13.3 columns with various types of supports:
DESCRIPTION
13.3 Columns with Various Types of Supports:. Fixed - Free. Euler’s Equation. P CR = 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 - PowerPoint PPT PresentationTRANSCRIPT
13.3 Columns with Various Types of Supports:
Fixed - Free
)(2
2
PM
dxdEI
2
2
4LEIPCR
2
2
)(KLEIPCR
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)
Column Types:
Where Le = effective length = KL
How would you model these columns???
2
2
2
/
,
rKLE
ArInote
CR
)/( rKL
where
= effective slenderness ratio
In terms of stress:
Examples:
