外文翻譯---靜力彈塑性分析法在側(cè)向荷載分布方式下的評(píng)估研究

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1、　　靜力彈塑性分析法在側(cè)向荷載分布方式下的評(píng)估研究　　Armagan KORKMAZ1, Ali SARI2　　1訪問學(xué)者,土木工程學(xué)院, 得克薩斯大學(xué), 奧斯汀, TX 78712, PH: 512-232-9216; armagan@mail.utexas.edu　　2博士, 土木工程學(xué)院,

2、得克薩斯大學(xué), 奧斯汀, TX 78712, PH: 512-232-9216; ali_sari@mail.utexas.edu　　摘要：　　這項(xiàng)研究的目的是通過彈塑性分析法和非線性時(shí)程分析法來評(píng)估框架結(jié)構(gòu)的性能或多種荷載形式及自然周期的多樣性。彈塑性分析法的荷載分布狀態(tài)有三角形、IBC（k=2），和矩形。在這個(gè)

3、研究中四種典型的鋼筋混凝土框架結(jié)構(gòu)被采用，它們分別有四種不同的自然周期。非線性時(shí)程分析法是計(jì)算地震的最好方法，但美國的FEMA-273容量震譜法和ATC-40位移系數(shù)法推薦使用靜力彈塑性分析法。這篇論文將比較分別利用靜力彈塑性分析法與非線性時(shí)程分析法分析所得到的結(jié)果。為了評(píng)估彈塑性分析法在三種不同荷載形式和四種自然周期下的結(jié)果，非線性時(shí)程分析法也被執(zhí)行來對(duì)照。在不同地震下分布在全球的50個(gè)站點(diǎn)紀(jì)錄了地面運(yùn)動(dòng)情況被用來做分析，通過比較靜力

4、彈塑性分析法和非線性時(shí)程分析法的結(jié)果來選擇這種典型框架結(jié)構(gòu)在特殊自然周期下最佳的荷載分布方式。　　關(guān)鍵詞：靜力彈塑性分析、非線性時(shí)程分析、荷載形式、抗彎矩框架　　前言　　一般的抗震設(shè)計(jì)中僅僅只有安全和碰撞是在地震設(shè)計(jì)規(guī)范中明確要求避免的，抗震設(shè)計(jì)一般基于結(jié)構(gòu)在地震中的性能表現(xiàn)

5、。這樣在低的地震水平下就要求考慮結(jié)構(gòu)的非彈性行為。FEMA-273和ATC-40采用靜力彈塑性分析法而不是非線性時(shí)程分析，因?yàn)榍罢咴诳拐鹩?jì)算中能得到更精確度結(jié)果。在抗震計(jì)算的目的是：（a）、在經(jīng)常發(fā)生的小震情況下避免非結(jié)構(gòu)破壞；（b）、在偶爾發(fā)生的中震情況下避免結(jié)構(gòu)破壞和最小限度的非結(jié)構(gòu)破壞；（c）、在罕遇大震下不倒塌或產(chǎn)生嚴(yán)重破壞。結(jié)構(gòu)設(shè)計(jì)要明確的在這三種情況下進(jìn)行。　　這項(xiàng)研究的目的是通過彈

6、塑性分析法和非線性時(shí)程分析法來評(píng)估框架結(jié)構(gòu)的性能或多種荷載形式及自然周期的多樣性。3、5、8和15層的四種框架結(jié)構(gòu)被用來分析，分析中荷載分布狀態(tài)選擇三角形IBC（k=1），IBC（k=2）和矩形。其中k是與結(jié)構(gòu)周期相關(guān)的系數(shù)，用來定義荷載豎向因素。這四種結(jié)構(gòu)用非線性程序DRAIN-2D (Prakash, V., Powell, G., Campbell, S., 1993)來分析，并把其結(jié)果與記錄的相應(yīng)數(shù)據(jù)比較。靜力彈塑性分析法和非線

7、性時(shí)程分析法都被執(zhí)行，這兩種非線性分析方法的聯(lián)系將被研究。　　在各種不同的地震運(yùn)動(dòng)下建筑物的性能將被檢查，最后比較靜力彈塑性分析法和非線性時(shí)程分析法的結(jié)果來選擇這種典型框架結(jié)構(gòu)在特殊自然周期下最佳的荷載分布方式。　　地表運(yùn)動(dòng)數(shù)據(jù)　　在這個(gè)研究中，50個(gè)不同的數(shù)據(jù)被用于非線性時(shí)

8、程分析法中，在表1中給出。所有數(shù)據(jù)來自四個(gè)A、B、C、D四個(gè)等級(jí)不同地點(diǎn)，它們的橫波速度分別是> 750 m/s, 360m/s至750 m/s, 180 m/s至360 m/s, ? 180 m/s。這些數(shù)據(jù)選至發(fā)生在世界不同地方的毀滅性地震，其中地震的名稱、數(shù)據(jù)源、記錄名稱、加速度峰值、有效期及過期類型都在表1中給出。　　地表加速度峰值大約在0.046g至0.395g，其中g(shù)為重力加速

9、度。所有地表運(yùn)動(dòng)數(shù)據(jù)取至距離地面最大為20km的近地范圍內(nèi)。　　框架結(jié)構(gòu)的描述　　有著典型截面和鋼筋的3、5、8和15層的鋼筋混凝土框架結(jié)構(gòu)見圖1，這些鋼筋混凝土結(jié)構(gòu)是按Turkish 規(guī)范設(shè)計(jì)?？紤]結(jié)構(gòu)所處環(huán)境為土質(zhì)類型Z1、地震1區(qū)，設(shè)計(jì)為等級(jí)為1級(jí)，其中恒載、活載以及地震荷載在設(shè)計(jì)中已經(jīng)被考慮。</p&g

10、t;　　所有這些鋼筋混凝土框架結(jié)構(gòu)都有3跨，長8m，層高3m。柱子假定與地基固結(jié)，鋼筋的屈服強(qiáng)度為22 kN/cm2 ，混凝土的抗壓強(qiáng)度為1.6kN/cm2.　　3層框架結(jié)構(gòu)的第一周期經(jīng)計(jì)算為0.54 s ，結(jié)構(gòu)中所有的框架梁截面為矩形，寬25 cm、高25cm，框架柱截面尺寸為30cmx30cm。5層框架結(jié)構(gòu)的第一周期經(jīng)計(jì)算為0.72 s ，框架梁截面為矩形，寬25 cm

11、、高50cm，框架柱截面尺寸前三層為40cmx40cm，后兩層為30cmx30cm。8層和15層的框架結(jié)構(gòu)的周期分別為0.90 s和1.20s ，兩者的框架梁截面為矩形，寬25 cm、高55cm。8層結(jié)構(gòu)框架柱截面尺寸前五層為50cmx50cm，后三層為40cmx40cm，而15層結(jié)構(gòu)框架柱截面尺寸前八層為80cmx80cm，后七層為60cmx60cm。　　框架結(jié)構(gòu)的靜力彈塑性分析法</p

12、>　　對(duì)于低等級(jí)的性能，為了估計(jì)其需求，就需要考慮結(jié)構(gòu)的非彈性行為。靜力彈塑性分析法可以用來識(shí)別地震的危險(xiǎn)，并選擇性能等級(jí)以此來設(shè)計(jì)性能目標(biāo)。在靜力彈塑性分析法中，以側(cè)向荷載近似代表由層間產(chǎn)生的相關(guān)慣性力并使結(jié)構(gòu)在這個(gè)側(cè)向荷載作用下產(chǎn)生的位移大于地震設(shè)計(jì)中預(yù)期的位移(Li, Y.R., 1996)。這種分析方法提供了剪力與位移的置換關(guān)系并指出非彈性的界限和結(jié)構(gòu)側(cè)面負(fù)荷能力，而曲線斜率方面的改變表明了各有限元

13、的屈服強(qiáng)度。靜力彈塑性分析法的主要目的是決定結(jié)構(gòu)的荷載數(shù)量和變形能力。這些信息都能夠用于評(píng)價(jià)結(jié)構(gòu)的整體性。　　在詳細(xì)設(shè)計(jì)了鋼筋混凝土框架結(jié)構(gòu)后，就用靜力彈塑性分析法評(píng)估結(jié)構(gòu)的地震反應(yīng)，為此電腦程序Drain 2D會(huì)被用到。有以下三種簡化荷載形式：三角形IBC（k=1），IBC（k=2）和矩形，其中k是與結(jié)構(gòu)周期相關(guān)的系數(shù)，用來定義荷載豎向因素。它們也會(huì)用于3、5、8和15層的鋼筋混凝土框架結(jié)構(gòu)的

14、靜力彈塑性分析。　　荷載標(biāo)準(zhǔn)的確定時(shí)基于設(shè)計(jì)參數(shù)中的慣性力的分布。簡化的荷載布置方式如均布分布、三角形分布、IBC分布是最常見的荷載參數(shù)。　　地震力的豎向分布：　?。?）　?。?

15、）　　式中：　　Cvx為豎向分布參數(shù)　　V為總側(cè)向力設(shè)計(jì)值，或結(jié)構(gòu)底部剪力　　wi和wx為部分結(jié)構(gòu)自重　　hi和hx為結(jié)構(gòu)高度（至基地算起）<

16、p>　　k為與結(jié)構(gòu)周期相關(guān)的參數(shù)　　除這些側(cè)向荷載外，結(jié)構(gòu)還承受恒載和活載。P-△作用在靜力彈塑性分析中同樣被考慮。側(cè)向荷載一直會(huì)增加，直到3、5和8層的框架結(jié)構(gòu)樓頂位移達(dá)到50cm?，15層的框架結(jié)構(gòu)樓頂位移達(dá)到100 cm?。梁柱單元用于結(jié)構(gòu)分析，假定梁在水平方向是剛性的，考慮非彈性影響單元是鉸接的，而應(yīng)變強(qiáng)化被忽略。雙線性彎矩—轉(zhuǎn)角關(guān)系假定用于所用梁柱單元，由ACI 318-89建議

17、的軸壓荷載—彎矩關(guān)系、P—M、交互關(guān)系被用于柱單元屈服表面。薄弱破碎區(qū)段的慣性矩Icr ，在分析的時(shí)候用于所有的梁柱。Icr取總慣性矩Ig的一半。　　由靜力彈塑性分析法所得的結(jié)果見圖2-5。每個(gè)框架結(jié)構(gòu)的彈塑性曲線都分均布荷載、三角形荷載以及IBC荷載三種荷載方式給出，顯示了剪重比與之相對(duì)應(yīng)的層間位移。基底剪力V由地面以上所有荷載相加得到，結(jié)構(gòu)重力W所有樓層重量之和。除此之外，這些曲線還表示結(jié)構(gòu)

18、抗側(cè)力的損失情況和柱位移下的剪切破壞。曲線中曲率的變化表明了不同結(jié)構(gòu)單元屈服情況，首先是梁屈服，接著是柱屈服和各單元的剪切破壞。隨著結(jié)構(gòu)自重的增加，頂層位移增大，出現(xiàn)首次屈服和剪切破壞（見圖2-5）。在相應(yīng)的結(jié)構(gòu)位移（水平位移）下，矩形荷載分布比其它荷載分布形式相比會(huì)造成更高的剪重比。 　　框架結(jié)構(gòu)的非線性時(shí)程分析　　前面對(duì)框架結(jié)構(gòu)進(jìn)行了靜力彈塑性分析，

19、下面用非線性時(shí)程分析法對(duì)其進(jìn)行分析。這些框架結(jié)構(gòu)都承受恒載和活載，同靜力彈塑性分析法一樣，P-△作用在非線性時(shí)程分析中也被考慮。在非線性時(shí)程分析中Drain 2D程序被利用，有限元程序也被用來模擬結(jié)構(gòu)。在靜力彈塑性分析中所描述的模型同樣用于非線性時(shí)程分析法中，且假定質(zhì)量集中在節(jié)點(diǎn)處。　　結(jié)構(gòu)承受的??種地震情況都是在以下地震中被記錄的，這些地震是美國南加州Anza地震、美國加州Parkfield

20、地震、美國西部Morgan Hill地震、土耳其Kocaeli地震、日本Coyota Lake地震、美國N. Palm Springs地震、美國加州Northridge地震、美國加州Santa Barbara地震、美國Imperial Valley地震、美國加州Cape Mendocino地震、日本神戶Kobe地震、美國Central California地震、美國加州Lytle Creek地震、美國南加州Whittier Narrow

21、s 地震、美國Hollister Westmoreland地震、美國Livermor地震、美國加州Cape Mendocino地震。這些數(shù)據(jù)取自A、B、C、D四類地區(qū)，來用于非線性時(shí)程分析。　　被選中的地震有著不同的頻率和地表加速度峰值，數(shù)據(jù)來自近地范圍因而可以用來評(píng)估結(jié)構(gòu)的反應(yīng)并與靜力彈塑性分析法所得到的結(jié)果比較。3、5、8和15層框架結(jié)構(gòu)的非線性時(shí)程分析的結(jié)果見圖-6。由此可以比較兩種分析方

22、法在不同周期、不同荷載情況，即矩形、三角形和IBC(k=2)下四種框架結(jié)構(gòu)的結(jié)果。　　結(jié)論　　在詳細(xì)設(shè)計(jì)了鋼筋混凝土框架結(jié)構(gòu)后，靜力彈塑性分析法和非線性時(shí)程分析法被執(zhí)行來評(píng)價(jià)在不同荷載情況下的地震反應(yīng)。靜力彈塑性分析法假定抗震所設(shè)的目標(biāo)位移量與實(shí)際地震下的最大位移大致一樣。

23、　從圖-2至圖-5可以看出，對(duì)于高層的框架結(jié)構(gòu)位移增大，出現(xiàn)首次屈服和剪切破壞。在相應(yīng)的結(jié)構(gòu)位移（水平位移）下，矩形荷載分布比其它荷載分布形式相比會(huì)造成更高的剪重比。 　　如圖-6所示，在所選的地表運(yùn)動(dòng)數(shù)據(jù)下，非線性時(shí)程分析法在三角形荷載、矩形荷載和IBC(k=2)荷載情況的結(jié)果相互比較知：靜力彈塑性曲線在高層框架結(jié)構(gòu)（8和15層框架結(jié)構(gòu)）下與非線性時(shí)程分析得出的結(jié)構(gòu)不是很相符。靜力彈塑性分析法

24、在矩形分布下所得的抗震要求要比其它荷載方式如三角形荷載、IBC(k=2)荷載形式下更合理。　　參考文獻(xiàn)　　1. ATC-40 (1996), “Seismic evaluation and Retrofit of Concrete Buildings”, Vol.1, Applied Technology Coun

25、cil, 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) “

26、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-

27、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 Calif

28、ornia, CA.　　EVALUATION OF LATERAL LOAD PATTERN　　IN PUSHOVER ANALYSIS　　Armagan KORKMAZ1, Ali SARI2　　1Visitor Researcher, Department of Ci

29、vil Engineering, University of Texas at Austin, Austin,TX78712, PH: 512-232-9216; armagan@mail.utexas.edu　　2Ph. D. Student, Department of Civil Engineering, University of Texas at Austin, Austin, TX

30、78712, PH: 512-232-9216; ali_sari@mail.utexas.edu　　ABSTRACT　　The objective of this study is to evaluate the performance of the frame structures or various load

31、 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 differen

32、t 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 analys　　Keywords: Push

33、over analysis, nonlinear time history, load patterns, moment-resisting frame　　INTRODUCTION　　Only the life safety and collapse prevention in general earthquake resistant design ph

34、enomena 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 the seismic dema

35、nds at low performance levels. FEMA-273 and ATC-40 use pushover analysis as nonlinear static analysis but nonlinear time history analysis has more accurate results on computing seismic demands (　　The

36、 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

37、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 p

38、eriod to define vertical distribution factor (IBC, 2000).　　The performance of the buildings subjected to various representative earthquake ground motions is examined. Finally, pushover and nonlinear

39、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 DATA</

40、p>　　For 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

41、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 wo

42、rld earthquake name, date of earthquake, data source, record name, peak ground a　　The peak ground accelerations are in the range 0.046 to 0.395g, where g is acceleration due to gravity. All ground m

43、otion data are recorded in near-field region as in maximum 20 km distance.　　DESCRIPTION OF THE FRAME STRUCTURES　　3, 5, 8 and 15-story R\C frame structures with typical cross-sect

44、ions 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 wi

45、th 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

46、 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

47、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 fi

48、rst 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 l

49、ast two stories, it is 30cmx30cm. The eight-story 　　NONLINEAR STATIC PUSHOVER ANALYSIS OF FRAME STRUCTURES　　For low performance levels, to estimate the demands, it is required to

50、 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 load

51、s 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 displacement

52、　　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 Drai

53、n 2D has been used. 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 no

54、nlinear static pushover analysis of 3, 5, 8 and 15-story R\C frame struct　　Load criteria are based on the distribution of inertial forces of design parameters. The simplified loading patterns as unif

55、orm distribution, triangular distribution and IBC distribution, these loading patterns are the most common loading parameters.　　Vertical Distribution of Seismic Forces:

56、?。?）　　（2）　　where:　　Cvx= Vertical distribution factor　　V = Total design lateral force or

57、 shear at the base of structure　　wi and wx = The portion of the total gravity load of the structure　　hi and hx = The height from the base　　k = An exponent re

58、lated to the structure period　　In 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 lat

59、eral 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

60、 horizontal plane. Inelastic effects are assigned to plastic hinges at member ends. Strain-hardening is neglecte　　The results of the pushover analyses are presented in Figures 2 to 5. The pushover cu

61、rves 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 calcula

62、ted 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 l　　NO

63、NLINEAR DYNAMIC TIME HISTORY ANALYSIS OF FRAME STRUCTURES　　After performing pushover analyses, nonlinear dynamic time history analyses have been employed to the four different story frame structures.

64、 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 em

65、ployed for the modeling of the structures during the nonlinear dynamic time history analyses. Drain 2D has been used for nonlinear time hist　　The frames are subjected to 50 earthquake ground motions,

66、 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 Nar

67、rows, 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 sele

68、cted 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 in this region and

69、 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

70、 are compared to for specific natural period 　　CONCLUSIONS　　After designing and detailing the reinforced concrete frame structures, a nonlinear pushover analysis and nonli

71、near 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 a

72、t 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 yielding and shear failure of

73、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.&l

74、t;/p>　　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 motio

75、n 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 l

76、oad distribution estimate maximum seismic demands during the given earthquakes mo　　REFERENCES　　1. ATC-40 (1996), “Seismic evaluation and Retrofit of Concrete Buildings”, Vol.1,

77、 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.</

78、p>　　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.&l

79、t;/p>　　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

80、(1995). Structural Engineering Association of California, CA.　　Table 1. Ground Motion Data Used in the Analyses　　60/603m　　fy= 22 kN/cm2&l

81、t;/p>　　Beams: 25x50 : As=10.30 cm2　　25x55 : As=13.26 cm2　　60/60　　60/60　　60

82、/60　　3m　　30/60　　3m　　30/603m&

83、lt;b>　　3m　　60/60　　30/30　　50x50 : As=45.20 cm2　　80x80 : As=145.00 cm2<p

84、>　　25/50　　3m　　25/50　　25/50　　3m</p&g

85、t;　　25/50　　25/50　　25/50　　25/50　　25/50<

86、;/b>　　40/40　　50/50　　50/50　　50/50<

87、b>　　50/50　　3m　　50/50　　25/55　　25/55&

88、lt;p>　　25/55　　60/60　　60/60　　3m　　80/80&

89、lt;/p>　　3m　　80/80　　3m　　80/80　　3m</

90、b>　　80/80　　3m80/80　　3m80/80　　3m80/80<p&

91、gt;　　30/603m　　30/603m　　30/603m　　30/603m　　30/60

92、3m　　30/603m　　30/60　　3m　　30/603m<p

93、>　　3m　　3m　　8m8m8m　　3-story　　8m8m8m

94、　　5-story　　8m8m8m　　8-story　　8m8m8m&

95、lt;b>　　15-Story　　(a)(b)(c)(d)　　Figure 1. Diagram of analyzed 3, 5, 8 and 15-story R\C frames with typical cross sections and steel reinforcements<p

96、>　　0.005.0010.0015.0020.00　　displacement (cm)　　0.005.0010.0015.0020.00　　displacement (cm)　　0.005.0010.0015.0020.00</p&

97、gt;　　displacement (cm)　　Figure 4. Push-over Curves of 8-story R\C Frame for three different Load Patterns　　0.10　　0.09

98、　　0.08　　0.07　　0.06　　0.05<b

99、>　　0.04　　0.03　　0.02　　0.01　　0.00<

100、p>　　RC Frame, Pushover Curve, Rectangular Load　　2nd floor　　3rd floor　　4th floor<p&

101、gt;　　5th floor　　6th floor　　7th floor　　8th floor　　9t

102、h floor　　10th floor　　11th floor　　12th floor　　13th floor　　14th floor　　15th floor</

103、p>　　Roof　　0.10　　0.09　　0.08　　0.07</

104、b>　　0.06　　0.05　　0.04　　0.03

105、　0.02　　0.01　　0.00　　RC Frame, Pushover Curve, Triangular Load　　2nd floor</b&g

106、t;　　3rd floor　　4th floor　　5th floor　　6th floor&l

107、t;p>　　7th floor　　8th floor　　9th floor　　10th floor　　11th floor<

108、;p>　　12th floor　　13th floor　　14th floor　　15th floor　　16th floor　　0.10<

109、;b>　　0.09　　0.08　　0.07　　0.06　　0.05&l

110、t;p>　　0.04　　0.03　　0.02　　0.01　　0.00<

111、/p>　　RC Frame, Pushover Curve, IBC (k=2) Load　　2nd floor　　3rd floor　　4th floor</p&g

112、t;　　5th floor　　6th floor　　7th floor　　8th floor<

113、;b>　　9th floor　　10th floor　　11th floor　　12th floor　　13th floor　　14th floor　　15th

114、floor　　Roof　　0.0020.0040.0060.0080.00　　displacement (cm)　　0.0020.0040.0060.0080.00　　disp

115、lacement (cm)　　0.0020.0040.0060.0080.00　　displacement (cm)　　Figure 5. Push-over Curves of 15-story R\C Frame for three different Load Patterns

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