6.1Compression members: UB and UC sections
6.2.4
6.2.4 (2)
(a) Design resistance of the cross section N_{c,Rd}
The design resistance is given by:
(i) For Class 1, 2 or 3 cross sections:
(ii) For Class 4 cross sections:
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 Annex) 
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 tabulated in the tables of dimensions and gross section properties and the tables of effective section properties within this website. The values are not shown in the tables.
None of the universal columns are Class 4 under axial compression alone according to BS EN 199311, but some universal beams are Class 4 and these sections are marked thus *.
Table 5.2
The sections concerned are UB where the width to thickness ratio for the web in compression is:
c / t = d / t_{w } > 42ε
where:
d 
is the depth of straight portion of the web (i.e. the depth between fillets) 
t_{w} 
is the thickness of the web 
ε 
= (235/f_{y})^{0.5} 
f_{y} 
is the yield strength. 
6.3.1.1
(b) Design buckling resistance
Design buckling resistances for two modes of buckling are given in the tables:
 Flexural buckling resistance, about each of the two principal axes: N_{b,y,Rd} and N_{b,z,Rd}
 Torsional buckling resistance, N_{b,T,Rd}
No resistances are given for torsionalflexural buckling because this mode of buckling does not occur in doubly symmetrical cross sections.
(i) Design flexural buckling resistance, N_{b,y,Rd} and N_{b,z,Rd}
The design flexural buckling resistances N_{b,y,Rd} and N_{b,z,Rd} depend on the nondimensional slenderness (), which in turn depends on:
 The buckling lengths (L_{cr}) given at the head of the table
 The properties of the cross section.
6.3.1.3
The nondimensional slenderness has been calculated as follows:
For Class 1, 2 or 3 cross sections:

for yy axis buckling 

for zz axis buckling 
For Class 4 cross sections:

for yy axis buckling 

for zz axis buckling 
where:
L_{cr,y}, L_{cr,z} 
are the buckling lengths for the yy and zz axes respectively 
i_{y}, i_{z} 
are the radii of gyration about yy and zz axes respectively. 
The tabulated buckling resistance is only based on Class 4 cross section properties if this value of 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.
An example is given below:
533 x 210 x 101 UB S275
For this section, c/t = d/t_{w} = 44.1 > 42ε = 39.6
Hence, the cross section is Class 4 under compression alone.
The value of axial force at which the section becomes Class 4 is N_{Ed} = 2890 kN (see axial force and bending table, where n = 0.845 and N_{pl,Rd} = 3420 kN).
For L_{cr,y} = 4 m, N_{b,y,Rd }= 3270 kN
The table shows 3270 kN in italic type because the value is greater than the value at which the cross section becomes Class 4
For L_{cr,y} = 14 m, N_{b,y,Rd } = 2860 kN
The table shows 2860 kN in normal type because the value is less than the value at which cross–section becomes Class 4 (2890 kN).
(ii) Design torsional buckling resistance, N_{b,T,Rd}
6.3.1.4
The design torsional buckling resistance N_{b,T,Rd} depends on the nondimensional 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 nondimensional slenderness has been calculated as follows:

for Class 1, 2 or 3 cross sections 

for Class 4 cross sections 
where:
N_{cr,T} 
is the elastic torsional buckling force, given by 
where:
i_{0}

= 
y_{0} 
is the distance from the shear centre to the centroid of the gross cross section along the yy axis (zero for doubly symmetric sections). 
6.2Compression members: hollow sections
6.2.4
6.2.4 (2)
(a) Design resistance of the cross section N_{c,Rd}
The design resistance is given by:
(i) For Class 1, 2 or 3 cross sections:
(ii) For Class 4 cross sections:
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 Annex). 
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 tabulated in the tables of dimensions and gross section properties and the tables of effective section properties within this website of this website. The values are not shown in the tables.
Sections that are Class 4 under axial compression are marked thus *. The sections concerned are:
Table 5.2
 Square hollow sections, where c / t > 42ε and c = h – 3t
 Rectangular hollow sections, where c_{w} / t > 42ε and c_{w} = h – 3t
 Circular hollow sections, where d/t > 90ε^{2}
where:
h 
is the overall depth of the cross section 
t 
is the thickness of the wall 
ε 
= (235/f_{y})^{0.5} 
f_{y} 
is the yield strength. 
 Elliptical hollow sections, where > 90ε^{2} (See Reference 15)
where D_{e} is defined in Section 4.2.
6.3.1.1
(b) Design buckling resistance
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 nondimensional slenderness (), which in turn depends on:
 The buckling lengths (L_{cr}) given at the head of the table
 The properties of the cross section.
6.3.1.3
The nondimensional slenderness has been calculated as follows:
For Class 1, 2 or 3 cross sections:

for yy axis buckling 

for zz axis buckling 
For Class 4 cross sections:

for yy axis buckling 

for zz axis buckling 
where:
L_{cr,y}, L_{cr,z} 
are the buckling lengths for the yy and zz axes respectively. 
i_{y}, i_{z} 
are the radii of gyration about the yy and zz 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, BS EN 199311 refers the user to BS EN 199316. 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 f_{y,reduced} =
D_{e} is defined in Section 4.2.
6.3Compression members: parallel flange channels
6.2.4
6.2.4 (2)
(a) Design resistance of the cross section N_{c,Rd}
The design resistance is given by:
where:
A 
is the gross area of the cross section 
f_{y} 
is the yield strength 
γ_{M0} 
is the partial factor for resistance of cross sections (γ_{M0} = 1.0 as given in the National Annex). 
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.
6.3.1
(b) Design buckling resistance
Design buckling resistance values are given for the following cases:
 Single channel subject to concentric axial force
 Single channel connected only through its web, by two or more bolts arranged symmetrically in a single row across the web.
1. Single channel subject to concentric axial force
Design buckling resistances for two modes of buckling are given in the tables:
 Flexural buckling resistance about the two principal axes: N_{b,y,Rd} and N_{b,z,Rd}
 Torsional or torsionalflexural buckling resistance, whichever is less, N_{b,T,Rd}
(i) Design flexural buckling resistance, N_{b,y,Rd} and N_{b,z,Rd}
The design flexural buckling resistances N_{b,y,Rd} and N_{b,z,Rd} depend on the nondimensional 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 nondimensional slenderness, which has been calculated as follows:
6.3.1.3

for yy axis buckling 

for zz axis buckling 
where:
L_{cr,y}, L_{cr,z} 
are the buckling lengths for the yy and zz axes respectively. 
6.3.1.4
(ii) Design torsional and torsionalflexural buckling resistance, N_{b,T,Rd}
The resistance tables give the lesser of the torsional and the torsionalflexural buckling resistances. These resistances depend on the nondimensional 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 nondimensional slenderness, which has been calculated as follows:
where:
N_{cr,T} 
is the elastic torsional buckling force, = 
i_{0} 
= 
y_{0} 
is the distance along the y axis from the shear centre to the centroid of the gross cross section. 
N_{cr,TF} 
is the elastic torsional‑flexural buckling force, = Aσ_{TF} 
σ_{TF} 
= 
σ_{Ey} 
= 
σ_{T} 
= N_{cr,T} / A 
b 
= 1 – (y_{0}/i_{0})^{2} 
L_{ey} 
is the unrestrained length considering buckling about the yy axis. 
2. Single channel connected only through its web, by two or more bolts arranged symmetrically in a single row across the web
Design buckling resistances for two modes of buckling are given in the tables:
6.3.1
 Flexural buckling resistance about each of the two principal axes: N_{b,y,Rd} and N_{b,z,Rd}
 Torsional or torsionalflexural buckling resistance, whichever is less, N_{b,T,Rd}
(i) Design flexural buckling resistance, N_{b,y,Rd} and N_{b,z,Rd}
The design flexural buckling resistances N_{b,y,Rd} and N_{b,z,Rd} depend on the nondimensional slenderness (), which in turn depends on:
 The system length (L) given at the head of the tables. L is the distance between intersections of the centroidal axes of the channel and the members to which it is connected.
 The properties of the cross section.
 The nondimensional slenderness, which has been calculated as follows:
Annex BB.1.2

for yy axis buckling 

where 

for zz axis buckling 
(Based on a similar rationale given in Annex BB.1.2 for angles)
where:
L_{cr,y}, L_{cr,z} 
are the lengths between intersections 
i_{y}, i_{z} 
are the radii of gyration about the yy and zz axes. 
ε 
= (235/f_{y})^{0.5}. 
6.3.1.4
(ii) Design torsional and torsionalflexural buckling resistance, N_{b,T,Rd}
The torsional and torsionalflexural buckling resistance has been calculated as given above for single channels subject to concentric force.
6.4Compression members: single angles
6.3.1.1
(a) Design buckling resistance
Design buckling resistances for 2 modes of buckling, noted as F and T, are given in the tables:
 F: Flexural buckling resistance (taking torsionalflexural buckling effects into account), N_{b,y,Rd} and N_{b,z,Rd}
 T: Torsional buckling resistance, N_{b,T,Rd}.
(i) Design flexural buckling resistance, N_{b,y,Rd}, N_{b,z,Rd}
The tables give the lesser of the design flexural buckling resistance and the torsional flexural buckling resistance.
The design flexural buckling resistances N_{b,y,Rd} and N_{b,z,Rd} depend on the nondimensional slenderness (), which in turn depends on:
 The system length (L) given at the head of the tables. L is the distance between intersections of the centroidal axes (or setting out line of the bolts) of the angle and the members to which it is connected.
 The properties of the cross section.
 The nondimensional slenderness, which has been calculated as follows:
For two or more bolts in standard clearance holes in line along the angle at each end or an equivalent welded connection, the slenderness has been taken as:
EN 199311 BB.1.2(2)
For Class 3 cross sections:
For Class 4 cross sections:
where:
L_{y}, L_{z} and L_{v} 
are the system lengths between intersections. 
These expressions take account of the torsional flexural buckling effects as well as the flexural buckling effects.
For the case of a single bolt at each end, BS EN 199311 refers the user to 6.2.9 to take account of the eccentricity. (Note: no values are given for this case).
6.3.1.3
(ii) Design torsional buckling resistance, N_{b,T,Rd}
The design torsional buckling resistance N_{b,T,Rd} depends on the nondimensional slenderness (), which in turn depends on:
 The system length (L) given at the head of the table
 The properties of the cross section
 The nondimensional slenderness, which has been calculated as follows:
6.3.1.4(2)

for Class 1, 2 or 3 cross sections 

for Class 4 cross sections 
where:
N_{cr,T} 
is the elastic torsional buckling force = 
G 
is the shear modulus 
E 
is the modulus of elasticity 
ν 
is Poisson’s ratio (= 0.3) 
I_{T} 
is the torsional constant 
I_{0 } 
= 
I_{u} 
is the second moment of area about the uu axis 
I_{v} 
is the second moment of area about the vv axis 
u_{0} 
is the distance from shear centre to the vv axis 
v_{0} 
is the distance from shear centre to the uu axis. 