1. 13.3 Columns with Various Types of Supports:
Fixed - Free
Figure: 13-11a

2. Euler’s Equation
PCR = critical or maximum axial load on the column just before it begins to buckle.
E = modulus of elasticity for the material
I = least moment of inertia of the column’s cross-section
L = unsupported length of the column, whose ends are pinned
K= effective length factor (i.e. 1 for pinned-pinned, 2 for fixed free)

3. Where Le = effective length = KL
Column Types:
Figure: 13-12a
Where Le = effective length = KL

4. How would you model these columns???
Figure: UN

5. = effective slenderness ratio
In terms of stress:
Figure: 13-08
where
= effective slenderness ratio

6. Examples:
Figure: 13-13aEx13.3

11. Figure: P13.02

12. Figure: P13.12

13. Figure: P13.26

14. Figure: P13.41