# Buckling of Columns

By Vishwajeet Sinha|Updated : December 30th, 2016

Columns and Struts:

• A structural member subjected to an axial compressive fore is called strut. As per definition strut may be horizontal, inclined or even vertical.
• Vertical strut is called a column.

Euler’s Column Theory: This theory has the following assumptions.

• Perfectly straight column and axial load apply.
• Uniform cross-section of the column throughout its length.
• Perfectly elastic, homogeneous and isotropic material.
• Length of column is large as compared to its cross-sectional dimensions.
• The shortening of column due to direct compression is neglected.
• The failure of column occurs due to buckling alone.

Limitation of Euler’s Formula

• There is always crookedness in the column and the load may not be exactly axial.
• This formula does not take into account the axial stress and the buckling load given by this formula may be much more than the actual buckling load.

Euler’s Buckling (or crippling load): The maximum load at which the column tends to have lateral displacement or tends to buckle is known as buckling or crippling load. Load columns can be analysed with the Euler’s column formulas can be given as

where, E = Modulus of elasticity, l = Effective Length of column, and I = Moment of inertia of column section.

1. For both end hinged:

n=1

1. For one end fixed and other free:

1. For both end fixed:

n=2,

1. For one end fixed and other hinged:

Effective Length for different End conditions:

Modes of failure of Columns

Slenderness Ratio ( λ) Slenderness ratio of a compression member is defined as the ratio of its effective length to least radius of gyration.

Buckling Stress:

• Rankine’s Formula for Columns: It is an empirical formula, takes into both crushing PCS and Euler critical load (PR).

PR = Crippling load by Rankine’s formula

Pcs = σcs A = Ultimate crushing load for column

Crippling load obtained by Euler’s formula

Where, A = Cross-section are of column, K = Least radius of gyration, and A = Rankine’s constant.

• To prevent any kid of stress reversal, force applied should be within an area near the cross section called as CORE or KERN.
• Shape of kern for rectangular and l-section is Rhombus and for square section shape is square for circular section shape is circular.

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Member since Jun 2016

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Jeevith stress reversal means stresses of opposite nature that may reduce the stability,like the uplift forces in gravity dams

Crushing means to fail in compression,associated with short column.

Sonu TiwariDec 31, 2016

Thanks

Akhil SantiJan 1, 2017

Nice

Harish SharmaJan 3, 2017

thanks

Mohit MathurJan 5, 2017

both ends fixed 4π^2EI/L^2

Manisha GhoshJan 13, 2017

Very effective...👌

Vi Sh NuJan 29, 2017

Nice app

JeevithSep 3, 2017

Aar Kay AttriApr 2, 2018

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