What is refuted here — page 23
Right mechanism, wrong accounting — continued
The physics named is the physics acting. The sum that usually accompanies it does not come out, and the missing term is generally the one that decides. 377 claims in this group.
A damper's effect can be estimated from its coefficient alone, since the brace that holds it only has to be strong enough to carry its force.
What decides it: The brace's stiffness sets the ceiling: the most damping the pair can add is (√(1+κ) − 1)/2, so a brace a quarter as stiff as the structure limits it to 5.9% whatever the damper, and 20% of added damping needs a brace 0.96 times as stiff as the structure.
Tested in The damper is only as good as its brace, at the figure it turns on · the essays about damping.
Safe rather than true
Not a misconception so much as a simplification that has stopped being labelled as one. Each of these errs on the safe side in the case it was chosen for — and each has a direction in which it does not. 5 claims in this group.
Truss joints are pins, so truss members carry axial force and nothing else.
What decides it: The same truss solved twice — pin-jointed, and with the joints continuous as welding actually makes them. The axial forces agree to about a per cent, which is why the idealisation is a good one; the bending it omits reaches a quarter of the axial stress in the worst member. It scales with EI/L, so a stocky truss of heavy members suffers more of it than a light one — which is the opposite of the way most reserves of strength work, and is the direction in which the simplification stops erring safe.
Tested in The joint that is not a pin, at the figure it turns on · the essays about truss.
Wind loading is a static problem: work out the pressure, multiply by the area, apply it.
What decides it: True for a stiff structure and badly wrong for a slender one. Split into its parts, a warehouse at 2 Hz takes 15% of its fluctuating response from resonance and a tower at 0.2 Hz takes 90% — and the resonant part is inversely proportional to a damping ratio that no static calculation contains. The static method survives because the gust factor it hides absorbs the difference for ordinary buildings.
Tested in The wind is a spectrum, at the figure it turns on · the essays about gust response.
The effective width of a flange is min(span/8, b) per side, and that expression comes from the elasticity of the problem.
What decides it: The exact elastic ceiling for an infinitely wide flange fed by a sinusoidal shear flow is L/2π = 0.1592L per side, from Airy's solution. The rule caps at L/8 = 0.125L, which is 0.7854 of it — exactly 2π/8. A rule that is a fixed fraction of the exact answer is a fit with a margin in it, not a derivation of it, and it is a straight line where the elasticity is a curve.
Tested in The flange that is not all there, at the figure it turns on · the essays about effective width.
Quoting k = 4 for a long plate is an approximation, so it could be wrong in either direction.
What decides it: It is the floor of the envelope and not an average through it. Every scallop rises above 4 and none falls below it, so the quoted value understates the critical stress by up to 12.5 per cent and never overstates it — and past an aspect ratio of 1.60 the error can never exceed 5 per cent again.
Tested in Four was never a fact about plates, at the figure it turns on · the essays about plate buckling.
One pass of the effective-width calculation is enough, because the correction is small.
What decides it: It is small in the moment and not in the width. One pass reports 278 mm of web removed against the converged 323, understating the loss by 16 per cent, while the moment capacity it reports is 10,079 kNm against 9,999 — an error of 0.8 per cent. The two errors differ by a factor of twenty because the width that goes missing sits near the neutral axis.
Tested in Classified by a gradient it does not have, at the figure it turns on · the essays about plate buckling.