Analytical Solution for Lateral-Torsional Buckling of Concrete-Filled Tubular Flange Girders with Torsional Bracing

<table class="table-group" id="tab9"><tr><td><table class="table"><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left">Parameter</td><td class="align_center"><i>H</i> (mm)</td><td class="align_center"><i>b</i><sub><i>f</i></sub> (mm)</td><td class="align_center"><i>t</i><sub><i>f</i></sub> (mm)</td><td class="align_center"><i>t</i> (mm)</td><td class="align_center"><svg height="12.5794pt" id="M107" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 13.8605 12.5794" width="13.8605pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 240 712C227 712 170 680 87 673L82 648H117C155 648 162 644 150 590L23 -4L30 -12C55 -4 81 3 105 8C113 53 131 150 143 187C199 281 323 387 372 387C390 387 393 369 380 311L328 86C313 19 319 -12 347 -12C379 -12 442 24 499 88Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.643,3.132)"><path d="M698 334C698 397 680 451 655 451C627 451 602 424 602 397C602 389 605 383 614 371C622 360 624 340 624 317C624 161 546 47 458 47C419 47 389 69 389 125C389 142 391 162 397 185L457 430L451 435L380 421L315 164C301 107 266 47 222 47C182 47 153 69 153 126C153 137 157 162 161 185C166 214 179 265 197 334C203 358 208 385 208 407C208 433 201 451 176 451C124 451 64 404 24 348L44 320C86 366 113 382 121 382C126 382 128 381 128 374C128 368 126 356 122 341C102 266 88 204 81 164C77 143 73 121 73 107C73 23 131 -12 187 -12C234 -12 281 10 322 45C343 5 383 -12 422 -12C559 -12 698 174 698 334Z"></path></g></svg> (mm)</td><td class="align_center"><svg height="11.1049pt" id="M108" style="vertical-align:-3.29108pt" version="1.1" viewbox="-0.0498162 -7.81382 11.577 11.1049" width="11.577pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.368,3.132)"><path d="M698 334C698 397 680 451 655 451C627 451 602 424 602 397C602 389 605 383 614 371C622 360 624 340 624 317C624 161 546 47 458 47C419 47 389 69 389 125C389 142 391 162 397 185L457 430L451 435L380 421L315 164C301 107 266 47 222 47C182 47 153 69 153 126C153 137 157 162 161 185C166 214 179 265 197 334C203 358 208 385 208 407C208 433 201 451 176 451C124 451 64 404 24 348L44 320C86 366 113 382 121 382C126 382 128 381 128 374C128 368 126 356 122 341C102 266 88 204 81 164C77 143 73 121 73 107C73 23 131 -12 187 -12C234 -12 281 10 322 45C343 5 383 -12 422 -12C559 -12 698 174 698 334Z"></path></g></svg> (mm)</td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td class="align_left">Section 1</td><td class="align_center">440</td><td class="align_center">160</td><td class="align_center">80</td><td class="align_center">3</td><td class="align_center">280</td><td class="align_center">4</td></tr><tr><td class="align_left">Section 2</td><td class="align_center">1260</td><td class="align_center">500</td><td class="align_center">300</td><td class="align_center">6</td><td class="align_center">660</td><td class="align_center">8</td></tr><tr><td class="align_left">Section 3</td><td class="align_center">600</td><td class="align_center">120</td><td class="align_center">60</td><td class="align_center">3</td><td class="align_center">480</td><td class="align_center">4</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The sizes of the three sections.</div>

Advances in Civil Engineering

tab9

Table 9

Table 9: Analytical Solution for Lateral-Torsional Buckling of Concrete-Filled Tubular Flange Girders with Torsional Bracing 