Feasibility Study on Tension Estimation Technique for Hanger Cables Using the FE Model-Based System Identification Method

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td align="left">Cable number</td><td align="center">Length (m)</td><td align="center">Diameter (mm)</td><td align="center">Young’s modulus (<svg height="12.1853pt" id="M47" style="vertical-align:-0.6303997pt" version="1.1" viewbox="-0.0498162 -11.5549 46.7056 12.1853" width="46.7056pt" 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="M513 0V26C475 28 448 43 413 81C379 116 277 234 258 264C301 314 319 334 344 359C383 396 404 407 473 418V443L269 434V408C317 403 320 395 299 364C280 337 250 298 228 276C213 260 195 247 165 241V712C126 699 69 682 21 677V653C82 648 87 642 87 576V104C87 40 81 32 14 26V0H237V26C173 32 165 38 165 104V215C171 217 176 218 181 218C189 218 198 212 212 196C267 129 330 49 376 -2L513 0Z" id="g190-108"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="496" vert-adv-y="496"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,6.448,0)"><path d="M719 650H483V622C553 619 576 606 581 560C585 532 588 487 588 394V148H585L167 650H20V622C67 618 88 610 109 585C127 562 129 557 129 484V264C129 173 126 124 123 93C118 44 92 31 35 28V0H272V28C204 32 181 44 176 95C173 124 170 172 170 264V515H172L598 -9H629V394C629 487 631 532 635 563C639 606 663 619 719 622V650Z" id="g190-79"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="743" vert-adv-y="743"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,16.107,0)"><path d="M298 665H241L25 -44H81L298 665Z" id="g190-48"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="331" vert-adv-y="331"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,20.487,0)"><path d="M797 0V26C739 32 732 36 732 103V296C732 394 682 449 605 449C576 449 550 437 529 423C504 407 475 389 446 366C425 418 382 449 334 449C303 449 279 437 253 421C222 403 201 385 180 371V452C135 432 85 419 41 411V388C99 379 102 374 102 310V103C102 38 93 32 27 26V0H238V26C189 32 180 38 180 103V338C210 363 250 390 289 390C351 390 377 348 377 275V103C377 37 368 32 306 26V0H520V26C465 32 456 38 456 101V296C456 314 455 326 453 338C491 369 529 390 565 390C628 390 653 345 653 274V107C653 36 642 32 583 26V0H797Z" id="g190-110"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="819" vert-adv-y="819"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,31.134,0)"><path d="M797 0V26C739 32 732 36 732 103V296C732 394 682 449 605 449C576 449 550 437 529 423C504 407 475 389 446 366C425 418 382 449 334 449C303 449 279 437 253 421C222 403 201 385 180 371V452C135 432 85 419 41 411V388C99 379 102 374 102 310V103C102 38 93 32 27 26V0H238V26C189 32 180 38 180 103V338C210 363 250 390 289 390C351 390 377 348 377 275V103C377 37 368 32 306 26V0H520V26C465 32 456 38 456 101V296C456 314 455 326 453 338C491 369 529 390 565 390C628 390 653 345 653 274V107C653 36 642 32 583 26V0H797Z" id="g190-110"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="819" vert-adv-y="819"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,41.86,-5.741)"><path d="M411 139C381 76 368 73 314 73H129L267 224C351 317 400 380 400 469C400 574 322 635 233 635C176 635 128 610 98 576L40 495L63 476C89 515 130 568 198 568C274 568 316 519 316 436C316 347 251 264 191 192C142 134 85 76 30 21V0H403C415 45 425 89 438 131L411 139Z" id="g190-243"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="465" vert-adv-y="465"></glyph.data></g></svg>)</td><td align="center">Weight (<svg height="12.1853pt" id="M48" style="vertical-align:-0.6303997pt" version="1.1" viewbox="-0.0498162 -11.5549 46.5868 12.1853" width="46.5868pt" 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="M513 0V26C475 28 448 43 413 81C379 116 277 234 258 264C301 314 319 334 344 359C383 396 404 407 473 418V443L269 434V408C317 403 320 395 299 364C280 337 250 298 228 276C213 260 195 247 165 241V712C126 699 69 682 21 677V653C82 648 87 642 87 576V104C87 40 81 32 14 26V0H237V26C173 32 165 38 165 104V215C171 217 176 218 181 218C189 218 198 212 212 196C267 129 330 49 376 -2L513 0Z" id="g190-108"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="496" vert-adv-y="496"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,6.448,0)"><path d="M719 650H483V622C553 619 576 606 581 560C585 532 588 487 588 394V148H585L167 650H20V622C67 618 88 610 109 585C127 562 129 557 129 484V264C129 173 126 124 123 93C118 44 92 31 35 28V0H272V28C204 32 181 44 176 95C173 124 170 172 170 264V515H172L598 -9H629V394C629 487 631 532 635 563C639 606 663 619 719 622V650Z" id="g190-79"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="743" vert-adv-y="743"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,16.107,0)"><path d="M298 665H241L25 -44H81L298 665Z" id="g190-48"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="331" vert-adv-y="331"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,20.487,0)"><path d="M797 0V26C739 32 732 36 732 103V296C732 394 682 449 605 449C576 449 550 437 529 423C504 407 475 389 446 366C425 418 382 449 334 449C303 449 279 437 253 421C222 403 201 385 180 371V452C135 432 85 419 41 411V388C99 379 102 374 102 310V103C102 38 93 32 27 26V0H238V26C189 32 180 38 180 103V338C210 363 250 390 289 390C351 390 377 348 377 275V103C377 37 368 32 306 26V0H520V26C465 32 456 38 456 101V296C456 314 455 326 453 338C491 369 529 390 565 390C628 390 653 345 653 274V107C653 36 642 32 583 26V0H797Z" id="g190-110"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="819" vert-adv-y="819"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,31.134,0)"><path d="M797 0V26C739 32 732 36 732 103V296C732 394 682 449 605 449C576 449 550 437 529 423C504 407 475 389 446 366C425 418 382 449 334 449C303 449 279 437 253 421C222 403 201 385 180 371V452C135 432 85 419 41 411V388C99 379 102 374 102 310V103C102 38 93 32 27 26V0H238V26C189 32 180 38 180 103V338C210 363 250 390 289 390C351 390 377 348 377 275V103C377 37 368 32 306 26V0H520V26C465 32 456 38 456 101V296C456 314 455 326 453 338C491 369 529 390 565 390C628 390 653 345 653 274V107C653 36 642 32 583 26V0H797Z" id="g190-110"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="819" vert-adv-y="819"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,41.86,-5.741)"><path d="M269 381C298 400 325 421 340 436C360 455 370 476 370 504C370 579 313 635 223 635H222C170 635 123 610 95 579L52 516L72 497C95 533 136 577 193 577C245 577 286 546 286 482C286 408 218 369 127 339L133 314C149 319 174 325 197 325C254 325 324 285 324 192C325 83 266 39 201 39C143 39 103 68 78 91C70 98 62 97 54 91C45 84 33 71 32 58C30 46 34 35 48 22C61 10 102 -12 148 -12C216 -12 410 57 410 225C410 298 357 362 269 379V381Z" id="g190-232"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="452" vert-adv-y="452"></glyph.data></g></svg>)</td><td align="center">Design tension (kN)</td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td align="left">29A</td><td align="center">25.3234</td><td align="center" rowspan="4">49.52</td><td align="center" rowspan="4"><span style="width: 65.3355ptpx;"><svg height="11.8774pt" id="M49" style="vertical-align:-0.3499002pt" version="1.1" viewbox="-0.0498162 -11.5275 65.3355 11.8774" width="65.3355pt" 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="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g121-47"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,6.24,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path><glyph.data ascent="3473" descent="-2876" 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71 555 71 471C71 400 113 353 178 316C143 295 107 268 91 252C70 231 46 202 46 157C46 50 132 -12 241 -12C329 -12 442 52 442 168C442 257 379 305 311 343C354 374 380 398 388 407C407 428 417 458 417 487C417 568 348 635 253 635ZM240 600C288 600 340 564 340 481C340 422 314 387 279 360C207 395 148 426 148 499C148 549 181 600 240 600ZM252 23C188 23 129 72 129 163C129 218 162 266 211 298C288 261 360 217 360 144C360 68 312 23 252 23Z" id="g58-54"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg></span></td><td align="center" rowspan="4">377.685</td></tr><tr><td align="left">29B</td><td align="center">24.9986</td></tr><tr><td align="left">36A</td><td align="center">9.0173</td></tr><tr><td align="left">36B</td><td align="center">8.8329</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Geometrical and material properties of the hanger cables.

Mathematical Problems in Engineering

tab1

Table 1

Table 1: Feasibility Study on Tension Estimation Technique for Hanger Cables Using the FE Model-Based System Identification Method 