What is refuted here — page 20

The strip-yield model's correction to the simple check is at most 23 per cent, whatever the plate.

What decides it: Only at the thickness the toughness was measured at. With each plate's own toughness, the simple check using the 25 mm value overstates a 60 mm flange by up to 36 per cent and a 100 mm plate by 45; a 12 mm web by 14.

Tested in The toughness that belongs to the plate, at the figure it turns on · the essays about fracture.

Resizing a redundant truss until every member is at its allowable stress converges to the fully stressed design of that truss.

What decides it: It converges to a fully stressed design, and which one depends on where it started. From six starting areas for the counters, an eight-panel counter-braced Pratt truss reached six different designs — the first panel's counter from 0.40 to 11.19 — every one needing 1,200 units of steel and deflecting 24.0 at mid-span.

Tested in The truss whose forces follow its sections, at the figure it turns on · the essays about truss deflection.

A pile in layered ground can be designed with an equivalent uniform ground, a modulus averaged over the depth the pile is working in.

What decides it: For the head it can: weighted by the square of the pile's own deflection, the average gives the head deflection within 8 per cent for any thickness of soft or stiff upper layer. For the moment it cannot: with a soft layer two characteristic lengths thick over stiff ground the pile's largest moment is 427 kN·m and the averaged ground gives 308.

Tested in The layer a pile feels, at the figure it turns on · the essays about lateral pile.

A block on ground with a bearing limit tips at a definite push, set by the ground's strength and the block's weight and width.

What decides it: On ground that softens toward its limit without reaching it, a block whose weight is at its base has no peak push at all: at a lean of 0.2 radians the push is 801 kN and still rising toward the 813 kN limit. Its weight 8 m up, it peaks at 676 kN, at a lean of 19 thousandths.

Tested in The ground that never quite gives way, at the figure it turns on · the essays about overturning.

A sandwich panel's resistance to a local load is set by its core's crushing strength.

What decides it: Only when the face is thick enough. Under a strip load 10 mm wide, a steel-faced polyurethane panel with 0.5 mm faces yields its face at 3.4 N per mm of width, before its core crushes at 5.0; with 3 mm faces the core crushes first, at 18.8, and the face yields at 23.7.

Tested in The face that dents and the core that crushes, at the figure it turns on · the essays about sandwich section.

A stiffer core makes a sandwich panel more resistant to local loads.

What decides it: It protects the face and not itself. At a fixed crushing strength of 0.12 N/mm², raising the core's modulus from 1 to 16 N/mm² raises the load at which the 0.5 mm steel face yields from 2.2 to 4.6 N/mm and lowers the load at which the core crushes from 7.0 to 3.6.

Tested in The face that dents and the core that crushes, at the figure it turns on · the essays about sandwich section.

A deck screwed to the top flange stops the beam twisting.

What decides it: It is a spring, not a wall. An 8 m open section on forks, carrying 12 kN/m at 75 mm from its shear centre, twists 6.25° with nothing fastened to it; a deck restraining the flange at 5 kNm per metre per radian leaves 4.20°. Halving the twist takes 10.2 kNm/m/rad, and the same beam held against warping at its ends takes 25.4.

Tested in A deck is a spring, not a wall, at the figure it turns on · the essays about twist serviceability.

Thickening the section at the weld until it can carry the parent's proof load restores the member's behaviour.

What decides it: It restores the strength and not the ductility. A land 1.41 times the parent's area lets the 6082-T6 parent reach its proof stress, and the member keeps 13 per cent of its stretch; it takes a land 1.68 times as thick, the parent's ultimate over the zone's, to move the neck out of the zone, and then the member keeps all of it.

Tested in The soft zone that takes all the stretch, at the figure it turns on · the essays about Heat-affected zone.

Past a few diameters of member thickness, making a doweled timber joint thicker buys nothing.

What decides it: It is true of Johansen's mechanisms and of a smooth dowel, and not of a screw. An 8 mm fully threaded screw joining two members of 350 kg/m³ timber reaches Johansen's plateau of 4.73 kN at about seven diameters; with its withdrawal resistance, which grows with the thread's length in each member, its capacity reaches 6.82 kN at ten diameters, 44 per cent above the plateau.

Tested in The pull that Johansen left out, at the figure it turns on · the essays about dowel yield.

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.