What is refuted here — page 8

A shallower lacing angle uses less steel per metre and is otherwise neutral.

What decides it: It is penalised three times. Taking the angle from 45° to 30° lowers the critical load from 3,832 kN to 3,456, raises the design shear at 2,000 kN from 32.4 kN to 45.8, and lengthens the diagonal from 1,131 mm to 1,600 — so a larger force is carried by a member buckling over a longer length.

Tested in The lacing decides the force it has to carry, at the figure it turns on · the essays about Built-up column.

A slip coating reduces downdrag in proportion to how much it reduces the friction.

What decides it: It reduces it faster, because the neutral plane moves as well. Taking the interface factor from 0.3 to 0.1 — a third — takes the drag from 1,131 kN to 177, a sixth, because the plane climbs from 18.86 m to 12.93 and sheds the deepest and hardest-pulling metres first.

Tested in The coating that takes the resistance with it, at the figure it turns on · the essays about downdrag.

The smoother the shaft, the better, since the drag is what is being designed against.

What decides it: Past 0.05 on this pile the calculation has no answer at all: the base takes 600 kN and the whole shaft 477, so 1,200 kN at the head has nowhere to go. The coating removes the resistance along the same length it removes the drag, and the pile fails in bearing before the drag has fully gone.

Tested in The coating that takes the resistance with it, at the figure it turns on · the essays about downdrag.

A bigger pile is a safer pile where downdrag is expected.

What decides it: It drags harder. Reducing the diameter from 750 mm to 400 takes the worst force from 2,331 kN to 1,663 — the perimeter that collects the drag has fallen by 47 per cent while the section carrying it has fallen by 72, so the stress goes up, but the force a connection or a splice must carry goes down.

Tested in The coating that takes the resistance with it, at the figure it turns on · the essays about downdrag.

A trapezoidal hook section is a founding and forging convenience.

What decides it: It is worth 39 per cent at the governing fibre. The same trapezoid at the same area, depth and moment gives 223.6 N/mm² at the inner fibre with its wide face inward and 311.6 with the wide face outward, because the shape moves the neutral axis and the section modulus in the same direction.

Tested in The wide side goes inside, at the figure it turns on · the essays about curved beam.

Making a Vierendeel girder deeper stiffens it, as it would a truss.

What decides it: It softens it. The same 21 m girder at 6,000 mm deep deflects 109.09 mm and at 9,000 mm deflects 139.85 — worse by 28 per cent — because the depth lengthens nothing that resists and the chord bending, which is 98 per cent of the movement, depends on the panel length rather than on the depth.

Tested in The frame is a girder stood on end, at the figure it turns on · the essays about vierendeel.

More panels means more members and more joints, so it is the expensive way to stiffen one.

What decides it: It is the only lever that works well. Going from 4 panels to 10 on the same span takes the deflection from 166.19 mm to 65.86 — a factor of 2.5 — and the panel moment from 196.9 kN·m to 78.8, because both go with the panel length and the deflection goes with its cube.

Tested in The frame is a girder stood on end, at the figure it turns on · the essays about vierendeel.

A frame's lateral stiffness comes from its columns' axial stiffness, as a truss's does.

What decides it: Ninety-eight per cent of it is bending. Doubling the chord's second moment of area alone — the axial areas untouched — takes the deflection from 109.09 mm to 55.72, while triangulating the same members takes it to 6.53. The frame is a bending structure wearing a truss's outline.

Tested in The frame is a girder stood on end, at the figure it turns on · the essays about vierendeel.

The tension field is a property of the web panel.

What decides it: It is a property of the panel and its boundary together. The band is anchored by the flanges above and below and by the stiffeners either side, and at the end panel one of those stiffeners has nothing beyond it — which is why an end panel is designed without tension field action or given a stiffener sized as a beam.

Tested in The tension has to pull on something, at the figure it turns on · the essays about tension field.

Shedding is free, since the spandrel is being relieved.

What decides it: It is bought with a rotation. Getting to a quarter of the torsional stiffness means the spandrel has cracked in torsion along its length, and the joint has rotated by whatever that cracking allows — a serviceability state with a crack width and a visible twist, neither of which appears in the strength calculation that licensed the release.

Tested in The torque that should not be shed, at the figure it turns on · the essays about compatibility torsion.

Whether a torque is compatibility or equilibrium is a property of the torque.

What decides it: It is a property of what else is available. The same spandrel carries a 197 kN·m fixed-end moment it can shed and a canopy's 116 kN·m it cannot — and at a 3.6 m canopy that second number is 311, on a member whose whole compatibility torque was 100.

Tested in The torque that should not be shed, at the figure it turns on · the essays about compatibility torsion.

Adding a diaphragm at midspan roughly halves a box girder's distortional stress.

What decides it: It removes a third of it. The bare 60 m box peaks at 73 N/mm²; one diaphragm at midspan takes it to 49, because at 30 m from each end it is further away than the 23.6 m decay length and neither end can feel it. Two take it to 18 and three to 10.

Tested in One diaphragm is nearly none, at the figure it turns on · the essays about box distortion.

A lighter box is a smaller distortion problem, since there is less load in it.

What decides it: It is a much larger one, and its own arithmetic disguises it. Taking the plates from 20 mm to 12 lengthens the decay from 23.6 m to 28.6 — which reads as needing diaphragms further apart — while raising the distortional stress at one decay length's spacing from 20 per cent of the bending stress to 55.

Tested in One diaphragm is nearly none, at the figure it turns on · the essays about box distortion.

Diaphragm spacing is a detailing rule, so a span-over-five sort of number is adequate.

What decides it: The quantity it should be measured against varies by a factor of 1.7 across ordinary boxes. The same span gives a decay length of 16.7 m on a 2.5 m wide box, 23.6 m on a 4 m one, and 28.6 m on the same 4 m box in thinner plate — and the stress at one decay length's spacing runs from 9 per cent to 55.

Tested in One diaphragm is nearly none, at the figure it turns on · the essays about box distortion.

Members that carry no force are redundant and can be taken out.

What decides it: They are the robustness. Removing member 12 from a Pratt truss with its counters leaves a structure at 1.97 times the worst survivor's force, with two previously idle members now working; removing the same member from the same truss without them leaves a mechanism. The counters carried nothing until they were needed.

Tested in A determinate truss has no robustness at all, at the figure it turns on · the essays about robustness.

A deeper truss is a more robust one, since its members are less heavily loaded.

What decides it: Its worst redistribution is larger. The same 8-panel Pratt truss at a depth of 1.6 asks a survivor for 5.51 times what it carried before; at 0.6 it asks for 2.01. A deep truss's members carry small forces, and a small force multiplied is still a large multiple.

Tested in A determinate truss has no robustness at all, at the figure it turns on · the essays about robustness.

Rocking response is a resonance, so a longer pulse at the same acceleration is not worse.

What decides it: It is much worse, and there is no resonance to speak of. Doubling the pulse from 0.8 s to 1.6 at the same 1.0 g overturns both blocks — the small one and the one three times its size — where the shorter pulse left the large one at 46 per cent. The block has no period to be tuned to.

Tested in The only damping is the landing, at the figure it turns on · the essays about rocking.

A torsional brace and a lateral brace are two ways of doing the same job, so a rule of thumb written for one can be scaled for the other.

What decides it: They scale differently and the difference is a whole power. The lateral brace's ideal stiffness is very nearly proportional to the moment it is holding; the torsional brace's is exactly quadratic in it, and steeper than quadratic over the useful range because the curve has its root at the unbraced capacity. On the 8 m beam drawn here, doubling the moment from 201 to 403 kNm multiplies the rotational demand by 7.1.

Tested in Twice the moment, four times the brace, at the figure it turns on · the essays about beam bracing.

A stiffener at a brace point is a detailing item.

What decides it: It is the bracing member. On the same girder a pair of 12 × 150 stiffeners takes the delivered stiffness from 87 to 2,036 kNm/rad and the capacity to 5,095 kNm, which is still 9 per cent short of the plastic moment; a pair of 20 × 150 reaches 3,335 and 6,172 kNm, which clears it. The size of the stiffener is decided by a bracing calculation and by nothing else on the drawing.

Tested in Twice the moment, four times the brace, at the figure it turns on · the essays about beam bracing.

The stiffener is a slender plate, so its buckling length is what decides it.

What decides it: Its slenderness is 0.25 and the column curve returns 0.98, so 98 per cent of the answer is the squash load of the area. Taking the buckling length as the full depth of the web rather than three quarters of it — a factor of 1.8 on the critical load — moves the resistance from 1,373 kN to 1,314, which is four per cent.

Tested in A column nine hundred millimetres long, at the figure it turns on · the essays about patch loading.

A chord's buckling check can use the mean axial force, since the member buckles over its whole length anyway.

What decides it: It does not buckle over its whole length once the force varies, and the mean is the wrong number twice over. On the 40 m chord drawn, the constant-force answer is 1,881 kN; put the mean force of a parabola into it and it permits a peak of 2,822 kN against a true 2,113 — 34 per cent unconservative, in a check that looked comfortable.

Tested in The buckle that will not spread out, at the figure it turns on · the essays about continuous restraint.

A stiffer U-frame moves the problem further from the middle of the span.

What decides it: It concentrates it. Raising the restraint from 0.35 to 1.4 N/mm per mm takes the critical peak force from 2,113 to 4,113 kN, and takes the buckle from 56 per cent of the length to 48 — the half-wave shortens as the fourth root of the stiffness, so a better-restrained chord buckles harder into a smaller piece of itself.

Tested in The buckle that will not spread out, at the figure it turns on · the essays about continuous restraint.

A steel loses strength after the ultimate load, which is what the falling branch of the curve shows.

What decides it: It hardens the whole way. At the ultimate load the engineering curve reads 431 MPa and the true stress is 538, and at twice the necking strain the true stress is higher again. The fall is the ratio between the two, which is exactly e^ε and nothing else — 1.25 at the ultimate load for this steel.

Tested in The curve was rising the whole time, at the figure it turns on · the essays about gauge length.

A stronger steel is a safer choice wherever fatigue governs, because its fatigue limit is higher.

What decides it: Its plain fatigue limit is higher and it keeps less of it. The same 1 mm notch returns a factor of 2.40 in a 430 MPa steel and 2.90 in a 1,400 MPa one, because the material length the peak is averaged over falls from 0.43 mm to 0.05 as the microstructure gets finer. The notched fatigue strengths of the two converge while their smooth ones diverge.

Tested in The notch a crack does not feel in full, at the figure it turns on · the essays about stress concentration.

A one-hour fire rating is a property of the steel and the protection, so the same protection gives the same rating.

What decides it: It is proportional to the section factor. The same board at 0.2 W/mK gives sixty minutes on a 76 per metre column at 11 mm and needs 21 mm on a 160 per metre beam and 35 on a 323 per metre one — twice the material for the lighter section, and the ratio is the ratio of the two section factors.

Tested in The temperature is a shape, at the figure it turns on · the essays about fire.

The reserve between first yield and collapse is a property of the section, so one factor covers the detail.

What decides it: It varies along the span from 2.6 at the support to exactly 1.0 at mid-span, because it is bought entirely by the local Vierendeel bending. Where the shear is nothing the tee is in pure axial force, and a member in pure tension or compression has no shape factor whatever.

Tested in Four corners and a mechanism, at the figure it turns on · the essays about web opening.

A tee carrying 20 per cent of its squash load has lost about 20 per cent of its moment capacity.

What decides it: It has lost 13 per cent. The interaction of a tee is much flatter than proportional near zero axial force, because the force is absorbed by moving the plastic neutral axis inside a flange that sits close to the plastic centroid — 301 kN out of 1,519 takes the plastic moment from 32.2 kNm to 28.1.

Tested in Four corners and a mechanism, at the figure it turns on · the essays about web opening.

A box girder checked for bending and for torsion, taking the worse of the two, has been checked.

What decides it: Neither check is about a wall. On the box drawn, bending puts 107 N/mm of shear flow into each web and torsion puts 50 round the cell, so one web carries 157 and the other 57 — and the equivalent stresses at the quarter point are 116 and 11 N/mm². Both checks would report numbers between those two.

Tested in Three actions on one web, at the figure it turns on · the essays about multicell torsion.

The eaves is the critical section of a portal rafter, because that is where the moment is largest.

What decides it: The depth is largest there too, and it is largest by more. On the rafter drawn the eaves is at 0.42 of capacity and the haunch tip at 0.46, with a moment of 226 kNm against the eaves' 500 — the section has just become the bare rafter and the moment has fallen by less than the modulus has.

Tested in The section that governs is inside the haunch, at the figure it turns on · the essays about tapered member.

A bigger damper gives more damping.

What decides it: Past the optimum it gives less, and the optimum is a ceiling rather than a plateau. On the 200 m stay drawn, a damper 4 m from the anchorage reaches 1.00 per cent of critical at its best size and 0.47 per cent at four times that size — a damper stiff enough to be a support supplies no damping at all, because nothing moves at a support.

Tested in The damper that is too near the end, at the figure it turns on · the essays about cable dynamics.

The damping available depends on the cable — its tension, its mass, its length.

What decides it: It depends on where the damper is, as a fraction of the length, and on nothing else. The exact complex root of the taut string with a damper in it returns x/2L to within a few per cent across the whole range, with the tension and the mass cancelling out of the answer entirely.

Tested in The damper that is too near the end, at the figure it turns on · the essays about cable dynamics.

With damping that large, a machine foundation is not a vibration problem.

What decides it: The mode that governs is the one that barely radiates. Rocking has two halves of the footing moving in opposite directions, so their wave fields cancel in the far field: 13 per cent here, a resonant peak of 4.1 against the vertical mode's absence of any peak at all, and the only mode of the three that behaves like an ordinary lightly damped oscillator.

Tested in The damping that is radiated, at the figure it turns on · the essays about vibration isolation.

Two buildings that pound will do so at the top of the shorter one, where the relative displacement is largest.

What decides it: They touch at the lowest level where the closure exceeds the gap and stay in contact above it. On the pair drawn — 24 m and 15 m, 50 mm apart — the first contact is at 7.6 m, less than a third of the taller building's height and half way up the shorter one.

Tested in The floor that arrives at a column, at the figure it turns on · the essays about pounding.

Deflection theory is a refinement of elastic theory, so the difference between them is a correction.

What decides it: At 500 m it is 30 per cent and at 1,500 it is a factor of fourteen. The elastic-theory deck moment is 80.1 MN·m against the deflection theory's 56.3 on the span drawn, and the ratio falls from 1.00 at 100 m to 0.07 at 1,500 — the two theories are not close on any span worth building a suspension bridge for.

Tested in The tension that was left out, at the figure it turns on · the essays about stiffening girder.

The difference between the theories is in how much extra tension the cable picks up.

What decides it: The two compute nearly the same extra tension — 6.20 MN against 6.11 on the span drawn, a difference of one and a half per cent. What separates them is the H·v″ term in the deck's own equilibrium, which is a stiffness rather than a force and appears in no cable calculation at all.

Tested in The tension that was left out, at the figure it turns on · the essays about stiffening girder.

Adding a second outrigger at the optimum height for a single one doubles what the system removes.

What decides it: Both arms move when a second is added — from 59 per cent of the height to 35 and 71 — and what the pair removes is 91.6 per cent against a single arm's 82.3. The second is worth 9.3 points, which is half of what was left rather than a second helping of what the first took.

Tested in What the second arm is worth, at the figure it turns on · the essays about outrigger.

A larger temperature drop gives wider cracks, whatever is restraining the member.

What decides it: Under end restraint it gives more cracks of the same width. The crack opens only until the steel can transfer the cracking force back into the concrete, and that force is a property of the section: 0.32 mm at every strain across the sweep, with the count rising from a handful to nineteen as the imposed movement grows.

Tested in The bay that is cast last, at the figure it turns on · the essays about restraint cracking.

Below the minimum reinforcement the cracks are somewhat wider than the calculation says.

What decides it: They are one crack, an order of magnitude wider. If the steel yields at the first crack no force is transferred back, no second crack can form, and the whole 6.1 mm of movement in this 20 m bay goes into it. The minimum is a threshold between two mechanisms rather than a point on a curve.

Tested in The bay that is cast last, at the figure it turns on · the essays about restraint cracking.

A wrong load vector shows up as a violation of equilibrium somewhere in the model.

What decides it: It does not, and that is what makes it dangerous. Both sets have the same resultant, so the support reactions and the fixed-end moment come out identical and correct — 180 kN·m on the cantilever drawn, from either. Only the displacements are wrong, and nothing in the output flags them.

Tested in Equivalent in work, not in resultant, at the figure it turns on · the essays about force couple.

If the bearing pressure is too high, the plate can be made larger.

What decides it: Past the effective area a larger plate delivers nothing extra, because the additional material is beyond the reach of the cantilever that would have to carry it. What works is a thicker plate: c is proportional to t, so 20 mm to 40 doubles the reach and takes the capacity from 1,564 kN to 3,153.

Tested in The plate that is only as big as it is thick, at the figure it turns on · the essays about base plate.

The plate is a detailing item once the bearing area is satisfied.

What decides it: Its thickness is the design variable and nothing else on the drawing is. The bare column footprint would deliver 168 kN; the 20 mm plate delivers nine times that and the plate's own outline promises thirty times. What separates those three numbers is one dimension nobody calls structural.

Tested in The plate that is only as big as it is thick, at the figure it turns on · the essays about base plate.

Since a weld across is √1.5 stronger, using the directional method is worth about 22 per cent.

What decides it: It is worth 22 per cent only where the critical force is square to the weld, and on a real group it never quite is. On the C-shaped group the gain peaks at 20 per cent at an eccentricity of 25 mm, falls to 7 per cent at 500, and is exactly zero at no eccentricity at all.

Tested in The weld that is stronger where it is pulled, at the figure it turns on · the essays about weld strength.

Because the capacity varies round the group, the critical point is not the most heavily loaded one.

What decides it: It nearly always is. The capacity varies by 22 per cent between its two extremes and the force varies by several times that round any group with an eccentric load on it, so the utilisation peak sits where the force peak does — which is why the simpler check finds the right place and only the wrong number.

Tested in The weld that is stronger where it is pulled, at the figure it turns on · the essays about weld strength.

A rigid joint gives the lightest beam, because it takes the most moment off the span.

What decides it: It takes too much. A rigid joint leaves wL²/12 at the support — 90 kN·m on the beam drawn — against wL²/16 at the balanced joint, which is 68. The beam is sized by the larger of its two moments, so overshooting the split is as expensive as undershooting it.

Tested in The joint that was chosen, at the figure it turns on · the essays about joint classification.

The fraction of the fixed-end moment a joint should deliver depends on the beam and the load.

What decides it: It is three quarters, always. The support moment is f·wL²/12 and the span moment is wL²/8 − f·wL²/12, so they are equal when 2f/12 = 1/8 — which contains no beam, no span and no load, and gives f = 0.75 for every uniformly loaded beam there has ever been.

Tested in The joint that was chosen, at the figure it turns on · the essays about joint classification.

A building sagging and a building hogging at the same angular distortion are equally damaged.

What decides it: Hogging is worse by exactly two. A sagging building's neutral axis is near mid-height and its tension face is half the wall; a hogging one's is near the bottom and the tension face is the whole of it. At the proportions drawn the limiting deflection ratios are 0.41 and 0.21 per mille.

Tested in The crack is a strain, not a slope, at the figure it turns on · the essays about differential settlement.

The damage criterion is a property of the ground movement, so a building's own proportions do not enter it.

What decides it: They decide which of two mechanisms cracks it. A squat building cracks diagonally in shear and a long low one cracks in bending, the two cross at a length-to-height ratio of about 1.6, and the limiting deflection ratio has its minimum there — 0.41 per mille against 0.78 at L/H = 0.3.

Tested in The crack is a strain, not a slope, at the figure it turns on · the essays about differential settlement.

Horizontal ground strain is a second-order effect beside the settlement itself.

What decides it: It subtracts directly from the strain the building has available. A horizontal tensile strain of 0.03 per cent — three millimetres over ten metres — takes the sagging limit from 0.41 per mille to 0.25, which is 40 per cent of the capacity gone before any settlement has happened.

Tested in The crack is a strain, not a slope, at the figure it turns on · the essays about differential settlement.

Sway is caused by horizontal load, so a frame under gravity alone does not need the correction.

What decides it: With the 60 kN horizontal load removed entirely, the same portal's no-sway pass leaves a hold force of 22.57 kN. The columns are 5 m and 3.5 m, they take unequal shares of the beam's moment, and their shears do not cancel. An asymmetric frame sways under a symmetric load.

Tested in Every joint balanced, and the frame still leaning, at the figure it turns on · the essays about moment distribution.

A modified stiffness is a shortcut, so it trades accuracy for speed.

What decides it: All three runs on the same three-span beam converge to 197.22 kNm over the first interior support, which is the value a stiffness solution of the same beam gives. Each modified stiffness is the exact rotational stiffness of a member whose far end is doing something already known. Nothing is approximated; a freedom is removed rather than guessed.

Tested in Told what the far end is doing, at the figure it turns on · the essays about moment distribution.

Kani's method converges faster than moment distribution, which is why it was preferred in continental Europe.

What decides it: The two error sequences are identical. On three spans of 8, 10 and 8 m at 24 kN/m both are 28.23, 7.84, 2.40 and 0.88 kNm from the answer after one, two, three and four passes, from two implementations sharing no arithmetic, and the largest gap between them over ten passes is at the last decimal place a double carries. They are one iteration in two notations.

Tested in The table that cannot be read halfway, at the figure it turns on · the essays about moment distribution.

A weld group under an out-of-plane moment is checked the same way as a bolt group under one.

What decides it: A bolt group cannot carry compression, so where its neutral axis sits is an assumption. Placed at the group's centroid it gives a top-row force of 53.6 kN; placed at the bearing edge it gives 34.1 kN, 57 per cent apart on one connection under one moment. A weld line carries compression across its throat, so its neutral axis is its centroid and there is nothing to assume.

Tested in The eccentricity at right angles to the drawing, at the figure it turns on · the essays about weld group.

An out-of-plane force is the awkward direction for a fillet weld.

What decides it: It is the strong one. A force normal to the plate resolves onto the 45° throat as equal normal and shear components, exactly as a transverse in-plane force does, so the whole group carries the across-value of 2146 N/mm rather than the along-value of 1752 — a factor of 1.2247, which is the square root of one and a half.

Tested in The eccentricity at right angles to the drawing, at the figure it turns on · the essays about weld group.

A connection with a weld and a bolt in it carries the sum of the two capacities.

What decides it: A 400 kN weld beside a 380 kN bolt in a 2 mm clearance hole carries 400 kN — the weld's own capacity and not one kilonewton more, because the hole has not closed when the weld ruptures at 0.4 mm of movement. The sum promises 780 and the pair reaches 51 per cent of it.

Tested in Two fasteners that never arrive together, at the figure it turns on · the essays about weld group.

Two fasteners in one joint share load in proportion to their capacities.

What decides it: They share in proportion to their stiffness at the displacement they are both at, which is a different quantity and can be zero. At 0.4 mm the weld is at 100 per cent of its capacity, the bearing bolt at nothing and the preloaded bolt at 75 per cent — three fasteners, one displacement, three unrelated fractions.

Tested in Two fasteners that never arrive together, at the figure it turns on · the essays about weld group.

A bolt row's effective length is the width of plate it has to itself.

What decides it: It is the length of the cheapest yield-line pattern, which is a fold rather than a share. The same bolt row on the same 200 mm plate is worth 200 mm as an inner row, 164 as an end row and 100 as a row outside the tension flange — and 137, 226 and 255 kN of resistance, from one bolt and one thickness.

Tested in How much of the plate is bending, at the figure it turns on · the essays about prying.

The effective length is one number, used throughout the calculation.

What decides it: There are two. Mode 1, where the flange folds and the bolt survives, takes the smaller of the circular and straight patterns. Every mode that breaks a bolt takes the straight one alone, because a collapse that breaks the bolt cannot fold the plate all the way round it. On this plate at m = 25 mm those are 157 mm and 169.

Tested in How much of the plate is bending, at the figure it turns on · the essays about prying.

An analysis that accounts for ninety per cent of the mass is ninety per cent accurate.

What decides it: It is not one accuracy. On the ten-storey frame here, one mode carries 84.8 per cent of the mass, 97.6 per cent of the base shear and 79.8 per cent of the force in the top storey. Three quantities, one truncation, three different fractions — and the rule is written in the one that is not being checked.

Tested in The modes that were left out, at the figure it turns on · the essays about mode shapes.

An adaptive analysis is more conservative than a fixed-pattern one.

What decides it: It is not systematically either. On this frame the adaptive run gives a larger base shear and a larger ground-storey drift, and smaller drifts at every floor from the third upward — 7.0 mm against 26.3 at the fourth. It is a different answer rather than a safer one.

Tested in The pattern that stopped describing the building, at the figure it turns on · the essays about pushover.

If the friction check passes along a support and passes across it, the support will not slide.

What decides it: The friction law bounds the length of the tangential force, not its components. A contact carrying 1000 kN at μ = 0.4 asked for 300 kN along and 300 kN across passes both checks at 75 per cent and is asked for 424 kN in total, which is 106 per cent of the 400 kN it can supply.

Tested in Seventy-five per cent each way, at the figure it turns on · the essays about friction.