Rankine Gordon Equation
Rankine Gordon Equation
Predictions of buckling loads by the Euler formula is only reasonable for very long and slender struts that have very small geometrical imperfections. In practice, however, most column struts suffer plastic knockdown and the experimentally obtained buckling loads are much less than the Euler predictions. For struts in this category, a suitable formula is the Rankine Gordon equation which is a semiempirical formula, and takes into account the crushing strength of the material, its Young's modulus and its slenderness ratio.
A comparison of the RankineGordon and Euler equation, for geometrically perfect struts, is given below:
Comparison of Euler and RankineGordon equation
Where:
σ = failure stress
σ_{c} = elastic limit in compression
a = constant
A = crosssectional area
k = least radius of gyration
L = Length
P = Buckling Load
I = Area moment of Inertia
Material

σ_{c} 
a


Pinned Ends

Fixed Ends


Mild Steel 
320

1/7500

1/30000

Wrough Steel

250

1/9000

1/36000

Cast Iron

550

1/1600

1/6400

Wood

35

1/3000

1/12000

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