Identification of Torsionally Coupled Shear Buildings Models Using a Vector Parameterization

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/sv/volume-2016/6731928/figures/6731928.fig.0013a.svgz" name="6731928.fig.0013a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b><svg height="11.927pt" id="M1072" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 14.4894 11.927" width="14.4894pt" 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="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z" id="g113-70"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="616" vert-adv-y="616"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.665,2.976)"><path d="M490 623L468 651C434 618 405 602 360 602C327 602 300 608 259 619C204 636 179 642 146 642C101 642 46 623 0 561L22 533C59 565 94 582 139 582C175 582 196 573 232 564C277 552 312 542 349 542C396 542 452 559 490 623Z" id="g56-25"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="490" vert-adv-y="490"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.943,3.132)"><path d="M624 292C624 400 569 451 537 451C520 451 497 442 490 436L489 427C521 404 550 351 550 280C550 170 513 51 423 51C383 51 361 87 361 150C361 197 384 301 397 339L391 343L310 328C307 297 301 249 293 212C270 102 223 56 182 56C144 56 114 93 114 172C114 278 161 369 243 430L223 457C99 392 24 290 24 156C24 43 81 -12 141 -12C187 -12 247 32 286 88C295 31 325 -12 380 -12C431 -12 475 16 511 49C581 113 624 195 624 292Z" id="g50-246"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="648" vert-adv-y="648"></glyph.data></g></svg> versus <svg height="9.49473pt" id="M1073" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.84582 9.49473" width="6.84582pt" 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="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z" id="g113-226"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="517" vert-adv-y="517"></glyph.data></g></svg> for the three-story model</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/sv/volume-2016/6731928/figures/6731928.fig.0013b.svgz" name="6731928.fig.0013b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b><svg height="11.927pt" id="M1074" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 14.4894 11.927" width="14.4894pt" 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="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z" id="g113-70"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="616" vert-adv-y="616"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.665,2.976)"><path d="M490 623L468 651C434 618 405 602 360 602C327 602 300 608 259 619C204 636 179 642 146 642C101 642 46 623 0 561L22 533C59 565 94 582 139 582C175 582 196 573 232 564C277 552 312 542 349 542C396 542 452 559 490 623Z" id="g56-25"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="490" vert-adv-y="490"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.943,3.132)"><path d="M624 292C624 400 569 451 537 451C520 451 497 442 490 436L489 427C521 404 550 351 550 280C550 170 513 51 423 51C383 51 361 87 361 150C361 197 384 301 397 339L391 343L310 328C307 297 301 249 293 212C270 102 223 56 182 56C144 56 114 93 114 172C114 278 161 369 243 430L223 457C99 392 24 290 24 156C24 43 81 -12 141 -12C187 -12 247 32 286 88C295 31 325 -12 380 -12C431 -12 475 16 511 49C581 113 624 195 624 292Z" id="g50-246"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="648" vert-adv-y="648"></glyph.data></g></svg> versus <svg height="9.25202pt" id="M1075" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 12.3507 9.25202" width="12.3507pt" 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="M615 290C615 392 563 448 529 448C511 448 491 441 484 434L483 425C518 400 546 349 546 273C546 158 504 46 417 46C381 46 356 77 356 142C356 184 380 293 392 334L387 340L307 323C305 288 296 228 287 188C265 94 221 52 180 52C144 52 112 89 112 171C112 278 164 372 241 430L226 454C106 394 23 288 23 155C23 40 79 -12 139 -12C184 -12 245 32 285 85C292 31 322 -12 376 -12C423 -12 470 18 501 45C570 104 615 184 615 290Z" id="g113-246"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="638" vert-adv-y="638"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.969,3.132)"><path d="M387 400C387 425 348 451 303 451C247 451 176 414 132 376C69 322 24 228 24 148C24 43 74 -12 147 -12C211 -12 301 33 363 103L346 128C319 99 249 51 193 51C148 51 112 84 112 165C112 230 130 287 154 330C170 359 199 400 243 400C277 400 304 383 326 354C333 345 343 343 354 348C378 360 387 382 387 400Z" id="g50-100"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="411" vert-adv-y="411"></glyph.data></g></svg> for the three-story model</td></tr></table>

<div>Plots of <svg height="11.927pt" id="M1068" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 14.4894 11.927" width="14.4894pt" 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="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z" id="g113-70"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="616" vert-adv-y="616"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.665,2.976)"><path d="M490 623L468 651C434 618 405 602 360 602C327 602 300 608 259 619C204 636 179 642 146 642C101 642 46 623 0 561L22 533C59 565 94 582 139 582C175 582 196 573 232 564C277 552 312 542 349 542C396 542 452 559 490 623Z" id="g56-25"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="490" vert-adv-y="490"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.943,3.132)"><path d="M624 292C624 400 569 451 537 451C520 451 497 442 490 436L489 427C521 404 550 351 550 280C550 170 513 51 423 51C383 51 361 87 361 150C361 197 384 301 397 339L391 343L310 328C307 297 301 249 293 212C270 102 223 56 182 56C144 56 114 93 114 172C114 278 161 369 243 430L223 457C99 392 24 290 24 156C24 43 81 -12 141 -12C187 -12 247 32 286 88C295 31 325 -12 380 -12C431 -12 475 16 511 49C581 113 624 195 624 292Z" id="g50-246"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="648" vert-adv-y="648"></glyph.data></g></svg> versus <svg height="9.49473pt" id="M1069" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.84582 9.49473" width="6.84582pt" 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="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z" id="g113-226"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="517" vert-adv-y="517"></glyph.data></g></svg> and <svg height="11.927pt" id="M1070" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 14.4894 11.927" width="14.4894pt" 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="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z" id="g113-70"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="616" vert-adv-y="616"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.665,2.976)"><path d="M490 623L468 651C434 618 405 602 360 602C327 602 300 608 259 619C204 636 179 642 146 642C101 642 46 623 0 561L22 533C59 565 94 582 139 582C175 582 196 573 232 564C277 552 312 542 349 542C396 542 452 559 490 623Z" id="g56-25"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="490" vert-adv-y="490"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.943,3.132)"><path d="M624 292C624 400 569 451 537 451C520 451 497 442 490 436L489 427C521 404 550 351 550 280C550 170 513 51 423 51C383 51 361 87 361 150C361 197 384 301 397 339L391 343L310 328C307 297 301 249 293 212C270 102 223 56 182 56C144 56 114 93 114 172C114 278 161 369 243 430L223 457C99 392 24 290 24 156C24 43 81 -12 141 -12C187 -12 247 32 286 88C295 31 325 -12 380 -12C431 -12 475 16 511 49C581 113 624 195 624 292Z" id="g50-246"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="648" vert-adv-y="648"></glyph.data></g></svg> versus <svg height="9.25202pt" id="M1071" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 12.3507 9.25202" width="12.3507pt" 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="M615 290C615 392 563 448 529 448C511 448 491 441 484 434L483 425C518 400 546 349 546 273C546 158 504 46 417 46C381 46 356 77 356 142C356 184 380 293 392 334L387 340L307 323C305 288 296 228 287 188C265 94 221 52 180 52C144 52 112 89 112 171C112 278 164 372 241 430L226 454C106 394 23 288 23 155C23 40 79 -12 139 -12C184 -12 245 32 285 85C292 31 322 -12 376 -12C423 -12 470 18 501 45C570 104 615 184 615 290Z" id="g113-246"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="638" vert-adv-y="638"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.969,3.132)"><path d="M387 400C387 425 348 451 303 451C247 451 176 414 132 376C69 322 24 228 24 148C24 43 74 -12 147 -12C211 -12 301 33 363 103L346 128C319 99 249 51 193 51C148 51 112 84 112 165C112 230 130 287 154 330C170 359 199 400 243 400C277 400 304 383 326 354C333 345 343 343 354 348C378 360 387 382 387 400Z" id="g50-100"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="411" vert-adv-y="411"></glyph.data></g></svg> corresponding to the three-story reduced model.</div>

Shock and Vibration

fig13

Figure 13

Figure 13: Identification of Torsionally Coupled Shear Buildings Models Using a Vector Parameterization 