Comparing Hysteretic Energy and Ductility Uniform Annual Failure Rate Spectra for Traditional and a Spectral Shape-Based Intensity Measure

<div>Ductility UAFR spectra for <svg height="11.5303pt" id="M22" style="vertical-align:-3.18148pt" version="1.1" viewbox="-0.0498162 -8.34882 55.0914 11.5303" width="55.0914pt" 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="M213 67C239 136 257 225 255 300C253 353 242 447 164 447C112 447 54 389 41 319L67 309C90 362 117 377 134 377C184 377 189 277 190 239C193 153 164 43 146 -12H176C278 73 450 253 450 390C450 439 410 463 396 463C384 463 380 459 382 449C385 440 389 415 389 402C389 284 312 146 216 67H213Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.902,3.132)"><path d="M606 650H137L129 618C217 609 221 609 203 518L129 129C115 46 106 40 26 32L18 0H300L307 32C210 40 203 45 218 129L249 305H358C454 305 455 296 457 219H491L531 425H497C465 353 463 350 366 350H259L300 569C306 605 310 611 346 611H444C522 611 535 598 541 578C550 557 553 519 552 485L588 489L606 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.65,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,26.912,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.152,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,36.116,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,42.356,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,48.596,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z"></path></g></svg> and the nonlinear hysteretic models: (a) elasto-perfectly plastic and elastoplastic with (b) 3%, (c) 5%, and (d) 10% of post-yielding stiffness.</div>

Advances in Civil Engineering

fig6

Figure 6

Figure 6: Comparing Hysteretic Energy and Ductility Uniform Annual Failure Rate Spectra for Traditional and a Spectral Shape-Based Intensity Measure 