# 6 Compression tables

## 6.1Design resistance of cross-section *N*_{c,Rd}

6.2.4 (2)

The design resistance is given by:

(i) For Class 1, 2 or 3 cross-sections:

N_{c,Rd} = |

(ii) For Class 4 cross-sections:

N_{c,Rd} = |

where:

A |
is the gross area of the cross-section |

f_{y} |
is the yield strength |

A_{eff} |
is the effective area of the cross-section in compression |

γ_{M0} |
is the partial factor for resistance of cross-sections (γ_{M0} = 1.0 as given in the National Annexes). |

For Class 1, 2 and 3 cross-sections, the value of *N*_{c,Rd} is the same as the plastic resistance, *N*_{pl,Rd} given in the tables for axial force and bending, and is therefore not given in the compression tables.

For Class 4 sections, the value of *N*_{c,Rd} can be calculated using the effective areas provided in the software. The values are not shown in the tables.

Sections that are Class 4 under axial compression are marked thus *. The sections concerned are:

- Square hollow sections, where
*c*/*t*> 42*ε*and*c*=*h*– 3*t* - Rectangular hollow sections, where
*c*_{w}/*t*> 42*ε*and*c*_{w}=*h*– 3*t* - Circular hollow sections, where
*d*/*t*> 90*ε*^{2}where:*h*is the overall depth of the cross section *t*is the thickness of the wall *ε*= (235 / *f*_{y})^{0.5} - Elliptical hollow sections, where (See Reference 5)

where:

*D*_{e}is defined in Section 4.2.

## 6.2 Design buckling resistance *N*_{b,Rd}

6.3.1.1

Design buckling resistances for flexural buckling are given in the tables.

The design flexural buckling resistances *N*_{b,y,Rd} and *N*_{b,z,Rd} depend on the non-dimensional slenderness (), which in turn depends on:

- The buckling lengths (
*L*_{cr}) given at the head of the table - The properties of the cross-section.

The non-dimensional slenderness has been calculated as follows:

For Class 1, 2 or 3 cross-sections:

_{y} = |
for y-y axis buckling |

_{z} = |
for z-z axis buckling |

For Class 4 cross-sections:

_{y} = |
for y-y axis buckling |

_{z} = |
for z-z axis buckling |

where:

L_{cr,y}, L_{cr,z} |
are the buckling lengths for the y-y and z-z axes respectively |

i_{y}, i_{z} |
are the radii of gyration about the y-y and z-z axes respectively |

The tabulated buckling resistance is only based on Class 4 cross-section properties when the value of the force is sufficient to make the cross section Class 4 under combined axial force and bending. The value of *n* (= *N*_{Ed} / *N*_{pl,Rd}) at which the cross-section becomes Class 4 is shown in the tables for axial force and bending. Otherwise, the buckling resistance is based on Class 3 cross-section properties. Tabulated values based on the Class 4 cross section properties are printed in italic type.

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

For Class 4 elliptical hollow sections, the design buckling resistance has been taken as the greater of:

- The design buckling resistance based on an effective area (see Section 4.2) and
- The design buckling resistance based on the gross area, but reducing the design strength such that the section remains Class 3. The reduced design strength
*f*_{y,reduced}is given by:*D*_{e}is defined in Section 4.2.