This cheat sheet is for calculating the flexural buckling or "strut buckling" capacity of a column in compression. It could also be used to calculate the capacity of a compression flange between effective restraints.
The rules in the cheat sheet are taken from the Eurocode 3, which is based on Euler buckling theory but also includes an allowance for geometric imperfections (via figure 6.4).
The relationship between non-dimensional slenderness and the critical buckling load from Euler theory Ncr is shown below:
Previous codes such as BS5950 used a slenderness "lambda" defined as Le/i and used this to determine a buckling stress based on the material strength. Eurocode 3 uses a "non-dimensional slenderness", which takes into account the material strength via lambda1, which is then used to find a buckling reduction factor using a single graph for all material strengths.
The effective length of the member (Lcr or Le) is determined by the restraint provided at each end, e.g. for a pin ended column Lcr = L, but for a cantilever Lcr = 2L.
You can find compatible effective length parameters published in numerous sources including BS 5950-1 Table 22; the diagram in the cheat sheet is from Design of Structural Elements (ISBN: 9780415467209), which is a book that I would highly recommend.
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