Related Resources: material science

### 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: Comparison of Euler and Rankine-Gordon equation   Where:
σ = failure stress
σc = elastic limit in compression
a = constant
A = cross-sectional area
k = least radius of gyration
L = Length
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  