Perry Robertson formula

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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 beams, and is the basis for the buckling formulation adopted in EN 1993. The formula in question can be expressed in the following form:

\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)

with \theta = \frac{w_{o,1}c}{i^2}


  • \sigma_m is the average longitudinal stress in the beam's cross section
  •  f_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 load
  •  w_{o,1} the amplitude of the initial geometrical imperfection
  •  c distance from the cross section's centroid to the section's most stressed fiber
  •  i the section's radius of gyration

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

See also[edit]


  1. "Perry Robertson formula (BS 449-2 )". Retrieved 2010-11-22. 
  2. The manual of bridge engineering. Retrieved 2010-11-22.