A New Unified Solution for Circular Opening considering Different Strength Criteria and the Postpeak Elastic Strain Form

<table class="table-group" id="tab4"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Strength criterion</td><td class="align_center"><span style="width: 40.631ptpx;"><svg height="12.5794pt" id="M288" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 40.631 12.5794" width="40.631pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 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480 485Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,30.978,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"></path></g><g transform="matrix(.013,0,0,-0.013,35.924,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg> <svg height="14.5707pt" id="M289" style="vertical-align:-5.28237pt" version="1.1" viewbox="-0.0498162 -9.28833 43.6318 14.5707" width="43.6318pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 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686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg></span></td><td class="align_center">Strength criterion</td><td class="align_center"><span style="width: 40.631ptpx;"><svg height="12.5794pt" id="M290" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 40.631 12.5794" width="40.631pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 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transform="matrix(.0091,0,0,-0.0091,30.978,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"></path></g><g transform="matrix(.013,0,0,-0.013,35.924,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg><svg height="14.5707pt" id="M291" style="vertical-align:-5.28237pt" version="1.1" viewbox="-0.0498162 -9.28833 43.6318 14.5707" width="43.6318pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.498,0)"><path d="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 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37V0H394Z"></path></g><g transform="matrix(.013,0,0,-0.013,21.241,0)"><path d="M368 703H309L44 -163H104L368 703Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.602,0)"><path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,33.986,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"></path></g><g transform="matrix(.013,0,0,-0.013,38.932,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">MC</td><td class="align_center">1.528 (0.413)</td><td class="align_center">VM</td><td class="align_center">2.728 (0.667)</td></tr><tr><td class="align_left">GMC</td><td class="align_center">1.318 (0.322)</td><td class="align_center">IDP</td><td class="align_center">1.556 (0.422)</td></tr><tr><td class="align_left">GLD</td><td class="align_center">1.294 (0.308)</td><td class="align_center">MDP</td><td class="align_center">1.456 (0.386)</td></tr><tr><td class="align_left">GSMP</td><td class="align_center">1.332 (0.329)</td><td class="align_center">CDP</td><td class="align_center">1.198 (0.242)</td></tr><tr><td class="align_left">TR</td><td class="align_center">3.442 (0.712)</td><td class="align_center">UST<sub>0.5</sub></td><td class="align_center">1.347 (0.337)</td></tr><tr><td class="align_left">GTSS</td><td class="align_center">1.266 (0.291)</td><td class="align_center">—</td><td class="align_center">—</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The radius of plastic zone and critical inner pressures under different criteria.</div>

Advances in Civil Engineering

tab4

Table 4

Table 4: A New Unified Solution for Circular Opening considering Different Strength Criteria and the Postpeak Elastic Strain Form 