What is refuted here — page 12

Shear and moment interact, so a section carrying both should be checked for the combination.

What decides it: True and almost never binding. The reduction is the web's share of the plastic modulus — 26% on the rolled section here — times one minus √(1 − v²), so the first per cent of moment is not lost until the shear reaches 27% of the web's capacity and half the shear costs 3.5%. The check is worth making at one section on a continuous beam and nowhere else.

Tested in Both at once, and neither matters until it does, at the figure it turns on · the shear moment interaction ladder.

Local buckling reduces the capacity of a thin section, and that is the whole of it.

What decides it: It also moves the centroid. The plates of this lipped channel lose their material in different places, so the section that is left has its centroid 8.0 mm from the one that was drawn, and a load applied along the axis it was designed to arrives eccentrically — 1.42 kNm of bending nobody put in the load case. On a plain channel the shift is the same size and the other way.

Tested in What is left after it ripples, at the figure it turns on · the Effective cross-section ladder.

A taller arch is a stiffer one, because its thrust is smaller.

What decides it: The buckling coefficient rises from 16 at a rise of a twentieth of the span to a maximum of 49.7 at 0.275, and then falls back to 38 at a half. Past the optimum the rib is getting longer faster than the thrust is falling, and a semicircular arch buckles at less than a segmental one of the same section.

Tested in The arch that leans instead of squashing, at the figure it turns on · the arch buckling ladder.

The best height for a single outrigger is about half way up.

What decides it: Only for a rigid arm and only if the question is top drift. With a rigid arm the drift optimum is at 0.549 of the height; at a realistic stiffness it climbs to 0.744, and at a soft one to 0.97. Ask instead for the smallest base moment and the answer moves down to 0.49. There is no single number, and which one is quoted depends on what was being minimised.

Tested in The arm that makes the columns work, at the figure it turns on · the outrigger ladder.

Whether a member is a two-force member is a matter of how it is connected.

What decides it: It is a matter of where the forces are applied. Put a transverse load anywhere between the pins and the end forces tilt off the chord immediately — at 10 kN/m on this member they leave it at 14 degrees — and no detailing of the pins recovers the theorem.

Tested in The member with only one direction, at the figure it turns on · the two force member ladder.

Differential settlement is a soil problem.

What decides it: It is a problem about the ratio of two stiffnesses. The same soil under the same loads gives 66.5 mm of tilt across a limp frame and 0.04 mm across a stiff one — and the stiff one is carrying 1,665 kNm of bending against the limp one's 237. The soil supplied the provocation; the split between movement and force is the structure's.

Tested in The settlement that matters is the difference, at the figure it turns on · the differential settlement ladder.

Diaphragms are put in a box girder at some fraction of the span, by convention.

What decides it: The distortion obeys a beam-on-elastic-foundation equation, so it has a decay length that belongs to the cross-section rather than to the span — 17.5 m for this box, whether the span is thirty metres or ninety. Diaphragms spaced further apart than that do not help each other and the curve of stress against spacing is flat there; inside it the same curve falls steeply. A fraction of the span is a rule that happens to work at one span.

Tested in The section that will not keep its shape, at the figure it turns on · the box distortion ladder.

A corrugated web is a way of getting a slender web to work without stiffeners, and otherwise behaves as a plate girder.

What decides it: It behaves as a plate girder in shear and as something else entirely in bending. Solving one corrugation period as a frame gives an effective modulus along the girder of 222 N/mm² against the steel's 210,000 — a thousandth — so the web carries a thousandth of the bending stress and the section has 8.7 per cent less second moment than the flat-webbed girder it replaces. The stiffeners are saved and the stiffness is spent.

Tested in The web that carries no bending, at the figure it turns on · the corrugated web ladder.

Shear lag is worst where the moment is largest, so the base is the place to check.

What decides it: The governing equation is driven by M′ rather than by M — by the shear — so a tube with no shear anywhere would have no lag whatever its proportions. The concentration is largest low down because the shear has accumulated there, and it falls to exactly one at the top where the moment is zero. Both statements point at the base and only one of them is the reason.

Tested in The corner columns take more than their share, at the figure it turns on · the framed tube ladder.

A guy goes slack under wind, and then the mast is held by one guy instead of two.

What decides it: It does not go slack, it goes soft, and the two are different in a way that matters. Solving each guy's tension properly rather than stepping it, the leeward guy on the lowest level keeps 37 per cent of its partner's tension at design wind — and supplies 40 per cent of the pair's stiffness at ten per cent pretension and eight per cent at three. A cable losing tension loses stiffness as the cube of it.

Tested in Held by something that goes soft, at the figure it turns on · the guyed mast ladder.

More pretension in the guys makes a stiffer mast.

What decides it: Up to a point, and the point arrives early. Between 2 and 11 per cent of breaking load the top deflection falls from 195 mm to 106; between 11 and 30 it falls from 106 to 89 and then rises again. Meanwhile the vertical components add up: at 30 per cent the guys are pushing 2,160 kN down a mast whose Euler load between guy levels is 2,467.

Tested in Held by something that goes soft, at the figure it turns on · the guyed mast ladder.

Saint-Venant's principle says local details do not matter.

What decides it: It says they stop mattering at a distance of the order of the loaded dimension, and it has a number in it. A self-equilibrating load of wavelength λ leaves (1 + 2π)e^(−2π) of itself at one wavelength — 1.36 per cent — and 0.005 per cent at two. What it does not say is that the details do not matter *where they are applied*, which is the region every bearing, anchorage and connection on this site lives in.

Tested in How far a wrong load reaches, at the figure it turns on · the Saint-Venant's principle ladder.

A cold-formed section is checked for local buckling and for column buckling, which between them cover the ways it can go.

What decides it: They cover the ends of the signature curve and miss its middle. The section here has minima at 200 mm and at 1,500 mm and a third at 689, where the flange and its lip rotate as a rigid pair about the web junction — a mode in which the fold lines move, which is exactly what an effective-width calculation assumes they cannot do.

Tested in The mode between the two that get checked, at the figure it turns on · the distortional buckling ladder.

Creep makes a structure deflect more, which is a serviceability problem.

What decides it: For a beam that is the whole of it. For a compression member the deflection is also the lever arm of the axial load, so the demand grows with the deflection it is causing — and the arithmetic is a division by (1 − N/N_cr) with a denominator that is closing. It stops being a serviceability problem at the load where that denominator reaches zero.

Tested in The column that fails years later, at the figure it turns on · the creep buckling ladder.

Stiffening a beam where the moment is largest is the efficient place to add material.

What decides it: It is the efficient place for strength and only coincidentally for stiffness. The deflection density is M·m/EI, a product of two diagrams, and it peaks where the product does — which for a mid-span deflection under a uniform load is indeed mid-span, and for a deflection asked at the quarter point is not. Stiffening the busy half of this beam is worth 5.2 times stiffening the quiet half, and the busy half is defined by the product rather than by the real moment.

Tested in Where a deflection comes from, at the figure it turns on · the deflection distribution ladder.

Squeezing a material harder makes it stronger.

What decides it: It does nothing at all to a metal. Von Mises's criterion contains only differences of principal stresses, so an equal pressure in three directions cancels out of it exactly and the yield surface is a cylinder along the hydrostatic axis. It does a great deal to concrete, soil and rock, whose surfaces are cones — which is why confinement is a design tool for one of them and not for the other.

Tested in The shear strength nobody measured, at the figure it turns on · the yield criterion ladder.

A lower-bound calculation is a conservative approximation to the real answer.

What decides it: Every lower bound is safe, and the best of them is not an approximation at all. Sweeping the one redundant of this frame and taking the largest load factor whose moment field stays inside the plastic moment everywhere returns 0.71429 — which meets the lowest mechanism exactly, so the collapse load is known rather than bracketed.

Tested in Two ways of being wrong, at the figure it turns on · the bound theorems ladder.

A development length is the length over which the bond stress reaches its design value.

What decides it: It is the length over which a *uniform* bond stress would do the job, and a uniform bond stress is what the interface looks like only after it has yielded along its whole length. Elastically the bond is crowded against the loaded end and dies away over one decay length, which for a 20 mm bar is about 470 mm — so at the code's own 40 diameters the bond is 55 per cent used, not 100.

Tested in The force that arrives along a length, at the figure it turns on · the bond ladder.

A haunch at the support of a beam adds depth where the moment is largest, so it helps.

What decides it: It helps twice over if the depth grows in the same direction as the moment, because the inclined chords then carry part of the shear as well. Put the same haunch at the other end and it hurts twice over: the web is left with more shear than was applied, and by exactly the reciprocal factor. A three-to-one haunch is worth a third of the shear one way round and three times it the other.

Tested in The shear the chords take, at the figure it turns on · the inclined chord ladder.

The reserve past first yield is a margin the designer gets for nothing.

What decides it: It is real and it is bought with curvature. A rectangle reaches 96.3 per cent of its plastic moment at three times the yield curvature and 99.5 per cent at ten, so the last of the reserve costs a ductility demand that a stocky compact section can supply and a slender one cannot. It is not a margin, it is a trade.

Tested in What is left after the first fibre yields, at the figure it turns on · the shape factor ladder.

An open section in torsion fails by shear, because its shear stresses are so much higher.

What decides it: Its stress penalty is 3(r/t) and its stiffness penalty 3(r/t)², so at r/t = 15 the stresses are 45 times higher and the twist 675 times larger. The serviceability limit therefore arrives long before the strength one, and an open section in torsion is nearly always ruled out by twisting too far rather than by shearing through.

Tested in The slit that costs a factor of six hundred, at the figure it turns on · the torsional constant ladder.

The stays carry the load, so the deck can be light.

What decides it: They carry the vertical part. The horizontal part goes into the deck and accumulates towards the tower, which for the fan drawn here reaches 1.55 times the entire load being lifted. A stayed deck is a strut before it is a beam, and the flatter the stays the more of one.

Tested in The cable that is a spring, at the figure it turns on · the Cable-stayed ladder.

The instantaneous centre is a convenience — the same answer comes out of writing the displacements directly.

What decides it: It is the same answer and it is not the same calculation. The centre replaces a set of trigonometric displacement relations with one line intersection and two ratios of lengths, and it makes the answer's dependence on the geometry visible: flatten the roof and the centre descends, make the two lines parallel and it goes to infinity, which is the statement that the body translates instead of turning.

Tested in The point the mechanism turns about, at the figure it turns on · the instantaneous centre ladder.

A connection's capacity is the lowest of a set of checks on its parts.

What decides it: Here it is the lowest of a set of checks on its MECHANISMS, which is a different thing. Modes c, d and e are not failures of the dowel or of the timber but of the two together in a particular shape, and each has its own expression combining both. The lowest is the answer for the same reason the lowest collapse mechanism is the answer for a frame.

Tested in The smallest of six failures, at the figure it turns on · the dowel yield ladder.

Thicker timber gives a stronger joint.

What decides it: Up to about six and a half diameters. Past that the two-hinge mode governs, and its capacity is 1.15√(2M_y f_h d) with no member thickness in it at all — 9.61 kN for the dowel here, whatever the timber — so the extra timber buys exactly nothing. That is why timber connection tables run in diameters and then stop.

Tested in The smallest of six failures, at the figure it turns on · the dowel yield ladder.

A thin pipe is a bit weaker than a thick one against external pressure.

What decides it: The relation is a cube. Halving the wall divides the critical pressure by eight, so a pipe ten per cent thin has lost a quarter of its resistance — and nothing about the geometry can be moved to compensate, because there is nowhere further out to put the material.

Tested in The pressure that needs no direction, at the figure it turns on · the ring buckling ladder.

A material's yield stress is a property of the material.

What decides it: It is a property of the material and the rate. Cowper and Symonds' fit for mild steel has the yield stress doubling at 40.4 per second, so the constant is not a fitting parameter with no meaning — it is the rate at which the material is exactly twice as strong. What is genuinely rate-independent is the modulus, which is a lattice property.

Tested in The steel that is stronger in a millisecond, at the figure it turns on · the strain rate ladder.

Rate enhancement is a bonus, so ignoring it is conservative.

What decides it: For strength it is. For behaviour it is not: the ultimate strength rises about a third as much as the yield, so the ultimate-to-yield ratio closes up and the material has less hardening, less warning and a shorter plateau than it started with. A grade 355 steel starts with less margin than a grade 275 and ends with almost none — 1.38 falling to 1.08 against 1.56 falling to 1.23 — so the higher grade loses more of what it had. A capacity-design argument that assumes a member yields before its connection does is a rate-sensitive argument in both directions.

Tested in The steel that is stronger in a millisecond, at the figure it turns on · the strain rate ladder.

Two shear walls either side of an opening share the load in proportion to their stiffnesses.

What decides it: They do, if the beams over the opening are released. Connect them and the pair stops being two structures: the beams force the walls to bend together, which they can only do by one going down and the other coming up, and 63% of the base overturning is then carried by that axial couple rather than by either wall's bending. Sharing a load in proportion to stiffness is what independent members do.

Tested in Two walls that agreed to be one, at the figure it turns on · the wall coupling ladder.

The rectangular stress block is an approximation, so it gives an approximate answer.

What decides it: It is an approximation to the SHAPE and an identity for the answer. The rectangle is constructed to have the same resultant and the same centroid as the curve, and a bending calculation asks the distribution nothing else — so the moment it gives is the curve's moment to machine precision, not to a few per cent. What is approximate is the rounding of 0.832 and 0.973 to the printed 0.8 and 1.0, and that costs 0.69%.

Tested in Deliberately the wrong shape, at the figure it turns on · the stress block ladder.

More strips always means a better answer, so use as many as the machine allows.

What decides it: The error falls but not monotonically. What it actually depends on is where the neutral axis falls relative to a strip boundary, so it can be worse at sixteen strips than at eight. Eight strips give 0.088% here and two thousand give nothing worth having; the useful reading of the convergence plot is not the trend but the noise around it.

Tested in The section calculation with no formula in it, at the figure it turns on · the fibre model ladder.

Rigid joints at the crossings solve it, since they can carry moment.

What decides it: They supply 0.35% of a continuous sheet's shear stiffness. The mechanism is member bending over a cell, which smears to 12EI/s³ — and on a 30 m span under asymmetric load that racks 1,205 mm against a span/250 limit of 120. Rigid nodes turn a mechanism into a structure and do not turn it into a shell.

Tested in A shell only if the grid takes shear, at the figure it turns on · the gridshell ladder.

Strength governs a lifting check, since the beam is being carried by two points.

What decides it: The bending strength check is real and it is not the one that governs. Nothing in the roll equation is a stress: it is a restoring moment W·y_r·θ against an overturning moment W·(e_i + z̄θ), and W cancels out of the comparison entirely. What decides it is a stiffness, a geometry and a manufacturing tolerance.

Tested in Hung from above and still unstable, at the figure it turns on · the lift stability ladder.

A stronger mortar or a stronger brick fixes a slender wall.

What decides it: It raises the squash load and multiplies the same reduction factor, so it never changes what is wrong. The reduction here is 0.438 and it is a function of e/t and h/t only: two geometries and no material. Doubling the strength doubles a number that has already been cut by more than half for reasons the strength has no bearing on.

Tested in It does not buckle, it runs out of width, at the figure it turns on · the wall slenderness ladder.

The wind load on a building is the pressure on the face the wind is blowing at.

What decides it: That face supplies 518 kN of an 842 kN base shear on this building. The other 324 kN — 38.5% — is a suction on the leeward face, which pulls the building downwind exactly as the windward pressure pushes it. A free body of the whole building contains both, and a drawing that shows arrows on one face has left out well over a third of the load.

Tested in Most of it is suction, at the figure it turns on · the wind pressure ladder.

The force method and the stiffness method are alternative formulations of equal standing.

What decides it: They are equally exact and they are not equally automatable. The stiffness method's unknowns are chosen by the geometry — one set per node, always the same set — while the force method's have to be chosen by a person, and a bad choice on six spans gives a matrix that is 100% full where a good one is 52%. What ended the force method was not accuracy but the need for judgement.

Tested in Choose what to take away, at the figure it turns on · the force method ladder.

A two-way slab is two beam strips sharing a load in proportion to their stiffnesses.

What decides it: Two strips can only bend, and 31% of the load on a square panel is carried by twisting moments — 54% of it at the centre. The strip reading gets the share between directions right and has no room at all for the third mechanism, which is why it predicts 4.05 mm of deflection where the plate gives 2.53.

Tested in A third of the load crosses sideways, at the figure it turns on · the plate torsion ladder.

A higher-grade concrete is the way to build a durable structure.

What decides it: Tensile strength enters the cracking pressure linearly and once. Cover enters twice — the pressure the cover can take is proportional to it, and the time for the front to reach the bar is proportional to its square. Going from 35 mm to 70 mm quadruples the initiation time from 9.1 years to 36.2; a comparable spend on strength buys a fraction of that.

Tested in The load that comes from inside, at the figure it turns on · the corrosion ladder.

Once the Whitmore stress is satisfactory the plate is adequate.

What decides it: On this plate the Whitmore section yields at 1,564 kN and buckles at 721 — the check the rule was written for gives an answer more than twice the one that governs. Two other limit states sit between them. The stress check is the one that is always made and it is fourth of five in severity.

Tested in The width nobody drew, at the figure it turns on · the gusset ladder.

Soil-structure interaction adds damping, because the foundation radiates energy away.

What decides it: For a slender building it removes damping. The structure's own is divided by the cube of the period lengthening — 5% becomes 2.2% at a ratio of 1.31 — and a slender building's foundation returns only 0.28%, because the rocking mode radiates almost nothing at these frequencies. A squat building on a big footing gains 7.9%; a tall one on a small one loses more than half of what it had.

Tested in The ground is a spring, at the figure it turns on · the Soil-structure ladder.

A snow load is the ground snow load multiplied by a coefficient for the roof's shape.

What decides it: That gives the balanced layer, which on this roof is 0.48 kN/m². The wedge standing against a one-metre parapet at the downwind end reaches 2.60 kN/m² — 5.4 times as much — and it is made of snow that came off the same roof. The multiplication describes the average and the member is designed on the peak.

Tested in The load that arrives where the wind stops, at the figure it turns on · the snow drift ladder.

Getting the frame plumb during erection removes the problem.

What decides it: An erection tolerance is what the lean is measured against, not what it is reduced to. And a perfectly plumb frame still contains bowed members: a member wandering one section depth from the line between its ends carries 6.00 times as much bending stress as axial, which is the same substitution one scale down.

Tested in The load that is really a lean, at the figure it turns on · the notional load ladder.

A structure that is not strong enough can be made stronger by making it bigger.

What decides it: Only while the added material adds more capacity than weight. On a member of fixed depth the two grow at different rates and the share of capacity consumed by self weight is exactly (L/L*)², where L* is a limiting span; at L* no amount of area solves the equation at all. A dome under its own weight is the pure case — its stress is γR/(1 + cos φ₀), with no thickness in it, so four times the thickness gives exactly the same stress.

Tested in The weight that has to be known before it can be found, at the figure it turns on · the dead load ladder.

Hanging a beam from a point above its centre of gravity guarantees it hangs stably.

What decides it: True of a rigid body and false of a beam. The 30 m beam here has a vertical asymptote at a hook height of 0.236 m, which is its own lateral sag under self weight applied sideways — below that there is no equilibrium at any tilt whatever, and the rigid-body answer is out by a factor of 1.90.

Tested in The load that moves with the twist, at the figure it turns on · the load height ladder.

A cross-braced bay is safe under reversal because one diagonal is always in tension.

What decides it: It is safe if the tension diagonal is stiff, and a slack one is not a weak spring but barely a spring. A guy at 3% of its breaking load offers 10% of its steel's stiffness, because the sag correction goes as the cube of the tension. The bay drifts until the slack comes out, and the drift is not a small number.

Tested in The tie that spends an afternoon as a strut, at the figure it turns on · the load reversal ladder.

Second-order effects magnify a deflection.

What decides it: They reduce a stiffness, and the deflection is what follows. The distinction matters because a stiffness that has fallen changes everything the stiffness decided — how load divides between parallel systems, which member attracts moment, what the natural frequency is — and a factor applied to a deflection changes none of those.

Tested in The stiffness the load takes away, at the figure it turns on · the geometric stiffness ladder.

The design moment over a support is the moment the analysis reports at the support node.

What decides it: That value belongs to a point support. A reaction R spread uniformly over a bearing of width b has its own moment about the centreline of Rb/8, and the moment at the face of the support is lower by exactly that. On the two-span beam here the hogging moment of 134.8 kNm falls by 9.6 on a 400 mm column and by 14.4 on a 600 mm one.

Tested in The support that is not a point, at the figure it turns on · the support width ladder.

The eccentric moment is shared equally between the column above and the column below.

What decides it: It is shared in proportion to 4EI/L, like any out-of-balance moment at a joint, so a column length half as long takes twice as much of it. The bottom storey of a building, with a longer lower length and often a pinned base, is where the split is furthest from equal.

Tested in The moment the beam left behind, at the figure it turns on · the column eccentricity ladder.

Doubling the reinforcement in a beam doubles its bending capacity.

What decides it: Doubling the steel doubles the tension force and lowers the lever arm, because the compression zone has to grow to balance the larger force. On the section here the couple is 541 kN on a lever arm of 462 mm — 0.856 of the effective depth — and adding steel moves the neutral axis down, so the capacity grows more slowly than the area does and eventually stops growing at all.

Tested in Where the steel is, not how much of it, at the figure it turns on · the lever arm ladder.

A deeper structure is better, so the answer is always the deepest thing that fits.

What decides it: Chord force is a reciprocal in the depth, so the first metre of depth is worth far more than the fifth. Three ways of moving the same 2000 kN column across 14 m weigh 24.1, 2.6 and 72.8 tonnes and settle 60.6, 15.8 and 1.71 mm — the lightest is not the stiffest, and the stiffest is twenty-eight times the weight of the lightest.

Tested in The same span, four ways, at the figure it turns on · the form selection ladder.

A diagonal is an addition to a frame, so a diagrid is a braced tube with more bracing.

What decides it: A diagrid has no vertical columns at all. The same inclined members carry the gravity load and the lateral load, which is what makes it efficient and what makes losing one serious — a pin-jointed panel that loses a diagonal is not a weaker structure, it is a mechanism, and nothing about the strength of the survivors enters the answer.

Tested in The columns that lean, at the figure it turns on · the diagrid ladder.

A long-term deflection calculation that includes creep has covered the time-dependent effects.

What decides it: Creep multiplies what the load did; shrinkage adds something the load never did. On a lightly loaded slab near its cracking moment they are of the same order, and the creep multiplier of 3.76 at one year applies to only one of the two.

Tested in The curvature nobody applied, at the figure it turns on · the shrinkage curvature ladder.

A finer mesh always gives a more accurate answer, so the question is how fine to make it.

What decides it: For a frame it gives the identical answer, because the cubic shape a beam element assumes is the exact deflected shape of a member loaded only at its ends. Dividing a beam into ten elements produces the same displacements as one, at ten times the cost. The mesh only matters where the assumed shape is wrong, which is inside a member carrying distributed load and in every two-dimensional element there is.

Tested in The answer that depends on how it was divided, at the figure it turns on · the discretisation ladder.

Improving a material means raising its strength.

What decides it: At a coefficient of variation of 0.20 the characteristic value is 71% of the mean; at 0.10 it is 84%. Halving the scatter is therefore worth the same as raising the mean by 19% and leaving the scatter alone — and the best specimens of the material have not changed in either move. The whole of the difference is in the tail.

Tested in The strength no specimen had, at the figure it turns on · the characteristic strength ladder.

Ignoring a material's tensile strength is conservative.

What decides it: Conservative for strength and not for stiffness. A cracked reinforced section loses 68% of its second moment, so a deflection computed on the uncracked section is wrong in the unsafe direction; and a foundation analysed with no tension loses contact past the middle third, after which the peak pressure runs away — 770 kPa on a base whose central value is 133.

Tested in The strength thrown away on purpose, at the figure it turns on · the no tension ladder.

A group of four anchors carries four times what one carries.

What decides it: Only if their cones do not overlap, which requires a spacing of about three times the embedment. Closer than that, the anchors share the same concrete and the group's capacity is the projected area of one merged cone rather than four separate ones — so packing anchors together buys steel and no concrete.

Tested in The failure that is in the concrete, at the figure it turns on · the anchor breakout ladder.

A splice designed for the member's force is a splice as strong as the member.

What decides it: Not if the force is delivered to the wrong parts of the section. A flange plate has to carry the flange's share of the moment, an angle connected through one leg loses 13.77% of its net area to shear lag, and a net section through staggered holes leaves 81.33% of the gross. Three separate reductions, none of them a strength check on the member.

Tested in The joint that has to be as good as the member, at the figure it turns on · the splice ladder.

A larger peak pressure is a more severe load.

What decides it: Only at a fixed duration. A 30 kN load applied for 0.020 s to a structure of 0.300 s period produces a peak displacement of 2.74 mm against a static deflection of 6.84 — a factor of 0.40. The same structure under a load applied suddenly and held reaches 1.94. Two loads of the same peak, differing by a factor of five in effect, and what separates them is a ratio of two times.

Tested in The load that is over before it has moved, at the figure it turns on · the blast ladder.

A stronger structure resists a blast better.

What decides it: In the impulsive regime the load has finished before the structure has moved, so what it delivers is a momentum and what resists it is an energy — a capacity times a displacement. Doubling the strength halves the required ductility for the same impulse; doubling the mass halves the velocity it acquires. Neither is what a static check computes.

Tested in The load that is over before it has moved, at the figure it turns on · the blast ladder.

Downdrag is a load, so a pile with 483 kN of drag on it must be designed for 483 kN more than it was.

What decides it: The drag and the applied load are not independent. Raising the head load from 800 kN to 1,600 kN drops the drag from 482.87 kN to 82.87 kN, because the neutral plane climbs from 13.77 m to 5.71 m and sheds every metre of shaft it passes. The worst force in the pile goes from 1,282.87 to 1,682.87 — 800 kN of extra load bought 400 kN of extra force, and the measured gradient over the whole sweep is 0.500.

Tested in The ground that hangs on instead of holding up, at the figure it turns on · the downdrag ladder.