Slide 1
Compression can become sideways motion
A slender column can buckle under compression. It bends sideways abruptly even when the material has not reached its crushing strength.
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Buckling is an instability of the member’s geometry. Small imperfections become amplified by the compressive load, so an ideally straight drawing is not a complete representation of a real column.
Slide 2
Length strongly affects stability
A longer unbraced column is easier to buckle than a shorter equivalent one. Bending stiffness and support conditions also matter.
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In the ideal Euler model, critical load varies inversely with effective length squared. Doubling effective length reduces that predicted load to one quarter, with the same material and cross section.
Slide 3
Ends determine the effective length
A pinned end and a rotationally restrained end permit different buckling shapes. Their influence is represented through effective length in simple models.
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Real connections have finite stiffness rather than being perfectly pinned or fixed. Overestimating restraint can therefore overestimate capacity, especially when the surrounding frame can sway.
Slide 4
Bracing shortens the vulnerable span
A brace can restrain sideways movement and raise buckling resistance. It must have sufficient strength and stiffness to do that work.
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A nominal brace that moves with the column provides little restraint. Its connections and the structure receiving the brace force must be included, otherwise the assumed support exists only in the model.
Slide 5
Thin parts can buckle locally
A column’s wall or flange can buckle even if the whole member remains fairly straight. Local and overall instability need different checks.
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Making a hollow section wider with very thin walls may improve one geometric stiffness measure while worsening local plate stability. Efficient design balances material distribution with resistance to these smaller-scale modes.
Sources
- Structural Stability in Bridge Construction
Federal Highway Administration
- Beam Displacements
MIT / David Roylance