What is Euler's Column Theory?

Welcome back MechanicalEI, did you know that Euler’s Column theory gives a rough estimate of buckling load for a strut? This makes us wonder, What is Euler's Column Theory? Before we jump in check out the previous part of this series to learn about What are Columns and Struts?
Now, First, let's look at assumptions for the Euler's Column theory. The column is perfectly straight and only axial load is applied. It is of uniform cross-section throughout it's length. The material is perfectly elastic, homogeneous and isotropic. The length of the column is large when compared with cross-sectional dimension. The change in length due to compression is neglected and lastly, the failure is due to buckling alone. Given these assumptions, Euler's Column formula for calculating allowable load F is given by n pi squared E I upon L squared. Where n, E, and I are the factor accounting for end conditions, Modulus of elasticity and moment of inertia respectively. Euler's Column theory however suffers from two basic limitations. One being the presence of crookedness in the column causing the load to not be exactly axial. Another being that this formula does not take into account the axial stress and that the buckling load given by this formula may be much more than the actual buckling load. 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 which is the ratio of Length L of the strut to its least radius of gyration, K. According to the Formula, The Buckling load P is given as the product of elastic limit in compression and cross-sectional area A upon one plus the product of slenderness ratio and empirical constant a, which is dependent upon the type of ends of strut and the material of the strut. Hence, we first saw what Euler's Column theory is and then went on to see what Rankine-Gordon formula is?
In the next episode of MechanicalEI find out what Laplace Transforms are?
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Doh De Oh by Kevin MacLeod is licensed under a Creative Commons Attribution licence (creativecommon...)
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