Columns

What is a column?
 A structural member subjected to axial
compressive force is called a column.
 Normally, columns carry heavy
compressive loads.
 Columns are used in concrete and steel
buildings.

Types Of Columns
 Long
 Short (Strut)
 Intermediate

Classification
 LONG COLUMN :
 When length of column is more as
compared to its c/s dimension, it is
called long column.
Long Column
Le/rmin > 50
Where,
Le = effective length of column
rmin = Minimum radius of gyration

Real world example:
 Here in picture we can see long columns
on front of building in “The White house”
Washington D.C(USA).

SHORT COLUMN :
 When length of column is less as
compared to its c/s dimension, it is called
Short column.
Short Column
Le/rmin <50
Or,
Le/d < 15
 Crushing Load : The load at which short
column fails by crushing is called crushing
load.

INTERMEDIATE COLUMN:
 Column is intermediate when
4d < L < 30d
and
30 < Le /r min < 100 or Critical
slenderness ratio.

Before we move onward….
 Crippling Load (Pcr)
 Radius of gyration (r)
 Moment of inertia (I)
 Area (A)
 Effective Length (Le)
 Slenderness ratio (λ)
 Stronger Axis
 Weaker Axis

Types of supports
 Roller type support (1)
 Pin type support (2)
 Fixed support (3)

Effective Length (L e)
 The distance between points of two zero
moments.
 Depends upon the type of support
conditions.

COLUMN END CONDITION
AND EFFECTIVE LENTH :
1.Both ends hinged.
2.Both ends fixed.
3.One end fixed and other hinged.
4.One end fixed and other free.

(Le) for different support
conditions.

Slenderness ratio (λ)
 Slenderness ratio is the ratio of the
length of a column and the least radius
of gyration of its cross section. Often
denoted by lambda. It is used
extensively for finding out the design
load as well as in classifying various
columns in short/intermediate/long.
 λ = le/rmin

Radius of Gyration(r) , r = √(I/A) or I = Ar²
K=radius of gyration
I = Moment of Inertia (mm4)
A = Area of Section (mm2)
Slenderness ratio,
Slenderness Ratio = effective length of
column/Minimum radius of gyration
λ = le/rmin

CRIPPLING LOAD OR
BUCKLING
LOAD The load at which, long column starts
buckling(bending) is called buckling load or
crippling load.
 Buckling of column depends upon the
following factors.
1. Amount of load.
2. Length of column
3. End condition of column
4. C/s dimensions of column
5. Material of column.

Euler’s Formula
Euler’s Crippling Load,
PE = ∏²EI /le²
Where, E is Modulus of Elasticity
(Mpa)
I is MOI or 2nd Moment of area
(mm4)
Le is Effective length (mm)
Also known as Critical Buckling Load

Columns

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