What is refuted here — page 21

The dead load on a parabolic arch does not bend it, so the rib's bending can be designed for the live load alone.

What decides it: Alone, 15 kN/m of dead load bends the rib by 9 kN·m. With 6 kN/m of live load on half the span it raises the live load's peak moment from 346 kN·m to 519, through the thrust it adds: 563 of the 676 kN.

Tested in The weight that bends a rib it cannot bend, at the figure it turns on · the essays about arch buckling.

Enveloping the rigid and flexible idealisations gives every wall at least its true force.

What decides it: On the same plan, designing each bay for the larger of its tributary and rigid shares understates a bay by up to 17 per cent where the plate is soft, because neither model is a continuous plate: the middle bay's true share climbs to 61 per cent against a tributary 50.

Tested in Rigid by one code and not by the other, at the figure it turns on · the essays about diaphragm.

A transverse fillet weld is the stronger arrangement, so orienting welds across the load is the better detail.

What decides it: Statically, across the weld is √1.5 = 1.22 times along. For a load range at two million cycles it is 0.45 times along, because the across component is checked against category 36 and the along component against 80: the two checks disagree by a factor of 2.72.

Tested in Strongest across, and first to crack across, at the figure it turns on · the essays about weld group.

In a member with two identical welds, the neck forms in one zone and the other unloads, so the second weld adds nothing to the member's stretch.

What decides it: Before either necks, both identical zones reach their ultimate strength at the same load and each has used its whole uniform strain: a 2 m 6082-T6 member extends 19.4 mm to its maximum load with two identical welds against 12.3 with one, twice the stretch beyond the elastic. What the second zone does not add is its neck.

Tested in Two welds, and the one that decides, at the figure it turns on · the essays about Heat-affected zone.

The strength of a welded member is the characteristic strength of its heat-affected zone, however many welds it has.

What decides it: The member is as strong as its weakest zone. With zone strengths scattered by 5 per cent, the mean strength falls from 1.00 of one zone's with one weld to 0.97 with two and 0.92 with ten, and the value 95 per cent of members exceed from 0.92 to 0.87.

Tested in Two welds, and the one that decides, at the figure it turns on · the essays about Heat-affected zone.

An edge column's punching shear is the gravity shear multiplied by 1.4, whatever the slab around it.

What decides it: The general expression on the truncated perimeter, measured from that perimeter's own centroid, gives a multiplier of 1.00 at a 5 m end span, 1.34 at 6 m and 1.78 at 7.2 m for a 400 mm column under a 260 mm slab. The shortcut agrees with it at one span, 6.17 m, and is lower everywhere beyond it.

Tested in The perimeter whose middle is not the column's, at the figure it turns on · the essays about punching shear.

A self-tapping screw in a timber joint is designed by Johansen's dowel-bending model, with the rope effect added on top.

What decides it: That is the square screw's model, and it gives 5.9 kN for an 8 mm screw through two 100 mm members. Driven at 45 degrees the same screw carries 13.4 kN, of which its bending contributes 1.3 kN at the joint's peak; the bending is the larger share only steeper than 86 degrees.

Tested in The screw that is pulled instead of bent, at the figure it turns on · the essays about dowel yield.

The code's storey reduction is always conservative, because the probability argument allows a larger reduction than the code takes.

What decides it: Only while the floors are close to independent. With a coefficient of variation of 0.6, EN 1991-1-1's storey rule is safe for a ten-storey column only while the correlation between floors is below 0.19, and for a very tall column below 0.16. At a correlation of 0.3 its twenty-storey load is exceeded 9.7 per cent of the time, against the 5 per cent intended.

Tested in The floors that fill up together, at the figure it turns on · the essays about live load reduction.

If the least storey sway factor is above the limit, the second-order effects are small everywhere in the building.

What decides it: Above the spine, yes, and exactly. Inside it the storeys read factors over 100 at the ground and estimate 0.8 per cent of second-order drift there, where the true amplification is 6.4 per cent, because the ground storey leans with every floor above it.

Tested in The storey above the core decides, at the figure it turns on · the essays about sway stability.

A closed box's shear centre is at its middle, so a vertical load through the middle of a box girder does not twist it.

What decides it: Only for a single cell, or two equal ones. A 600 mm box 300 mm deep with an interior web 200 mm from one side, every wall 10 mm, has its shear centre at 273 mm, 27 mm from the middle toward the web. A load through the middle twists it by 27 mm of lever.

Tested in The web that moves the centre and not the twist, at the figure it turns on · the essays about shear centre.

Catenary action can carry a floor across a lost column at loads well above the beam's bending capacity.

What decides it: Only if the connections can turn far enough first. A sudden loss at 1.5 times the plastic collapse load asks the beam's ends for 0.103 radians. Connections good for 0.03 radians carry a sudden loss only up to 0.94 of the collapse load, and connections good for 0.07 up to 1.19.

Tested in The cable that pays the factor back, at the figure it turns on · the essays about robustness.

The force a camber locks into a redundant truss is the thing to control when it is fabricated.

What decides it: The cutting lists lock in 0, 2 and 91 kN. Random errors of 1 mm on every member lock 174 kN into some member at the median draw and 288 kN at one draw in twenty; 2 mm, twice that. Fitting the counters after the dead load is on removes all of it.

Tested in The counter fitted after the load, at the figure it turns on · the essays about camber.

While a stressed ribbon is erected span by span, an intermediate pier must resist the full thrust of the first span hung beside it.

What decides it: Only if the tendons are anchored at the pier with nothing beyond. Strung over both 100 m spans at the length the finished ribbon needs, the bare tendons already pull 17,766 kN, and a rigid pier carries 4,109 kN of the hung span's 21,875 — less than the 9,440 kN a crowd on one finished span asks of it.

Tested in The tendon that pulls before the deck arrives, at the figure it turns on · the essays about stressed ribbon.

A slender plate girder web has a useful shear reserve beyond buckling only if it has intermediate transverse stiffeners to anchor a tension field.

What decides it: That is Basler's model, and in it the 1,500 × 8 mm web in S355 with no intermediate stiffeners carries only its buckling shear, 0.14 of its plastic shear. The rotated stress field gives the same unstiffened web 0.41, nearly three times as much, provided its end post is rigid.

Tested in Two reserves for one buckled web, at the figure it turns on · the essays about tension field.

Adding intermediate stiffeners to a slender plate girder web saves steel, whichever post-buckling model it is checked by.

What decides it: For 1,500 kN on a 1,500 mm web in S355, with each stiffener 2,000 mm² in section and its steel counted, Basler's model needs 8.2 mm of steel with stiffeners at 0.7 depths against 13.1 mm unstiffened, a saving of 37 per cent. The rotated stress field needs 9.95 mm at best against 10.05 unstiffened: one per cent, before any welding is paid for.

Tested in Two reserves for one buckled web, at the figure it turns on · the essays about tension field.

The effective width of a flange over an interior support is a property of the girder's spans and flange.

What decides it: It also depends on the length the reaction is spread over. On the same girder a reaction over 0.3 m leaves 0.25 of the overhang working, over 1 m 0.33 and over 4 m 0.48, while EN 1993-1-5 gives 0.34 and EN 1994-1-1 0.42 whatever the support bears on.

Tested in The reaction that is made of short waves, at the figure it turns on · the essays about effective width.

Replacing the yielded fuse after an earthquake returns a fused rocking wall to its original condition.

What decides it: It restores the tendon's prestress but not the yielding bars, which keep their plastic stretch. A second identical pulse takes the wall with a new fuse to 134 mrad against 110 the first time; only renewing the bars as well brings it back to 110.

Tested in The fuse that protects the strand and not the wall, at the figure it turns on · the essays about rocking.

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.