. Differentiate Between Column & strut 2. Buckling Load 3. Limitations of Euler’s Formula CONTENTS Strut Column Differentiate Between Column & Strut Failure Of Column Or Strut Long Column Short Column Buckling Load Column End Condition And Effective Length What Is Euler’s Formula Some Assumptions Of The Euler’s Formula Euler’s Formula Limitation Of Euler’s Formula

2. 1. Differentiate Between Column & strut
2. Buckling Load
3. Limitations of Euler’s Formula

3. Contents
1) Strut
2) Column
3) Differentiate Between Column & Strut
4) Failure Of Column Or Strut
5) Long Column
6) Short Column
7) Buckling Load
8) Column End Condition And Effective Length
9) What Is Euler’s Formula
10) Some Assumptions Of The Euler’s Formula
11) Euler’s Formula
12) Limitation Of Euler’s Formula

4. STRUT
1) A structural member subjected to axial compressive force is called
strut.
1) Strut may be vertical, horizontal inclined.
2) The cross – sectional dimensions of strut are small.
3) Normally, struts carry smaller compressive loads.
4) Struts are used in roof truss and bridge trusses.
5) A strut is a structural component designed to resist longitudinal
compression.

5. STRUT:

6. 1) When strut is vertical it is known as a column
2) The cross – sectional dimensions of column are large.
3) Normally, columns carry heavy compressive loads.
4) Columns are used in concrete and steel buildings.
5) columns may be designed to resist lateral forces.
6) . Columns are frequently used to support beams or arches on which the
upper parts of walls or ceilings rest.
Column

7. Column
DESIGN USEDIN A COLUMN

8. S/No Column Strut
1
It is a vertical member subjected to axial
compressive load
It is a inclined member subject
ed to axial load.
2
Slenderness ratio of column is low Slenderness ratio of struts is
high
3
columns fail in compression. Struts fail due to buckling
4
Compressive member of frame structure Compressive member of truss
structure
Differentiate Between Column & strut

9. S/No Column Strut
5
Loads are applied any were throughout the
column
Loads are applied only on joints
6
Column is subjected to gravity load Strut is subjected to gravity load
7 It is generally failed by buckling It is generally failed by crushing
8
It is generally supported by fixed supports
at both ends.
It is generally supported by hinged or
pin joint at both ends
9
It is designed to take up the compressive
loads only.
It is designed to take up both the
compressive as well as tensile load
Differentiate Between Column & strut

10. Failure of Column or Strut
The failure of a column takes place due to the anyone of the following
stresses set up in the columns.
a)Direct compressive stresses.
b)Buckling stresses.
c)Combined of direct compressive and buckling stresses.
The mode of failure of columns depends upon their lengths
and depending
on the mode of failure columns are classified as
a. Shortcolumns
b. Longcolumns

11. When length of column is more as compared to its c/s dimension, it is calle
d long column.
Long Column Le/kmin > 50
Or,
Le/d > 15 for Long Where,
Le = effective length of column
d = least lateral dimension of column.
Kmin = Minimum radius of gyration
Long Column

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

13. BUCKLING LOAD
The load at which, long column starts buckling(bending) is called buckling
load or crippling load.
Long columns, which are also called slender columns, when subjected to
compression, deflects or bends in a lateral direction. The lateral deflection
of the long column is called buckling
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.

14. COLUMN END CONDITION AND EFFECTIVE LENTH :
1.Both end hinged.
2.Both end fixed.
3.One end fixed and other hinged.
4.One end fixed and other free.
Effective length (le)
Where l is actual lengt
h

15. COLUMN END CONDITION AND EFFECTIVE LENTH :

16. What is Euler’s Formula
This formula was derived in 1757, by the Swiss
mathematician Leonhard Euler. The column will
remain straight for loads less than the critical
load. The "critical load" is the greatest load that
will not cause lateral deflection (buckling).
For loads greater than the critical load, the column
will deflect laterally

17. Some Assumptions of the Euler’s Formula
The following assumptions are made while deriving Euler’s formula:
1) The material of the column is homogeneous and isotropic..
2) The compressive load on the column is axial only.
3) The column is free from initial stress.
4) The weight of the column is neglected.
5) The column is initially straight (no eccentricity of the axial load).
6) Pin joints are friction-less (no moment constraint) and fixed ends are rigid (no rot
ation deflection).
7) The cross section of the column is uniform throughout its length.
8) The direct stress is very small as compared to the Bending stress (the material is c
ompressed only within the elastic range of strains).
9) The length of the column is very large as compared to the cross-sectional dimensi
ons of the column.
10)The column fails only by buckling.

18. Euler’s formula

19. 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 mo
re than the actual buckling load
failure is due to buckling. The Euler’s formula for crippling is
Pcr
= (π 2 EI) / Le
2
But I =Ak2
∴Pcr/A= π 2E/(Le/K)2
σcr = π2E/(Le/K)2
Where σcr is crippling stress or critical stress or stress at failure The term Le/K is called slenderness
ratio. As slenderness ratio
increases critical load/stress reduces. The variation of critical stress with respect to slenderness ratio i
s shown in figure 1. As Le/K approaches to zero the critical stress tends to infinity. But this cannot h
appen. Before this stage the material will get crushed.

20. Limitation of Euler’s Formula

21. REFERENCES
1. BOOK (Strength of materials by Andrew pytel) fourt edition
2. BOOK (Strength of materials by William a nash) third edition
3. https://librarycivil.blogspot.com/2016/06/eulers-theory-of-columns.h
tml
4. You tube (https://www.youtube.com/watch?v=E52yWyIuEVM)
5. https://civildigital.com/buckling-columns-euler-theory-elastic-buckli
ng/
6. https://librarycivil.blogspot.com/2016/06/eulers-theory-of-columns.h
tml
7. http://www.prajval.in/edudetail/210/1383/%3Cp%3E%3Cstrong%3E
What-are-the-limitations-of-Euler&rsquo;s-equation-how-they-are-o
vercome=?-Explain-the-two-empirical-formulas-with-the-name%3C-
strong%3E%3C-p%3E-=
8. https://en.wikipedia.org/wiki/Euler%27s_critical_load
9. https://www.youtube.com/watch?v=E52yWyIuEVM