10.1 Axial load and bending: UB sections, UC sections, joists, and parallel flange channels
Generally, members subject to axial compression and bending should be checked for cross-section capacity (Clause 4.8.3.2) and member buckling (Clause 4.8.3.3).
Columns in simple construction should be checked in accordance with Clause 4.7.7.
All the relevant parameters required to evaluate the interaction equations given in the above clauses have been presented in tabular form, as follows:
4.8.3.2
(a) Cross-section capacity check
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.
Values are given in the tables for:
(i) Pz = Ag py (py is the design strength)
(ii) F/Pz limits
The compact and semi-compact limits are the maximum values of F/Pz up to which the section is either compact or semi‑compact, respectively. The compact limit is given in bold type.
(iii) Mcx and Mcy
These are the moment capacities (with low shear load) about the major and minor
axes respectively. They have been calculated as in Section 8.1 using Sx, Sxeff, and Sy, Syeff, as appropriate.
Note: Sxeff and Syeff can change with F/PZ values.
When F/Pz exceeds the semi-compact limit, the section is slender, due to the web and the moment capacities tabulated are based on a reduced design strength and the gross section properties, instead of pyZeff
The symbol $ indicates that the section would be overloaded due to axial load alone i.e. the section is slender and F > Aeff py .
(iv) Mrx and Mry
4.8.2.3
Annex 1.2.1
4.8.3.3
These have been determined using the reduced plastic moduli given in the section property tables for the values of F/Pz at the head of the table. Values of Mrx and Mry are not valid for semi-compact and slender sections hence, no values are shown when F/Pz exceeds the limit for a compact section (shown as “ – ” in the tables).
| Mrx = py Srx ≤ Mcx |
| Mry = py Sry ≤ Mcy |
(b) Member buckling check
The symbol * denotes that the section is slender when fully stressed under axial compression only (due to the web becoming slender). None of the sections listed are slender due to the flanges being slender. Under combined axial compression and bending, the section would be compact or semi‑compact up to the given F/Pz limits.
Values are given in the table for:
(i) Pz = Ag py
(ii) py Zx
4.8.3.3.1
This is used in the simplified method for member buckling.
(iii) py Zy
4.7.7
4.8.3.3.1
This is used for columns in simple construction and in the simplified method for member buckling.
(iv) F/Pz limit
The limits in normal and bold type are the maximum values up to which the section is either semi‑compact or compact, respectively. The tabulated resistances are only valid up to the given F/Pz limit.
(v) Pcx and Pcy
These are the compression resistances for buckling about the major and minor axes
respectively. The adjacent F/Pz limit, ensures that the section is not slender and have been calculated as in Section 6.1.
(vi) Mb is the buckling resistance moment, used in both the simplified and the more exact method. Values of Mb are given for two F/Pz limits the higher limit ensures the section is semi-compact and the lower limit (in bold) ensures the section is compact, Mb is calculated accordingly as in Section 8.1.
4.7.7
(vii) Mbs is the buckling resistance moment for use with columns in simple construction and has been calculated as for Mb except that pb has been obtained using a value of λLT = 0.5λ, where λ = L/ry. As for Mb there are two sets of values that apply to the two adjacent F/Pz limits.
10.2 Axial load and bending: hollow sections
Generally, members subject to axial compression and bending should be checked for cross‑section capacity and member buckling.
Columns in simple construction should be checked in accordance with Clause 4.7.7.
All the relevant parameters required to evaluate the interaction equations given in the above clauses have been presented in tabular form, as follows:
4.8.3.2
(a) Cross-section capacity check
The symbol * denotes that the section is slender when fully stressed under axial compression only.
Values are given in the tables for:
(i) Pz = Agpy (py is the design strength)
(ii) F/Pz limits
The compact and semi-compact limits are the maximum values of F/Pz up to which the section is either compact or semi‑compact, respectively. The compact limit is given in bold type. There are no F/Pz values for circular hollow sections.
(iii) Mc , Mcx and Mcy
Mc for circular and square hollow sections, Mcx and Mcy for rectangular hollow sections. These are the moment capacities (with low shear load) about the major and minor axes respectively. They have been calculated as in Section 8.2 using Sx, Sxeff, Zx and Zxeff, Sy, Syeff, Zy and Zyeff, as appropriate.
When F/Pz exceeds the semi-compact limit, and therefore the section is slender, if it is the web of the section that is slender the moment capacities tabulated are based on a reduced design strength and the gross section properties.
The symbol $ indicates that the section would be overloaded due to axial load alone i.e. the section is slender and F > Aeff py .
(iv) Mr , Mrx and Mry
4.8.2.3
Annex I.2.1
Mr for circular and square hollow sections, Mrx and Mry for rectangular hollow sections. These have been determined using the reduced plastic moduli given in the section property tables for the values of F/Pz at the head of the table. The Mr, Mrx and Mry values have been limited to the corresponding values of Mc, Mcx and Mcy. Values of Mrx and Mry are not valid for semi-compact and slender sections therefore, no values are shown when F/Pz exceeds the limit for a compact section, shown as “ – ” in the tables.
| Mrx = py Srx ≤ Mcx |
| Mry = py Sry ≤ Mcy |
4.8.3.3
(b) Member buckling check
The simplified method (Clause 4.8.3.3.1) assumes that out‑of‑plane, lateral torsional buckling controls. However, in certain instances, it is likely that in‑plane buckling, e.g. chord of truss with purlins not at node point, will be more critical. Thus, it is recommended that the more exact method should be used.
The symbol * denotes that the section is slender when fully stressed under axial compression only. Under combined axial compression and bending, the section would be compact or semi‑compact up to the given F/Pz limits.
Values are given in the tables for:
(i) py Z
4.7.7
4.8.3.3.1
For circular and square hollow sections. This is used for columns in simple construction and in the simplified method for member buckling.
(ii) py Zx
4.8.3.3.1
For rectangular hollow sections. This is used in the simplified method for member buckling.
(iii) py Zy
4.7.7
4.8.3.3.1
For rectangular hollow sections. This is used for columns in simple construction and in the simplified method for member buckling.
(iv) F/Pz limit
For square and rectangular hollow sections. The compact and semi-compact limits are the maximum values of F/Pz up to which the section is either compact or semi‑compact, respectively. The compact limit is given in bold type.
(v) Pc , Pcx and Pcy
Pc for circular and square hollow sections, Pcx and Pcy for rectangular hollow sections. These are the compression resistances for buckling about the relevant axes. They have been calculated as in Section 6.1. The adjacent F/Pz limit ensures that the section is not slender except where the F/Pz limit is zero. For this case the section is slender and allowance has been made in calculating the compression resistance, the values are displayed in italic type.
(vi) Mb
4.3.6.1
Mb is the buckling resistance moment, used in both the simplified and the more exact method. Values of Mb are given for two F/Pz limits. The higher limit ensures the section is semi-compact and the lower limit (in bold) ensures the section is compact, Mb is calculated accordingly. For circular and square hollow sections, Mb equals Mc. For rectangular hollow sections, Mb equals Mc provided that LE is within the limiting length Lc given in the Bending tables; see Section 8.2.2.
(vii) Mbs
4.7.7
Mbs is the buckling resistance moment for use with columns in simple construction. For hollow sections, Mbs equals Mb therefore values are not tabulated separately.
