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When a column buckles, then yields, and finally fractures fractures, along the most stressed point, this will initially reduce the axial and bending strains along other points. The apparent conclusion would be that the column can only fracture on one point. But is this necessarily true?

It seems to me that this only applies in an idealized scenario, where the column

  1. Has no mass

  2. Experiences no additional axial displacement at its ends when it buckles

  3. Ceases to bear on itself upon fracture.

My argument is that,

  1. Neither condition applies in practice, and bending may continue post fracture

  2. This may lead to a fracture at another point

Am I correct?

I'm especially interested in the role of assumptions 1 and 2, as they are virtually inevitable in practice, even if assumption 3 does not hold up, and the column ends miss each other due to some lateral displacement of the collapsing building.

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2 Answers 2

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For a pin-jointed column, that would be true. But even simple buckling equations are for fixed-end columns, where, after the column has buckled, it can continue to push sideways, causing bending strain. So you will see characteristic failure of light aluminium spars with multiple failure points.

For stiff materials like chalk, where the energy is not dissipated in plastic deformation, after buckling the released energy will cause shattering, with further characteristic breaks

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Fracture would mean complete detachment. So yes, this will happen at one point, because after this happens and the column breaks into two, there is no original structure to fracture. After fracture, the adhered region will release the elastic strain and will assume a position with only the residual plastic strains. Maybe you meant failure, and not fracture?

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