13.3 Columns with Various Types of Supports:
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13.3 Columns with Various Types of Supports: Fixed - Free ) ( 2 2 P M dx d EI 2 2 4 L EI P CR
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 Presentation
Transcript of 13.3 Columns with Various Types of Supports:
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13.3 Columns with Various Types of Supports:
Fixed - Free
)(2
2
PM
dxdEI
2
2
4LEIPCR
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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)
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Column Types:
Where Le = effective length = KL
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How would you model these columns???
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2
2
2
/
,
rKLE
ArInote
CR
)/( rKL
where
= effective slenderness ratio
In terms of stress:
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Examples:
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