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water table 39.2 kN/m² upward, everywhere weight 18.7 MN 6 m uplift 23.54 MN · weight 18.72 MN factor against flotation 0.80 no strength appears anywhere in that ratio
Uplift
1
A basement is a boat
1 rung · equilibrium
0 0.5 1 1.5 2 2.5 3 3.5 4 0 5 10 15 20 25 forcing frequency ÷ natural frequency force out ÷ force in √2 — nothing gained, at any damping 2% damping 5% damping 20% damping
Vibration isolation
1
The machine that shakes the building
1 rung · dynamics
100 kN chord moment 25.0 kNm from the panel shear · axial 200 kN from the global moment 6.20 mm against 3.18 mm triangulated — 68% of it is chord bending
Vierendeel
1
The truss with no diagonals
1 rung · structures
real M peak 32.0 a unit load, here and nowhere else unit m M × m area ÷ EI = 213.33 the unit load is the only place the question 'deflection where?' is asked
Virtual work
1
One deflection, without solving everything
1 rung · deflection
0 2 4 6 8 10 12 14 16 18 20 0 1 2 3 shedding frequency (Hz) 1.2 m across · St 0.18 · 0.9 Hz lock-in 6 m/s 0 2 4 6 8 10 12 14 16 18 20 0 50 100 150 200 wind speed (m/s) cross-wind amplitude (mm) 0.40% damping — Sc = 11.2, peak 180.94 mm
Vortex shedding
1
The wind that brings its own frequency
1 rung · dynamics
0 0.02 0.04 0.06 0.08 0.1 0.12 0 10 20 30 40 50 60 lateral deflection (m) height (m) released: two cantilevers as built: DoC 63% rigid beams: one wall
Wall coupling
1
Two walls that agreed to be one
1 rung · internal-forces
0 0.1 0.2 0.3 0.4 0.5 0 0.2 0.4 0.6 0.8 1 eccentricity ÷ thickness capacity ÷ squash load the kern 66.7% at the kern no tension only 1 − 2e/t slenderness 14.0 adds e_a = 17.4 mm Euler is 10× above all of this
Wall slenderness
1
It does not buckle, it runs out of width
1 rung · stability
+67.0 N/mm² −67.0 N/mm² +67.0 N/mm² −67.0 N/mm² I-section, ω = ±12169 mm² at a tip top flange bottom flange h = 295 V_f = 1.69 kN each way · V_f × h = 0.500 kN·m = the torque at the built-in end M_f = 3.04 kN·m each way · M_f × h = 0.897 kN·m² = the bimoment flange plan, sideways movement ×20 against the length
Warping
1
The section that cannot stay flat
1 rung · sections
contraflexure at the middle of the hole from the moment: 70.3 N/mm² from the shear: 167.6 N/mm² total 237.9 of 355 second moment lost: 30% deflection up by 0.7% the shear the tees must carry: 63 kN, half each, over 400 mm
Web opening
1
The hole that costs nothing, and everything
1 rung · sections
100 kN peak 0.88 Two points at maximum radius the radius rule finds the peak here equal radius, stresses differ ×1
Weld group
1
The corner that is not the worst point
1 rung · connections
0 10 20 30 40 50 60 70 80 90 0 20 40 60 80 100 120 140 160 angle between the weld and the load, degrees capacity, kN 0° · 116.83 kN 45° · 127.98 kN 90° · 143.09 kN ×1.22 along
Weld strength
1
The weld that is stronger across than along
1 rung · connections
windward c_p = 0.8 leeward c_p = -0.5 side c_p = -0.7 side c_p = -0.7 842 kN 38% of it from the back face 30 × 20 m
Wind pressure
1
Most of it is suction
1 rung · equilibrium
-1 -0.5 0.5 1 -1 -0.5 0.5 1 σ₁ ÷ f_y σ₂ ÷ f_y von Mises Tresca pure shear the widest gap is 2/√3 = 1.1547, at pure shear
Yield criterion
1
The shear strength nobody measured
1 rung · materials
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