1 Introduction
2 Description of the Selected Buildings
City | No. of stories | 5 | 10 | 15 | 20 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Ductility level | Conv. | Mod. Duct. | Duct. | Conv. | Mod. Duct. | Duct. | Conv. | Mod. Duct. | Duct. | Conv. | Mod. Duct. | Duct. | |
Toronto | tw (m) | 0.25 | 0.25 | 0.30 | 0.25 | 0.25 | 0.30 | 0.25 | 0.25 | 0.30 | 0.40 | 0.40 | 0.40 |
Lw (m) | 3.0 | 2.0 | 2.0 | 4.0 | 4.0 | 4.0 | 6.0 | 6.0 | 6.0 | 7.0 | 7.0 | 7.0 | |
Ta (s) | 1.26 | 2.30 | 2.37 | 2.90 | 3.20 | 3.31 | 3.76 | 3.88 | 4.04 | 4.00 | 4.42 | 4.93 | |
Governing case | S | S | W | W | W | W | W | W | W | W | W | W | |
Correspond. Max. I.D. (%) | 0.38 | 0.84 | 0.10 | 0.14 | 0.14 | 0.12 | 0.16 | 0.16 | 0.14 | 0.16 | 0.16 | 0.16 | |
Vf (kN)ǂ | 524 | 395 | 212 | 463 | 463 | 463 | 767 | 767 | 767 | 1103 | 1103 | 1103 | |
Mf (kN m)ǂ | 3847 | 1765 | 1601 | 7195 | 7195 | 7195 | 18,118 | 18,118 | 18,118 | 34,977 | 34,977 | 34,977 | |
Montreal | tw (m) | 0.25 | 0.25 | 0.30 | 0.25 | 0.25 | 0.30 | Not permitted | 0.25 | 0.30 | Not permitted | 0.35 | 0.35 |
Lw (m) | 6.0 | 5.0 | 4.0 | 7.0 | 5.0 | 5.0 | 6.0 | 6.0 | 7.0 | 7.0 | |||
Ta (s) | 0.50 | 0.69 | 1.00 | 1.37 | 2.36 | 2.45 | 3.90 | 4.05 | 4.35 | 4.84 | |||
Governing case | S | S | S | S | S | W | W | W | W | W | |||
Correspond. Max. I.D. (%) | 0.26 | 0.40 | 0.50 | 0.37 | 0.49 | 0.06 | 0.14 | 0.12 | 0.17 | 0.17 | |||
Vf (kN)ǂ | 1957 | 1122 | 463 | 2248 | 1003 | 505* | 1393* | 706* | 1385* | 1002* | |||
Mf (kN m)ǂ | 19,312 | 9961 | 3065 | 24,855 | 7736 | 6540 | 16,470 | 16,470 | 31,797 | 31,797 | |||
Vancouver | tw (m) | 0.25 | 0.25 | 0.30 | 0.25 | 0.25 | 0.30 | Not permitted | 0.25 | 0.30 | Not permitted | 0.35 | 0.35 |
Lw (m) | 7.0 | 7.0 | 6.0 | 8.0 | 7.0 | 7.0 | 9.0 | 9.0 | 9.0 | 9.0 | |||
Ta (s) | 0.41 | 0.46 | 0.58 | 1.14 | 1.53 | 1.60 | 2.26 | 2.36 | 3.33 | 3.73 | |||
Governing case | S | S | S | S | S | S | S | S | S | W | |||
Correspond. Max. I.D. (%) | 0.39 | 0.46 | 0.60 | 0.66 | 1.00 | 1.03 | 0.95 | 1.03 | 1.11 | 0.10 | |||
Vf (kN)ǂ | 4267 | 2769 | 1093 | 4002 | 2466 | 1219 | 2873 | 1463 | 3094 | 1419* | |||
Mf (kN m)ǂ | 46,011 | 29,464 | 11,266 | 62,725 | 35,709 | 17,326 | 50,878 | 25,748 | 65,751 | 35,772 |
3 Analysis and Design of Shear Walls
3.1 Analysis Assumptions
3.2 Shear Wall Design
3.3 Analysis Results
City | No. of stories | 5 | 10 | 15 | 20 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Ductility level | Conv. | Mod. Duct. | Duct. | Conv. | Mod. Duct. | Duct. | Conv. | Mod. Duct. | Duct. | Conv. | Mod. Duct. | Duct. | |
Toronto | Vr/Vf | 1.73 | 1.61 | 3.42 | 1.75 | 2.65 | 3.33 | 2.36 | 2.14 | 3.03 | 3.47 | 3.22 | 3.22 |
Mr/Mf | 0.95 | 1.06 | 1.34 | 1.05 | 1.15 | 1.30 | 1.10 | 1.06 | 1.18 | 1.02 | 1.06 | 1.20 | |
Δf Rd Ro (mm) | 41 | 86 | 81 | 85 | 95 | 101 | 100 | 103 | 109 | 70 | 85 | 105 | |
θid | N.R. | 0.003 | 0.004 | N.R | 0.003 | 0.004 | N.R. | 0.004 | 0.005 | N.R. | 0.003 | 0.004 | |
θic | 0.006 | 0.005 | 0.005 | 0.007 | 0.005 | 0.006 | 0.005 | 0.005 | |||||
Montreal | Vr/Vf | 1.05 | 1.46 | 3.33 | 1.06 | 1.58 | 3.83 | Not permitted | 1.37 | 3.28 | Not permitted | 2.30 | 3.17 |
Mr/Mf | 1.03 | 1.08 | 2.40 | 0.98 | 1.64 | 1.85 | 1.22 | 1.40 | 1.22 | 1.22 | |||
Δf Rd Ro (mm) | 30 | 44 | 53 | 78 | 96 | 104 | 210 | 225 | 224 | 254 | |||
θid | N.R. | 0.003 | 0.004 | N.R. | 0.003 | 0.004 | 0.003 | 0.004 | 0.003 | 0.004 | |||
θic | 0.011 | 0.011 | 0.006 | 0.007 | 0.005 | 0.005 | 0.005 | 0.005 | |||||
Vancouver | Vr/Vf | 1.00 | 1.00 | 2.12 | 1.00 | 1.01 | 2.12 | Not permitted | 1.00 | 2.28 | Not permitted | 1.17 | 2.88 |
Mr/Mf | 1.00 | 0.98 | 1.32 | 0.95 | 0.96 | 1.33 | 1.05 | 1.87 | 1.02 | 1.64 | |||
Δf Rd Ro (mm) | 46 | 50 | 68 | 152 | 201 | 227 | 308 | 336 | 479 | 510 | |||
θid | N.R. | 0.003 | 0.004 | N.R. | 0.004 | 0.006 | 0.004 | 0.005 | 0.004 | 0.005 | |||
θic | 0.01 | 0.014 | 0.007 | 0.009 | 0.006 | 0.007 | 0.006 | 0.006 |
4 Ductility and Material Quantities
City | No. of stories | 5 | 10 | 15 | 20 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Ductility level | Conv. | Mod. Duct. | Duct. | Conv. | Mod. Duct. | Duct. | Conv. | Mod. Duct. | Duct. | Conv. | Mod. Duct. | Duct. | |
Toronto | Concrete vol. (m3) | 45 | 30 | 36 | 120 | 120 | 144 | 270 | 270 | 324 | 672 | 672 | 672 |
Walls reinf. (tons) | 2.47 | 2.62 | 3.15 | 4.96 | 7.93 | 10.39 | 13.06 | 17.13 | 21.53 | 28.54 | 38.35 | 43.63 | |
Steel/conc. (kg/m3) | 55 | 87 | 88 | 41 | 66 | 72 | 48 | 63 | 66 | 42 | 57 | 65 | |
Total cost (unit) | 70 | 56 | 68 | 170 | 199 | 248 | 401 | 441 | 539 | 957 | 1056 | 1108 | |
Montreal | Concrete Vol. (m3) | 90 | 75 | 72 | 210 | 150 | 180 | Not permitted | 270 | 324 | Not permitted | 588 | 588 |
Walls reinf. (tons) | 9.48 | 7.49 | 5.19 | 13.96 | 10.57 | 13.72 | 18.97 | 22.75 | 40.79 | 40.79 | |||
Steel/Conc. (kg/m3) | 105 | 100 | 72 | 66 | 70 | 76 | 70 | 70 | 69 | 69 | |||
Total cost (unit) | 185 | 150 | 124 | 350 | 256 | 317 | 460 | 551 | 996 | 996 | |||
Vancouver | Concrete Vol. (m3) | 105 | 105 | 108 | 240 | 210 | 252 | Not permitted | 405 | 486 | Not permitted | 756 | 756 |
Walls reinf. (tons) | 23.11 | 14.78 | 7.40 | 49.13 | 29.00 | 16.24 | 42.79 | 32.18 | 54.00 | 54.20 | |||
Steel/Conc. (kg/m3) | 220 | 141 | 68 | 205 | 138 | 64 | 106 | 69 | 71 | 72 | |||
Total cost (unit) | 336 | 253 | 182 | 731 | 500 | 414 | 833 | 808 | 1296 | 1298 |
5 Ductility and Rebar Constructability
City | No. of stories | 5 | 10 | 15 | 20 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Ductility level | Conv. | Mod. Duct. | Duct. | Conv. | Mod. Duct. | Duct. | Conv. | Mod. Duct. | Duct. | Conv. | Mod. Duct. | Duct. | |
Toronto | SVL (mm) | 500 | 320 | 260 | 500 | 320 | 260 | 500 | 320 | 260 | 320 | 200 | 200 |
SHZ (mm) | 500 | 320 | 260 | 500 | 320 | 260 | 500 | 320 | 260 | 260 | 200 | 200 | |
Asconc (M) | 8–20 | 8–15 | 8–30 | 8–15 | 8–20 | 8–25 | 8–25 | 12–20 | 16–20 | 16–20 | 8–30 | 12–30 | |
SHoops (mm) | 250 | 90 | 120 | 250 | 120 | 150 | 250 | 120 | 120 | 320 | 180 | 180 | |
LCOL (mm) | 250 | 250 | 300 | 250 | 250 | 300 | 250 | 250 | 300 | 400 | 400 | 400 | |
No. of B. | 738 | 1870 | 1499 | 1462 | 2903 | 2496 | 2190 | 4359 | 4498 | 4727 | 5937 | 5941 | |
No. of C. | 216 | 553 | 401 | 404 | 931 | 699 | 600 | 1405 | 1208 | 1320 | 2073 | 2081 | |
No. of T. | 780 | 1708 | 1577 | 1800 | 3875 | 4600 | 3420 | 8531 | 11,423 | 11,769 | 21,933 | 22,600 | |
C.F. | 1734 | 4131 | 3477 | 3666 | 7709 | 7794 | 6210 | 14,294 | 17,130 | 17,816 | 29,943 | 30,622 | |
Relative | 1.00 | 2.38 | 2.01 | 1.00 | 2.10 | 2.13 | 1.00 | 2.30 | 2.76 | 1.00 | 1.68 | 1.72 | |
Montreal | SVL (mm) | 500 | 320 | 260 | 500 | 320 | 260 | Not permitted | 320 | 260 | Not permitted | 220 | 220 |
SHZ (mm) | 400 | 320 | 260 | 400 | 320 | 260 | 320 | 260 | 220 | 220 | |||
Asconc (M) | 20–30 | 12–25 | 8–25 | 16–25 | 8–25 | 12–25 | 16–20 | 12–25 | 16–25 | 16–25 | |||
SHoops (mm) | 250 | 125 | 150 | 250 | 125 | 150 | 120 | 150 | 150 | 150 | |||
LCOL (mm) | 600 | 400 | 300 | 400 | 250 | 300 | 300 | 300 | 300 | 300 | |||
No. of B. | 1028 | 1426 | 1265 | 2740 | 2811 | 2508 | 4361 | 3744 | 5165 | 5165 | |||
No. of C. | 391 | 504 | 383 | 710 | 927 | 723 | 1409 | 1050 | 1493 | 1493 | |||
No. of T. | 1635 | 2419 | 2300 | 3720 | 4545 | 5923 | 9000 | 9923 | 20,618 | 20,618 | |||
C.F. | 3054 | 4348 | 3948 | 7170 | 8283 | 9153 | 14,769 | 14,718 | 27,277 | 27,277 | |||
Relative | 1.00 | 1.42 | 1.29 | 1.00 | 1.16 | 1.28 | 1.00 | 1.00 | 1.00 | 1.00 | |||
Vancouver | SVL (mm) | 400 | 320 | 260 | 500 | 320 | 260 | Not permitted | 320 | 260 | Not permitted | 280 | 220 |
SHZ (mm) | 170 | 220 | 260 | 220 | 260 | 260 | 320 | 260 | 280 | 220 | |||
Asconc (M) | 52–30 | 36–25 | 8–30 | 56–30 | 36–25 | 8–25 | 32–25 | 16–25 | 20–30 | 20–25 | |||
SHoops (mm) | 250 | 125 | 150 | 250 | 125 | 150 | 175 | 150 | 175 | 150 | |||
LCOL (mm) | 1150 | 900 | 300 | 1800 | 900 | 300 | 900 | 350 | 500 | 400 | |||
No. of B. | 2227 | 2741 | 1281 | 4219 | 5330 | 2520 | 5783 | 3772 | 7792 | 9187 | |||
No. of C. | 684 | 889 | 415 | 1141 | 1558 | 747 | 1747 | 1106 | 2385 | 2337 | |||
No. of T. | 4221 | 5302 | 3223 | 7255 | 9932 | 7369 | 12,640 | 14,677 | 18,600 | 27,927 | |||
C.F. | 7133 | 8931 | 4919 | 12,615 | 16,819 | 10,636 | 20,171 | 19,555 | 28,777 | 39,452 | |||
Relative | 1.00 | 1.25 | 0.69 | 1.00 | 1.33 | 0.84 | 1.00 | 0.97 | 1.00 | 1.37 |