What is refuted here — page 26

A crack-arrest hole is a standard detail: a hole of 20 to 25 mm drilled at the crack tip stops a fatigue crack.

What decides it: The hole has to be sized for the crack, because its radius goes as the square of the stress intensity at the tip, which grows with the crack. At the cope of a stringer reacting 350 kN, 70 per cent of it traffic, a 25 mm hole stops a crack up to about 64 mm deep; a 100 mm crack needs a hole the size a site drill cannot make.

Tested in The hole at the tip of the crack, at the figure it turns on · the essays about coped beam.

A girder that has been checked for lifting can be lifted whenever it is needed.

What decides it: Only if the check used the camber on the day. A pretensioned girder's camber grows by creep in storage, from 60 mm at release to 113 mm at four weeks and 133 mm at three months for the girder drawn, and its factor of safety against roll falls from 1.77 to 1.31 and then 1.12 — the same girder, slings and hook.

Tested in The camber that lowers the hook, at the figure it turns on · the essays about camber.

A filler whose crush strength rises with its crushing rate is soft for the slow contacts and firm for the fast ones, and so does at every depth what a graded filler does only at different depths.

What decides it: It does rank collisions by speed, and it treats a middling 1.94 m/s collision at 32.2 MN against a graded filler's 44.4. But its strength is highest at the first instant of every collision, so stopping the hardest one, 2.85 m/s and 761 kJ, in 24 mm costs a peak of 38.4 MN with half its strength on speed and 63.4 with all of it, against 30.5 for a uniform filler.

Tested in The filler that knows how fast it is hit, at the figure it turns on · the essays about pounding.

A shallow arch fails by snapping through: its strength is the maximum of its symmetric load-deflection path.

What decides it: Only while its rise is below √22 = 4.69 radii of gyration. Above that a sideways path branches off first: at a rise of 6 the arch fails at p = 311 where the symmetric maximum is 375, and at a rise of 8 at 461 against 844. An analysis that keeps the arch symmetric overstates its strength by 17 and 45 per cent.

Tested in The arch that turns aside before it snaps, at the figure it turns on · the essays about Snap-through.

An arch dam of constant radius is the natural and economical form, its thickness simply growing with the water pressure.

What decides it: Only in a canyon as wide at its foot as at its crest. In a V-shaped canyon 200 m wide and 100 m deep, a constant-radius dam is 21.3 m thick at its foot and needs two-thirds more concrete than one kept at 133.6° all the way down, whose rings shrink with the canyon and which is thickest, 5.3 m, half-way down.

Tested in The angle that saves the most concrete, at the figure it turns on · the essays about curved surface pressure.

The higher the preload in the holding-down bolts, the stiffer the base and the larger the moment it can take before its plate lifts.

What decides it: Before any storm, yes: 45 kN·m at 120 kN a bolt, 76 at 200. After four reversals to 170 kN·m the base preloaded to 120 kN keeps all of its 45.5 kN·m, while the one preloaded to 200 kN keeps 37.3, because its bolts started nearer their yield and the storm stretched them further past it.

Tested in The base that lets go and closes again, at the figure it turns on · the essays about base plate.

An I-section develops its plastic moment almost as soon as it yields, so a plastic hinge in a steel I-section needs little rotation.

What decides it: As a beam it does: 98 per cent of its plastic moment at 1.2 times its first-yield curvature. As a column under three-fifths of its squash load it needs 6.4 times the same curvature, more than five times as much, because the compression has yielded its web before the bending begins.

Tested in The hinge a squeezed section has to work for, at the figure it turns on · the essays about Moment-curvature.

A slab panel within a continuous floor can be credited with compressive membrane action, since its ends are restrained by the surrounding construction.

What decides it: Only if the restraint is stiff. A 4 m strip 200 mm thick gains half of its 3.89-fold enhancement with end springs of 0.56 times its own axial stiffness and nine tenths with 5.6 times it. An edge panel held by a 2 m edge band between columns 8 m apart gets springs of a twentieth of that stiffness and peaks at 1.69 times its flexural load.

Tested in The edge that cannot hold the arch, at the figure it turns on · the essays about membrane action.

An elevated tank can be analysed with the ground tank's impulsive and convective masses, each on its own oscillator, and the two responses combined.

What decides it: Only on a stiff tower. The convective mass hangs off the container, not off the ground, and once the tower's period approaches the sloshing period the system's two modes belong to neither: on a tower of 2.5 s the separate answer overstates the coupled base shear by 35%, and near 3.25 s by 48%.

Tested in The tank that sloshes the tower, at the figure it turns on · the essays about sloshing.

For a given amount of flange steel, a girder in bending is strongest with equal flanges.

What decides it: Only by its gross section. With a slender web the effective section is strongest top-heavy: 40 mm of flange on a 1,500 by 8 mm web is best at 22 mm on top and 18 below, 14.24 × 10⁶ mm³, against 13.37 with equal flanges, because the extra steel in compression raises the axis and shrinks the hole the web's buckling cuts.

Tested in The flange a slender web wants heavier, at the figure it turns on · the essays about Effective cross-section.

A network arch's hangers are lightly stressed, because crossing them shares the load among more of them than vertical hangers would.

What decides it: Their largest forces are moderate; their ranges are not. On a 100 m arch with 32 hangers under 60 kN/m of dead load, a 60 kN/m live load running on from either end swings the worst crossed hanger from 49 kN to 727 — a range of 90% of the largest force in any hanger — where the worst vertical hanger swings from 194 to 388, half of its own.

Tested in The hangers that carry the shear twice, at the figure it turns on · the essays about network arch.

Each horizontal ring of an arch dam carries the water at its own depth, so its stress is the ring formula pR/t.

What decides it: The rings share the water with the crown cantilever, in whatever proportion makes the two deflect alike. In a V-shaped canyon the ring 4 m below the crest carries 195% of the water there, 1.48 N/mm² where pR/t says 0.76, and the ring formula's peak of 2.04 N/mm² falls to 1.77 divided.

Tested in The water the valley floor takes, at the figure it turns on · the essays about curved surface pressure.

A building over a settlement trough can be assessed by the deflection ratio of the greenfield trough beneath it.

What decides it: Only if the building is soft against the ground. A building 30 m long, centred on a trough 30 mm deep, takes 95% of the ground's deflection ratio at a relative stiffness EI/(kₛ·B⁴) of 10⁻⁴, 66% at 10⁻³ and 17% at 10⁻². The greenfield ratio is an upper bound that a stiff building is nowhere near.

Tested in The building the trough cannot bend, at the figure it turns on · the essays about differential settlement.

A stiffer building is safer over a settlement trough, because it deflects less.

What decides it: It deflects less because it carries the trough's curvature as bending moment instead. Its largest moment rises from 53 kN·m per metre of width at 10⁻⁴ to 967 at 10⁻² and levels at 1,159, the moment a rigid building needs to hold the ground's shape off itself. Its damage criterion moves from strain in its finishes to strength in its structure.

Tested in The building the trough cannot bend, at the figure it turns on · the essays about differential settlement.

A damper's effect can be estimated from its coefficient alone, since the brace that holds it only has to be strong enough to carry its force.

What decides it: The brace's stiffness sets the ceiling: the most damping the pair can add is (√(1+κ) − 1)/2, so a brace a quarter as stiff as the structure limits it to 5.9% whatever the damper, and 20% of added damping needs a brace 0.96 times as stiff as the structure.

Tested in The damper is only as good as its brace, at the figure it turns on · the essays about damping.

An opening beside a column takes more from the outer punching perimeter than from the control perimeter.

What decides it: In length, yes: a 300 × 300 mm opening a depth from the face removes 458 mm of the control perimeter and 1,093 mm of the outer one. As a share it does not: 0.10 of the control perimeter and 0.11 of the outer, both close to the shadow's 38.9 degrees over a full turn.

Tested in A hole takes a tenth of every perimeter, at the figure it turns on · the essays about punching shear.

A flexible retaining stem relieves the compaction pressure on it by moving, so the more flexible the stem the less the residual.

What decides it: Free at the top, the 300 mm stem leans 2.6 mm and keeps 87% of a stiff stem's base moment. Propped first, it bows 0.15 mm and keeps 99% of the base moment and of the prop force; even a stem of a sixty-seventh of its stiffness, bowing 6.5 mm, keeps 64% of the moment and 72% of the force.

Tested in The prop that holds what the roller left, at the figure it turns on · the essays about lateral pressure.

Heave is downdrag with the sign changed: the pile carries the same force in tension, at the same neutral plane.

What decides it: The plane is nearly where it was: 17.3 m in heave against 17.2 m in settlement, for a 24 m pile carrying 200 kN with 100 mm of ground movement. The force is not: 520 kN of tension against 910 kN of compression, because the head load adds to downdrag and subtracts from uplift, and the toe that carried 324 kN in settlement lifts and carries nothing.

Tested in The pile the ground pulls apart, at the figure it turns on · the essays about downdrag.

A shrink-fitted compound tube, which prestresses its bore without ever yielding the steel, carries more pressure elastically than an autofrettaged tube of the same wall.

What decides it: Not with two layers: on a wall 2.5 times its bore, two layers carry 1.43 times the plain tube's first-yield pressure where the best autofrettage carries 2.00, or 1.70 in a steel whose reverse yield is 0.7 of its forward one. Four layers carry 1.75, which beats that steel's overstrain; nothing reaches past 2.

Tested in The ceiling the bore sets, at the figure it turns on · the essays about unloading.

The differential shortening an outrigger restrains comes from the columns working at a higher stress than the core, so columns no busier than the core load it with nothing.

What decides it: With the columns at the core's own 6 N/mm² the arm connected at topping out still ends with 1.22 MN, because the 600 mm columns creep and dry more slowly than 300 mm walls and more of their shortening arrives after the connection. With columns as thin as the walls and as stressed, there is none.

Tested in The arm connected late, at the figure it turns on · the essays about outrigger.

A cover plate needs to run between one and two plate widths beyond the section where it is needed before it can be counted.

What decides it: For a plate carrying only axial force, the shear lag between its two welded edges does give nine tenths of its share at about 1.2 widths, which sits between the two terminal lengths. A doubler on a coped web carries its share mostly as bending and is already welded along the whole cope behind the cut: welded on its edges it reaches nine tenths at about 160 mm, four tenths of its 392 mm depth, and with a weld across its end at about 30 mm.

Tested in How far a doubler has to run, at the figure it turns on · the essays about coped beam.

The settlement a building above a tunnel has to tolerate is the trough's deflection ratio along the building's length.

What decides it: Only for a building square to the trough. A 30 × 12 m building at 45° to a trough 30 mm deep, with its inflection 15 m from the tunnel's axis, sits on ground whose sag along it is 6.4 mm and whose warp — one corner off the plane of the other three — is 18 mm. Beyond about 21° of skew the warp is the larger.

Tested in The building the trough twists, at the figure it turns on · the essays about differential settlement.

A building whose floors are tied into its walls is better placed to resist a twisting settlement, because it is stiffer.

What decides it: It is about a thousand times stiffer in torsion than the same walls standing open, and it takes under a fifth of the ground's twist where the open walls take nearly all of it. But it holds the rest off with a torque: at 45° its 300 mm walls carry about 48 kPa of shear, half the lower end of masonry's initial shear strength, and every floor-to-wall connection carries a shear flow of 14.5 kN/m. The open walls take the twist by tilting, and strain very little doing it.

Tested in The building the trough twists, at the figure it turns on · the essays about differential settlement.

The longer a branch runs before it is braced, the safer the branch connection.

What decides it: Safer for the branch: held along its length it falls from 70 N/mm² at 0.5 m to 10 at 2 m and 5 at 6 m. Not for the riser, which stays between 63 and 73 N/mm² at every length, because what loads it is the branch's stiffness along its own axis, and a pipe's axial stiffness hardly depends on how long it is.

Tested in The branch that holds the riser to a floor, at the figure it turns on · the essays about floor spectrum.

A thicker base slab makes a basement less sensitive to a rise in the water table, because it is heavier.

What decides it: Less sensitive as a whole, because its weight counts against the uplift. More sensitive in its own bending, because the slab carries the uplift less its own weight, and a metre of rise is a larger share of a smaller difference: 20 per cent a metre for a 0.4 m slab under a 6 m head, 26 for 0.9 m and 90 for 2 m.

Tested in The basement that leaks before it floats, at the figure it turns on · the essays about uplift.

Torsional braces along a girder are best spaced equally, since the bracing requirement depends on their number and not their positions.

What decides it: Under uniform moment, nearly: the best clustering of three braces on a 24 m girder saves 6 per cent of the total stiffness needed to reach 5,627 kN·m. Under a uniform load the best, 3.75 m either side of the middle brace rather than 6, saves 26 per cent; under a central point load, 34.

Tested in Three braces where the moment is, at the figure it turns on · the essays about beam bracing.

Moving braces away from the supports lengthens the end bays and so lowers the moment the girder can reach.

What decides it: Only where the end bays carry the full moment. With every brace rigid, under uniform moment the girder's ceiling falls from 9,704 kN·m as soon as the braces close in. Under a uniform load it rises, from 12,019 equally spaced to 14,320 with the outer braces 5 m from the middle one, because the shortened middle bays are where the moment is and the lengthened end bays carry little of it.

Tested in Three braces where the moment is, at the figure it turns on · the essays about beam bracing.

For a given number of ductile shear studs, how they are spaced along a composite beam does not affect its plastic moment or the slip its studs must give.

What decides it: It does not affect the plastic moment, which depends only on the slab force the studs can deliver. It halves the slip: nineteen studs a half-span on a 12 m beam with half connection must slip 8.8 mm at their ends to reach 95 per cent of the plastic moment when spaced evenly, and 4.4 mm when graded toward the supports.

Tested in The same studs, moved to where the slip is, at the figure it turns on · the essays about composite action.

EN 1994-1-1's minimum degree of shear connection is a property of the span and the steel grade.

What decides it: It is a property of the span, the steel grade and the spacing it was fitted for, which is even. The same 6 mm slip requirement allows 0.69 of full connection at 12 m with even spacing and 0.40 with the studs graded toward the supports; at 20 m, 0.88 and 0.51.

Tested in The same studs, moved to where the slip is, at the figure it turns on · the essays about composite action.

The stress in the steel between two holes in a twisted shaft depends on how far apart they are.

What decides it: It depends on how far apart their islands float. With 2 mm between them, the steel carries 0.04 of the solid shaft's surface stress when the holes lie across the radius and 1.71 when they lie along it, the inner island floating 81 above the outer.

Tested in Two islands in one film, at the figure it turns on · the essays about membrane analogy.

The deck chord of a Vierendeel girder is designed by its share of the girder's shear, like the other chord.

What decides it: Only where its share is large. With equal chords, a load between the posts adds 14 per cent to the deck chord's moment in the middle panels, where the shear is small, and nothing in the end panels. With a deck chord of an eighth of the chord stiffness, it adds 107 per cent in the middle panels and 47 in the end ones: the deck chord's own bending between posts governs everywhere.

Tested in The load that visits every panel, at the figure it turns on · the essays about vierendeel.

A joint that makes precast beams continuous over a pier carries hogging moment, so it needs top reinforcement and nothing more.

What decides it: Under the superimposed and imposed load it does. But a joint cast when the beams are 28 days old is sagged by the beams' creep to 211 kN·m at thirty years, against a sagging cracking moment of 140, and under the load the pier is then hogged by only 48 kN·m where the load alone hogs it by 259. Without bottom reinforcement across the joint, the beams' ends open at the soffit.

Tested in The joint cast over the pier, at the figure it turns on · the essays about end rotation.

A stack of identical pretensioned beams is safe in the yard if each beam is safe on its own bearers.

What decides it: Only if the bearers line up. With two beams stacked on it and their bearers landing 100 mm outside its own, the bottom beam's top fibre reaches −3.24 N/mm² against a limit of −3.0 and a value of −2.98 lined up; 250 mm out, −3.63. Each beam above costs 0.13 N/mm² for every 100 mm out of line, at every section between the bearers.

Tested in The beam at the bottom of the stack, at the figure it turns on · the essays about prestress limits.

A core drilled beside a column should be placed between the rails of shear studs, so that no stud is cut and the slab keeps its punching resistance.

What decides it: Between rails the studs' check is at 0.79 of what remains; on a rail, with that rail lost, 0.86. Both pass, because the studs were rounded up to a stock size. What decides is the outer perimeter, at 1.00 either way one depth from the face and over 1 closer in: the hole pushes the perimeter the slab needs outward and the studs that reach it do not move.

Tested in The core drilled after the slab was built, at the figure it turns on · the essays about punching shear.

A slab that passes its punching check with shear studs has no spare resistance for a hole that was not on the drawing.

What decides it: It has whatever the rounding of its studs left, which is not designed and not small. Laid out exactly as the check asked, the slab on a 10 m bay fails with a 150 mm core one depth out; rounded to 14 mm studs and six whole rings, it passes. The largest core it can take there swings between nothing and 434 mm as the bay changes by a quarter of a metre.

Tested in The core drilled after the slab was built, at the figure it turns on · the essays about punching shear.

A damper's coefficient and exponent, certified on a test rig at the design velocity, define the damping it adds to the building.

What decides it: They define it at one amplitude. Through a brace of the structure's stiffness the same damper behaves as one of size 0.27 at three times the design amplitude, 0.59 at the design amplitude and 36 at a tenth, so the damping it adds runs from 13% through 20.7% to nothing over a factor of thirty in motion.

Tested in The damper sized for the earthquake, at the figure it turns on · the essays about damping.

The linked counterweight's half-payload position is set by the step at pick-up, and a crane that can follow the payload has no reason to keep it.

What decides it: With no hoisting surge and no rebound, the share that balances lifting the payload against losing it is exactly one half — the linked crane's position — so the half was already a hedge between pick-up and release. A surge moves it down, and a rebound moves it further: 0.35 with a hoisting factor of 1.2 and a rebound of 0.5, 0.10 with a rebound of 1.

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

A roof's rain load is fixed by the drainage designer's static and hydraulic heads, and the structural engineer's ponding check only multiplies it.

What decides it: The same 50 mm head on an 18 by 12 m bay gives 168 mm of water at mid-bay with a scupper fixing the level, 75 mm with a drain on the girder line and 50 mm with a drain at the bay's middle. Where the outlet sits changes the members' load by a factor of 3.4 for one head, so the outlet's position belongs to the structure's calculation as much as its height does.

Tested in The roof that drains towards its sag, at the figure it turns on · the essays about serviceability.

A footing's rocking stiffness for a dynamic analysis can be taken from the subgrade modulus that gives its settlement under the column.

What decides it: That modulus describes ground being loaded. Rocking unloads half the footing, and ground that has carried the column unloads more stiffly: on ground that reloads four times as stiffly, the 8 m strip's rocking stiffness is 0.90 GN·m/rad in its first storm and 1.15 from its third, against 0.70 from the loading modulus alone.

Tested in The footing the storms press down, at the figure it turns on · the essays about elastic foundation.

A plastic hinge in steel holds its moment as it rotates, and only local buckling or fracture makes it lose moment.

What decides it: With its compression rising in proportion to its rotation, an I-section's hinge loses 0.02 of its unloaded plastic moment for every first-yield curvature if the load rises to 0.35 of the squash load, 0.04 if to 0.6 and 0.07 if to 0.85, in a steel modelled as perfectly plastic, with no buckling and no fracture.

Tested in The hinge squeezed while it turns, at the figure it turns on · the essays about Moment-curvature.

A brace that stops an arch turning sideways only has to be stiff, since a perfect arch puts no force through it until it buckles.

What decides it: A perfect arch's brace carries nothing until the peak. An arch rising eight radii of gyration and built a tenth of one out of shape sideways puts 12% of its whole load through a brace of exactly the stiffness that would suffice for the perfect arch, and 6% through one twice as stiff; built three-tenths out, 21% and 17%.

Tested in The brace that holds a mode, at the figure it turns on · the essays about Snap-through.

The elbow is always the weak point of a branch connection, because piping codes intensify its stress and make it more flexible than straight pipe.

What decides it: Only while the leg past it is short. With a long-radius elbow the elbow's intensified stress is above the tee's for second legs under about 400 mm, 146 against 82 N/mm² at 100 mm, and below it beyond, 39 against 53 at 1 m; a bend of three diameters, intensified only 1.09 times, stays below the tee at every length drawn.

Tested in The elbow that takes the strut away, at the figure it turns on · the essays about floor spectrum.

Floors let in large tenancies are correlated, so the storey rule's reduction for a tall column is unsafe whenever a building is let to a few large occupiers.

What decides it: For office loading, whose characteristic floor load is set mostly by short intermittent visits that do not coincide between floors, twenty floors let to a single tenant still need only 0.60 of their summed loads against the rule's 0.73, and the rule's load is exceeded in 1.4% of fifty-year lives. The correlation the tenancy creates is real, but it applies only to the sustained part, and for an office that part is small.

Tested in The load that stays and the load that visits, at the figure it turns on · the essays about live load reduction.

Coupling beams should be made deep enough to carry the shear an elastic analysis gives them, after which the walls act as one.

What decides it: The elastic coupling holds only until the first beam reaches its capacity. With beams 0.6 m deep limited to 2 N/mm², the first yields at 1.9 times the storey force and all twenty by 3.4; the degree of coupling then falls from 0.63 to 0.44 at four times the storey force and 0.17 at ten, because the couple is capped at the beams' summed capacity and every further increment is carried by the walls in bending.

Tested in The coupling beam asked for shear, at the figure it turns on · the essays about shear deflection.

A thicker end plate makes the component method's stiffness estimate for an end-plate joint more accurate.

What decides it: Lever arm matters more than thickness. With its bolt 65 mm from its web against the column flange's 30, a 14 mm end plate is 0.85 of its series sum and an 18 mm one 0.86; only at 25 mm, stiff enough that its own bending is a small part of the pair, does it come back to 0.93.

Tested in The flanges that lean on each other, at the figure it turns on · the essays about prying.

The secondary moments in a continuous prestressed beam are those of the finished beam under the full tendon force; how the beam was built does not enter.

What decides it: True only of a beam stressed in one operation once every span exists. Four 16 m spans prestressed with 2,400 kN, cast and stressed one bay at a time: the secondary moment at the first interior support is 164 kN·m against the 350 the finished-beam analysis gives, and the secondary shear in the first span is 10.3 kN against 21.9.

Tested in The beam stressed one bay at a time, at the figure it turns on · the essays about secondary prestress.

A pinned-base portal has no moment at its bases, so it cannot suffer alternating plasticity, and a shakedown check adds nothing to its collapse check.

What decides it: True while gravity leads: under 160 kN of gravity and 60 kN of reversing wind the pinned portal shakes down and collapses at the same factor, 0.73. The alternation has not gone, it has moved to the knees, which on pinned bases sweep from −300 to +150 kNm. Above about 102 kN of wind the knees alternate before the frame collapses, and shakedown falls below collapse.

Tested in The base that sends the wind to the knees, at the figure it turns on · the essays about shakedown.

A cracked deck and an uncracked one work over the same effective width, which is why EN 1994 gives one width for both.

What decides it: True when the bars run equally both ways at about 1.7%, where the cracked deck's modulus ratio is the uncracked plate's. Half as much transverse steel as longitudinal narrows the width over the pier from 0.328 to 0.281 of the overhang; a quarter as much to 0.238. Twice as much widens it to 0.373.

Tested in The deck that cracks over the pier, at the figure it turns on · the essays about effective width.

The traces of a frame's flexibility give a useful lower bound on its critical load factor from the first trace or two.

What decides it: On a six-storey frame whose factor is 14.96 the first trace gives 5.12 and the second 10.82; four traces give 14.07. A frame whose storeys all have the same critical factor is bounded at one sixth of it by the first trace, because the first trace adds every storey's sway as though each were the frame's mode.

Tested in The trace that adds up every storey, at the figure it turns on · the essays about stability energy.

Keeping every hanger of a network arch taut under every load is what decides the hangers.

What decides it: Softened to a tenth of a plain bar's stiffness, none of the 32 hangers goes slack under any stage of the live load, and the worst still swings through 635 kN — 212 N/mm² on a 3,000 mm² bar. A threaded bar needs about 13,800 mm² to bring its 678 kN range to its detail category of 50 N/mm².

Tested in The hanger that cannot be made soft enough, at the figure it turns on · the essays about network arch.

The storey rule's reduction is conservative for any building whose floors are let separately, since separate tenants do not load their floors together.

What decides it: Let floor by floor, twenty floors need 0.26 of their summed loads when visits are independent. When a third of the visits are made by the whole building at once — a fire drill, a building-wide event, the end of a school day — they need the rule's 0.73, and with every visit shared 0.96. Separate tenancies decorrelate the sustained load, not the visits.

Tested in The visits that come to every floor at once, at the figure it turns on · the essays about live load reduction.

A beam splice's web plates carry the web's share of the moment, and the flange covers the flange's.

What decides it: Only if the splice plates happen to divide their stiffness as the beam's flanges and web do. Two 8 mm web plates 480 mm deep carry 14 per cent of the moment across the gap, where the web carried 19, so their edge stress is 158 N/mm² against the 218 the web's share gives, and the flange covers carry 990 kN of flange force against the 955 the flange's share gives.

Tested in The splice that bends as one section, at the figure it turns on · the essays about single lap.

A characteristic strength for an existing structure should be estimated from its cores alone, because the specification describes what was ordered and not what was built.

What decides it: The cores alone do say what was built, but three of them cannot say how scattered it is, and the penalty for that is large: three cores of mean 33 N/mm² and 12 per cent scatter give 21.9. With the specification's population as a prior of three specimens' weight they give 26.5, which cores alone reach only at 21, and the population they come from has 26.9.

Tested in The strength three cores revise, at the figure it turns on · the essays about characteristic strength.

Leaving an arch three-hinged until its creep and shrinkage are nearly over can only reduce its moments, since a three-hinged arch carries the movements without moment.

What decides it: It carries them without restraint moment, but the crown drops while it waits and the axis stops being the funicular of its load. Closed at ten years, the rib's springing moment is −15 kN·m, but the dropped crown has locked enough shape into it that its largest moment is 126 kN·m, more than closing at a year leaves anywhere. Only a camber set for the drop recovers the benefit.

Tested in The arch that waits with its hinges open, at the figure it turns on · the essays about rib shortening.

A tuned liquid damper can be kept in tune with a building whose period drifts either way, since water can always be added or let out.

What decides it: Only within its walls and its deep-water limit. A stiffer building needs deeper water: a 10 m tank whose walls hold 2.2 m cannot be retuned below 4.5 s, and at 3.9 s it detunes to a peak of 25 against 9 had it been deep enough. No depth at all makes a 10 m tank faster than 3.58 s.

Tested in The tank that follows the building, at the figure it turns on · the essays about sloshing.

If phased evacuation reduces a stair column's load below the storey rule's, the rule is conservative for that column and its reduction can be taken with confidence.

What decides it: Only if full evacuations are rarer than about one alarm in two hundred. Phased alone, the half-corridor column on twenty floors needs 0.29 against the rule's 0.73, and no life exceeds the rule; with one alarm in twenty escalating it needs 0.75, and the rule is exceeded in 6.1 per cent of fifty-year lives.

Tested in The stair that empties three floors at a time, at the figure it turns on · the essays about live load reduction.

Crossbeams at every 4 m make a box rigid enough against distortion that its cross-frames can be spaced as widely as the crossbeams' strength allows.

What decides it: Only if the crossbeams are ring frames. Open tee crossbeams, with no web or bottom stiffener, give the box a decay length of 21 m against the ring frames' 6.5; with cross-frames every 20 m the peak warping stress is 21.7 N/mm² with the open tees and 21.8 with nothing at all.

Tested in The stiff frame among soft ones, at the figure it turns on · the essays about box distortion.

A few degrees between the casting temperatures of adjacent spans cannot matter to the piers of a stressed ribbon, which are designed for the far larger unbalance of a crowd on one span.

What decides it: It depends on the sag. At a sag of 2 per cent a 20 °C difference leaves a seventh of a crowd's pier force, 713 kN against 4,953. At a sag of 1 per cent the same difference leaves 82 per cent of a crowd's, and at 0.8 per cent more than a crowd's; at 4 per cent, 1 per cent.

Tested in The span cast in the afternoon, at the figure it turns on · the essays about stressed ribbon.

Setting the largest shear in the group, from any direction, against the largest tension, from any direction, gives a bracket's capacity close enough to design by.

What decides it: It gives a floor, and a costly one. For the six-bolt bracket it is 0.90 of the least capacity in the plate's plane and falls to 0.82 when the load is 300 mm in front of the column, because the worst shear and the worst tension occur in different directions and often at different bolts; under the straight-line interaction it falls to 0.81.

Tested in The worst direction is an eigenvector, at the figure it turns on · the essays about bolt group.

A few millimetres of clearance in a cross-frame's bolt holes cannot matter to a girder's bracing, because the braces still engage well before the girder reaches its buckling moment.

What decides it: They do engage early — at 579 kN·m on the 24 m girder, below its unbraced 947 — but the girder has twisted into them by then, and the braces hold a more crooked girder for the rest of the load. At the target of 5,627 kN·m, 3 mrad of slack raises the twist at midspan from 11.0 to 18.2 mrad and the middle brace's moment from 34.1 to 58.1 kN·m.

Tested in The braces with slack in their bolts, at the figure it turns on · the essays about beam bracing.