1. Introduction¶
Scope¶
This book explains how to check a steel member, a beam or a column, for the most common failure modes:
- the strength of the cross-section,
- buckling of a member in compression,
- lateral torsional buckling of a beam,
- the combined effect of bending and compression.
Notation¶
| Symbol | Meaning | Unit |
|---|---|---|
| \(A\) | cross-sectional area | cm² |
| \(f_y\) | yield strength | N/mm² |
| \(E\) | modulus of elasticity, 210 000 | N/mm² |
| \(i\) | radius of gyration | mm |
| \(L_{cr}\) | buckling length | m |
| \(N_{Ed}\) | design axial force (compression positive) | kN |
| \(N_{b,Rd}\) | design buckling resistance | kN |
| \(\gamma_{M1}\) | partial factor for stability | - |
Units¶
Forces are in kN, moments in kNm, lengths in mm or m (stated in each equation) and stresses in N/mm². The examples show the unit of every result.
Sign convention
Compression is positive. A negative axial force is tension.
How the examples are calculated¶
All numbers in the examples were calculated with a short Python program, shown at the end of each chapter. You can copy the code and change the inputs.