What is refuted here — page 19
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. 283 claims in this group.
A truss sized so every member works at the same stress is a strength design, and its deflection is whatever it happens to be.
What decides it: For the same volume of steel, an eight-panel Pratt truss sized fully stressed deflects at mid-span 1.044 times as much as the stiffest division possible; with equal areas, 1.39 times. A Howe truss gives 1.050 and 1.35, a Warren 1.026 and 1.40.
Tested in The truss that is stiff by accident, at the figure it turns on · the essays about truss deflection.
A frame that has as many unknowns as equations and a non-zero determinant is rigid, and its computed forces describe it.
What decides it: Two bars of 200 MN axial stiffness over an 8 m span, meeting at a joint raised 3 degrees and loaded with 50 kN, pass both tests. Each carries 478 kN, and the joint sags 183 mm under the load on a rise of 210 — 87 per cent of the geometry the forces were computed on.
Tested in Rigid by every test, and still folding, at the figure it turns on · the essays about determinacy.
The quarter-point formula for the moment-gradient factor is conservative, because it was calibrated to err on the safe side.
What decides it: It is conservative on straight-line diagrams, by up to 21 per cent. For a fixed-ended beam under a central point load its quarter-point readings are zero and it gives 1.923, against an exact 1.723: 12 per cent on the unsafe side.
Tested in The formula that reads four numbers, at the figure it turns on · the essays about moment gradient.
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.