# Column Theory - Column Strength Curve

## Presentation on theme: "Column Theory - Column Strength Curve"— Presentation transcript:

Column Theory - Column Strength Curve

Example I OK – Column is Stable
A W12x50 is used as a column to support a compressive load of 145 kips. The length is 20 ft and the ends are pinned. Without regard to LRFD or ASD investigate the stability of the column For a W12x50 OK – Column is Stable

Example I NG – Column is Unstable
A W12x50 is used as a column to support a compressive load of 145 kips. The length is 20 ft the bottom is fixed and the top is free. Without regard to LRFD or ASD investigate the stability of the column For a W12x50 NG – Column is Unstable

AISC Requirements CHAPTER E pp 16.1-32 Nominal Compressive Strength
AISC Eqtn E3-1

AISC Requirements LRFD

AISC Requirements ASD

AISC Requirements ASD – Allowable Stress

To compute Fcr – ELASTIC BUCKLING
Recall Assumptions

Column is perfectly straight The load is axial, with no eccentricity
Assumptions Column is perfectly straight The load is axial, with no eccentricity The column is pinned at both ends

To compute Fcr – ELASTIC BUCKLING
Accounts for Imperfections

To compute Fcr – INELASTIC BUCKLING

Design Strength

Alternatively Inelastic Buckling

In Summary

Example A W14x74 of A992 steel has a length of 20 feet and pinned ends. Compute the design strength for LRFD and the allowable compressive strength for ASD Slenderness Ratio

Example

Example LRFD ASD