# 3 Section properties

## 3.1 General

All section properties have been accurately calculated and rounded to three significant figures. They have been calculated from the metric dimensions given in the appropriate standards (see Section 1.1).

Section properties are given for both hot-finished and cold-formed hollow sections (but not for cold-formed elliptical hollow sections). For the same overall dimensions and wall thickness, the section properties for square and rectangular hot-finished and cold-formed sections are different because the corner radii are different.

For hot-finished square and rectangular hollow sections, the section properties have been calculated using corner radii of 1.5t externally and 1.0t internally, as specified by EN 10210-2.

For cold-formed square and rectangular hollow sections, the section properties have been calculated using the external corner radii of 2t if t ≤ 6 mm, 2.5t if 6 mm < t ≤ 10 mm and 3t if t > 10 mm, as specified by EN 10219-2. The internal corner radii used are 1.0t if t ≤ 6 mm, 1.5t if 6 mm < t ≤ 10 mm and 2t if t > 10 mm, as specified by EN 10219-2.

## 3.2 Second moment of area (I) and radius of gyration (i)

The second moment of area has been calculated taking into account all radii of the sections. Values are given about both the y-y and z-z axes.

The radius of gyration is a parameter used in the calculation of buckling resistance and is derived as follows:

i = [I / A]1/2

where:

 I is the second moment of area about the relevant axis A is the area of the cross section

## 3.3 Elastic and plastic section modulus (Wel and Wpl)

The elastic section modulus is used to calculate the elastic design resistance for bending or to calculate the stress at the extreme fibre of the section due to a moment. It is derived as follows:

Wel,y = Iy / z

Wel,z = Iz / y

where:

 z, y are the distances to the extreme fibres of the section from the elastic y-y and z-z axes, respectively

The elastic (Wel) and plastic section moduli (Wpl) about both principal axes are given in the tables.

## 3.4 Torsional constant (IT)

For circular hollow sections:

IT = 2I

For square, rectangular and elliptical hollow sections:

IT = where:

 I is the second moment of area of a CHS t is the thickness of the section p is the mean perimeter length For square and rectangular hollow sections: p = 2 [(b – t) + (h – t)] – 2 Rc (4 - π) For elliptical hollow sections: p = Ap is the area enclosed by the mean perimeter For square and rectangular hollow sections: Ap = (b – t) (h – t) – Rc2 (4 - π) For elliptical hollow sections: Ap = Rc is the average of the internal and external corner radii

## 3.5Torsional section modulus (Wt)

 Wt = 2 Wel for circular hollow sections Wt = for square, rectangular and elliptical hollow sections

where:

 Wel is the elastic modulus and IT, t, Ap and p are as defined in Section 3.4.