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The '''Perry-Robertson formula''' is a mathematical formula which is able to produce a good approximation of [[buckling]] loads in long slender [[Beam (structure)|beams]], and is the basis for the buckling formulation adopted in [[EN 1993]].  
The formula in question can be expressed in the following form:

<math>\sigma_m = \frac{1}{2} \left(f_y +\sigma_e\left(1+\theta\right) - \sqrt{ \left(f_y + \sigma_e\left(1+\theta\right)\right)^2 - 4f_y\sigma_e} \right) </math>

with 
<math>\theta = \frac{w_{o,1}c}{i^2} </math>

where:
* <math>\sigma_m</math> is the average longitudinal stress in the beam's cross section
* <math> f_y</math> is the material's elastic limit
* <math> \sigma_e</math> is the average tension measured in the cross section which correspond to the beam's Euler load
* <math> w_{o,1}</math> the amplitude of the initial geometrical imperfection
* <math> c</math> distance from the cross section's [[centroid]] to the section's most stressed fiber
* <math> i</math> the section's [[radius of gyration]]

Robertson then proposed that <math>\theta = 0.003\lambda</math>, where <math>\lambda</math> represents the beam's slenderness.

==See also==
* [[Buckling]]
* [[EN 1993]]

==References==
<references/>
#{{cite web |title=Perry Robertson formula (BS 449-2 )|url=http://www.roymech.co.uk/Useful_Tables/Mechanics/Struts.html#Perry|accessdate=2010-11-22}}
#{{Cite book |title=The manual of bridge engineering|url=http://books.google.com/books?id=8PGk81gtCywC&pg=PA154&lpg=PA154&dq=perry+robertson+buckling+formula&source=bl&ots=5J_yV5LPa6&sig=7WaScf45LQYSOm-ZMCHmIqDSmt4&hl=en&ei=gbnpTNqeKNGahQfaqLwP&sa=X&oi=book_result&ct=result&resnum=9&ved=0CEkQ6AEwCA|accessdate=2010-11-22}}

[[Category:Elasticity (physics)]]


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