Overturning Axis Selection in Curved Box-Girder Bridges with Single-Column Piers

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/mpe/volume-2018/9206138/figures/9206138.fig.007a.svgz" name="9206138.fig.007a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Schematic diagram of overturning axis selection</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/mpe/volume-2018/9206138/figures/9206138.fig.007b.svgz" name="9206138.fig.007b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Parameters Ω and <svg height="9.49473pt" id="M34" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 7.34169 9.49473" width="7.34169pt" 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="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z" id="g113-101"></path></g></svg> for overturning axis 1</td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/mpe/volume-2018/9206138/figures/9206138.fig.007c.svgz" name="9206138.fig.007c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>Parameters Ω and <svg height="9.49473pt" id="M35" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 7.34169 9.49473" width="7.34169pt" 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="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z" id="g113-101"></path></g></svg> for overturning axis 2</td></tr><tr class="fig-image" id="d"><td><object data="https://static.hindawi.com/articles/mpe/volume-2018/9206138/figures/9206138.fig.007d.svgz" name="9206138.fig.007d" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(d) </b>Distances <svg height="9.25202pt" id="M36" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 10.3843 9.25202" width="10.3843pt" 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="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z" id="g113-121"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path></g></svg> for axis 1 and axis 2 (the red is for axis 1, and the blue is for axis 2)</td></tr></table>

<div>Overturning axis selection analysis.</div>

Mathematical Problems in Engineering

fig7

Figure 7

Figure 7: Overturning Axis Selection in Curved Box-Girder Bridges with Single-Column Piers 