Note: G40.21M-350W (Fy =350 MPa, Fu = 450 MPa) steel is to be used, unless otherwise specified. None of the beams in this assignment are cambered. It is not permitted to use M, values obtained from the beam selection tables found in the HSC - code calculations must be performed. 1. A W310x143 section is used as an interior column (column B) of a steel frame as shown in Figure 1. Assume that the lateral sways of the frame are prevented by the lateral load resisting system of the building (ex. shear wall or bracing) and the columns are laterally braced by the load bearing wall in the direction which is perpendicular to the frame plane. The column bases are pinned supports. Complete the following: a) Calculate the equivalent length factors K, for column B (for both the upper and lower columns). b) Evaluate the factored axial compressive resistance of both the upper and lower columns of column B based on the corresponding Ky values obtained from item a). W410x54 W410x67 34001 W410x60 W410x74 4300 column B W310x143 9500 11200 + * X Figure 1. Unit: mm W SHAPES W360 - W310 H W SHAPES W360 - W310 T H. Theo Warping Constant C. Nominal Mass retical Mass Depth Flange Flange Flange Web Width Thick Thick- ness ness d D t w mm mm mm mm DIMENSIONS AND SURFACE AREAS Distances Surface Area per metre of length Imperial T Kk6-21 Total of mm mm mm Top Flange a Mnus Top Designation kg/m kg/m mm 57 51 45 56.6 50.6 45.0 358 355 352 172 171 171 332 13.1 11.6 9.8 7.9 7.2 6.9 82 82 82 295 295 296 31 30 28 21 20 20 332 1.39 1.38 1.37 122 1.21 120 W14x38 W14x34 W14x30 332 39 33 39.1 32.7 353 349 128 127 10.7 8.5 6.5 5.8 61 61 295 296 29 27 20 20 332 332 1.21 1.19 1.08 1.07 W14x26 W14x22 PROPERTIES Torsional Axis Y-Y Axis X-X Dead Constant Area Designation Load 1 Sx Fy Z ly Sy Zy J kNm mm 106mm 10mm mm 10 mm 10 mm 10 mm mm 10 mm 10 mm 10mm W360 x57 0.555 7230 160 896 149 1010 11.1 129 39.3 199 333 331 X51 0.496 6 450 141 796 148 893 9.68 113 38.8 174 237 285 x45 0.441 5710 122 691146 778 8.18 95.7 378 148 159 239 W360 x39 0.383 4960 102 580 143 662 3.75 58.6 274 91.6 150 110 x33 0.321 4 190 82.6 473 141 541 2.91 45.8 26.4 71.8 85.3 84.3 W310 x500 4.91 63 700 1 690 7910 163 9 880494 2 910 88.0 4 490 101 000 15 300 X454 4.45 57 8001480 7 130 160 8820 436 2 600 86.8 4 000 77 200 13 100 X415 4.07 52 8001 300 6 450 157 7 900 391 2 340 86.0 3610 59 500 11 300 X375 3.68 47 800 1 130 5 770 154 7000 344 2 080 84.8 3210 44 900 9 570 x342 3.37 43 700 1 010 5260152 6 330 | 310 1 890 84.2 2 910 34 900 8 420 x313 3.07 39 900 896 4 790 150 5 720 277 1 700 83.3 2 620 27 000 7350 x283 2.77 36 000 787 4 310 148 5 100 246 1 530 82.6 2 340 20 300 6330 X253 2.48 32 300 682 3830 146 4490215 1 350 81.6 2 060 14 800 5 370 X226 2.22 28 800 596 3 420 144 3 970189 1 190 81.0 1830 10 800 4 620 X202 1.99 25700 520 3 050 142 3510 166 1 050 80.2 1 610 7730 3 960 x179 1.75 22 800 445 2 2 670 140 3 050 144 919 79.5 1 400 5 370 3 340 x158 1.54 20 100 386 2 360 139 2 670125 805 78.9 1 220 3770 2 840 X143 1.40 18 200 348 2 150 138 2 420113 729 78.6 1 110 2 860 2 540 x129 1.27 16 500 308 1 940137 2 160 100 652 78.0 991 2 130 2 220 x118 1.15 15 000 275 1 750 136 1 950 90.2 588 77.6 893 1 600 1970 X107 1.05 13 600 248 1 590 135 1 760 81.2 531 77.2 806 1 210 1 760 X97 0.949 12 300 222 1440 134 72.9 478 76.9 725 909 1 560 W310 x86 0.847 11 000 198 1 280 134 1420 44.5 351 63.6 533 874 961 x79 0.773 10 100 177 1 150 133 1 280 39.9 314 63.0 478 655 847 500 454 415 375 342 313 283 253 226 202 179 158 143 129 118 107 97 500.4 454.0 415.1 374.8 343.2 313.3 282.9 252.9 226.7 202.6 178.7 157.4 143.1 129.6 117.5 106.9 96.8 427 415 403 391 382 374 365 356 348 341 333 327 323 318 314 311 308 340 336 334 330 328 325 322 319 317 315 313 310 309 308 307 306 305 75.1 68.7 62.7 57.2 52.6 48.3 44.1 39.6 35.6 31.8 28.1 25.1 22.9 20.6 18.7 17.0 15.4 45.1 41.3 38.9 35.4 32.6 30.0 26.9 24.4 22.1 20.1 18.0 15.5 14.0 13.1 11.9 10.9 9.9 147 147 148 147 148 148 148 147 147 147 148 147 148 147 148 148 148 233 234 234 233 233 234 233 233 233 234 233 233 234 233 233 233 234 97 91 85 79 74 70 66 61 57 54 50 47 45 42 41 39 37 43 41 40 38 37 35 34 33 31 30 29 28 27 27 26 26 25 277 278 278 277 277 277 277 277 277 277 277 277 277 277 277 277 277 2.12 2.09 2.06 2.03 2.01 1.99 1.96 1.94 1.92 1.90 1.88 1.86 1.85 1.84 1.83 1.82 1.82 1.78 1.76 173 1.70 1.68 1.66 1.64 1.62 1.60 1.59 1.57 1.55 1.55 1.53 1.53 1 52 1.51 W122336 W12,305 W12279 W12,252 W12x230 W12x210 W12x190 W12x 170 W12x152 W12x136 W12x120 W12x106 W12x96 W12x87 W12x79 W12x72 W12x55 1 590 25 86 79 86.3 78.9 310 306 254 254 16.3 14.6 9.1 8.8 122 123 234 234 38 36 277 277 1 62 161 1.36 1.36 W12x58 W12x53 24 W310 x74 X67 x60 0.726 9 480 0.650 8520 0.580 7 610 164 144 128 1 060 132 942 131 842130 1 180 23.4 1 050 20.7 933 18.3 229 203 180 49.9 49.5 49.3 350 310 275 718 522 378 505 439 384 74 67 60 74.0 66.3 59.1 310 306 303 205 204 203 16.3 14.6 13.1 9.4 8.5 7.5 98 98 98 234 234 234 38 36 35 25 24 24 277 277 277 142 1.41 1 40 1.22 121 1.20 W12250 W12x45 W12x40 W310 x52 X45 x39 0.513 6 650 0.438 5670 0.380 4 940 118 99.2 85.1 747133 634 132 549 131 837 708 610 10.3 8.55 7.27 123 39.2 103 38.8 88.138.4 189 158 135 308 191 126 237 195 164 52 45 39 52.3 44.6 38.7 317 313 310 167 166 165 13.2 11.2 9.7 7.6 6.6 5.8 80 256 80 256 80 256 31 29 27 20 19 19 291 291 291 1.29 128 1 27 1.12 1.11 1.10 W12x35 W12x30 W12x26 15 W310 x33 x28 X24 X21 48 48 15 0.321 0.278 0.234 0.207 4 180 3 590 3040 2 680 65.0 54.3 42.7 37.0 415 125 351 123 280 119 244117 480 407 328 287 1.92 1.58 1.16 0.983 37.6 21.4 31.0 20.9 22.9 19.5 19.5 19.1 59.6 49.2 36.7 31.2 122 75.7 425 29.4 43.8 35.6 257 21.7 33 28 24 21 32.8 28.4 23.8 21.1 313 309 305 303 102 102 101 101 10.8 8.9 6.7 5.7 6.6 6.0 5.6 5.1 264 264 265 265 24 22 20 19 291 291 292 292 1.02 1.01 1.00 1.00 0.919 0.912 0902 0.899 W12x22 W12x19 W12x16 W12x14 15 15 48 Sections Highlighted in yellow are commonly used sizes and are generally readily available When subject to tension, bolted connections are preferred for these sections. Note: G40.21M-350W (Fy =350 MPa, Fu = 450 MPa) steel is to be used, unless otherwise specified. None of the beams in this assignment are cambered. It is not permitted to use M, values obtained from the beam selection tables found in the HSC - code calculations must be performed. 1. A W310x143 section is used as an interior column (column B) of a steel frame as shown in Figure 1. Assume that the lateral sways of the frame are prevented by the lateral load resisting system of the building (ex. shear wall or bracing) and the columns are laterally braced by the load bearing wall in the direction which is perpendicular to the frame plane. The column bases are pinned supports. Complete the following: a) Calculate the equivalent length factors K, for column B (for both the upper and lower columns). b) Evaluate the factored axial compressive resistance of both the upper and lower columns of column B based on the corresponding Ky values obtained from item a). W410x54 W410x67 34001 W410x60 W410x74 4300 column B W310x143 9500 11200 + * X Figure 1. Unit: mm W SHAPES W360 - W310 H W SHAPES W360 - W310 T H. Theo Warping Constant C. Nominal Mass retical Mass Depth Flange Flange Flange Web Width Thick Thick- ness ness d D t w mm mm mm mm DIMENSIONS AND SURFACE AREAS Distances Surface Area per metre of length Imperial T Kk6-21 Total of mm mm mm Top Flange a Mnus Top Designation kg/m kg/m mm 57 51 45 56.6 50.6 45.0 358 355 352 172 171 171 332 13.1 11.6 9.8 7.9 7.2 6.9 82 82 82 295 295 296 31 30 28 21 20 20 332 1.39 1.38 1.37 122 1.21 120 W14x38 W14x34 W14x30 332 39 33 39.1 32.7 353 349 128 127 10.7 8.5 6.5 5.8 61 61 295 296 29 27 20 20 332 332 1.21 1.19 1.08 1.07 W14x26 W14x22 PROPERTIES Torsional Axis Y-Y Axis X-X Dead Constant Area Designation Load 1 Sx Fy Z ly Sy Zy J kNm mm 106mm 10mm mm 10 mm 10 mm 10 mm mm 10 mm 10 mm 10mm W360 x57 0.555 7230 160 896 149 1010 11.1 129 39.3 199 333 331 X51 0.496 6 450 141 796 148 893 9.68 113 38.8 174 237 285 x45 0.441 5710 122 691146 778 8.18 95.7 378 148 159 239 W360 x39 0.383 4960 102 580 143 662 3.75 58.6 274 91.6 150 110 x33 0.321 4 190 82.6 473 141 541 2.91 45.8 26.4 71.8 85.3 84.3 W310 x500 4.91 63 700 1 690 7910 163 9 880494 2 910 88.0 4 490 101 000 15 300 X454 4.45 57 8001480 7 130 160 8820 436 2 600 86.8 4 000 77 200 13 100 X415 4.07 52 8001 300 6 450 157 7 900 391 2 340 86.0 3610 59 500 11 300 X375 3.68 47 800 1 130 5 770 154 7000 344 2 080 84.8 3210 44 900 9 570 x342 3.37 43 700 1 010 5260152 6 330 | 310 1 890 84.2 2 910 34 900 8 420 x313 3.07 39 900 896 4 790 150 5 720 277 1 700 83.3 2 620 27 000 7350 x283 2.77 36 000 787 4 310 148 5 100 246 1 530 82.6 2 340 20 300 6330 X253 2.48 32 300 682 3830 146 4490215 1 350 81.6 2 060 14 800 5 370 X226 2.22 28 800 596 3 420 144 3 970189 1 190 81.0 1830 10 800 4 620 X202 1.99 25700 520 3 050 142 3510 166 1 050 80.2 1 610 7730 3 960 x179 1.75 22 800 445 2 2 670 140 3 050 144 919 79.5 1 400 5 370 3 340 x158 1.54 20 100 386 2 360 139 2 670125 805 78.9 1 220 3770 2 840 X143 1.40 18 200 348 2 150 138 2 420113 729 78.6 1 110 2 860 2 540 x129 1.27 16 500 308 1 940137 2 160 100 652 78.0 991 2 130 2 220 x118 1.15 15 000 275 1 750 136 1 950 90.2 588 77.6 893 1 600 1970 X107 1.05 13 600 248 1 590 135 1 760 81.2 531 77.2 806 1 210 1 760 X97 0.949 12 300 222 1440 134 72.9 478 76.9 725 909 1 560 W310 x86 0.847 11 000 198 1 280 134 1420 44.5 351 63.6 533 874 961 x79 0.773 10 100 177 1 150 133 1 280 39.9 314 63.0 478 655 847 500 454 415 375 342 313 283 253 226 202 179 158 143 129 118 107 97 500.4 454.0 415.1 374.8 343.2 313.3 282.9 252.9 226.7 202.6 178.7 157.4 143.1 129.6 117.5 106.9 96.8 427 415 403 391 382 374 365 356 348 341 333 327 323 318 314 311 308 340 336 334 330 328 325 322 319 317 315 313 310 309 308 307 306 305 75.1 68.7 62.7 57.2 52.6 48.3 44.1 39.6 35.6 31.8 28.1 25.1 22.9 20.6 18.7 17.0 15.4 45.1 41.3 38.9 35.4 32.6 30.0 26.9 24.4 22.1 20.1 18.0 15.5 14.0 13.1 11.9 10.9 9.9 147 147 148 147 148 148 148 147 147 147 148 147 148 147 148 148 148 233 234 234 233 233 234 233 233 233 234 233 233 234 233 233 233 234 97 91 85 79 74 70 66 61 57 54 50 47 45 42 41 39 37 43 41 40 38 37 35 34 33 31 30 29 28 27 27 26 26 25 277 278 278 277 277 277 277 277 277 277 277 277 277 277 277 277 277 2.12 2.09 2.06 2.03 2.01 1.99 1.96 1.94 1.92 1.90 1.88 1.86 1.85 1.84 1.83 1.82 1.82 1.78 1.76 173 1.70 1.68 1.66 1.64 1.62 1.60 1.59 1.57 1.55 1.55 1.53 1.53 1 52 1.51 W122336 W12,305 W12279 W12,252 W12x230 W12x210 W12x190 W12x 170 W12x152 W12x136 W12x120 W12x106 W12x96 W12x87 W12x79 W12x72 W12x55 1 590 25 86 79 86.3 78.9 310 306 254 254 16.3 14.6 9.1 8.8 122 123 234 234 38 36 277 277 1 62 161 1.36 1.36 W12x58 W12x53 24 W310 x74 X67 x60 0.726 9 480 0.650 8520 0.580 7 610 164 144 128 1 060 132 942 131 842130 1 180 23.4 1 050 20.7 933 18.3 229 203 180 49.9 49.5 49.3 350 310 275 718 522 378 505 439 384 74 67 60 74.0 66.3 59.1 310 306 303 205 204 203 16.3 14.6 13.1 9.4 8.5 7.5 98 98 98 234 234 234 38 36 35 25 24 24 277 277 277 142 1.41 1 40 1.22 121 1.20 W12250 W12x45 W12x40 W310 x52 X45 x39 0.513 6 650 0.438 5670 0.380 4 940 118 99.2 85.1 747133 634 132 549 131 837 708 610 10.3 8.55 7.27 123 39.2 103 38.8 88.138.4 189 158 135 308 191 126 237 195 164 52 45 39 52.3 44.6 38.7 317 313 310 167 166 165 13.2 11.2 9.7 7.6 6.6 5.8 80 256 80 256 80 256 31 29 27 20 19 19 291 291 291 1.29 128 1 27 1.12 1.11 1.10 W12x35 W12x30 W12x26 15 W310 x33 x28 X24 X21 48 48 15 0.321 0.278 0.234 0.207 4 180 3 590 3040 2 680 65.0 54.3 42.7 37.0 415 125 351 123 280 119 244117 480 407 328 287 1.92 1.58 1.16 0.983 37.6 21.4 31.0 20.9 22.9 19.5 19.5 19.1 59.6 49.2 36.7 31.2 122 75.7 425 29.4 43.8 35.6 257 21.7 33 28 24 21 32.8 28.4 23.8 21.1 313 309 305 303 102 102 101 101 10.8 8.9 6.7 5.7 6.6 6.0 5.6 5.1 264 264 265 265 24 22 20 19 291 291 292 292 1.02 1.01 1.00 1.00 0.919 0.912 0902 0.899 W12x22 W12x19 W12x16 W12x14 15 15 48 Sections Highlighted in yellow are commonly used sizes and are generally readily available When subject to tension, bolted connections are preferred for these sections