column and strut difference between them

. 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

1. 1. Differentiate Between Column & strut 2. Buckling Load 3. Limitations of Euler’s Formula BY: NOOR AHMED Roll no: 17CE71 Presentation is About

2. Contents S t r u t 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

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

4. S T R U T :

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

6. Column DESIGN USED IN A COLUMN

7. S/No Column Strut 1 It is a vertical member subjected to axial compressive load It is a inclined member subjected 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

8. 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

9. 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. Direct compressive stresses. Buckling stresses. C o m b i n ed o f d i r e c t co m pr e s s i v e an d b u c k l i ng stresses. The mode of failure of columns depends upon their lengths and depending on the mode of failure columns are classified as Short columns Long columns

10. When length of column is more as compared to its c/s dimension, it is called long column. Long Column Le/k min > 50 Or, Le/d > 15 for Long Where, Le = effective length of column d = least lateral dimension of column. K min = Minimum radius of gyration Long Column

11. When length of column is less as compared to its 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

12. 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. Amount of load. Length of column End condition of column C/s dimensions of column Material of column .

13. 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 ( l e ) Where l is actual length

14. COLUMN END CONDITION AND EFFECTIVE LENTH :

15. 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

16. Some Assumptions of the Euler’s Formula The following assumptions are made while deriving Euler’s formula: The material of the column is homogeneous and isotropic.. The compressive load on the column is axial only. The column is free from initial stress. The weight of the column is neglected. The column is initially straight (no eccentricity of the axial load). Pin joints are friction-less (no moment constraint) and fixed ends are rigid (no rotation deflection). The cross section of the column is uniform throughout its length. The direct stress is very small as compared to the Bending stress (the material is compressed only within the elastic range of strains). The length of the column is very large as compared to the cross-sectional dimensions of the column. The column fails only by buckling. 

17. Euler’s formula

18. 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 more than the actual buckling load failure is due to buckling. The Euler’s formula for crippling is P cr = (π 2 EI) / L e 2 But I =Ak 2 ∴ P cr /A= π 2 E/(L e /K) 2 σ cr = π 2 E/(L e /K) 2 Where σ cr is crippling stress or critical stress or stress at failure The term L e /K is called slenderness ratio. As slenderness ratio increases critical load/stress reduces. The variation of critical stress with respect to slenderness ratio is shown in figure 1. As L e /K approaches to zero the critical stress tends to infinity. But this cannot happen. Before this stage the material will get crushed.

19. Limitation of Euler’s Formula

20. REFERENCES BOOK (Strength of materials by Andrew pytel ) fourt edition BOOK (Strength of materials by William a nash ) third edition https://librarycivil.blogspot.com/2016/06/eulers-theory-of-columns.html You tube ( https://www.youtube.com/watch?v=E52yWyIuEVM ) https://civildigital.com/buckling-columns-euler-theory-elastic-buckling/ https://librarycivil.blogspot.com/2016/06/eulers-theory-of-columns.html http://www.prajval.in/edudetail/210/1383/%3Cp%3E%3Cstrong%3EWhat-are-the-limitations-of-Euler&rsquo;s-equation-how-they-are-overcome=?-Explain-the-two-empirical-formulas-with-the-name%3C-strong%3E%3C-p%3E-= https://en.wikipedia.org/wiki/Euler%27s_critical_load https://www.youtube.com/watch?v=E52yWyIuEVM