The collection

Every essay — page 10

Essays 217 to 226 of 226, in the same order.
pinneda mechanismno shear stiffness at allrigid1205 mmGt = 0.35% of a sheet'sbraced6.4 mmGt = 65% of a sheet'striangulated4.3 mmGt = 98% of a sheet's Structural form

A shell only if the grid takes shear

A curved surface carries load in its own plane at a fraction of the material a flat one needs, and every gridshell ever built is an attempt to buy that with members instead of with a surface. The attempt succeeds or fails on one property nobody draws — whether four bars meeting at a corner can resist being racked — and a pinned quadrilateral grid cannot resist it at all.

8 figures · gridshell
1015202530354045500510152025beam length (m)factor of safety against rolling1.5, a working factorpast 42 m30 m: 13.3 Stability

Hung from above and still unstable

A rigid body hanging from a point above its centre of gravity is a pendulum and cannot fall over. A beam is not rigid, and tilting it puts a component of its own weight sideways — which bows it, which moves its centre of gravity further out. Past a length there is no hook height at which it hangs stably at all, and the length arrives as a fourth power.

8 figures · lift stability
00.10.20.30.40.500.20.40.60.81eccentricity ÷ thicknesscapacity ÷ squash loadthe kern66.7% at the kernno tension only1 − 2e/tslenderness 14.0adds e_a = 17.4 mmEuler is 10×above all of this Stability

It does not buckle, it runs out of width

Every stability failure in this collection is a member that could have carried tension deciding to go sideways instead. Masonry cannot carry tension, and its failure under an eccentric load is not a bifurcation at all — the bearing area simply shrinks until it runs out. The capacity is exactly linear in the eccentricity, Euler's load is ten times anything allowed, and no material property appears until the very end.

8 figures · wall slenderness
windward c_p = 0.8leeward c_p = -0.5sidec_p = -0.7sidec_p = -0.7842 kN38% of it fromthe back face30 × 20 m Equilibrium

Most of it is suction

A wind load is drawn as arrows pressing on the windward face, which is where about three fifths of it comes from. The rest is a pull on the back. The two side faces carry the largest suctions on the building and contribute nothing at all to the answer — and the inside of the building, which nobody draws, decides whether the roof stays on.

8 figures · wind pressure
0510152025-100-5050position along the beam (m)bending moment (kNm)-98.6-98.6hinges releasedsupports released Deflection

Choose what to take away

The other machine for a redundant structure works by removing restraints until what is left can be solved by statics, then putting back exactly enough force to close the gaps that opened. Which restraints are removed does not change the answer at all, and changes the arithmetic completely — one choice gives a tridiagonal matrix a person can solve on paper, and another gives a full one.

8 figures · force method
6 × 6 m, simply supported on four sidescorner hold-down 2M_xy = 26.7 kN, 7.42% of the whole loadM_xy ≈ 0 Deflection

A third of the load crosses sideways

A slab spanning both ways is usually explained as two beams sharing a load by a fourth power, and the explanation is not merely approximate — it is missing a mechanism. A real plate carries load three ways, and the third one has no beam strip in it: it is twisting, it accounts for a third of the load on a square panel, and it is why the corners lift.

8 figures · plate torsion
2.62.833.23.43.63.811.522.5density log₁₀(kg/m³)modulus log₁₀(GPa)mild steelhigh-strength steelaluminiumconcretetimbercast ironcarbon fibreglassE/ρ — a tieE^½/ρ — a beamE^⅓/ρ — a plate Materials

The ranking belongs to the load case

Every table of material properties ever printed ranks by strength, and every one of them answers a question nobody asked. What a structure wants is the least mass for a stated performance, and the combination of properties that gives it changes with the shape of the member — so timber beats steel four to one as a beam and loses to it as a tie, without either material changing.

8 figures · material index
204060800102030405060cover (mm)years to a split coverinitiation ∝ c²and propagation35 mm: 9.1 yr70 mm: 36.2 yrthe cover splits at a section loss of 0.21% Materials

The load that comes from inside

Every action in this collection has been applied from outside — a weight, a pressure, a movement, a temperature. Corrosion is not applied at all, and the reason it belongs to statics rather than to durability is that what does the damage is a load: rust occupies three times the volume of the steel it came from, and the only place to make room is by pushing the cover apart.

8 figures · corrosion
the brace force30°b_eff = 367 mm90 mm4.08× the width anything is actually attached togoverns on the Whitmore section buckles, at 721 kN Connections

The width nobody drew

Every other member in this collection arrives with a cross-section. A gusset plate does not — it is a piece of steel with a brace bolted to it somewhere in the middle, and no geometry says how much of it is working. The profession's answer is a thirty-degree spread from a 1952 master's thesis, it invents three quarters of the area being checked, and the check it was written for is not the one that governs.

8 figures · gusset
10020030040050060070000.20.40.60.811.21.41.6shear wave velocity of the ground (m/s)÷ the fixed-base answerperiodbase sheardampingfixed base200 m/speriod 1.311 times · shear 0.88 times · drift 1.51 timessoft groundrock Dynamics

The ground is a spring

Every dynamic result in this collection has assumed a structure rising from something that does not move. Nothing does. A foundation can slide and it can rock, both are flexibilities in series with the structure's own, and the rocking one carries a square of the height — so the period lengthens, the force falls, the drift rises, and the damping goes the wrong way.

8 figures · soil structure