What is refuted here — page 15

A long thin column is worse than a square one of the same area for punching, because its perimeter resists the twist less well.

What decides it: True for one orientation and false for the other, and the perimeter beats both. At 300 mm of eccentricity a 450 × 450 column runs at 1.009 of its resistance; the same area as 800 × 250 runs at 0.974 and as 250 × 800 at 0.921. The rectangle wins in both orientations because it is 300 mm longer round.

Tested in Turn the column, and the slab passes, at the figure it turns on · the punching shear ladder.

The shear in a built-up column's lacing can be taken as the axial load over a hundred.

What decides it: It is right at low utilisation and increasingly wrong as the load approaches the critical one. At 1,500 kN on this column the rule gives 15 kN against a computed 17.4; at 2,000 kN it gives 20 against 32.4 — a factor of 1.62 — because the second-order amplification is not linear in the load and the rule is.

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

A curved bar is checked by finding the bending stress and correcting it.

What decides it: Not for a hook, where the free body carries a direct tension as well. At 100 kN the bending alone gives 445.5 N/mm² at the inner fibre and the direct tension adds a uniform 51.9 — the peak is 497.5, and the straight-beam calculation that omits both is 54 per cent under it.

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

Closer stiffeners make a girder web more efficient, at the cost of a few more stiffeners.

What decides it: They also multiply what the flange is asked to hold. Taking the stiffener spacing from 4,500 mm to 800 on a 1,500 mm web raises the panel's shear capacity from 716 kN to 2,498 and the pull on the flange from 72.5 N/mm to 602.8 — a factor of 8.3, on a member sized for bending.

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

A compatibility torsion can be ignored, because the structure does not need it.

What decides it: It can be shed and it cannot be ignored. Releasing the spandrel takes its torque from 100 kN·m to 41, and the floor beam's midspan moment from 147 kN·m to 177 — the two always add to the same free moment of 197, so what is shed arrives somewhere that has to be checked for it.

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

Robustness is a property a structure has more or less of.

What decides it: Not below a threshold. All 31 members of an 8-panel Warren truss leave a mechanism when removed, and all 29 of a Howe. There is no redistribution anywhere in either to measure, so the quantity a member-removal study reports is not small — it does not exist, and the answer is the same for every member.

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

A rocking block's survival is decided by how hard the ground shakes.

What decides it: It is decided as much by what happens between shakes. The same block under the same 1.0 g pulse overturns at a restitution of 0.93 and survives at 87 per cent of the toppling angle at 0.75 — the ground motion identical, and the difference entirely in how much energy each landing takes out.

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

A slender block is worse at rocking than a stocky one, because it topples at a smaller angle.

What decides it: It is worse twice over and the second reason is the impact. A 4.4-to-1 block loses 14 per cent of its energy per landing and a 2.4-to-1 block loses 38 — because the classical restitution falls with the toppling angle, so the slender block is both nearer to going over and worse at losing the energy that would stop it.

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

A wider stiffener is always a stronger one.

What decides it: Only up to its own slenderness limit. A 150 mm outstand on a 10 mm plate is past the 114 mm that 14ε t_s allows, so the outstand buckles locally before the stub column reaches the squash load the area promises — a check on the plate that the stub-column arithmetic does not contain.

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

The stress in a necked specimen is the load divided by the neck's area.

What decides it: That is the axial stress, and it is larger than the flow stress that caused it, because the neck's curvature puts a hydrostatic tension into the middle of the section. At a neck sharpness of 0.8 the measured value is 18 per cent above the flow stress and at 2.0 it is 39 per cent, and the correction is read off the shape of the neck rather than off any instrument.

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

Notch sensitivity is a correction applied to the elastic solution.

What decides it: It is a statement that the elastic solution answers a different question. The stress at a point is not what starts a crack; the stress over a process volume is, and the peak at a sharp notch is confined to a volume smaller than that. The correction is what is left when a point calculation is asked a question about a region.

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

An unprotected steel member fails within a few minutes of a fire starting.

What decides it: A few minutes for a light section and half an hour for a heavy one. At a load ratio of 0.6 the critical temperature is 558 °C, and the six sections drawn reach it between 8.0 and 29.3 minutes — so the lightest is at its limit before the heaviest has passed 300 °C.

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

An opening is safe when the peak stress at its worst corner is below the yield stress.

What decides it: That is a first-yield criterion on a detail with three more corners to give. On the opening drawn, first yield arrives at a load factor of 1.49 and the four-hinge mechanism at 3.89 — the elastic check finds one corner and the failure needs all four.

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

Distortion is a serviceability matter, since it produces small stresses.

What decides it: On a box with no interior diaphragms its warping stress at the quarter point is 60 N/mm² against a bending stress of 54 — more than the action it is a correction to — and the transverse plate bending it produces in the walls is 151 N/mm². Whether it is small is a property of the diaphragm spacing rather than of the phenomenon.

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

A longer haunch is a safer rafter.

What decides it: Only until the tip reaches a part of the rafter where the moment is small. Past 3.3 m on this frame the governing station jumps back to the eaves and the worst utilisation is flat at 0.42 however much longer the haunch is made — every millimetre past the knee is steel protecting a section that is no longer being checked.

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

A damper has to be tuned to the mode that is causing trouble.

What decides it: Every mode reaches the same ceiling and the peaks are flat: half the optimum coefficient gives 80 per cent of the ceiling and so does twice it. A damper sized for mode 1 delivers 0.8 per cent to mode 2 and 0.6 to mode 4, which is why one damper is fitted for a whole spectrum of excitation.

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

A heavier foundation block is a better one.

What decides it: It lowers the natural frequency, which is usually what is wanted, and it lowers the damping while doing it. Five times the mass takes the vertical damping from 47 per cent to 21 and the rocking mode from 13 to 2 — mass buys frequency and costs damping, and the two have to be traded rather than assumed to agree.

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

A pounding check is a check on the separation, so a building that has been given the gap the code asks for has been dealt with.

What decides it: The gap decides whether contact happens; the floor levels decide what contact does. Storey heights of 3.00 and 3.75 m put two of the taller building's floors 40 and 20 per cent up a column of the shorter one, and no separation calculation contains a floor level.

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

More outriggers is a way of reducing the core's base moment when the drift is already acceptable.

What decides it: They reduce it, and by less than they reduce drift, and by progressively less again: one arm takes 51 per cent of the base moment, two 65, three 73 and four 74. A core sized by its base moment gets much less from an outrigger system than one sized by drift, which is the usual case above about thirty storeys.

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

The error is a coarse-mesh artefact, so it goes away in any model anybody would build.

What decides it: It converges as the square of the mesh size — 33.3 per cent on one element, 8.3 on two, 2.1 on four — so it is still 0.5 per cent at eight and it is being paid for with elements rather than with a load vector. The consistent set is exact on every mesh drawn, including the coarsest.

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

A weld group is checked by comparing its largest force per unit length with the weld's capacity.

What decides it: The weld has more than one capacity. At 47 degrees to its axis the critical point on the group drawn has 1,612 N/mm available against the 1,460 an along-the-weld check would use and the 1,789 a square pull would give — three numbers for one weld, and the check needs the one that belongs to the direction the force is in.

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

Classifying a joint as pinned, semi-rigid or rigid tells a designer what to do with it.

What decides it: It tells them which analysis is permissible, and it is a set of lines drawn across a continuous curve at 0.5EI/L and 8EI/L. The design question is which point of that curve to buy, and the answer — three quarters of the fixed-end moment — falls inside the semi-rigid band that the classification exists to make people avoid.

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

Truss joints are pins, so truss members carry axial force and nothing else.

What decides it: The same truss solved twice — pin-jointed, and with the joints continuous as welding actually makes them. The axial forces agree to about a per cent, which is why the idealisation is a good one; the bending it omits reaches a quarter of the axial stress in the worst member. It scales with EI/L, so a stocky truss of heavy members suffers more of it than a light one — which is the opposite of the way most reserves of strength work, and is the direction in which the simplification stops erring safe.

Tested in The joint that is not a pin, at the figure it turns on · the truss ladder.

Wind loading is a static problem: work out the pressure, multiply by the area, apply it.

What decides it: True for a stiff structure and badly wrong for a slender one. Split into its parts, a warehouse at 2 Hz takes 15% of its fluctuating response from resonance and a tower at 0.2 Hz takes 90% — and the resonant part is inversely proportional to a damping ratio that no static calculation contains. The static method survives because the gust factor it hides absorbs the difference for ordinary buildings.

Tested in The wind is a spectrum, at the figure it turns on · the gust response ladder.

The effective width of a flange is min(span/8, b) per side, and that expression comes from the elasticity of the problem.

What decides it: The exact elastic ceiling for an infinitely wide flange fed by a sinusoidal shear flow is L/2π = 0.1592L per side, from Airy's solution. The rule caps at L/8 = 0.125L, which is 0.7854 of it — exactly 2π/8. A rule that is a fixed fraction of the exact answer is a fit with a margin in it, not a derivation of it, and it is a straight line where the elasticity is a curve.

Tested in The flange that is not all there, at the figure it turns on · the effective width ladder.