Report - PEER - University of California, Berkeley
Report - PEER - University of California, Berkeley Report - PEER - University of California, Berkeley
where a is the constant peculiar to the type of restoring force characteristics. γ 1 ranges2N⎛ ⎞⎜ ∑ mj⎟j i2 k1 ≤ γ1≤ ∑ si,⎜ = ⎟1si= ・ - α 1⎜ ・M⎟(23)k⎜ ⎟i⎝ ⎠−where αiis the optimum yield shear force coefficient which produces the equal--distribution of µi. The upper bound of γ 1 (=∑ Si ) is attained in the case where µiisequal in all stories. By equating W p in the case of the evenly distributed damage andthat in the case of arbitrarily distributed damage, - -µ can be related to µi. W p iswritten in two ways.1WPMg=4π2 2T022 2T022α1µi・κ12 −1µ1s aMg α γ1a2WP= ・4πκ1The balance of energy results inα2 −1µ1γ1κ12 -1∑α µai=κ1−∑i(24)sia, (25)−− r1µ1= (26)∑ siiµ5. ILLUSTRATIVE EXAMPLE OF EFFECTIVE PERIOD OF MULTI-MASSSYSTEMSThe general form of shear type multi-mass systems is identified to be the flexible-stiffmixed system as is indicated in Fig.3. The system consists of the flexible elementwhich remains elastic and the stiff element which has a high elastic rigidity andbehaves inelastically. The extent of combinations is measured by the participationratio of the flexible element, f defined byf-f Q m= (27)sQY392
−-wheref Qm= kfδmis the average maximum stress in the flexible element, s Q Y theyield strength of the stiff element, δ m the average maximum deformation of thepositive and negative directions and k f the spring constant of flexible element.(a) flexible element (b) stiff element (c) mixed systemFigure 3. Flexible-stiff mixed system.Ordinary shear type structures belong to the case of f=0. By adding the flexibleelement, the structural behavior is highly improved in suppressing the excessivedevelopment of the maximum deformation and the damage concentration into acertain story. The effectiveness of the system appears clearly in the following range off ≥ 0.7(28)As illustrative examples, ten storied frames of the flexible-stiff mixed type aretaken. The restoring force characteristics of the stiff element is of the elastic-perfectlyplastic type. The stiffness of the flexible element is defined by the fictitious yieldpoint as follows.fQYkf= (29)fδYwhere f Q Y =the fictitious yield shear force of the flexible element and f δ Y =thefictitious yield deformation of the flexible element. The yield shear force coefficientis defined as follows.fQYisQYiαfi= , α = (30)NSiNg m g m∑j=ij∑j=ijwhere α fi is the fictitious yield shear coefficient of the flexible element and α si =theyield shear force coefficient of the stiff element. The distribution of α fi and α si isspecified to beαfiαsi-= = αi(31)αfIαsIfδi sδimifδ i , s δ i , and m i are assumed to be = = = const.δ δ mf1s11393
- Page 356 and 357: 5. EVALUATION OF MPA: UNSYMMETRIC-P
- Page 358 and 359: Without additional conceptual compl
- Page 360 and 361: AN IMPROVED PUSHOVER PROCEDURE FOR
- Page 362 and 363: for a response governed by the fund
- Page 364 and 365: 2.2 Modal ScalingThe principal aim
- Page 366 and 367: 2.3 Pushover-History AnalysisSubsti
- Page 368 and 369: (3) Calculate cumulative scale fact
- Page 370 and 371: 46.4 58 58 58 58 58 58 58 58 58 58
- Page 372 and 373: EXTENSIONS OF THE N2 METHOD — ASY
- Page 374 and 375: The strength reduction factor due t
- Page 376 and 377: The relations apply to SDOF systems
- Page 378 and 379: in X-direction pushover curves prac
- Page 380 and 381: As an example, an idealized force-d
- Page 382 and 383: The IN2 curve can be used in the pr
- Page 384 and 385: HORIZONTALLY IRREGULAR STRUCTURES:
- Page 386 and 387: Dutta and Das (2002, 2002b and refs
- Page 388 and 389: They tested the procedure on three
- Page 390 and 391: Table 1. Properties of the 4 WallsW
- Page 392 and 393: The following is a summary of two s
- Page 394 and 395: ectangular concrete deck supported
- Page 396 and 397: REFERENCESAlmazan, J. L., and J. C.
- Page 398 and 399: Rosenblueth, E. (1957). “Consider
- Page 400 and 401: instantaneous period of vibration a
- Page 402 and 403: value of the maximum plastic deform
- Page 404 and 405: (a) elastic-perfectly plastic type(
- Page 408 and 409: Referring to Eq. (15), the natural
- Page 410 and 411: -The effective period obtained by u
- Page 412 and 413: eal damage data, rather than theore
- Page 414 and 415: liquefaction-induced damage. This i
- Page 416 and 417: Figure 5. Selected damage distribut
- Page 418 and 419: Figure 6. Idealized capacity spectr
- Page 420 and 421: I’ for the ductile case, as expec
- Page 422 and 423: This study has shown that a modific
- Page 424 and 425: thickness of the inner wall is usua
- Page 426 and 427: 4. EARTHQUAKE GROUND MOTION INPUT A
- Page 428 and 429: 5.2 Performance Levels and Limit St
- Page 430 and 431: where λ I jis the occurrence rate
- Page 432 and 433: intensity VI because the number of
- Page 434 and 435: and thus are not considered in seis
- Page 436 and 437: The values of the displacement modi
- Page 438 and 439: constant amplitude loading (CA) or
- Page 440 and 441: deterioration. These are the type o
- Page 442 and 443: members, is the main feature of the
- Page 444 and 445: RESULTS, DISCUSSIONS AND CONCLUSION
- Page 446 and 447: systems, where FEMA estimations are
- Page 448 and 449: The case study is a Hospital in the
- Page 450 and 451: Table 1. Dimensions and amount of r
- Page 452 and 453: 4.2 Incremental AnalysisBase shear
- Page 454 and 455: When adding jackets to columns, the
where a is the constant peculiar to the type <strong>of</strong> restoring force characteristics. γ 1 ranges2N⎛ ⎞⎜ ∑ mj⎟j i2 k1 ≤ γ1≤ ∑ si,⎜ = ⎟1si= ・ - α 1⎜ ・M⎟(23)k⎜ ⎟i⎝ ⎠−where αiis the optimum yield shear force coefficient which produces the equal--distribution <strong>of</strong> µi. The upper bound <strong>of</strong> γ 1 (=∑ Si ) is attained in the case where µiisequal in all stories. By equating W p in the case <strong>of</strong> the evenly distributed damage andthat in the case <strong>of</strong> arbitrarily distributed damage, - -µ can be related to µi. W p iswritten in two ways.1WPMg=4π2 2T022 2T022α1µi・κ12 −1µ1s aMg α γ1a2WP= ・4πκ1The balance <strong>of</strong> energy results inα2 −1µ1γ1κ12 -1∑α µai=κ1−∑i(24)sia, (25)−− r1µ1= (26)∑ siiµ5. ILLUSTRATIVE EXAMPLE OF EFFECTIVE PERIOD OF MULTI-MASSSYSTEMSThe general form <strong>of</strong> shear type multi-mass systems is identified to be the flexible-stiffmixed system as is indicated in Fig.3. The system consists <strong>of</strong> the flexible elementwhich remains elastic and the stiff element which has a high elastic rigidity andbehaves inelastically. The extent <strong>of</strong> combinations is measured by the participationratio <strong>of</strong> the flexible element, f defined byf-f Q m= (27)sQY392
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