# 7 Bending tables

## 7.1 Circular and square hollow sections

6.2.8 (2)

The design resistances for bending Mc,Rd and shear Vc,Rd are tabulated for circular and square hollow sections in S355 and S420 (hot finished only) steel. No values have been calculated for S275 circular and square hollow sections.

The design resistances for bending about the principal axes of the cross section, Mc,Rd are given by:

(i) For Class 1, 2 cross-sections:

 Mc,y,Rd = Mc,z,Rd = (ii) For Class 3 cross-sections with a Class 1 or 2 flange:

Mc,y,Rd = Where:

Wpl,eff,y is calculated according to EN 1993-1-5, 4.4.

(iii) For other Class 3 cross-sections:

 Mc,y,Rd = Mc,z,Rd = (iv) For Class 4 cross-sections:

 Mc,y,Rd = Mc,z,Rd = 6.2.6 (2)

The design shear force resistance Vc,Rd is given by

Vc,Rd = 6.2.6 (3)

where:

 Av is the shear area For circular hollow sections Av = 2 A / π For square hollow sections Av = A / 2 γM0 is the partial factor for resistance of cross sections (γM0 = 1.0 as given in the National Annexes).

The second moment of area (I) is included in the tables because it is required for deflection checks.

For Class 4 CHS, EN 1993-1-4 refers the user to EN 1993-1-6. Moment resistance values for these sections have not been calculated and the symbol \$ is shown instead.

6.2.6 (3)

Where the design shear force is high (> 50% of the shear resistance), a reduced value of resistance for bending Mc,b,Rd and shear Mc,z,Rd should be calculated. No values are tabulated in this publication. Values of the design shear resistance, Vc,Rd are given in the tables of web bearing and buckling resistance.

## 7.2 Rectangular hollow sections

The following information is presented in the tables for rectangular hollow sections in S355 and S420 steel. No values have been calculated for S275 rectangular hollow sections.

(i) Design resistance for bending about the y-y and z-z axes and design shear resistance:

The values of Mc,y,Rd and Mc,z,Rd and Vc,Rd have been calculated as detailed in Section 8.1(a) of Steel Building Design: Design Data - 'Blue Book' (SCI publication P363) and Section 7.1 respectively, with the shear area for bending about the major axis taken as Av = A h / (b + h).

(ii) The section classification given in the tables applies to members subject to bending only about the appropriate axes. Sections may be Class 4 for pure bending about the y-y or z-z axis. It should be noted that a section may be Class 4 when bending about the z-z axis and not Class 4 when bending about the y-y axis.

(iii) The limiting length, Lc, is the length above which the design buckling resistance moment is reduced below the cross-sectional resistance due to lateral torsional buckling. The value of the limiting length is that at which the slenderness LT = 0.4, which is the value of LT,0 recommended in the CIDECT Design Guide 2 .

The slenderness for lateral torsional buckling has been calculated as follows: LT = And for RHS the elastic critical buckling moment is:

Mcr = From these expressions, conservatively assuming C1 = 1.0, the limiting length above which LTB needs to be checked can be derived as follows:

Lc = For lengths up to the limiting length, Mb,Rd is equal to Mc,y,Rd.

In the resistance tables for bending alone, no values of Mb,Rd are tabulated for lengths in excess of the limiting length. Values for lengths in excess of the limiting length are provided in the tables of combined bending and compression.

(iv) The second moment of area (I) is repeated in the tables as it is required for deflection checks.

## 7.3 Elliptical hollow sections

The following information is presented in the tables for hot rolled elliptical hollow sections in S355 steel.

(i) Design resistance for bending about the y-y axis

For Class 1, 2 and 3 sections, the design resistances are calculated in accordance with Section 7.1.

(ii) Design resistance for bending about the z-z axis

For Class 1, 2 and 3 sections, the design resistances are calculated in accordance with Section 7.1.

For Class 4 sections, the design resistances are calculated as if the section were Class 3, using a reduced design strength such that the section remains Class 3.

The reduced design strength is taken as where:

 De,minor is the equivalent diameter for buckling about the minor axis and is given by:De,minor = (iii) Design resistance for shear

The design resistance for shear in the major axis of the elliptical section is calculated in accordance with Section 7.1. For an elliptical section, the shear area Av is taken in accordance with Reference 7 as:

Av = (2 h – 2 t) t

(iv) Limiting length, Lc

The limiting length, Lc above which the design buckling resistance moment is reduced below the cross-sectional resistance due to lateral torsional buckling has been calculated in accordance with Section 7.2.