What is refuted here — page 25

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.

A chimney that locks in to vortex shedding is made safer by making it stiffer, because a stiffer chimney locks in at a stronger wind, which is rarer.

What decides it: Only above a critical speed of 1.22 times the wind's Rayleigh scale. Below it a stronger critical wind is met more often per cycle of the band, not less. In a climate of scale 5.5 m/s the 1.2 m chimney at 0.90 Hz locks in at 6.0 m/s and its base lasts 22 days; stiffened to 1.35 Hz it locks in at 9.0 m/s and lasts 27 days, while at 0.45 Hz it lasts 72.

Tested in The breeze that uses up a chimney, at the figure it turns on · the essays about Vortex-shedding.

Back-analysing a failed slope by setting its factor of safety to one measures the strength of the soil it failed in.

What decides it: It measures one relation between two strengths. The 10 m slope at 35° fails at F = 1 with 32.1 kPa of cohesion and no friction, with 12.4 kPa and 20°, with 2.0 kPa and 40°, and with no cohesion at 48.1°. The second equation is the slip's own depth: 13.6, 5.2 and 2.3 m for those three.

Tested in A failed slope gives a line, not a soil, at the figure it turns on · the essays about slope stability.

A frame's joints are checked under the load combination that governs its members, since that is the combination with the largest moments.

What decides it: Gravity plus sway gives the members of the two-bay frame their largest moment, 146.5 kN·m, and puts 89 kN through the floor interior panel. One bay loaded plus sway gives the members less, 124.4 kN·m, and puts 242 kN through the same panel, more than any exterior panel carries in any case.

Tested in The panel that gravity leaves empty, at the figure it turns on · the essays about corner moment.

The torsion constant of an open I-section is the sum of bt³/3 over its flanges and web.

What decides it: For the 457 × 191 × 67 UB the sum is 34.7 cm⁴ and the published constant 37.1. The film over the same three plates with sharp corners gives 34.2, and over the rolled outline, with root fillets of 10.2 mm that are 1.0 per cent of the area, 37.15 — the fillets are worth 8.7 per cent of the constant, and across seven standard sections 9 to 13.

Tested in The corner the rolling mill rounds, at the figure it turns on · the essays about torsional constant.

A storey-by-storey sway check can only err on the safe side, because the least storey factor is never above the building's own critical factor.

What decides it: The least storey factor is on the safe side: 3.88 for a 20-storey bending tower whose own critical factor is 5. But a storey's own factor used as its own amplifier is not: the tower's ground storey reads 1/(1 − 1/α) = 1.019, and a second-order analysis of the whole building gives that storey 1.199.

Tested in The storey that cannot see the building lean, at the figure it turns on · the essays about sway stability.

The ratio of the maximum to the average edge drift measures how much a plan's torsion amplifies its corner displacements.

What decides it: Only for a plan with no natural eccentricity. For the core-and-façade plan it is 1.63 while the far edge moves 1.98 times the translation of a plan with no torsion, because the average it divides by has itself moved to 1.21; a symmetric plan reading the same 1.63 moves its corner 1.63.

Tested in A measure of twist that divides by the twist, at the figure it turns on · the essays about plan torsion.

A column base with a thick plate and anchor bolts on a lever arm can be taken as fixed in the frame analysis.

What decides it: The 500 × 400 × 20 mm base on two M24 bolts is 9.1 times the column's EI/L, against the 30 that EN 1993-1-8 requires of a rigid base in a sway frame. Its bolts are 59 per cent of its flexibility, so a 40 mm plate reaches 13.7 and a perfectly rigid one 15.3; the portal on it drifts 1.28 times as far as on fixed bases.

Tested in The fixed base the bolts decide, at the figure it turns on · the essays about base plate.

A truss is precambered by making its chords the right lengths, since the chords carry the bending.

What decides it: The chords carry the bending and not all of the deflection. In the 24 m Pratt truss the webs are 26 per cent of the 48.8 mm dead-load sag; building only the chords to their dead-load strain takes out 36.2 mm and leaves 12.6. Only every member built to its own strain removes the whole sag.

Tested in The camber that lives in the member lengths, at the figure it turns on · the essays about camber.

A retaining wall that can move far enough to mobilise active pressure needs to be designed only for the active triangle.

What decides it: Only if its backfill was not compacted. A 3 m wall with backfill of 20 kN/m³ and φ′ = 30° has an active base moment of 30 kN·m per metre; compacted by a 60 kN/m roller its backfill locks in a constant 27.6 kPa below 0.46 m, and the moment is 106 kN·m — more than the 45 of the same soil at rest against a wall that cannot move.

Tested in The pressure the roller leaves behind, at the figure it turns on · the essays about lateral pressure.

Lighter compaction plant near a wall removes the problem of compaction pressure.

What decides it: It reduces it by the square root of the plant's weight, not in proportion. A 15 kN/m roller still gives the 3 m wall a base moment of 58 kN·m, nearly twice the active 30, and a 10 kN/m pedestrian roller dominates the top 1.7 m of any wall.

Tested in The pressure the roller leaves behind, at the figure it turns on · the essays about lateral pressure.

Widening a prestressed tee's flange raises the load it can be prestressed for, since it raises its section modulus.

What decides it: It raises the top fibre's modulus, which was not the limit. From a 200 to a 1,400 mm flange, the load the top fibre can be prestressed for goes from 18.9 to 72.2 kN/m and the bottom fibre's from 13.8 to 19.6, and the bottom fibre decides.

Tested in The flange the prestress cannot use, at the figure it turns on · the essays about prestress limits.

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.

A double-cover splice has no eccentricity, because the covers lie on both faces of the plate.

What decides it: Only equal covers put their centroid on the main plate's centre line. A 15 mm and an 8 mm cover put it 6.5 mm off, and the cure is not to make the covers' areas equal but their first moments about that line: with inner covers 160 mm wide under a 200 mm outer cover of 15 mm, equal area needs 18.8 mm and balance needs 17.5.

Tested in The thinner cover carries more, at the figure it turns on · the essays about single lap.

In a prestressed beam the shear the tendon carries is its vertical component, P sin θ, so the shear to be resisted is the applied shear less P sin θ.

What decides it: True of a beam on two supports. Two 16 m spans prestressed with 2,400 kN under 45 kN/m: 0.8 m inside the end support the applied shear is 234 kN and the tendon's slope relieves 209 of it, leaving 25. The reactions the tendon provokes add a constant 26 kN back, and the shear left for the links is 51 — twice the figure the rule gives.

Tested in The relief that belongs to the pressure line, at the figure it turns on · the essays about secondary prestress.

A slope that has failed twice, at two different places or heights, fixes both strength parameters of its soil.

What decides it: Only if the two slips loaded the soil at very different normal stresses. Slopes of 35° and 28° failing in a soil of 8 kPa and 24° cross exactly there, but if each was within five per cent of failure rather than exactly at it, the crossing is anywhere from 18° to 30°. Two slopes at one angle and different heights cross only at zero cohesion.

Tested in Two slips are a shear test, at the figure it turns on · the essays about slope stability.

The advantage of an active mass driver is that it does more with the same mass in the same space.

What decides it: In the same space it does a little more: 7.38 against 8.72 with half the applied force, as good as a 3.0 per cent passive mass. Most of its advantage is space: half as much stroke again takes it to 4.49, as good as 9.3 per cent.

Tested in The law that throws the tuning away, at the figure it turns on · the essays about tuned mass damper.

An interior web added to a box girder moves its shear centre sideways toward the web, and nothing else.

What decides it: True of a vertical web. In a trapezoidal box 1.5 m deep, an interior web from the middle of the top flange to a point 500 mm left of the middle of the bottom flange moves the shear centre 69 mm sideways and 10 mm up; leaned the other way round, from 500 mm left at the top to the middle at the bottom, 88 mm sideways and 12 mm down.

Tested in The web that leans and lifts the centre, at the figure it turns on · the essays about shear centre.

A floor plate hands its shear to a brace line uniformly along the line, so the collector feeding a short braced bay carries the line's share times the fraction of the line the bay does not occupy.

What decides it: That is the force a steel deck delivers: 689 kN against the rule's 720 for a 6 m bay on a 24 m line. A 150 mm concrete slab sends its shear into the bay directly: the collector carries 171 kN, about a quarter, and the slab beside the bay averages 132 kN/m against the rule's 40.

Tested in The collector the slab does not need, at the figure it turns on · the essays about diaphragm.

Preloading the holding-down bolts makes a column base rigid.

What decides it: At 150 kN a bolt the base is 45.6 times EI/L — up to 57 kN·m, where the bed under the plate first lets go; its secant stiffness falls below the rigid boundary at 120 kN·m. And 0.1 mm of creep in the grout takes a fifth of the preload from a bonded anchor.

Tested in The base that is rigid until the bed lets go, at the figure it turns on · the essays about base plate.

The neutral plane of a pile in settling ground can be found from equilibrium alone: head load and drag above it balanced by shaft resistance and base resistance below.

What decides it: Only once the base resistance is known, and it is not an input. For a 24 m pile carrying 800 kN in ground settling 100 mm, the toe mobilises 623 kN; equilibrium given that number puts the plane at 15.9 m, as compatibility does. Given an assumed 300 kN it puts it at 13.8 m and the largest force at 1,283 kN instead of 1,407.

Tested in The plane where the pile and the ground agree, at the figure it turns on · the essays about downdrag.

Each kilonewton added to the head of a pile with downdrag raises the largest force in it by half a kilonewton, because the neutral plane rises to meet it.

What decides it: True with the toe's force fixed. With the toe mobilised by its movement, added load pushes it down and it takes some of the load itself; by compatibility the largest force rises 0.77 kN per kilonewton added — a half plus half the toe's share.

Tested in The plane where the pile and the ground agree, at the figure it turns on · the essays about downdrag.

The more flexible the stem, the more of the compaction pressure it sheds, down to the active pressure for a stem flexible enough.

What decides it: The relief flattens out. A 200 mm stem keeps 70 per cent of the rigid stem's base moment and the softest stem drawn, moving nearly 30 mm at its top, still keeps 68 per cent — where active pressure would be 32 — because the pressure at the base and in the last lifts cannot relax however much the stem bends.

Tested in The stem that bends away from the roller, at the figure it turns on · the essays about lateral pressure.

A rigid restraint against twist at mid-span removes the beam's twist.

What decides it: It removes the twist at mid-span and leaves 0.40° at 1.7 m from each end, where the two halves now twist as beams of half the length; and it takes 4.38 kN·m of the 7.20 kN·m applied torque through one connection.

Tested in The restraint that works where the twist is, at the figure it turns on · the essays about twist serviceability.

Backprops are soft enough that their stiffness has to be designed for.

What decides it: A steel prop of 36 kN/mm on a 1.2 m grid is 6.8 times stiffer per square metre than the slab, and takes the struck slab from 1.49 to only 1.52 of its weight; halving the stiffness gives 1.55. What has to be specified is the slack: a millimetre of it takes the worst use of strength from 1.95 to 2.29.

Tested in The backprop that takes load nobody gave it, at the figure it turns on · the essays about maturity.

A hole bored along a shaft weakens it in torsion like any other cut, by crowding the stress function's film into the nearest wall.

What decides it: A 10 mm hole 15 mm off the axis of a 50 mm shaft leaves 93 per cent of the solid shaft's stiffness, because the film over the hole is an island that floats at 55 per cent of the solid film's peak height. Pin the island at the outline's height, which is the same shaft slit from the hole to the surface, and it keeps 67 per cent.

Tested in The island the film floats, at the figure it turns on · the essays about membrane analogy.

The effective number n⁰·⁹ for a row of axially loaded screws is a safe allowance for the softening of each screw after its peak.

What decides it: It is safe, and far below what the row reaches in members of ordinary depth with a thread that peaks at 1.5 mm. With a brittle thread peaking at 0.5 mm, in members with 40 mm of depth per row, thirty screws reach an effective number of 21.7 against n⁰·⁹ = 21.4, and the rule is then exact rather than generous.

Tested in Twenty screws that peak together, at the figure it turns on · the essays about dowel yield.

A semi-rigid interior joint relieves its column-web panel at no cost, because a joint that takes less moment needs a lighter panel.

What decides it: The panel shear under a load on one bay falls from 154 kN with rigid joints to 104 at a joint stiffness of three times the beam's EI/L — and the loaded beam's sagging moment rises from 71 to 102 kN·m, because the span's free moment wL²/8 = 160 kN·m is fixed and a softer joint only lowers the support moments it hangs from.

Tested in The panel a soft joint empties into the span, at the figure it turns on · the essays about corner moment.

Which of ovalisation and local buckling ends a thin tube in bending is decided by the shell knockdown factor and not by how thin the tube is.

What decides it: Only with no pressure on it. A pressure scales the ovalisation limit by the square root of one plus the pressure over the ring's buckling pressure, and that pressure goes as (t/r)³: 1 kPa of suction is 0.002 of the ring's buckling pressure of a tube with r/t = 50 and a quarter of that of one with r/t = 240. Over r/t from 40 to 500 at one knockdown, ovalisation governs from r/t = 187 with no pressure and from r/t = 50 near the ring's buckling pressure outside.

Tested in Three kilopascals that halve a tube in bending, at the figure it turns on · the essays about brazier buckling.

In a Vierendeel girder with unequal chords, the shear in each panel divides between the chords in proportion to their second moments, because the stiffer member attracts the load.

What decides it: Only if the posts are rigid. Six 2 m panels, 1.5 m deep, the top chord four times as stiff as the bottom and the posts as stiff as the bottom chord: the top chord carries 0.56, 0.59 and 0.70 of the shear from the support to the load, where the rule gives 0.80 in every panel. With posts a hundred times stiffer it carries 0.76, 0.78 and 0.80.

Tested in The heavy chord the posts will not let work, at the figure it turns on · the essays about vierendeel.

A basement whose finished building is heavy enough to hold it down against the groundwater needs no tension piles.

What decides it: Only if the pumps keep the water away until enough of the building is there. The 20 × 30 m basement, eight storeys of 8 kN/m² over it leaving 16.1 MN to spare when finished, needs ties of 9.4 MN — twenty-one tension piles — if the pumps stop as the basement is completed and the water returns with a recovery time of 7 days, 5.0 MN after one floor, 0.7 after two and none after three.

Tested in The water that comes back while the floors go up, at the figure it turns on · the essays about uplift.

The pumps under a basement must run until the building above it is heavy enough to hold it down by itself.

What decides it: Only if the water comes back at once. With a floor a week, that rule asks for five floors on the basement before the pumps stop; the water's recovery time lowers it to four at 3 days, three at 7, one at 14 and none from about 20 days, because the frame keeps adding weight while the ground refills.

Tested in The water that comes back while the floors go up, at the figure it turns on · the essays about uplift.

An edge column designed for its axial load and the simple-construction eccentricity is adequate in a semi-continuous frame, because the joint moments bend it in double curvature.

What decides it: The double curvature protects the buckling check, which moves only from 0.25 to 0.42 in the top storey. It does not protect the section at the floor, where the end moment arrives in full: the top storey's section check goes from 0.24 under the rule to 0.74 at the design load, 0.97 at the beams' collapse load, and above 1.0 if the joints are 10 per cent stronger than their design resistance.

Tested in The column on the other side of the joint, at the figure it turns on · the essays about joint classification.

The higher the overstrain pressure used in autofrettage, the higher the pressure the cylinder can afterwards carry elastically, up to the pressure that yields its whole wall.

What decides it: Only for walls up to 2.22 times the bore with a steel that yields equally in reverse. A tube 2.5 times its bore in a 900 N/mm² steel can take 756 N/mm² elastically after an overstrain to 756, and still only 756 after one to 825, which yields the whole wall: the release from 825 reverses the bore past yield and gives the difference back.

Tested in The overstrain the release gives back, at the figure it turns on · the essays about unloading.

Putting the strands of a pretensioned beam as low as the section allows is always the economic choice, because it needs the least prestress.

What decides it: It needs the fewest strands at mid-span — twelve at 100 mm, eight at 220, six at 300 — and the most debonding at the ends: none up to 200 mm, two at 220, three from 260. Past about 230 mm more than a quarter of the strands must be sleeved, more than owners commonly allow, so the depth that is cheapest at mid-span is decided by the ends.

Tested in The strands that are sleeved at the ends, at the figure it turns on · the essays about prestress limits.

A secondary beam framing into a primary from one side twists it, because its reaction acts off the primary's shear centre.

What decides it: It does if its connection is very flexible: at 10 kN·m/rad its 3.6 kN·m of torque takes the mid-span twist from 6.25° to 9.12°. Above about 33 kN·m/rad the restraint the same secondary gives outweighs its torque, and at 1,000 the twist falls to 0.47°. Whether it twists or holds is decided by the connection, not by the eccentricity.

Tested in The secondary beam that twists what it holds, at the figure it turns on · the essays about twist serviceability.

A crane's counterweight is sized for the heaviest payload at the longest radius.

What decides it: On a luffing crane the jib's own moment about the mast changes by 6,591 kN·m between 15° and 85°, more than twice the 2,898 kN·m that 60 kN at the tip ever adds. A fixed counterweight centred on the whole range leaves the mast ±4,744 kN·m, of which the jib's change accounts for 3,295.

Tested in The counterweight that follows the jib, at the figure it turns on · the essays about counterweight.

Letting the springs of a Winkler foundation go slack in tension makes only a small correction, because the uplift it removes is small.

What decides it: The pressure under the column rises 8 per cent and the moment 9 per cent, which is small. But the contact length stops depending on the strip at all: every weightless strip longer than 8.05 m — π/β for 1/β = 2.56 m — keeps exactly 8.05 m on the ground, and the 117 kN·m of reverse moment the linear answer puts 3.8 m from the column does not exist.

Tested in The ends the ground was holding down, at the figure it turns on · the essays about elastic foundation.

The more torsional braces a beam has, the stiffer each one must be, because each brace added raises the moment the braces are working to reach.

What decides it: True only of the ceiling. For the 24 m girder the stiffness each brace needs to reach 95 per cent of its row's ceiling rises from 1,615 kN·m/rad for one brace to 118,954 for eight. Asked instead for 5,627 kN·m, each brace needs 3,510 kN·m/rad with three and 1,477 with eight, and the total stays between 10,530 and 11,813.

Tested in The stiffness a row of braces shares out, at the figure it turns on · the essays about beam bracing.

Jacking a backprop to a preload relieves the young slab it supports by the amount of the preload.

What decides it: At the moment of jacking it does. But snug backprops would have taken 0.23 of a slab's weight off the young slab by creep within the week anyway, and a preload leaves creep less to do: of 0.30 w jacked, 0.16 w is still relief at the end of the week, and the same holds in proportion at every preload, about half.

Tested in The backprop jacked tight lands on the floor below, at the figure it turns on · the essays about maturity.

Top lateral bracing turns an open tub girder into a closed box, so the closed box's section properties apply while the deck is poured.

What decides it: For torsion very nearly: bracing equivalent to a 0.5 mm plate multiplies the trough's torsion constant 1,950 times, to 9 per cent of the finished box's. For the shear centre not at all: it rises only from 706 to 538 mm below the bottom flange, 9 per cent of the way to the finished box's 1,127 mm above it.

Tested in The box that is a trough until its deck is cast, at the figure it turns on · the essays about shear centre.