8. Bending tables
8.1. Bending: UB sections, UC sections, joists and parallel flange channels
6.2.5 (2)
(a) Design resistance of cross-section
The design resistances for bending about the principal axes of the cross-section are given by:
(i) For Class 1, 2 cross-sections:
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(ii) For Class 3 cross-sections with a Class 1 or 2 flange:
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(iii) For other Class 3 sections
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(iv) For Class 4 cross-sections
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Note:
- Some I and H sections in S275 and S355 are Class 4 under bending alone. Although the effective section properties are not tabulated, effective properties have been used to derive the bending resistance tables.
- Where the design shear force is high ( > 50% of the shear resistance), a reduced value of resistance for bending Mv,y,Rd and Mv,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 (see Section 9.1).
(b) Design lateral torsional buckling resistance moment
The lateral torsional buckling resistance moment Mb,Rd is given in the tables for a range of values of the following parameters:
- The length between lateral restraints, L, given at the head of the tables
- The value of factor C1
The lateral torsional buckling resistance moment, Mb,Rd, is given by:
where:
| W y | = Wpl,y | for Class 1, 2 cross-sections |
| W y | = Wel,y | for Class 3 cross-sections, with Class 3 flanges |
| W y | = Wpl,eff,y | for Class 3 cross-sections with Class 1 or 2 flanges |
| W y | = Weff,y | for Class 4 cross-sections |
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is the reduction factor for lateral-torsional buckling. It depends on the non-dimensional slenderness  and the imperfection factor corresponding to the appropriate buckling curve. |
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| M cr | is the elastic critical moment for lateral-torsional buckling based on gross sectional properties and takes into account the following:
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| C 1 | is a factor that takes into account the shape of the bending moment diagram. Values of C1 given in the tables include 1.0; 1.13; 1.35; 1.5; 1.77; 2.0 and 2.5. Access Steel document SN003 Elastic critical moment for lateral torsional buckling [24] gives background information related to this factor. To take C1 = 1.0 is conservative. | |
The C1 values of 1.13, 1.35 and 1.77 correspond to common design situations, as shown below.
| Loading | Bending moment diagram | C 1 factor |
|---|---|---|
| UDL, pin-ended beam |  |
1.13 |
| Central point load, pin-ended beam |  |
1.35 |
| Triangular bending moment diagram, pin at one end |  |
1.77 |
For linear bending moment diagrams, C1 may be determined from the following table, based on psi;, the ratio of the end moments.
| End moment loading | ψ | C 1 |
|---|---|---|
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+ 1.00 | 1.00 |
| + 0.75 | 1.17 | |
| + 0.50 | 1.36 | |
| + 0.25 | 1.56 | |
| 0.00 | 1.77 | |
| - 0.25 | 2.00 | |
| - 0.50 | 2.24 | |
| - 0.75 | 2.49 | |
| - 1.00 | 2.76 |
For other shapes of bending moment diagram, the factor C1 may be determined from the ratio:
M cr may be determined by using the software LTBeam, freely available from www.cticm.com
The reduction factor is calculated for the 'rolled sections' case, using buckling curves "b" or "c" as appropriate and the values of 
LT,0 and β given by the National Annex. The UK National Annex gives the following values:
| LT,0 |
= 0.4 |
| β | = 0.75 |
The reduction factor is modified to take account of the moment distribution between the lateral restraints of members using the modification factor β :
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