What is refuted here — page 17
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. 254 claims in this group.
Shear deformation changes how far a beam deflects but not its bending moments.
What decides it: True of a statically determinate beam and false of a redundant one. A 300 × 600 steel rectangle fixed at one end and propped at the other carries 0.105 wL² at its wall at a span-to-depth ratio of 2 rather than the 0.125 of bending theory, and 0.070 at a ratio of 1, where the span moment has risen from 0.070 wL² to 0.092 — 31 per cent more than the calculation without shear gives.
Tested in The shear that moves the moments, at the figure it turns on · the essays about shear deflection.
The carry-over factor of a prismatic member is one half.
What decides it: It is (2 − φ)/(4 + φ), with φ = 12EI/(GAs L²). One half is the value for a member rigid in shear. It is zero at φ = 2, which a 300 × 600 steel rectangle reaches at a span-to-depth ratio of 1.25, and −0.5 at φ = 8, where turning one end turns the far end's moment the other way.
Tested in The shear that moves the moments, at the figure it turns on · the essays about shear deflection.
Peak counting is a slightly conservative approximation to rainflow.
What decides it: It is an upper bound, not an approximation, and how far above the answer it sits depends on the record. Pairing the highest peak with the lowest valley whether or not they ever made a loop gives this record a Miner sum of 4.36 against rainflow's 2.97, and a life of 23 years against 34.
Tested in Which reversal closes the loop, at the figure it turns on · the essays about fatigue.
The hottest fire a compartment can produce is the worst one for its structure.
What decides it: For bare steel, yes: its peak rises from 839 °C with an opening factor of 0.02 to 1,074 °C at 0.10. For the same member protected, it runs the other way, from 734 °C to 593 °C, because a hot short fire is out before the board has let its heat through and a cool long one is not.
Tested in The fire that goes out, at the figure it turns on · the essays about fire.
A concrete's creep coefficient is a property of the mix.
What decides it: Part of it is. The part drying does not add is 1.28 after fifty years for this concrete in any member at all. The rest belongs to the member: in air at 50 per cent humidity the same mix, poured on the same day, reaches 2.45 in a 150 mm slab open on both faces and 1.93 in a 1.2 m transfer beam.
Tested in The creep that belongs to the member, at the figure it turns on · the essays about creep.
A partial-penetration butt weld is designed on the fillet-weld rules, so the directional criterion sets its strength.
What decides it: It is designed on those rules, and for a butt throat in transverse tension it is their second condition, σ⊥ ≤ 0.9fu, that governs, in every grade: 324 N/mm² against the criterion's 450 in S235, 441 against 544 in S355, and 486 against 540 in S460.
Tested in The throat that misses the load, at the figure it turns on · the essays about weld strength.
A repair welded under load is only worth the live-load share of its benefit, whatever check is being made.
What decides it: For the checks that read a stress, roughly so: flexure runs from 0.27 with no load present to 0.46 with all of it, and shear and local buckling move the same way. Tear-out does not move at all. A block tearing out of the web is a plastic mechanism, and the doubler takes it from 0.57 to 0.30 at every share.
Tested in The plate that arrives after the load, at the figure it turns on · the essays about coped beam.
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. 3 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.