vilas Nikam - Mechanics oof Structure-Column

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Text of vilas Nikam - Mechanics oof Structure-Column


PRESENTED BY Prof V N NIKAM(Lecturer) Sandip Institute of PolytechnicNashik


Important definitionColumn: A vertical member of a structure use to support axial compressive load called as column.

Strut:inclined structural member subjected to axial compressive load called as strut.

Buckling: The bending action of column is called as buckling.

Radius of Gyration (k):k = (I/A)k = radius of gyrationI = Moment of InertiaA = Cross sectional area of column section

Effective length of column: The length of column which deflects or bends as if it is hinged at its ends is called as effective length.

Effective length for various end condition

Classification of column

Short Column

Medium Column

Long Column

Short Column

Column fails in crushing only.

In design of short column, compressive stress are considered and bending stress are neglected.

Slenderness ratio () < 30

Medium size column

A column fails in crushing and bending both direct stresses as well as bending stresses are developed.

For medium column, 30< < 100

Long column

Long column fails only in bending or buckling.

Slenderness ratio for long column is very large.

In design of long column bending stress are considered and direct stresses are neglected.

For long column > 100

Failure of column

a) Failure by crushingShort column fails in compression only due to crushing.Let A = cross sectional area of column.

PC = crushing load c = Crushing stress PS = Safe load on column Crushing load PC = C . A


b) Failure by buckling or bendingBefore crushing, at a certain load column start bending called as buckling load or critical load or crippling load.It may be calculated by a) Euler's formulab) Rankine's Formula

Euler's Theory of column

Euler's theory is applicable for only long column.

He had considered bending stress only and compressive stress are completely neglected.Assumption in Euler's column theory.1. The material of column is perfectly homogenous and isotropic.2. The column is initially straight and of uniform lateral dimensions.3. The load on column is exactly axial.4. The column is long and fails due to bending or buckling only.5. The self weight of column is neglected.6. The column is stressed upto limit proportionality.

Euler's Formula

Euler's buckling load or crippling load is given by

PE = Euler's buckling load.E = Modulus of elasticity of column materialI = minimum moment of inertia of column sectionLe = Effective length of column.

Also Crushing stress

Euler's formula is applicable when > 80

Factor of safety

Factor of safety for mild steel and cast iron is taken as 3 and 5 respectively.

Safe Load

Strength of column

Load carrying capacity of column is called as strength of column. It is given by

Rankine's formula

Rankine had derived formula for long column as follows.


PR = Rankine's Crippling loadLe = Effective length of columnk = Minimum radius of gyrationc or fc = Ultimate crushing stressA = Area of cross sectiona or = Rankine's constant

Value of crushing stress for and Rankine's constant for different material

SR NOMaterial

c = Crushing stress in N/mm2

A = Rankine's constant


2Wrought Iron2501/9000

3Mild steel3251/7500

4Cast Iron5501/1600

Thank you !!!!!!!!!!!!!!!!!!!