Columns, slenderness ratio, types of columns, buckling and crushing load, euler theory

1. COLUMNS
Concept of Column and Modes of Failure
Slenderness Ratio
Types of Columns
Buckling load and Crushing Load
Euler’s Theory for long columns
By:-
Er. Bharat Bansal
Lect. Mechanical Engineering
Govt. Polytechnic College Bathinda

2. COLUMN
• Vertical member of
structure subjected to
axial compressive load is
called column.

3. MODES OF FAILURE
• Direct Compressive stress
• Buckling Stress
• Combination of direct compressive
stress and buckling stress

4. SLENDERNESS RATIO
The ratio of length of column to minimum radius
of gyration of cross sectional area of column is
called Slenderness Ratio.

5. TYPES OF COLUMNS
(Based on length of Column)
LENGHT SLENDERNESS RATIO
Short Column Less than 8 times of their
Diameter
Less than 32
Medium
Column
Varying from 8 to 30 times of
their Diameter
Varying from 32 to 120
Long Column More than 30 times of their
Diameter
More than 120

6. TYPES OF COLUMNS
(Based on End Conditions of Column)

7. BUCKLING LOAD
• The maximum axial compressive load which a
column can take without failure by buckling is
called Buckling Load. It is also called Crippling
load or Critical load.

8. BUCKLING FACTOR
• It is the ratio of equivalent length of column to
minimum radius of gyration.

9. CRUSHING LOAD
• The load that fails the column by directly
crushing it, without undergoing to Buckling, is
called Crushing Load.
• It more frequently occurs in Short Columns.

10. ASSUMPTIONS IN EULER’S THEORY

11. EULER’S FORMULA

12. LIMITATIONS OF EULER’S FORMULA