{h/2}$
RHS	$W_{el} = \frac{I}{h/2}$
CHS	$W_{el} = \frac{\pi(D^4-d^4)}{32D}$

The elastic section modulus will directly affecting:

📐 Elastic moment capacity

The equation of elastic moment capacity is:

$M_{el} = f_y \cdot W_{el}$

This is the moment at which the extreme fibre just reaches yield — the section is still fully elastic.

4️⃣ Plastic Section Modules, Z, W_pl

The plastic section modulus represents the section's capacity once it has fully yielded. The stress in section is experiencing redistribution of stress, as shown below.

The Symbols of Plastic Section Modules are a bit different across eurcodoe and AISC:

Item	Eurocode	AISC
Plastic Section Modulus(Major)	$W_{pl,y}$	$Z_{x}$
Plastic Section Modulus(Minor)	$W_{pl,z}$	$Z_{y}$

General Calculation of Plastic Section Modules of different shapes:

Section	Equation
General	$W_{pl} = \sum A_i d_i$
Rectangle	$W_{pl} = \frac{bh^2}{4}$
Circle	$W_{pl} = \frac{4r^3}{3}$
I / H-section	$W_{pl} = bt_f(h-t_f)+\frac{t_w(h-2t_f)^2}{4}$
RHS	$W_{pl} = \frac{bh^2 - (b - 2t)(h - 2t)^{2}}{4}$
CHS	$W_{pl} = \frac{4}{3}(R^3-r^3)$

The plasic section modulus will directly affecting:

📐 Plastic moment capacity

The equation of plastic moment capacity is:

$M_{el} = f_y \cdot W_{pl}$

This is the moment at which the whole section has yielded — the maximum moment it can carry before forming a plastic hinge.

🔢 Example: how geometry affects section properties across three angle/section types

Since these properties are used directly to compute structural analysis and capacity, let's look at how different geometries (I-section, CHS, RHS) with similar area affect the properties, so we can make a better decision to suit the situation.

To illustrate how the geometry will affect the properties:

	I Section	RHS	CHS	which better
Standard	457x191x67	250x150x12.5	355.6x8.0	(with similar area)
$A(mm^2)$	8550	8700	8740	similar
$I_{y}(cm^4)$	29400	6600	13200	I section better
$I_{z}(cm^4)$	1450	3000	13200	CHS better
$W_{el,y}(cm^3)$	1470	530	740	I section better
$W_{el,z}(cm^3)$	150	400	740	CHS better
$W_{pl,y}(cm^3)$	1450	680	970	I section better
$W_{pl,z}(cm^3)$	240	480	970	CHS better

From the table above, we can see that even with the same area, different geometries produce very different value of the properties. Details of calculation of each value can be found in I-section , RHS and CHS

I-section: is efficient at resisting moment in its main axis but is comparatively weak in the other axis.
CHS: is more balanced in both directions.
RHS: falls between the two — its properties are lower than the CHS's for the same area, but it's relatively easier to fabricate and connect.

So the right choice really depends on the structural situation at hand.

📄 Need to calculate the values of each section for I section, CHS or RHS?

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#steel design #glossary

CivilSimple Team

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