The collection

Every essay — page 7

Essays 145 to 151 of 151, in the same order.
0.020.1011025000.20.40.60.8floor-plate stiffness ÷ wall stiffnessshare of the storey forcethe middle wallan end walltributary arearigid plate← soft plate Structural form

The floor is a beam lying down

A floor plate spans horizontally between the walls that resist a lateral load, carries a distributed inertia load, and has chords, a web and a span-to-depth ratio like any other beam. Its stiffness decides whether the walls share the load by their stiffness or by the area of floor nearest them — and the familiar tributary answer turns out to be neither limit.

11 figures · diaphragm
s_s = 100l_y = 559flangewebspread 5.6 times the bearingyield resistance 1586 kN · elastic critical 510 kNresistance 450 kN at a slenderness of 1.76 Stability

The load that chooses its own length

Every other load in this collection arrives over a length somebody decided. A wheel on a crane girder does not — the flange bends under it and spreads it along the web, and how far it spreads is an output of the flange's own stiffness against the web's own strength. The effective length is 5.6 times the bearing that produced it.

11 figures · patch loading
bending, as a solid column doesP_E = 1341 kNracking, which a solid column cannotS_v = 31500 kN1/P꜀ᵣ = 1/P_E + 1/S_v → 1287 kNthe smaller of the two governs, and here it is the bending Stability

The column made of two columns

A solid column buckles when its bending stiffness runs out. A laced one has a second way to go — the lattice shears, the chords stay straight — and the two flexibilities add rather than the two stiffnesses. A battened column reaches 23% of its own Euler load and behaves as though its slenderness were twice what it is.

11 figures · built up column
02040608000.20.40.60.811.21.41.6brace stiffness (units of EI/L³)effective length factor k23.2 EI/L³ = 1.41 N꜀ᵣ/L0.77 — held1.32 — freepast the threshold the frame buckles in a mode the brace does not hold Stability

The most dangerous day is before it is finished

A structure is analysed once, complete, with every restraint present. It spends weeks in states nobody drew — a beam landed with no deck on it holds 17% of the moment its section is worth, a frame not yet braced buckles at a third of the load it will, and a bolt not yet tightened is a pin where the analysis assumed a fixity.

11 figures · erection stability
-40-30-20-10010020406080100120140column shorter than core (mm)height (m)from loadfrom shrinkagethe sumworst 43 mmat level 40one in 208 Deflection

The columns are shorter than the core

Every column in a tall building gets shorter as the building is built on top of it, and the core beside it gets shorter by a different amount. The floors between them tilt by the difference — and the difference is largest exactly half way up, because a floor near the top has almost nothing built above it and a floor near the bottom has almost nothing beneath it.

11 figures · differential shortening
4020080030002000000.20.40.60.81stiffness of each supportfraction of the deflection that is bendingrigid supportsare over here1%the beam drawn Deflection

The deflection that belongs to the support

A beam calculation answers a question about a beam sitting on things that do not move. Real ones sit on bearings, on other beams and on columns that shorten, and every one of those is a spring in series with the member — so a deflection is the sum of two things and only one of them is a property of the beam.

11 figures · support flexibility
water table39.2 kN/m² upward, everywhereweight 18.7 MN6 muplift 23.54 MN · weight 18.72 MNfactor against flotation 0.80no strength appears anywhere in that ratio Equilibrium

A basement is a boat

Every load in this collection presses down and is resisted by strength. Hydrostatic uplift presses up, is resisted by weight, and does not care what is built on it — so the check contains no material property at all. It is a ratio of two weights, and one of them is water.

11 figures · uplift