外文翻译---静力弹塑性分析法在侧向荷载分布方式下的评估研究

静力弹塑性分析法在侧向荷载分布方式下的评估研究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;armagan@2博士, 土木工程学院, 得克萨斯大学, 奥斯汀, TX 78712, PH: 512-232-9216;ali_sari@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中仅仅只有安全和碰撞是在地震设计规范中明确要求避免的，抗震设计一般基于结构在地震中的性能表现。

这样在低的地震水平下就要求考虑结构的非弹性行为。

FEMA-273和ATC-40采用静力弹塑性分析法而不是非线性时程分析，因为前者在抗震计算中能得到更精确度结果。

在抗震计算的目的是：（a）、在经常发生的小震情况下避免非结构破坏；（b）、在偶尔发生的中震情况下避免结构破坏和最小限度的非结构破坏；（c）、在罕遇大震下不倒塌或产生严重破坏。

结构设计要明确的在这三种情况下进行。

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。

3、5、8和15层的四种框架结构被用来分析，分析中荷载分布状态选择三角形IBC（k=1），IBC（k=2）和矩形。

其中k是与结构周期相关的系数，用来定义荷载竖向因素。

这四种结构用非线性程序DRAIN-2D (Prakash, V., Powell, G., Campbell, S., 1993)来分析，并把其结果与记录的相应数分布方式。

地表运动数据在这个研究中，50个不同的数据被用于非线性时程分析法中，在表1中给出。

所有数据来自四个A、B、C、D四个等级不同地点，它们的横波速度分别是> 750 m/s, 360m/s至750 m/s, 180 m/s至360 m/s, 180 m/s。

这些数据选至发生在世界不同地方的毁灭性地震，其中地震的名称、数据源、记录名称、加速度峰值、有效期及过期类型都在表1中给出。

地表加速度峰值大约在0.046g至0.395g，其中g为重力加速度。

所有地表运动数据取至距离地面最大为20km的近地范围内。

框架结构的描述有着典型截面和钢筋的3、5、8和15层的钢筋混凝土框架结构见图1，这些钢筋混凝土结构是按Turkish 规范设计。

考虑结构所处环境为土质类型Z1、地震1区，设计为等级为1级，其中恒载、活载以及地震荷载在设计中已经被考虑。

所有这些钢筋混凝土框架结构都有3跨，长8m，层高3m。

柱子假定与地基固结，钢筋的屈服强度为22 kN/cm2 ，混凝土的抗压强度为1.6kN/cm2.3层框架结构的第一周期经计算为0.54 s ，结构中所有的框架梁截面为矩形，宽25 cm、高25cm，框架柱截面尺寸为30cmx30cm。

5层框架结构的第一周期经计算为0.72 s ，框架梁截面为矩形，宽25 cm、高50cm，框架柱截面尺寸前三层为40cmx40cm，后两层为30cmx30cm。

8层和15层的框架结构的周期分别为0.90 s和1.20s ，两者的框架梁截面为矩形，宽25 cm、高55cm。

8层结构框架柱截面尺寸前五层为50cmx50cm，后三层为40cmx40cm，而15层结构框架柱截面尺寸前八层为80cmx80cm，后七层为60cmx60cm。

框架结构的静力弹塑性分析法对于低等级的性能，为了估计其需求，就需要考虑结构的非弹性行为。

静力弹塑性分析法可以用来识别地震的危险，并选择性能等级以此来设计性能目标。

在静力弹塑性分析法中，以侧向荷载近似代表由层间产生的相关惯性力并使结构在这个侧向荷载作用下产生的位移大于地震设计中预期的位移(Li, Y.R., 1996)。

这种分析方法提供了剪力与位移的置换关系并指出非弹性的界限和结构侧面负荷能力，而曲线斜率方面的改变表明了各有限元的屈服强度。

静力弹塑性分析法的主要目的是决定结构的荷载数量和变形能力。

这些信息都能够用于评价结构的整体性。

在详细设计了钢筋混凝土框架结构后，就用静力弹塑性分析法评估结构的地震反应，为此电脑程序Drain 2D会被用到。

有以下三种简化荷载形式：三角形IBC （k=1），IBC（k=2）和矩形，其中k是与结构周期相关的系数，用来定义荷载竖向因素。

它们也会用于3、5、8和15层的钢筋混凝土框架结构的静力弹塑性分析。

VC F vx x = （1） =VX C ∑=n i ki ik x x h w h w 1（2） 式中：C vx 为竖向分布参数V 为总侧向力设计值，或结构底部剪力w i 和w x 为部分结构自重h i 和h x 为结构高度（至基地算起）k 为与结构周期相关的参数除这些侧向荷载外，结构还承受恒载和活载。

P-△作用在静力弹塑性分析中同样被考虑。

侧向荷载一直会增加，直到3、5和8层的框架结构楼顶位移达到50cm ，15层的框架结构楼顶位移达到100 cm 。

梁柱单元用于结构分析，假定梁在水平方向是刚性的，考虑非弹性影响单元是铰接的，而应变强化被忽略。

双线性弯矩—转角关系假定用于所用梁柱单元，由ACI 318-89建议的轴压荷载—弯矩关系、P —M 、交互关系被用于柱单元屈服表面。

薄弱破碎区段的惯性矩I cr ，在分析的时候用于所有的梁柱。

I cr 取总惯性矩I g 的一半。

由静力弹塑性分析法所得的结果见图2-5。

每个框架结构的弹塑性曲线都分均布荷载、三角形荷载以及IBC 荷载三种荷载方式给出，显示了剪重比与之相对应的层间位移。

基底剪力V 由地面以上所有荷载相加得到，结构重力W 所有楼层重量之和。

除此之外，这些曲线还表示结构抗侧力的损失情况和柱位移下的剪切破坏。

曲线中曲率的变化表明了不同结构单元屈服情况，首先是梁屈服，接着是柱屈服和各单元的剪切破坏。

随着结构自重的增加，顶层位移增大，出现首次屈服和剪切破坏（见图2-5）。

在相应的结构位移（水平位移）下，矩形荷载分布比其它荷载分布形式相比会造成更高的剪重比。

框架结构的非线性时程分析前面对框架结构进行了静力弹塑性分析，下面用非线性时程分析法对其进行分析。

这些框架结构都承受恒载和活载，同静力弹塑性分析法一样，P-△作用在非线性时程分析中也被考虑。

在非线性时程分析中Drain 2D 程序被利用，有限元程序也被用来模拟结构。

在静力弹塑性分析中所描述的模型同样用于非线性时程分析法中，且假定质量集中在节点处。

结构承受的种地震情况都是在以下地震中被记录的，这些地震是美国南加州Anza 地震、美国加州Parkfield 地震、美国西部Morgan Hill 地震、土耳其Kocaeli 地震、日本Coyota Lake 地震、美国N. Palm Springs 地震、美国加州Northridge 地震、美国加州Santa Barbara 地震、美国Imperial Valley 地震、美国加州Cape Mendocino 地震、日本神户Kobe 地震、美国Central California 地震、美国加州Lytle Creek 地震、美国南加州Whittier Narrows 地震、美国Hollister Westmoreland 地震、美国Livermor 地震、美国加州Cape Mendocino 地震。

这些数据取自A 、B 、C 、D 四类地区，来用不同荷载情况，即矩形、三角形和IBC(k=2)下四种框架结构的结果。

结论在详细设计了钢筋混凝土框架结构后，静力弹塑性分析法和非线性时程分析法被执行来评价在不同荷载情况下的地震反应。

静力弹塑性分析法假定抗震所设的目标位移量与实际地震下的最大位移大致一样。

从图-2至图-5可以看出，对于高层的框架结构位移增大，出现首次屈服和剪切破坏。

在相应的结构位移（水平位移）下，矩形荷载分布比其它荷载分布形式相比会造成更高的剪重比。

如图-6所示，在所选的地表运动数据下，非线性时程分析法在三角形荷载、矩形荷载和IBC(k=2)荷载情况的结果相互比较知：静力弹塑性曲线在高层框架结构（8和15层框架结构）下与非线性时程分析得出的结构不是很相符。

静力弹塑性分析法在矩形分布下所得的抗震要求要比其它荷载方式如三角形荷载、IBC(k=2)荷载形式下更合理。

参考文献1. ATC-40 (1996), “Seismic evaluation and Retrofit of Concrete Buildings”,Vol.1, Applied Technology Council, Redwood City, CA.2. FEMA-273 (1997),“NEHRP Guidelines for the Seismic Rehabilitation of Buildings, federal Emergency Managem ent Agency”, Washington D.C.3. IBC (2000) “International Building Code”.4. Prakash, V., Powell,G., Campbell, S. (1993), DRAIN 2D User Guide 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.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; armagan@2Ph. D. Student, Department of Civil Engineering, University of Texas at Austin, Austin, TX 78712, PH: 512-232-9216; ali_sari@ABSTRACTThe 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 for pushover analyses are chosen as triangular, IBC (k=2) and rectangular. Four different framed structures are used, which are typical reinforced concrete (R\C) frame systems and have four different natural periods. Even though the nonlinear dynamic time history analysis is the best way to compute seismic 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 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 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 codes. The design is generally based on evaluating the seismic performance of structures. It is required to consider inelastic behavior while evaluating the1996, 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 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 various load patterns and variety of natural periods by performing pushover and nonlinear dynamic time history analyses. 3, 5, 8 and 15 story R\C 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, where 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 nonlinear 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 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 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 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 acceleration 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 R\C frame structures with typical cross-sections and steel reinforcements are shown in Figure 1. The reinforced concrete frame structures have 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 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/cm2and 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 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 columns 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 the 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 estimate 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 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 the 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 information can be used to assessused. Three simplified 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 R\C frame structures.Load criteria are based on the distribution 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:V C F vx x = （1）=VX C ∑=n i k iikx x h w h w 1 （2） where:C vx = Vertical distribution factorV = Total design lateral force or shear at the base of structurew i and w x = The portion of the total gravity load of the structureh i and h x = The height from the basek = An exponent related to the structure periodIn addition these lateral loadings, frames are subjected live loads and dead weights. 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 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 yielding surface of column elements. Inertial moment of cracked section, I cr , is used for both column and beam members during analyses. I cr is computed as half of the gross moment of inertia, I g .The results of the pushover analyses are presented in Figures 2 to 5. The pushover curves are shown for three 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 the 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 beam, first yielding of column and shear failure in the members. By the increase in the height of the frame structures,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 structures. These frames are subjected live and dead weights. Also P- △effects are under consideration as in pushover analysis. For time history analysis P-effects have been taken into the account. Finite element procedure is employed for the modeling of the structures during the nonlinear dynamic time 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 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 dynamic 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. T he ground motion data are chosen from near-field region to evaluate the response of the frame structures in 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 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 response 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, firstcorresponding story displacement.As it is presented in Figure 6, nonlinear static pushover 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 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), “Seis mic evaluation and Retrofit of Concrete Build ings”, Vol.1, AppliedTechnology Council, Redwood City, CA.2. FEMA 273 (1997). “NEHRP Guidelines for the Seismic Rehabilitation of Buildings,Federal Emergency Managem ent Agency”, Washington D.C.3. IBC (2000) “International Building Code”.4. Prakash, V., Powell, G., Campbell, S. (1993), DRAIN 2D User Guide V 1.10,University of California at Berkeley, CA.5. Li, Y.R. (1996), “Non-Linear Time History And Pushover Analyses for Seismic Design andEvaluation” PhD Thesis, Universit y of Texas, Austin, TX.6. Vision 2000 Committee (1995). Structural Engineering Association of California, CA.Table 1. Ground Motion Data Used in the Analyses60/603mf y=22kN/cm2Beams: 25x50 : As=10.30 cm225x55 : As=13.26 cm260/6060/6060/603m30/603m30/603m3m 60/6030/3050x50 : As=45.20 cm280x80 : As=145.00 cm225/503m25/5025/503m25/5025/5025/5025/5025/5040/4050/5050/5050/5050/503m50/5025/5525/5525/5560/6060/603m80/803m80/803m80/803m80/803m80/803m80/803m80/8030/603m30/603m30/603m30/603m30/603m30/603m30/603m30/603m3m3m8m8m8m3-story8m8m8m5-story8m8m8m8-story8m8m8m15-Story(a) (b) (c) (d)F igure 1. Diagram of analyzed 3, 5, 8 and 15-story R\C frames with typical cross sections and steel reinforcementsV /WV /WV /WV /WV /WV /WRC Frame, Pushover Curve, Rectangular LoadRC Frame, Pushover Curve, Triangular LoadRC Frame, Pushover Curve, IBC (k=2) Load0.080.080.080.07 0.070.070.06 0.06 0.060.050.05 0.050.04 2nd floor 0.04 0.04 2nd floor 3rd floor 3rd floor 0.03 4th Floor 0.03 0.03 4th floor 5th floor 5th floor 0.02 6th floor 0.02 0.02 6th floor 7th floor 7th floor 0.018th floor 0.01 0.01 8th floorRoofRoof0.000.00 0.000.005.00 10.00 15.0020.00displacement (cm)0.005.0010.0015.0020.00displacement (cm) 0.005.00 10.00 15.0020.00displacement (cm)Figure 4. Push-over Curves of 8-story R\C Frame for three different Load Patterns0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00RC Frame, Pushover Curve, Rectangular Load2nd floor 3rd floor 4th floor 5th floor 6th floor 7th floor 8th floor 9th floor 10th floor 11th floor 12th floor 13th floor 14th floor 15th floor Roof0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.010.00RC Frame, Pushover Curve, Triangular Load2nd floor 3rd floor 4th floor 5th floor 6th floor 7th floor 8th floor 9th floor 10th floor 11th floor 12th floor 13th floor 14th floor 15th floor 16th floor0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.010.00RC Frame, Pushover Curve, IBC (k=2) Load2nd floor 3rd floor 4th floor 5th floor 6th floor 7th floor 8th floor 9th floor 10th floor 11th floor 12th floor 13th floor 14th floor 15th floor Roof0.0020.00 40.00 60.00 80.00 displacement (cm) 0.0020.00 40.00 60.00 80.00 displacement (cm) 0.0020.00 40.00 60.00 80.00displacement (cm)V /WV /WV /WV /WFigure 5. Push-over Curves of 15-story R\C Fram e for three different Load Patterns0.200.18 0.160.140.12 0.160.14 0.120.10 0.100.080.060.04 0.020.080.06 0.040.020.0024681012displacement (cm)0.0024681 01 21 41 6dis p la cem en t (c m )RectangularIBCA andB site classes D site class R e c t a n g u larTrian g u la r IB CA a n dB s i te c l a s s esC s i te c l a s sD s i te c l a s sa) 3-Story Frameb) 5-Story Frame0.120.120.10 0.100.08 0.080.06 0.060.04 0.040.020.020.002468101214161820displacement (cm)0.0024681012141618202224262830displacement (cm)RectangularTriangular IBCA andB site classesC site classD site classRectangularTriangularIBCA andB site classesC site classD site classc) 8-Story Frame d) 15-Story Frame Figure 6. Pushover and Nonlinear Time History Results of 3, 5, 8 and 15-story Frames。