Rankine Gordon Equation

Strength of Materials

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 semi-empirical formula, and takes into account the crushing strength of the material, its Young's modulus and its slenderness ratio.

A comparison of the Rankine-Gordon and Euler equation, for geometrically perfect struts, is given below:

Rankine Gordon Equation

Comparison of Euler and Rankine-Gordon equation

Columns

Rankine Gordon Equation

least radius of gyration

Where:
σ = failure stress
σc = elastic limit in compression
a = constant
A = cross-sectional area
k = least radius of gyration
L = Length
P = Buckling Load
I = Area moment of Inertia

Material

σc
Mpa

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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