Axial & bending tables
Generally, members subject to axial compression forces and bending should be verified for cross-section resistance
(EN 1993-1-1, §6.2.9) and for member buckling resistance (EN 1993-1-1, §6.3.3.(4)).
The relevant parameters required to evaluate the interaction equations given in the above clauses are presented in tabular form.
The tables are applicable to members subject to combined tension and bending and also to members subject to combined compression and bending. However, the values in the tables are conservative for tension, as the more onerous compression section classification limits have been used for calculating resistances to axial force.
Tables are given for cross-section resistances and for member buckling resistances, as explained below.
10.1. Axial force and bending: Rolled I and H sections and channels
10.1.1. Cross-section resistance check
Code ref
§6.2.9
§6.2.1 (7)
For Class 1,2 and 3 cross-sections the following conservative approximation may be used:
Eq (6.2)
Values of Npl,Rd, Mc,y,Rd and Mc,z,Rd are given in the tables. The section classification depends on the axial force applied and therefore Mc,Rd values are given for different values of NEd / Npl,Rd. The values of these resistances have been calculated as given in the following sections.
No values are given for combined axial force and bending on Class 4 sections. Refer to EN 1993-1-1, §6.2.9.3(2).
(a) Design resistance for axial force
Eq (6.6)
where:
| A | is the gross area of the cross-section |
| f y | is the yield strength |
| γ M0 | is the partial factor for cross-sections ( γ M0 = 1.0 given in the National Annex). |
(b) Design resistance for bending about the principal axis of the cross-section
The design resistances for bending about the major and minor axes M c,y,Rd and M c,z,Rd have been calculated as in Section 8.1 using W pl,y, W el,y and W pl,z and W el,z as appropriate. No values are given for the reduced resistances in the presence of high shear.
Code ref
§6.2.5 (2)
M c,Rd values for these sections are not given in the tables. For cross-sectional checks of Class 4 sections, see EN 1993-1-1, §6.2.9.3(2).
The symbol x indicates that the section is Class 4 for a given value of N Ed / N pl,Rd
The symbol $ indicates that the section is Class 4 and that it would be overloaded due to compressive axial force alone i.e. the section is Class 4 and N Ed > A eff f y. for the given value of N Ed / N pl,Rd.
The Class 2 and Class 3 limits for the section subject to bending and compression are the maximum values of N Ed / N pl,Rd up to which the section is either Class 2 or Class 3, respectively. The Class 2 limit is given in bold type.
Code ref
§5.5.2 (8)
§6.2.9.1 (2)
As an alternative to equation (6.2) for Class 1 and 2 sections a less conservative criterion may be used as follows:
M Ed ≤ M N,Rd
Eq (6.31)
Values of M N,Rd are given in the tables.
(c) Design moment resistance reduced due to axial force
The reduced moment resistance M N,y,Rd has been calculated as follows:
Code ref
§6.2.9
(i) Where both the following criteria are satisfied:
Eq (6.33 and 6.34)
where:
Code ref
§6.2.9.1 (4)
| h w | is the clear web depth between flanges = h - 2tf |
| γ M0 | is a partial factor (γ M0 = 1.0 see Section 5.1) |
The reduced design moment resistance is equal to the plastic resistance moment:
M N,y,Rd = M pl,y,Rd
(ii) Where the above criteria are not satisfied the reduced design moment resistance is given by:
Code ref
§6.2.9.1 (5)
Eq (6.36)
where:
| M pl,y,Rd | is the plastic resistance moment about the y-y axis |
| n | is the ratio N Ed / N pl,Rd |
(d) Design moment resistance about the z-z axis reduced due to axial force
The reduced moment resistance M N,z,Rd has been calculated as follows:
(i) Where both the following criteria are satisfied:
Code ref
§6.2.9.1 (4)
Eq (6.35)
where:
| h w | is the clear web depth between flanges = h - 2tf |
| γ M0 | is a partial factor for cross-sections ( γ M0 = 1.0 see Section 5.1) |
In this case no allowance has been made for the effect of the axial force on the plastic resistance moment about the z-z axis and the reduced design moment resistance in this case is equal to the plastic resistance moment:
M N,z,Rd = M pl,z,Rd
(ii) Where the above criterion is not satisfied the reduced design moment resistance is given by:
Code ref
§6.2.9.1 (5)
For n ≤ a
M N,z,Rd = M pl,z,Rd
Eq(6.37)
For n ≥ a
Eq(6.38)
where:
Code ref
§6.2.9.5
| M pl,z,Rd | is the plastic resistance moment about the z-z axis |
| n | is the ratio N Ed / N pl,Rd |
| a | is as given in (c) |
Because the values of M N,y,Rd and M N,z,Rd are only valid for Class 1 and Class 2 sections, no values are shown when
N Ed / N pl,Rd exceeds the limit for a Class 2 section (shown as the symbol " - " in the tables).
Reduced design moment resistances for channels are not presented in the tables. This is because EN 1993-1-1, §6.2.9 does not specifically cover the requirements for channels.
10.1.2. Member buckling check
Interaction equations (6.61) and (6.62) from EN 1993-1-1, §6.3.3(4) must be satisfied for members subject to combined axial compression and bending. To check these interaction equations the following parameters given in (a), (b) and (c) are needed:
(a) 
These are given in the tables as N b,y,Rd and N b,z,Rd. They are the compression resistances for buckling about the y-y and the z-z axis respectively. The adjacent N Ed / N pl,Rd limit, ensures that the section is not Class 4 and have been calculated as in Section 6.1.
(b) 
This term is given in the tables as M b,Rd. Values are given for two N Ed / N pl,Rd limits. The higher limit ensures the section is Class 3 and the lower limit (in bold) ensures the section is Class 2, M b,Rd is calculated accordingly, as described in Section 8.1 In both cases it is conservatively assumed that C1 = 1.0 .
(c) 
M z,Rk may be based on the elastic or plastic modulus, depending on the section classification, as shown in Table 6.7 of
EN 1993-1-1. Values of f y W el,z are given. Values of f y W pl,z are given as Mc,z,Rd in the tables for cross-section resistance check. Values are quoted with γ M1 = 1.0 , as given in the National Annex.
In addition values of f y W el,y and N pl,Rd are given in the tables for completeness.
According to the UK National Annex, either Annex A or Annex B of EN 1993-1-1 should be used to calculate the interaction factors k for I and H sections. Annex B of EN 1993-1-1 should be used to calculate the interaction factors k for parallel flange channels.
The symbol * denotes that the cross-section is Class 4 under axial compression only. Under combined axial compression and bending, the Class of the cross-section depends on the axial force, expressed in terms of n ( = N Ed / N pl,Rd ). Values of n are given, up to which the cross-section would be Class 2 or Class 3.
The limits in normal and bold type are the maximum values up to which the section is either Class 3 or Class 2, respectively. The tabulated resistances are only valid up to the given N Ed / N pl,Rd limit.