The document is a PowerPoint presentation about columns. It defines columns as vertical structural members that support axial compressive loads and struts as inclined members under compression. It discusses buckling as the bending action of columns. It classifies columns as short, medium or long based on their slenderness ratio and describes their failure modes. It presents Euler's formula and Rankine's formula for calculating the buckling/critical load of long columns based on the column's effective length, moment of inertia and modulus of elasticity. It provides crushing stress values and Rankine's constants for different materials.

1. A
POWERPOINT PRESEMTATION
ON
COLUMN
PRESENTED
BY
Prof V N NIKAM
(Lecturer)
vilas5151@gmail.com
Sandip Institute of Polytechnic
Nashik

2. 6. COLUMNS
Important definition
➲ Column: A vertical member of a structure use to sup-
port 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 gyration
I = Moment of Inertia
A = Cross sectional area of column section
Important definition
➲ Column: A vertical member of a structure use to sup-
port 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 gyration
I = Moment of Inertia
A = Cross sectional area of column section

3. ➲ 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.

4. Effective length for various end condition

5. Classification of column
➲ Short Column
➲ Medium Column
➲ Long Column

6. Short Column
➲ Column fails in crushing only.
➲ In design of short column, compressive stress are con-
sidered and bending stress are neglected.
➲ Slenderness ratio (λ) < 30

7. Medium size column
➲ A column fails in crushing and bending both direct stresses
as well as bending stresses are developed.
➲ For medium column, 30< λ < 100

8. 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 λ > 100

9. Failure of column
a) Failure by crushing
Short column fails in compression only due to crushing.
Let A = cross sectional area of column.
PC = crushing load
σc = Crushing stress
PS = Safe load on column
Crushing load PC = бC . A

10. .b) Failure by buckling or bending
➲ Before 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 formula
b) Rankine's Formula

12. 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 dimen-
sions.
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.

13. Euler's Formula
Euler's buckling load or crippling load is given by
PE = Euler's buckling load.
E = Modulus of elasticity of column material
I = minimum moment of inertia of column section
Le = Effective length of column.

14. Also Crushing stress
Euler's formula is applicable when λ > 80

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

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

17. Rankine's formula
Rankine had derived formula for long column as follows.
➲ Where
➲ PR = Rankine's Crippling load
Le = Effective length of column
k = Minimum radius of gyration
σc or fc = Ultimate crushing stress
A = Area of cross section
a or α = Rankine's constant

18. Value of crushing stress for and Rank-
ine's constant for different material
SR NO Material σc = Crushing
stress in N/mm2
A = Rankine's
constant
1 Timber 50 1/750
2 Wrought Iron 250 1/9000
3 Mild steel 325 1/7500
4 Cast Iron 550 1/1600

19. Thank you !!!!!!!!!!!!!!!!!!!