Perry–Robertson formula explained

The Perry–Robertson formula is a mathematical formula which is able to produce a good approximation of buckling loads in long slender columns or struts, and is the basis for the buckling formulation adopted in EN 1993. The formula in question can be expressed in the following form:

$$\backslash sigma\_m\; =\; \backslash frac\; \backslash left(f\_y\; +\backslash sigma\_e\backslash left(1+\backslash theta\backslash right)\; -\; \backslash sqrt\; \backslash right)$$

with

\theta = (w _{o,1} c)/(i ^{2})

where:

\sigma _{m} is the average longitudinal stress in the beam's cross sectionf _{y} is the material's elastic limit\sigma _{e} is the average tension measured in the cross section which correspond to the beam's Euler loadw _{o,1} the amplitude of the initial geometrical imperfectionc distance from the cross section's centroid to the section's most stressed fiberi the section's radius of gyration

Robertson then proposed that

\theta = 0 . 003λ , where λ represents the beam's slenderness.

References

1. Web site: Perry Robertson formula (BS 449-2). 2010-11-22. https://web.archive.org/web/20110108101926/http://roymech.co.uk/Useful_Tables/Mechanics/Struts.html#Perry. 2011-01-08. dead.
2. Book: The manual of bridge engineering. 9780727727749. 2010-11-22. Ryall. M. J.. Hewson. Nigel. Parke. G. A. R.. Harding. J. E.. 2000.