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1、EVALUATION OF LATERAL LOAD PATTERNIN PUSHOVER ANALYSISArmagan KORKMAZ1, Ali SARI21Visitor Researcher, Department of Civil Engineering, University of Texas at Austin, Austin,TX78712, PH: 512-232-9216; armaganmail.utexas.edu2Ph. D. Student, Department of Civil Engineering, University of Texas at Austi
2、n, Austin, TX 78712, PH: 512-232-9216; ali_sarimail.utexas.eduABSTRACTThe objective of this study is to evaluate the performance of the frame structures or various load patterns and variety of natural periods by performing pushover and nonlinear dynamic time history analyses. The load distributions
3、for pushover analyses are chosen as triangular, IBC (k=2) and rectangular. Four different framed structures are used, which are typical reinforced concrete (RC) frame systems and have four different natural periods. Even though the nonlinear dynamic time history analysis is the best way to compute s
4、eismic demands FEMA-273 and ATC-40 proposes to use of nonlinear static procedure or pushover analysis. This paper is also intended to compare the results of pushover and nonlinear dynamic time history analyses. To evaluate the results from the pushover analyses for three load patterns and also four
5、natural periods, nonlinear dynamic time history analyses are performed. Earthquake ground motions recorded at 50 stations during various earthquakes overall the world are used in the analyses. Pushover and nonlinear time history analyses results are compared to choose the best load distribution for
6、specific natural period for this type of frame structure. Keywords: Pushover analysis, nonlinear time history, load patterns, moment-resisting frameINTRODUCTIONOnly the life safety and collapse prevention in general earthquake resistant design phenomena are explicitly prevented in seismic design cod
7、es. The design is generally based on evaluating the seismic performance of structures. It is required to consider inelastic behavior while evaluating the seismic demands at low performance levels. FEMA-273 and ATC-40 use pushover analysis as nonlinear static analysis but nonlinear time history analy
8、sis has more accurate results on computing seismic demands (ATC-40, 1996, FEMA-273, 1997). The purposes in earthquake-resistance design are: (a) to prevent non-structural damage in minor earthquakes, which may occur frequently in life time, (b)to prevent structural damage and minimize non-structural
9、 damage in moderate earthquakes which may occur occasionally, (c) to prevent collapsing or serious damage in major earthquakes which may occur rarely. Designs are explicitly done only under the third condition.The objective of this study is to evaluate the performance of the frame structures for var
10、ious load patterns and variety of natural periods by performing pushover and nonlinear dynamic time history analyses. 3, 5, 8 and 15 story RC frame structures are used in the analyses and the load distributions for pushover analyses are chosen as triangular (IBC, k=1), IBC (k=2) and rectangular, whe
11、re k is the an exponent related to the structure period to define vertical distribution factor (IBC, 2000). The four frame structures have been analyzed using nonlinear program DRAIN-2D (Prakash, V., Powell, G., Campbell, S., 1993) and the results have been compared by recorded response data. Both n
12、onlinear static pushover analysis and nonlinear dynamic time history analysis are performed. The correlations between these nonlinear analyses are studied.The performance of the buildings subjected to various representative earthquake ground motions is examined. Finally, pushover and nonlinear time
13、history analyses results are compared to choose the best load distribution (pattern) for specific natural period for these types of reinforced concrete frame structures.GROUND MOTION DATAFor this study, it is considered as 50 different data used in the nonlinear dynamic time history analyses, given
14、in the Table 1. All the data are from different site classes as A, B, C and D. The shear velocities for the site classes A, B, C and D are Vs 750 m/s, 360m/s to 750 m/s, 180 m/s to 360 m/s, and 180 m/s, respectively. The ground motion data are chosen from different destructive earthquakes around the
15、 world earthquake name, date of earthquake, data source, record name, peak ground accelerations (pga) for the components, effective durations and fault types for each data are presented in the Table1., respectively.The peak ground accelerations are in the range 0.046 to 0.395g, where g is accelerati
16、on due to gravity. All ground motion data are recorded in near-field region as in maximum 20 km distance.DESCRIPTION OF THE FRAME STRUCTURES3, 5, 8 and 15-story RC frame structures with typical cross-sections and steel reinforcements are shown in Figure 1. The reinforced concrete frame structures ha
17、ve been designed according to the rules of the Turkish Code. The structures have been considered as an important class 1 with subsoil type of Z1 and in seismic region 1. The dead, live and seismic loads have been taken account during design.All reinforced concrete frame structures consist three-bay
18、frame, spaced at 800 cm. The story height is 300 cm. The columns are assumed as fixed on the ground. Yield strength of the steel reinforcements is 22 kN/cm2 and compressive strength of concrete is 1.6kN/cm2.The first natural period of the 3-story frame structure is computed 0.54 s. The cross-section
19、 of all beams in this frame is rectangular-shapes with 25cm width and 50cm height. The cross-section of all columns is 30cmx30cm. The first natural period of 5-story frame structure is 0.72 s and the cross-section of beams is 25cm width and 50cm height similar to 3-story frame. Cross-section of colu
20、mns at the first three stories is 40cmx40cm and at the last two stories, it is 30cmx30cm. The eight-story and 15-story frame structures have natural period of 0.90 s and 1.20 s. The cross section of beams for both frame structures is 25cmx55cm. The 8-story frame structure has 50cmx50cm columns for t
21、he first five stories and 40cmx40cm for the last three stories. The cross section of columns for first eight stories in the 15-story frame structures is 80cmx80cm and at the last seven stories, it is 60cmx60cm.NONLINEAR STATIC PUSHOVER ANALYSIS OF FRAME STRUCTURESFor low performance levels, to estim
22、ate the demands, it is required to consider inelastic behavior of the structure. Pushover analysis is used to identify the seismic hazards, selection of the performance levels and design performance objectives. In Pushover analysis, applying lateral loads in patterns that represent approximately the
23、 relative inertial forces generated at each floor level and pushing the structure under lateral loads to displacements that are larger than the maximum displacements expected in design earthquakes (Li, Y.R., 1996). The pushover analysis provides a shear vs. displacement relationship and indicates th
24、e inelastic limit as well as lateral load capacity of the structure. The changes in slope of this curve give an indication of yielding of various structural elements. The main aim of the pushover analysis is to determine member forces and global and local deformation capacity of a structure. The inf
25、ormation can be used to assess the integrity of the structure.After designing and detailing the reinforced concrete frame structures, a nonlinear pushover analysis is carried out for evaluating the structural seismic response. For this purpose the computer program Drain 2D has been used. Three simpl
26、ified loading patterns; triangular, (IBC, k=1), (IBC, k=2) and rectangular, where k is an exponent related to the structure period to define vertical distribution factor, are used in the nonlinear static pushover analysis of 3, 5, 8 and 15-story RC frame structures.Load criteria are based on the dis
27、tribution of inertial forces of design parameters. The simplified loading patterns as uniform distribution, triangular distribution and IBC distribution, these loading patterns are the most common loading parameters.Vertical Distribution of Seismic Forces: （1） （2）where:Cvx= Vertical distribution fac
28、torV = Total design lateral force or shear at the base of structurewi and wx = The portion of the total gravity load of the structurehi and hx = The height from the basek = An exponent related to the structure periodIn addition these lateral loadings, frames are subjected live loads and dead weights
29、. P- effects have been taken into the account during the pushover analyses. The lateral force is increased for 3, 5 and 8-story frames until the roof displacement reached 50 cm and 100cm for15-story frame. Beam and column elements are used to analyze the frames. The beams are assumed to be rigid in
30、the horizontal plane. Inelastic effects are assigned to plastic hinges at member ends. Strain-hardening is neglected in all elements. Bilinear moment-rotation relationship is assumed for both beam and column members. Axial load-Moment, P-M, interaction relation, suggested by ACI 318-89, is used as y
31、ielding surface of column elements. Inertial moment of cracked section, Icr, is used for both column and beam members during analyses. Icr is computed as half of the gross moment of inertia, Ig.The results of the pushover analyses are presented in Figures 2 to 5. The pushover curves are shown for th
32、ree distributions, and for each frame structures. The curves represent base shear-weight ratio versus story level displacements for uniform, triangular and IBC load distribution. Shear V was calculated by summing all applied lateral loads above the ground level, and the weight of the building W is t
33、he summation of the weights of all floors. Beside these, these curves represent the lost of lateral load resisting capacity and shear failures of a column at the displacement level. The changes in slope of these curves give an indication of yielding of various structural elements, first yielding of
34、beam, first yielding of column and shear failure in the members. By the increase in the height of the frame structures, first yielding and shear failure of the columns is experienced at a larger roof displacements (Figures 2-5.) and rectangular distribution always give the higher base shear-weight r
35、atio comparing to other load distributions for the corresponding story displacement (horizontal displacement).NONLINEAR DYNAMIC TIME HISTORY ANALYSIS OF FRAME STRUCTURESAfter performing pushover analyses, nonlinear dynamic time history analyses have been employed to the four different story frame st
36、ructures. These frames are subjected live and dead weights. Also P- effects are under consideration as in pushover analysis. For time history analysis P-D effects have been taken into the account. Finite element procedure is employed for the modeling of the structures during the nonlinear dynamic ti
37、me history analyses. Drain 2D has been used for nonlinear time history analysis and modeling. The model described for pushover analyses has been used for the time history analyses. Mass is assumed to be lumped at the joints.The frames are subjected to 50 earthquake ground motions, which are recorded
38、 during Anza (Horse Cany), Parkfield, Morgan Hill, Kocaeli, Coyota Lake, N. Palm Springs, Northridge, Santa Barbara, Imperial Valley, Cape Mendocino, Kobe, Central California, Lytle Creek, Whittier Narrows, Hollister Westmoreland, Landers, Livermor and Cape Mendocino earthquakes, for the nonlinear d
39、ynamic time history analyses. These data are from different site classes as A, B, C and D.The selected earthquake ground motions have different frequency contents and peak ground accelerations.The ground motion data are chosen from near-field region to evaluate the response of the frame structures i
40、n this region and comparison of them with pushover analyses results. The results of nonlinear time history analysis for 3, 5, 8 and15-story frame structures are presented in Figure 6. Pushover and nonlinear time history analyses results are compared to for specific natural period for four different
41、frame structure and for each load distributions; rectangular, triangular and IBC (k=2).CONCLUSIONSAfter designing and detailing the reinforced concrete frame structures, a nonlinear pushover analysis and nonlinear dynamic time history analysis are carried out for evaluating the structural seismic re
42、sponse for the acceptance of load distribution for inelastic behavior. It is assumed for pushover analysis that seismic demands at the target displacement are approximately maximum seismic demands during the earthquake.According to Figures 2, 3, 4 and 5, for higher story frame structures, first yiel
43、ding and shear failure of the columns is experienced at the larger story displacements and rectangular distribution always give the higher base shear-weight ratio comparing to other load distributions for the corresponding story displacement.As it is presented in Figure 6, nonlinear static pushover
44、analyses for IBC (k=2), rectangular, and triangular load distribution and nonlinear time history analyses results for the chosen ground motion data (all of them are near-field data) are compared. Pushover curves do not match with nonlinear dynamic time history analysis results especially for higher
45、story reinforced pushover analyses results for rectangular load distribution estimate maximum seismic demands during the given earthquakes more reasonable than the other load distributions, IBC (k=2), and triangular.REFERENCES1. ATC-40 (1996), “Seismic evaluation and Retrofit of Concrete Buildings”,
46、 Vol.1, Applied Technology Council, Redwood City, CA.2. FEMA 273 (1997). “NEHRP Guidelines for the Seismic Rehabilitation of Buildings, Federal Emergency Management Agency”, Washington D.C.3. IBC (2000) “International Building Code”.4. Prakash, V., Powell, G., Campbell, S. (1993), DRAIN 2D User Guid
47、e V 1.10, University of California at Berkeley, CA.5. Li, Y.R. (1996), “Non-Linear Time History And Pushover Analyses for Seismic Design and Evaluation” PhD Thesis, University of Texas, Austin, TX.6. Vision 2000 Committee (1995). Structural Engineering Association of California, CA.静力弹塑性分析法在侧向荷载分布方式
48、下的评估研究Armagan KORKMAZ1, Ali SARI21访问学者,土木工程学院, 得克萨斯大学, 奥斯汀, TX 78712, PH: 512-232-9216; armaganmail.utexas.edu2博士, 土木工程学院, 得克萨斯大学, 奥斯汀, TX 78712, PH: 512-232-9216; ali_sarimail.utexas.edu摘要：这项研究的目的是通过弹塑性分析法和非线性时程分析法来评估框架结构的性能或多种荷载形式及自然周期的多样性。弹塑性分析法的荷载分布状态有三角形、IBC（k=2），和矩形。在这个研究中四种典型的钢筋混凝土框架结构被采用，它们分别有四种不同的自然周期。非线性时程分析法是计算地震的最好方法，但美国的FEMA-273容量震谱法和ATC-40位移系数法推荐使用静力弹塑性分析法。这篇论文将比较分别利用静力弹塑性分析法与非线性时程分析法分析所得到的结果。为了评估弹塑性分析法在三种不同荷载形式和四种自然周期下的结果，非线性时程分析法也被执行来对照。在不同地震下分布在全球的50个站点纪录了地面运动情况被用来做分析，通过比较静力弹塑性分析法和非线性时程分析法的结果来选择这种典型框架结构在特殊自然周期下最佳的荷载分布方式。关键词：静力弹塑性分析、非线性时程分析、荷载形式、抗弯矩框架前言一般的抗震设计
