A POWERPOINT PRESEMTATION ON COLUMN
PRESENTED BY Prof V N NIKAM(Lecturer)[email protected] Sandip
Institute of PolytechnicNashik
6. COLUMNS
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.
Where
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
1Timber501/750
2Wrought Iron2501/9000
3Mild steel3251/7500
4Cast Iron5501/1600
Thank you !!!!!!!!!!!!!!!!!!!
