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1、Seismic Collapse Safety of Reinforced Concrete Buildings. II: Comparative Assessment of Nonductile and Ductile Moment Frames Abbie B. Liel, M.ASCE1; Curt B. Haselton, M.ASCE2; and Gregory G. Deierlein, F.ASCE3 Abstract: This study is the second of two companion papers to examine the seismic collapse

2、 safety of reinforced concrete frame buildings, and examines nonductile moment frames that are representative of those built before the mid-1970s in California. The probabilistic assessment relies on nonlinear dynamic simulation of structural response to calculate the collapse risk, accounting for u

3、ncertainties in ground-motion characteristics and structural modeling. The evaluation considers a set of archetypical nonductile RC frame structures of varying height that are designed according to the seismic provisions of the 1967 Uniform Building Code. The results indicate that nonductile RC fram

4、e structures have a mean annual frequency of collapse ranging from 5 to 14 10?3at a typical high-seismic California site, which is approximately 40 times higher than corresponding results for modern code-conforming special RC moment frames. These metrics demonstrate the effectiveness of ductile deta

5、iling and capacity design requirements, which have been introduced over the past 30 years to improve the safety of RC buildings. Data on comparative safety between nonductile and ductile frames may also inform the development of policies for appraising and mitigating seismic collapse risk of existin

6、g RC frame buildings. DOI: 10.1061/(ASCE)ST.1943-541X .0000275. 2011 American Society of Civil Engineers. CE Database subject headings: Structural failures; Earthquake engineering; Structural reliability; Reinforced concrete; Concrete structures; Seismic effects; Frames. Author keywords: Collapse; E

7、arthquake engineering; Structural reliability; Reinforced concrete structures; Buildings; Commercial; Seismic effects. Introduction Reinforced concrete (RC) frame structures constructed in Califor- nia before the mid-1970s lack important features of good seismic design, such as strong columns and du

8、ctile detailing of reinforce- ment, making them potentially vulnerable to earthquake-induced collapse. These nonductile RC frame structures have incurred significant earthquake damage in the 1971 San Fernando, 1979 Imperial Valley, 1987 Whittier Narrows, and 1994 Northridge earthquakes in California

9、, and many other earthquakes worldwide. These factors raise concerns that some of Californias approxi- mately 40,000 nonductile RC structures may present a significant hazard to life and safety in future earthquakes. However, data are lacking to gauge the significance of this risk, in relation to ei

10、ther the building population at large or to specific buildings. The collapse risk of an individual building depends not only on the building code provisions employed in its original design, but also structural configuration, construction quality, building location, and site-spe- cific seismic hazard

11、 information. Apart from the challenges of ac- curately evaluating the collapse risk is the question of risk tolerance and the minimum level of safety that is appropriate for buildings. In this regard, comparative assessment of buildings designed accord- ing to old versus modern building codes provi

12、des a means of evalu- ating the level of acceptable risk implied by current design practice. Building code requirements for seismic design and detailing of reinforced concrete have changed significantly since the mid- 1970s, in response to observed earthquake damage and an in- creased understanding

13、of the importance of ductile detailing of reinforcement. In contrast to older nonductile RC frames, modern code-conforming special moment frames for high-seismic regions employ a variety of capacity design provisions that prevent or delay unfavorable failure modes such as column shear failure, beam-

14、 column joint failure, and soft-story mechanisms. Although there is general agreement that these changes to building code require- ments are appropriate, there is little data to quantify the associated improvements in seismic safety. Performance-based earthquake engineering methods are applied in th

15、is study to assess the likelihood of earthquake-induced collapse in archetypical nonductile RC frame structures. Performance-based earthquake engineering provides a probabilistic framework for re- lating ground-motion intensity to structural response and building performance through nonlinear time-h

16、istory simulation (Deierlein 2004). The evaluation of nonductile RC frame structures is based on a set of archetypical structures designed according to the pro- visions of the 1967 Uniform Building Code (UBC) (ICBO 1967). These archetype structures are representative of regular well- designed RC fra

17、me structures constructed in California between approximately 1950 and 1975. Collapse is predicted through 1Assistant Professor, Dept. of Civil, Environmental and Architectural Engineering, Univ. of Colorado, Boulder, CO 80309. E-mail: abbie . 2Assistant Professor, Dept. of Civil Eng

18、ineering, California State Univ., Chico, CA 95929 (corresponding author). E-mail: chaseltoncsuchico .edu 3Professor, Dept. of Civil and Environmental Engineering, Stanford Univ., Stanford, CA 94305. Note. This manuscript was submitted on July 14, 2009; approved on June 30, 2010; published online on

19、July 15, 2010. Discussion period open until September 1, 2011; separate discussions must be submitted for individual papers. This paper is part of the Journal of Structural Engineer- ing, Vol. 137, No. 4, April 1, 2011. ASCE, ISSN 0733-9445/2011/4- 492502/$25.00. 492 / JOURNAL OF STRUCTURAL ENGINEER

20、ING ASCE / APRIL 2011 J. Struct. Eng. 2011.137:492-502. Downloaded from by Sultan Qaboos University on 06/21/14. Copyright ASCE. For personal use only; all rights reserved. nonlinear dynamic analysis of the archetype nonductile RC frames, using simulation models capable of capturing

21、the critical aspects of strength and stiffness deterioration as the structure collapses. The outcome of the collapse performance assessment is a set of measures of building safety and relating seismic collapse resistance to seismic hazard. These results are compared with the metrics for ductile RC f

22、rames reported in a companion paper (Haselton et al. 2011b). Archetypical Reinforced Concrete Frame Structures The archetype nonductile RC frame structures represent the expected range in design and performance in Californias older RC frame buildings, considering variations in structural height, con

23、figuration and design details. The archetype configurations explore key design parameters for RC components and frames, which were identified through previous analytical and experimental studies reviewed by Haselton et al. (2008). The complete set of archetype nonductile RC frame buildings developed

24、 for this study includes 26 designs (Liel and Deierlein 2008). This paper focuses primarily on 12 of these designs, varying in height from two to 12 stories, and including both perimeter (P) and space (S) frame lateral resisting systems with alternative design details. All archetype buildings are de

25、signed for office occupancies with an 8-in. (20-cm) flat-slab floor system and 25-ft (7.6-m) column spacing. The 2- and 4-story buildings have a footprint of 125 ft by 175 ft (38.1 m by 53.3 m), and the 8- and 12-story buildings measure 125 ft (38.1 m) square in plan. Story heights are 15 ft (4.6 m)

26、 in the first story and 13 ft (4.0 m) in all other stories. Origi- nal structural drawings for RC frame buildings constructed in California in the 1960s were used to establish typical structural configurations and geometry for archetype structures (Liel and Deierlein 2008). The archetypes are limite

27、d to RC moment frames without infill walls, and are regular in elevation and plan, without major strength or stiffness irregularities. The nonductile RC archetype structures are designed for the highest seismic zone in the 1967 UBC, Zone 3, which at that time included most of California. Structural

28、designs of two-dimensional frames are governed by the required strength and stiffness to satisfy gravity and seismic loading combinations. The designs also satisfy all relevant building code requirements, including maximum and minimum reinforcement ratios and maximum stirrup spacing. The 1967 UBC pe

29、rmitted an optional reduction in the design base shear if ductile detailing requirements were employed, however, this reduction is not applied and only standard levels of detailing are considered in this study. Design details for each structure are Table 1. Design Characteristics of Archetype Nonduc

30、tile and Ductile RC Frames Stucture Design base shear coefficienta,b Column sizec (in: in.) Column reinforcement ratio, Column hoop spacingd,e(in.) Beam sizef (in: in.) Beam reinforcement ratios (0) Beam hoop spacing (in.) Nonductile 2S0.08624 240.0101224 240.006 (0.011)11 2P0.08630 300.0151530 300.

31、003 (0.011)11 4S0.06820 200.0281020 260.007 (0.014)12 4P0.06824 280.0331424 320.007 (0.009)15 8S0.05428 280.0141424 260.006 (0.013)11 8P0.05430 360.0331526 360.008 (0.010)17 12S0.04732 320.025926 300.006 (0.011)17 12P0.04732 400.032930 380.006 (0.013)18 4Sg0.06820 200.0286.720 260.007 (0.014)8 4Sh0.

32、06820 200.0281020 260.007 (0.014)12 12Sg0.04732 320.025626 300.006 (0.011)11 12Sh0.04732 320.025926 300.006 (0.011)17 Ductile 2S0.12522 220.017518 220.006 (0.012)3.5 2P0.12528 300.018528 280.007 (0.008)5 4S0.09222 220.016522 240.004 (0.008)5 4P0.09232 380.0163.524 320.011 (0.012)5 8S0.05022 220.0114

33、22 220.006 (0.011)4.5 8P0.05026 340.0183.526 300.007 (0.008)5 12S0.04422 220.016522 280.005 (0.008)5 12P0.04428 320.0223.528 380.006 (0.007)6 aThe design base shear coefficient in the 1967 UBC is given by C 0:05=T1=3 0:10. For moment resisting frames, T 0:1N, where N is the number of stories (ICBO 1

34、967). bThe design base shear coefficient for modern buildings depends on the response spectrum at the site of interest. The Los Angeles site has a design spectrum definedby SDS 1:0 g and SD1 0:60 g. The periodused in calculation of the design base shear is derivedfrom the code equation T 0:016h0:9 n

35、 , where hnis the height of the structure in feet, and uses the coefficient for upper limit of calculated period (Cu 1:4) (ASCE 2002). cColumn properties vary over the height of the structure and are reported here for an interior first-story column. dConfiguration of transverse reinforcement in each

36、 member depends on the required shear strength. There are at least two No. 3 bars at every location. eConfiguration of transverse reinforcement in ductile RC frames depends on the required shear strength. All hooks have seismic detailing and use No. 4 bars (ACI 2005). fBeam properties vary over the

37、height of the structure and are reported here are for a second-floor beam. gThese design variants have better-than-average beam and column detailing. hThese design variants have better-than-average joint detailing. JOURNAL OF STRUCTURAL ENGINEERING ASCE / APRIL 2011 / 493 J. Struct. Eng. 2011.137:49

38、2-502. Downloaded from by Sultan Qaboos University on 06/21/14. Copyright ASCE. For personal use only; all rights reserved. summarized in Table 1, and complete documentation of the non- ductile RC archetypes is available in Liel and Deierlein (2008). Four of the 4- and 12-story desig

39、ns have enhanced detailing, as described subsequently. The collapse performance of archetypical nonductile RC frame structures is compared to the set of ductile RC frame archetypes presented in the companion paper (Haselton et al. 2011b). As sum- marized in Table 2, these ductile frames are designed

40、 according to the provisions of the International Building Code (ICC 2003), ASCE 7 (ASCE 2002), and ACI 318 (ACI 2005); and meet all gov- erning code requirements for strength, stiffness, capacity design, and detailing for special moment frames. The structures benefit from the provisions that have b

41、een incorporated into seismic design codes for reinforced concrete since the 1970s, including an assort- ment of capacity design provisions e.g., strong column-weak beam (SCWB) ratios, beam-column and joint shear capacity design and detailing improvements (e.g., transverse confinement in beam- colum

42、n hinge regions, increased lap splice requirements, closed hooks). The ductile RC frames are designed for a typical high- seismic Los Angeles site with soil class Sdthat is located in the transition region of the 2003 IBC design maps (Haselton and Deierlein 2007). A comparison of the structures desc

43、ribed in Table 1 reflects four decades of changes to seismic design provisions for RC moment frames. Despite modifications to the period-based equation for design base shear, the resulting base shear coefficient is relatively similar for nonductile and ductile RC frames of the same height, except in

44、 the shortest structures. More significant differences between the two sets of buildings are apparent in member design and detailing, especially in the quantity, distribution, and detailing of transverse reinforcement. Modern RC frames are subject to shear capacity design provisions and more stringe

45、nt limitations on stirrup spacing, such that transverse reinforcement is spaced two to four times more closely in ductile RC beams and columns. The SCWB ratio enforces minimum column strengths to delay the formation of story mechanisms. As a result, the ratio of column to beam strength at each joint

46、 is approximately 30% higher (on average) in the duc- tile RC frames than the nonductile RC frames. Nonductile RC frames also have no special provision for design or reinforcement of the beam-column joint region, whereas columns in ductile RC frames are sized to meet joint shear demands with transve

47、rse reinforcement in the joints. Joint shear strength requirements in special moment frames tend to increase the column size, thereby reducing axial load ratios in columns. Nonlinear Simulation Models Nonlinear analysis models for each archetype nonductile RC frame consist of a two-dimensional three

48、-bay representation of the lateral resisting system, as shown in Fig. 1. The analytical model repre- sents material nonlinearities in beams, columns, beam-column joints, and large deformation (P-) effects that are important for simulating collapse of frames. Beam and column ends and the beam-column

49、joint regions are modeled with member end hinges that are kinematically constrained to represent finite joint size Table 2. Representative Modeling Parameters in Archetype Nonductile and Ductile RC Frame Structures Structure Axial loada,b (P=Agf0c) Initial stiffnessc Plastic rotation capacity (cap;p

50、l, rad) Postcapping rotation capacity (pc, rad) Cyclic deteriorationd() First mode periode(T1, s) Nonductile 2S0.110:35EIg0.0180.040411.1 2P0.030:35EIg0.0170.051571.0 4S0.300:57EIg0.0210.033332.0 4P0.090:35EIg0.0310.100432.0 8S0.310:53EIg0.0130.028322.2 8P0.110:35EIg0.0250.100512.4 12S0.350:54EIg0.0

51、290.063532.3 12P0.140:35EIg0.0450.100822.8 4Sf0.300:57EIg0.0320.047482.0 4Sg0.300:57EIg0.0210.033332.0 12Sf0.350:54EIg0.0430.094672.3 12Sg0.350:54EIg0.0290.063532.3 Ductile 2S0.060:35EIg0.0650.100870.63 2P0.010:35EIg0.0750.1001110.66 4S0.130:38EIg0.0570.100800.94 4P0.020:35EIg0.0860.1001331.1 8S0.21

52、0:51EIg0.0510.100801.8 8P0.060:35EIg0.0870.1001221.7 12S0.380:68EIg0.0360.058572.1 12P0.070:35EIg0.0700.1001182.1 aProperties reported for representative interior column in the first story. (Column model properties data from Haselton et al. 2008.) bExpected axial loads include the unfactored dead lo

53、ad and 25% of the design live load. cEffective secant stiffness through 40% of yield strength. d is defined such that the hysteretic energy dissipation capacity is given by Et M yy(Haselton et al. 2008). eObtained from eigenvalue analysis of frame model. fThese design variants have better-than-avera

54、ge beam and column detailing. gThese design variants have better-than-average joint detailing. 494 / JOURNAL OF STRUCTURAL ENGINEERING ASCE / APRIL 2011 J. Struct. Eng. 2011.137:492-502. Downloaded from by Sultan Qaboos University on 06/21/14. Copyright ASCE. For personal use only; a

55、ll rights reserved. effects and connected to a joint shear spring (Lowes and Altoontash 2003). The structural models do not include any contribution from nonstructural components or from gravity-load resisting structural elements that are not part of the lateral resisting system. The model is implem

56、ented in OpenSees with robust convergence algorithms (OpenSees 2009). As in the companion paper, inelastic beams, columns, and joints are modeled with concentrated springs idealized by a trilinear back- bone curveand associated hysteretic rules developed by Ibarra et al. (2005). Properties of the no

57、nlinear springs representing beam and column elements are predicted from a series of empirical relation- ships relating column design characteristics to modeling parame- ters and calibrated to experimentaldatafor RC columns (Haselton et al. 2008). Tests used to develop empirical relationships includ

58、e a large number of RC columns with nonductile detailing, and predicted model parameters reflect the observed differences in moment-rotation behavior between nonductile and ductile RC elements. As in the companion paper, calibration of model param- eters for RC beams is established on columns tested

59、 with low axial load levels because of the sparse available beam data. Fig. 2(a) shows column monotonic backbone curve properties for a ductile and nonductile column (each from a 4-story building). The plastic rotation capacity cap;pl, which is known to have an important influence on collapse prediction, is a function of the amount of column confinement reinforcement and axial load levels, and is approximately 2.7 times greater for the ductile RC column. The ductile RC column also has a larger postcapping rotation capacity (pc) that affects t