Structural Engineering & Statics
where the load goes
Series

Robustness — the series

3 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Take that one away and the load finds another route. A 6-panel pratt truss under 20 kN at each top node, before and after member 2 is removed. The load redistributes. The worst-affected survivor now carries 2.03 times what it did, and four members that carried nothing before are now working. Whether that is survival depends on how much spare capacity was there, which is a different question from whether the frame was strong enough.

    The structure that survives losing a member

    Every check in this collection asks what a structure carries. None of them asks what is left when part of it is gone — and two frames with the same members, the same weight and the same factor of safety can answer that question completely differently.

    part 1 · structures
  2. Removing each member in turn. Every member of a 8-panel pratt truss removed one at a time, with the worst demand on the survivors plotted against the member removed. Four of the 35 leave a mechanism — the bars drawn to the top of the frame — and for those there is no redistribution to compute, because there is no structure left. The rest redistribute, and the worst of them asks a survivor for 2.04 times what it carried before. A single number for robustness does not exist: it depends on which member goes.

    A determinate truss has no robustness at all

    Remove any one of a Warren truss's thirty-one members and what is left is a mechanism. Not weakened — gone, with no set of forces that holds the load in any position. Robustness is not a property a structure has by degree; it is bought by adding members that carry nothing until something else stops carrying, and a truss without them has none of it to measure.

    part 2 · structures
  3. Three members after a diagonal goes. The forces in three members of the counter-braced truss when the diagonal 9–2, carrying 242 kN, is removed instantaneously, with 2 per cent damping, over one and a half of the damaged truss's first periods (0.57 s); dashed, the static force each settles to. The counter-diagonal 1–10 goes from −112 kN to −354 kN and peaks at −491 kN, 1.57 times its change. The bottom chord 3–4 ends exactly where it started, 750 kN, and on the way peaks at 1,115 kN. The bottom chord 2–3 settles lower, at 556 kN, after a first swing the other way, to 905 kN.

    The factor of two belongs to one mode

    A member that fails suddenly hands its force to the structure around it all at once, and the convention is to double the static answer: a load applied suddenly to a spring overshoots to twice its static deflection. A truss is not one spring. Take a diagonal out of a counter-braced truss in an instant and some members swing to three times their change of force, one swings the wrong way first, and a bottom chord whose force does not change at all passes through half as much again as it carries — because every mode overshoots by two, at its own time, and a member is a sum of modes.

    part 3 · structures

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