Seismic Retrofit of a Multispan Prestressed Concrete Girder Bridge with Friction Pendulum Devices

<table class="fixed-width table-group" id="tab6"><tr><td><table class="table"><colgroup><col style="width:7.46em"/><col style="width:6.95em"/><col style="width:7.02em"/><col style="width:6.86em"/><col style="width:6.93em"/></colgroup><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left">Direction</td><td class="align_center"><svg height="10.3116pt" id="M178" style="vertical-align:-4.35069pt" version="1.1" viewbox="-0.0498162 -5.96091 23.6392 10.3116" width="23.6392pt" 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="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z" id="g113-100"></path></g><g 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251 420C226 404 205 389 185 374V453C142 434 94 422 43 413V386C98 378 104 373 104 309V107C104 41 100 38 31 30V0H251V30C191 35 185 40 185 107V337C216 364 255 389 295 389C360 389 386 347 386 276V110C386 44 380 35 321 30V0H532Z" id="g58-108"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.116,3.132)"><path d="M303 37L293 66C280 59 256 49 231 49S173 63 173 143V396H281C294 404 298 428 287 439H173V575L158 577L92 509V439H46L17 408L22 396H92V107C92 27 128 -12 192 -12C203 -12 218 -9 237 2L303 37Z" id="g58-114"></path></g></svg> [kN⋅s/m]</td><td class="align_center"><svg height="10.3116pt" id="M179" style="vertical-align:-4.35069pt" version="1.1" viewbox="-0.0498162 -5.96091 24.5891 10.3116" width="24.5891pt" 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="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z" id="g113-100"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.173,3.132)"><path d="M682 0V33C615 38 603 49 571 134C507 305 441 494 378 665L343 655L136 136C101 48 86 41 22 33V0H246V33C170 41 161 50 183 112C196 152 209 192 224 232H441C461 176 478 126 493 87C504 49 499 41 433 33V0H682ZM425 279H242C273 363 303 448 335 533H337L425 279Z" id="g58-63"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.57,3.132)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.727,3.132)"><path d="M384 109C349 76 310 59 268 59C197 59 123 113 120 245C240 248 367 259 384 262C403 266 407 275 407 296C407 376 338 451 254 451H253C201 451 148 425 105 378C65 334 39 272 39 203C39 88 112 -12 235 -12C266 -12 339 5 402 84L384 109ZM230 411C285 411 319 365 319 313C319 298 313 293 294 293C236 291 180 290 125 290C141 370 185 411 230 411Z" id="g58-99"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.676,3.132)"><path d="M482 0V30C420 38 407 48 370 103L273 248C308 299 331 332 352 357C387 397 401 404 463 409V439H277V409C318 405 324 400 307 369C290 337 270 307 251 279L194 367C175 396 180 402 220 409V439H18V409C74 401 87 395 117 349L204 213C173 168 147 130 119 95C78 46 67 38 5 30V0H195V30C144 38 143 47 162 79C181 112 202 149 225 181L297 70C314 43 307 35 264 30V0H482Z" id="g58-118"></path></g><g transform="matrix(.0091,0,0,-0.0091,21.063,3.132)"><path d="M303 37L293 66C280 59 256 49 231 49S173 63 173 143V396H281C294 404 298 428 287 439H173V575L158 577L92 509V439H46L17 408L22 396H92V107C92 27 128 -12 192 -12C203 -12 218 -9 237 2L303 37Z" id="g58-114"></path></g></svg> [kN⋅s/m]</td><td class="align_center"><svg height="10.3116pt" id="M180" style="vertical-align:-4.35069pt" version="1.1" viewbox="-0.0498162 -5.96091 22.4517 10.3116" width="22.4517pt" 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="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z" id="g113-100"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.173,3.132)"><path d="M46 650V618C122 613 130 611 130 522V128C130 46 123 40 40 32V0H319V32C227 40 217 42 217 128V279L292 260C303 259 322 258 338 261C436 272 534 337 534 467C534 534 508 580 469 609C428 640 371 650 299 650H46ZM217 558C217 585 220 596 228 603C235 610 256 615 284 615C367 615 435 571 435 463C435 339 358 304 291 304C256 304 229 310 217 317V558Z" id="g58-78"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.387,3.132)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.544,3.132)"><path d="M138 535C169 535 191 560 191 589C191 620 168 644 139 644S85 620 85 589C85 560 110 535 138 535ZM257 0V30C192 35 185 43 185 109V453C142 435 94 422 40 414V386C101 378 104 372 104 311V109C104 41 97 35 33 30V0H257Z" id="g58-103"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.046,3.132)"><path d="M532 0V30C473 38 467 38 467 107V298C467 395 416 451 336 451C307 451 279 439 251 420C226 404 205 389 185 374V453C142 434 94 422 43 413V386C98 378 104 373 104 309V107C104 41 100 38 31 30V0H251V30C191 35 185 40 185 107V337C216 364 255 389 295 389C360 389 386 347 386 276V110C386 44 380 35 321 30V0H532Z" id="g58-108"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.932,3.132)"><path d="M303 37L293 66C280 59 256 49 231 49S173 63 173 143V396H281C294 404 298 428 287 439H173V575L158 577L92 509V439H46L17 408L22 396H92V107C92 27 128 -12 192 -12C203 -12 218 -9 237 2L303 37Z" id="g58-114"></path></g></svg> [kN⋅s/m]</td><td class="align_center"><svg height="10.3116pt" id="M181" style="vertical-align:-4.35069pt" version="1.1" viewbox="-0.0498162 -5.96091 23.4017 10.3116" width="23.4017pt" 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="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z" id="g113-100"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.173,3.132)"><path d="M46 650V618C122 613 130 611 130 522V128C130 46 123 40 40 32V0H319V32C227 40 217 42 217 128V279L292 260C303 259 322 258 338 261C436 272 534 337 534 467C534 534 508 580 469 609C428 640 371 650 299 650H46ZM217 558C217 585 220 596 228 603C235 610 256 615 284 615C367 615 435 571 435 463C435 339 358 304 291 304C256 304 229 310 217 317V558Z" id="g58-78"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.387,3.132)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.544,3.132)"><path d="M384 109C349 76 310 59 268 59C197 59 123 113 120 245C240 248 367 259 384 262C403 266 407 275 407 296C407 376 338 451 254 451H253C201 451 148 425 105 378C65 334 39 272 39 203C39 88 112 -12 235 -12C266 -12 339 5 402 84L384 109ZM230 411C285 411 319 365 319 313C319 298 313 293 294 293C236 291 180 290 125 290C141 370 185 411 230 411Z" id="g58-99"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.493,3.132)"><path d="M482 0V30C420 38 407 48 370 103L273 248C308 299 331 332 352 357C387 397 401 404 463 409V439H277V409C318 405 324 400 307 369C290 337 270 307 251 279L194 367C175 396 180 402 220 409V439H18V409C74 401 87 395 117 349L204 213C173 168 147 130 119 95C78 46 67 38 5 30V0H195V30C144 38 143 47 162 79C181 112 202 149 225 181L297 70C314 43 307 35 264 30V0H482Z" id="g58-118"></path></g><g transform="matrix(.0091,0,0,-0.0091,19.88,3.132)"><path d="M303 37L293 66C280 59 256 49 231 49S173 63 173 143V396H281C294 404 298 428 287 439H173V575L158 577L92 509V439H46L17 408L22 396H92V107C92 27 128 -12 192 -12C203 -12 218 -9 237 2L303 37Z" id="g58-114"></path></g></svg> [kN⋅s/m]</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">Longitudinal <svg height="8.68572pt" id="M182" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 10.0819 8.68572" width="10.0819pt" 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="M748 650H522L515 622L546 617C580 611 587 604 565 575C518 513 469 451 419 393C376 474 349 534 330 580C318 609 325 612 361 618L383 622L392 650H151L144 622C214 616 224 612 257 543L360 327C270 218 187 124 159 95C106 40 92 34 26 28L17 0H252L259 28L236 31C189 37 188 47 209 78C249 136 308 210 377 294L478 79C494 44 487 37 449 32L418 28L409 0H673L680 28C596 34 591 39 554 116L436 361C526 469 574 521 604 553C659 612 669 614 739 622L748 650Z" id="g113-89"></path></g></svg></td><td class="align_center">215.94</td><td class="align_center">179.95</td><td class="align_center">223.68</td><td class="align_center">186.40</td></tr><tr><td class="align_left">Transverse <svg height="8.68572pt" id="M183" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 8.6074 8.68572" width="8.6074pt" 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="M640 650H413L406 622L438 617C475 611 483 605 463 571C422 503 346 400 296 333C264 403 215 529 199 575C189 604 191 614 228 618L262 622L271 650H30L23 622C90 615 97 609 119 553L212 321C222 295 223 285 218 259L193 127C176 39 167 33 82 28L76 0H350L356 28C266 36 257 40 275 127L303 266C308 290 314 302 328 322C396 418 454 493 498 546C551 610 565 616 631 622L640 650Z" id="g113-90"></path></g></svg></td><td class="align_center">120.84</td><td class="align_center">100.70</td><td class="align_center">125.22</td><td class="align_center">104.35</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Values of the damping constants of the substructure elements.</div>

Shock and Vibration

tab6

Table 6

Table 6: Seismic Retrofit of a Multispan Prestressed Concrete Girder Bridge with Friction Pendulum Devices 