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0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 0 10 20 30 40 50 forcing frequency ÷ the structure's own amplitude ÷ static deflection no absorber — peak 50 3.0% absorber — peak 7.34 a factor of 6.8, for 3.0% of the mass
Tuned mass damper
1
The mass that helps by being late
1 rung · dynamics
200 kN 200 kN the chord — and the line of action 1.20 m bending moment = P × offset peak 240 kNm bending stress is 24.0 times the axial stress at the worst section
Two force member
1
The member with only one direction
1 rung · equilibrium
1 1.5 2 2.5 3 0.4 0.5 0.6 0.7 0.8 0.9 1 long span ÷ short span share taken by the short strips 6 × 8 m: 76.0% by 2 : 1 it is a one-way slab
Two way spanning
1
The slab that spans both ways
1 rung · structures
-0.6% -0.4% -0.2% 0.2% 0.4% 0.6% -300 -200 -100 100 200 300 strain stress, N/mm² 0.469% of the strain never came back
Unloading
1
What is left when the load comes off
1 rung · materials
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
+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
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