C C ONSIDERATION OF ONSIDERATION OF C C OLLAPSE AND OLLAPSE AND R R ESIDUAL ESIDUAL D D EFORMATION IN EFORMATION IN R R ELI ELI ABILITY-BASED ABILITY-BASED P P ERFORMANCE ERFORMANCE E E VALUATION OF VALUATION OF B B UILDINGS UILDINGS Chiun-lin WU 1 , Chin-Hsiung LOH 2 , Yang-Sen Yang 1 and Chia-hung LIN 2 1 National Center for Research on Earthquake Engineering, Taiwan, ROC 2 Department of Civil Engineering, National Taiwan University, Taiwan, ROC Numerical hysteretic models having post-peak negative stiffness (1 st row) and experimental results showing similar characteristics (2 nd row). Framework for Residual-Maximum Deformation Based Approach: Performance Matrix (Pampanin et al. 2003) : The reasons to evolve a currently popular and comparatively simple evalua tion method into a more knowledge-demanding performance evaluation method is based on an understanding of the following aspects: The consideration of near-fault motions with severe direc tivity velocity pulses and/or static displacement fling c ould lead to permanent deformation of the structural syst em when highly nonlinear structural behavior occurs. In addition, a 2% in 50 years hazard level usually make an o rdinary structure almost reach its collapse state. Buildings designed to older code documents are susceptib le to severe damage or may even collapse during a severe seismic event. This is especially true for the observed low-cycle collapse of reinforced concrete frame building s with light transverse column reinforcement during the 1999 Chi-Chi Taiwan earthquake. Modern advanced structural systems, in contrast to tradi tional systems, may be capable of re-centering itself ba ck to the original position after earthquakes. 1. 2. 3. () ( ) () ( () ( ) k p l y k l y k p l y k l y c k u r FS c k u r r k r FS Mu M x Mu Nx Nu Nx Nu M x u x Nx Nx M x Nu Nx M x M x Nx Mu N Nx Nu Nx ) () ( ) FS r k r FS x M x Mu N x -10 -8 -6 -4 -2 0 2 4 6 8 10 D isplacem ent(cm ) -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 State V ariable (cm ) Pinching + Strength D eterioration + StiffnessD egradation + Collapse k (1-) k c x x m 1 1 n n i i g i mx cx kx k u mx u x y Failure Surface u r y u r y y r r (1 ) (2 ) (3 ) (4 ) Failure Surface 1 1 () k k ht 1 1 () l l ht 1 y c r u tiffness-degradation function Load-deterioration function Post-peak stiffness function ary State Variable (deformation of slider-spring element) -10 -8 -6 -4 -2 0 2 4 6 8 10 D isplacem ent(cm ) -50 -40 -30 -20 -10 0 10 20 30 40 50 R estoring Force (K N) Bilinear+ Strength D eterioration + StiffnessD egradation + Capping -10 -8 -6 -4 -2 0 2 4 6 8 10 D isplacem ent(cm ) -50 -40 -30 -20 -10 0 10 20 30 40 50 R estoring F orce (K N) Pinching + Strength D eterioration + StiffnessD egradation + Collapse -10 -8 -6 -4 -2 0 2 4 6 8 10 D isplacem ent(cm ) -50 -40 -30 -20 -10 0 10 20 30 40 50 R estoring F orce (K N) Pinching + Strength D eterioration + StiffnessD egradation + Collapse Uang et al. (2000) Oh et al. (2002) Elwood and Moehle (2002) -60 -40 -20 0 20 40 60 D isplacem ent(cm ) -400 -300 -200 -100 0 100 200 300 400 R estoring Force -8 -6 -4 -2 0 2 4 6 8 T = 1.01 sec,D y =7.3 cm D uctility Example hysteretic loops of a 5-story RC building under seismic excitation Collapse Prevention Near Collapse Structurally Stable Immediate Occupancy Fully Functional Life Safety Operational Collapse 13th World Conference on Earthquake Engineering Vancouver, B.C., Canada, August 1-6, 2004, Paper No. 716 INTRODUCTION MATHEMATICAL REPRESENTATION OF HYSTERESIS LOOP WITH CONSIDERATION OF POST-PEAK BEHAVIOR u x u y Evolved Failure Surface d u 1 c d u u y d u 1 c d u 1 u y 1 u y r r (1 )’ (2) ’ (3) ’ (4) ’ Evolved Failure Surface Schematic representation of failure surface. Evolution of failure surface and its controlling parame Design spectra compared with median, 16- and 84-percentile spectra of 10 selected ground motions at 10%, 5% and 2% in 50 years hazard levels. 0 1 2 3 4 Period (sec) 0.0 0.2 0.4 0.6 0.8 1.0 SpectralA cceleration (g) 0 245 490 735 980 (cm /sec 2 ) D esign Spectrum M edian 16-& 84-percentile X inyi district, Taipei Basin (10% in 50 yrs.) 0 1 2 3 4 Period (sec) 0.0 0.2 0.4 0.6 0.8 1.0 SpectralA cceleration (g) 0 245 490 735 980 (cm /sec 2 ) D esign Spectrum M edian 16-& 84-percentile X inyi district, Taipei Basin (5% in 50 yrs.) 0 1 2 3 4 Period (sec) 0.0 0.2 0.4 0.6 0.8 1.0 SpectralA cceleration (g) 0 245 490 735 980 (cm /sec 2 ) D esign Spectrum M edian 16-& 84-percentile X inyi district, Taipei Basin (2% in 50 yrs.) m Hazard Ground Motion Suites – Xinyi District, Taipei basin, Taiwan PERFORMANCE EVALUATION METHOD CONSIDERING PEAK AND RESIDUAL DEFORMATIONS
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CCONSIDERATION OF ONSIDERATION OF CCOLLAPSE AND OLLAPSE AND RRESIDUAL ESIDUAL DDEFORMATION IN EFORMATION IN RREE
LIABILITY-BASED LIABILITY-BASED PPERFORMANCE ERFORMANCE EEVALUATION OF VALUATION OF BBUILDINGSUILDINGS
Chiun-lin WU 1, Chin-Hsiung LOH 2, Yang-Sen Yang 1 and Chia-hung LIN 2
1 National Center for Research on Earthquake Engineering, Taiwan, ROC2 Department of Civil Engineering, National Taiwan University, Taiwan, ROC
Numerical hysteretic models having post-peak negative stiffness (1st row) and experimental results showing similar characteristics (2nd row).
Framework for Residual-Maximum Deformation Based Approach: Performance Matrix (Pampanin et al. 2003) :The reasons to evolve a currently popular and comparatively simple evaluation method into a more knowledge-demanding performance evaluation method is based on an understanding of the following aspects:
The consideration of near-fault motions with severe directivity velocity pulses and/or static displacement fling could lead to permanent deformation of the structural system when highly nonlinear structural behavior occurs. In addition, a 2% in 50 years hazard level usually make an ordinary structure almost reach its collapse state.
Buildings designed to older code documents are susceptible to severe damage or may even collapse during a severe seismic event. This is especially true for the observed low-cycle collapse of reinforced concrete frame buildings with light transverse column reinforcement during the 1999 Chi-Chi Taiwan earthquake.
Modern advanced structural systems, in contrast to traditional systems, may be capable of re-centering itself back to the original position after earthquakes.
13th World Conference on Earthquake Engineering Vancouver, B.C., Canada, August 1-6, 2004, Paper No. 716
INTRODUCTIONINTRODUCTION
MATHEMATICAL REPRESENTATION OF HYSTERESIS LOOP WITH CONSIDERATION OF POST-PEAK BEHAVIOR MATHEMATICAL REPRESENTATION OF HYSTERESIS LOOP WITH CONSIDERATION OF POST-PEAK BEHAVIOR
u
x
u y Evolved Failure Surface
d u 1c d u
u y
d u 1c d u
1u y
1u y
r
r
(1)’
(2)’
(3)’
(4)’
Evolved Failure Surface
Schematic representation of failure surface.
Evolution of failure surface and its controlling parameters
Design spectra compared with median, 16- and 84-percentile spectra of 10 selected ground motions at 10%, 5% and 2% in 50 years hazard levels.
PERFORMANCE EVALUATION METHOD CONSIDERING PEAK AND RESIDUAL DEFORMATIONS PERFORMANCE EVALUATION METHOD CONSIDERING PEAK AND RESIDUAL DEFORMATIONS
13th World Conference on Earthquake Engineering Vancouver, B.C., Canada, August 1-6, 2004, Paper No. 716
A new mathematical form is presented in this study to describe hysteretic loops with post-peak behavior. Unlike other rule-based models, the proposed mathematical form can be readily incorporated into existing in-house and commercial software with no excessive coding efforts. In addition, a preliminary finding of this study is the introduction of performance-based earthquake engineering into the seismic design documents has indicates the necessity of considering post-peak behavior of structural systems into nonlinear dynamic analysis especially at the hazard level of very rare events such as 2% exceedance probability in 50 years.
SHAKE TABLE TESTS ON DYNAMIC GRAVITY LOAD COLLAPSE OF RC FRAMES WITH LOW-DUCTILITY COLUMNS SHAKE TABLE TESTS ON DYNAMIC GRAVITY LOAD COLLAPSE OF RC FRAMES WITH LOW-DUCTILITY COLUMNS
2% in 50 yrs. (w/o Collapse)2 % in 50 yrs (collapse)5% in 50 yrs. (w/o Collapse)5% in 50 yrs. (collapse)10% in 50 yrs. (w/o Collapse)10% in 50yrs. (collapse)
2% in 50 yrs. (w/o Collapse)2 % in 50 yrs (collapse)5% in 50 yrs. (w/o Collapse)5% in 50 yrs. (collapse)10% in 50 yrs. (w/o Collapse)10% in 50yrs. (collapse)
0
5
10
15
20
25
30
Duct
ilit
y
Performance Matrix of the 12-story RC model building with bilinear (left) and pinching (right) hysteretic behavior.
PERFORMANCE EVALUATION METHOD CONSIDERING PEAK AND RESIDUAL DEFORMATIONS
PERFORMANCE EVALUATION METHOD CONSIDERING PEAK AND RESIDUAL DEFORMATIONS
While considerable advances have been made in the use of analytical and/or numerical methods to evaluate seismic performance of civil structures, recently there is a clear trend that more RC collapse experiments are being conducted or planned worldwide to gain more knowledge on failure mechanism in view that the fundamental characteristics of structural collapse are not easily amenable to an analytical/numerical treatment at the present stage. On the other hand, older buildings built before 1982 in Taiwan are known to have poor seismic performance in terms of ductility and energy dissipation capacity during severe seismic events. Shake table tests, therefore, were conducted in this paper to study low-ductility collapse of old RC columns due to poor detailing. To do so, ½-scale 1-story RC frames composed of 2 low-ductility columns inter-connected by a strong beam were built to represent a typical 4-story commercial-resident complex and its soft 1st story columns in central Taiwan. A steel supporting beam system was built outside the table to catch frame specimens when structural collapse occurred. Two near-fault records from the 1999 Chi-Chi Taiwan earthquake were applied to excite frame specimens. This instrumented observation of dynamic collapse helps gain further insight into dynamic stability problems. During the tests, digital camcorders were used to record the progress of structural collapse; displacement histories were obtained through both LVDTs and image processing technique, the latter of which was shown very helpful when collapse or large displacement was expected. Flexural and flexural-shear failures were both observed in two individual experiments, which implies column design and loading history both play an important role in collapse mechanism. On the other hand, collapse analysis usually indicates involvement of discontinuum mechanics; however, experimental data show that hysteretic modeling approach may be sufficient to fit the needs of engineering practice in description of nonlinear structural dynamic response at structural collapse. In this regard, the authors’ experience in using OpenSees shows that more efforts still need to be made among engineering community in order to predict structural response with more accuracy, and, as such, experimental data from collapse tests provide a great platform for setting up benchmark problems for verification of new numerical simulation methods. It is concluded that if a higher hazard level at 2% exceedance probability in 50 years and near-fault ground motions are to be considered in performance-based earthquake engineering, global/local collapse needs to be carefully accounted for in structural dynamic analysis.
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