Structural Engineering & Statics
where the load goes
Series

Effective length — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. The ends decide the length that matters. Four columns of identical height and section, buckling under four sets of end conditions. The effective length factor is the fraction of the column that behaves like a pin-ended one, and the buckling load goes as its inverse square.

    The ends decide the length that matters

    Four columns of identical height and section, buckling at loads sixteen times apart. Nothing differs but what is holding the two ends.

    part 1 · stability
  2. A brace is a stiffness requirement, not a strength one. Critical load against brace stiffness for a pinned column braced at mid-height. The curve climbs from the unbraced Euler load of 9.87EI/L² and flattens at 39.48EI/L², which is the Euler load of the braced segment — past that the column buckles in a shape the brace does not obstruct, and further stiffness buys nothing. The knee is at about 159EI/L³. A stiffness of 60EI/L³ is marked, reaching 21.75EI/L².

    The brace that need not be strong

    A brace holding a column at mid-height carries almost no force. What it has to be is stiff — and the stiffness required is exact, large, and reached at a knee past which more buys nothing at all.

    part 2 · stability

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