Columns

theory of column

1. Columns Designing

2. 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.

3. Real world examples

4. Real world examples

5. Types Of Columns Long Short (Strut) Intermediate

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

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

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

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

10. Before we move onward…. Crippling Load ( P cr ) Radius of gyration (r) Moment of inertia (I) Area (A) Effective Length (L e ) Slenderness ratio ( λ ) Stronger Axis Weaker Axis

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

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

13. 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.

14. (L e ) for different support conditions.

15. 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 = l e / r min

16. Radius of Gyration(r) , r = √(I/A) or I = Ar² K=radius of gyration I = Moment of Inertia (mm 4 ) A = Area of Section (mm 2 ) Slenderness ratio, Slenderness Ratio = effective length of column/Minimum radius of gyration λ = le/ r min

17. 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.

18. Euler’s Formula Euler’s Crippling Load, P E = ∏ ²EI /le² Where, E is Modulus of Elasticity ( Mpa ) I is MOI or 2 nd Moment of area (mm 4 ) Le is Effective length (mm) Also known as Critical Buckling Load