高層結(jié)構(gòu)建筑外文翻譯--框架橫向剛度估計(jì)和橫向剛度線性與非線性的連續(xù)模型的靜力分析

1、<p><b>　　中文2597字</b></p><p>　　Lateral stiffness estimation in frames and its implementation to continuum models</p><p>　　for linear and nonlinear static analysis</p><

2、p>　　Tuba Ero?glu · Sinan Akkar</p><p>　　Abstract：Continuum model is a useful tool for approximate analysis of tall structures including moment-resisting frames and shear wall-frame systems. In contin

3、uum model, discrete buildings are simplified such that their overall behavior is described through the contributions of flexural and shear stiffnesses at the story levels. Therefore, accurate determination of these later

4、al stiffness components constitutes one of the major issues in establishing reliable continuum models even if the propose</p><p>　　Key words: Approximate nonlinear methods Continuum model Global capacit

5、y Nonlinear response Frames and dual systems</p><p>　　1 Introduction</p><p>　　Reliable estimation of structural response is essential in the seismic performance assessment and design because

6、it provides the major input while describing the global capacity of structures under strong ground motions.With the advent of computer technology and sophisticated structural analysis programs, the analysts are now able

7、to refine their structural models to compute more accurate structural response. However, at the expense of capturing detailed structural behavior, the increased unknow</p><p>　　new buildings. The continuum m

8、odel, in this sense, is an accomplished approximate tool for estimating the overall dynamic behavior of moment resisting frames (MRFs) and shear wall-frame (dual) systems.</p><p>　　Continuum model, as an app

9、roximation to complex discrete models, has been used extensively in the literature. Westergaard (1933) used equivalent undamped shear beam concept for modeling tall buildings under earthquake induced shocks through the i

10、mplementation of shear waves propagating in the continuum media. Later, the continuous shear beam model has been implemented by many researchers (e.g. Iwan 1997; Gülkan and Akkar 2002; Akkar et al. 2005; Chopra and

11、Chintanapakdee 2001) to approximate the</p><p>　　Heidebrecht and Stafford Smith (1973) defined a continuum model (hereinafter HS73) for approximating tall shear wall-frame type structures that is based on th

12、e solution of a fourthorder partial differential equation (PDE). Miranda (1999) presented the solution of this PDE under a set of lateral static loading cases to approximate the maximum roof and interstory drift demands

13、on first-mode dominant structures. Later, Heidebrecht and Rutenberg (2000) showed a different version of HS73 method to dr</p><p>　　While the theoretical applications of continuum model are abundant as brief

14、ly addressed above, its practical implementation is rather limited as the determination of equivalent flexural (EI) and shear (GA) stiffnesses to represent the actual lateral stiffness variation in discrete systems have

15、not been fully addressed in the literature. This flaw has also restricted the efficient use of continuum model beyond elastic limits because the nonlinear behavior of continuum models is dictated by the ch</p><

16、;p>　　This paper focuses on the realistic determination of lateral stiffness for continuum models. EI and GA defined in discrete systems are adapted to continuum models through an analytical expression that considers t

17、he heightwise variation of boundary conditions in discrete systems. The HS73 model is used as the base continuum model since it is capable of representing the structural response between pure flexure and shear behavior.

18、The proposed analytical expression is evaluated by comparing the def</p><p>　　2 Continuum model characteristics</p><p>　　The HS73 model is composed of a flexural and shear beam to define the fl

19、exural (EI) and shear (GA) stiffness contributions to the overall lateral stiffness. Themajor model parameters EI and GA are related to each other through the coefficient α (Eq.1).</p><p>　　As α goes to infi

20、nity the model would exhibit pure shear deformation whereas α = 0 indicates pure flexural deformation. Note that it is essential to identify the structural members of discrete buildings for their flexural and shear beam

21、contributions because the overall behavior of continuum model is governed by the changes in EI and GA. Equation 2 shows the computation of GA for a single column member in HS73. The variables Ic and h denote the column m

22、oment of inertia and story height, respecti</p><p>　　Equation 2 indicates that GA (shear component of total lateral stiffness) is computed as a fraction of flexural stiffness of frames oriented in the latera

23、l loading direction. Accordingly, the flexural part (EI) of total stiffness is computed either by considering the shear-wall members in the loading direction and/or other columns that do not span into a frame in the dire

24、ction of loading. This assumption works fairly well for dual systems. However, it may fail in MRFs because it will discard the</p><p>　　3 Lateral stiffness approximations for MRFs</p><p>　　Ther

25、e are numerous studies on the determination of lateral stiffness in MRFs. The methods proposed in Muto (1974) and Hosseini and Imagh-e-Naiini (1999) (hereinafter M74 and HI99, respectively) are presented in this paper an

26、d they are compared with the HS73 approach for its enhancement in describing the lateral deformation behavior of structural systems. Equation 3 shows the total lateral stiffness, k, definition of M74 for a column at an i

27、ntermediate story.</p><p>　　The parameters Ic, h, Ib1, Ib2, l1 and l2 have the samemeanings as in Eq. (2). </p><p>　　Note that Eq. (2) proposed in HS73 is a simplified version of Eq. (3) for a u

28、nit rotation. The former expression assumes that the dimensions of beams spanning into the column from top are the same as those spanning into the column from bottom. However, Eqs. (2) and (3) exhibit a significant conce

29、ptual difference: the HS73 approach interprets the resulting stiffness term as the shear contribution whereas M74 considers it as the total lateral stiffness. </p><p>　　The HI99 method defines the lateral st

30、iffness of MRFs through an equivalent simple system that consists of sub-modules of one-bay/one-story frames. Each sub-module represents a story in the original structure and the column inertia (Ic) of a sub-module is ca

31、lculated by taking half of the total moment of inertia of all columns in the original story. The relative rigidities of upper (ku) and lower (kl ) beams in a sub-module are calculated by summing all the relative beam rig

32、idities at the top and</p><p>　　The parameter kc and h denote the relative rigidity and length of the column in the submodule,respectively. The total lateral stiffness at ground story is computed by assignin

33、g relatively large stiffness values to kl to represent the fixed-base conditions. Equation (5) has a similar functional format as Eqs. (2) and (3). Since the lateral stiffness computed stands for the total lateral stiffn

34、ess, it exhibits a more similar theoretical framework to M74. </p><p>　　Discussions presented above indicate that both M74 and HI99 consider the variations in lateral stiffness at the ground story due to fix

35、ed-base boundary conditions. However, they ignore the free end conditions at the top story. As a matter of fact, Schultz (1992) pointed that lateral stiffness changes along the building height might be abrupt at boundary

36、 stories. The boundary stories defined by Schultz (1992) not only consist of ground and top floors but also the 2nd story because the propagation</p><p>　　References</p><p>　　1.Akkar S, Yazgan U

37、, Gülkan P (2005) Drift estimates in frame buildings subjected to near-fault ground motions. J Struct Eng ASCE 131(7):1014–1024</p><p>　　2.American Society of Civil Engineers (ASCE) (2007) Seismic rehab

38、ilitation of existing buildings: ASCE standard, report no. ASCE/SEI 41-06. Reston, Virginia</p><p>　　3.Applied Technology Council (ATC) (2004) FEMA-440 Improvement of nonlinear static seismic analysis pro-ce

39、dures, ATC-55 project report. prepared by the Applied technology Council for the Federal Emergency Management Agency, Washington, DC.</p><p>　　4.Blume JA (1968) Dynamic characteristics of multi-story buildin

40、gs. J Struct Div ASCE 94(2):377–402 </p><p>　　5.Borzi B, Pinho R, Crowley H (2008) Simpli?ed pushover-based vulnerability analysis for large-scale assessment of RC buildings. Eng Struct 30:804–820</p>

41、<p>　　框架橫向剛度估計(jì)和橫向剛度線性</p><p>　　與非線性的連續(xù)模型的靜力分析</p><p>　　吐哈埃爾奧盧?思南阿卡爾</p><p><b>　　摘要：</b></p><p>　　連續(xù)模型是高層結(jié)構(gòu)的近似分析，包括抗彎框架剪力墻系統(tǒng)都是非常有用的工具。在連續(xù)介質(zhì)模型，離散的建筑物被簡(jiǎn)化

42、，這樣他們的整體性能可以通過(guò)樓層層面的彎曲和剪切剛度來(lái)描述。因此，這些組件橫向剛度的準(zhǔn)確測(cè)定，是建立可靠的連續(xù)模型的主要問(wèn)題之一，即提出的解決方案是一個(gè)實(shí)際的近似結(jié)構(gòu)。本研究首先探討通過(guò)與精確結(jié)果的比較，通過(guò)對(duì)橫向剛度組件（即彎曲和剪切剛度）以往文獻(xiàn)的計(jì)算來(lái)獲得離散模型?；谶@些比較，一種適用于橫向剛度連續(xù)模型變化的新方法被提出來(lái)。建議的方法是進(jìn)行延伸來(lái)估計(jì)非線性抗彎矩框架的整體能力。該核查是比較與建議的過(guò)程，而估計(jì)的實(shí)際系統(tǒng)的非線性特

43、性表明其對(duì)大型建筑表現(xiàn)出類(lèi)似的結(jié)構(gòu)特征，并被有效利用。這一結(jié)論是通過(guò)比較，來(lái)進(jìn)一步說(shuō)明單自由度的非線性特性歷史分析（單自由度），它們從實(shí)際系統(tǒng)和擬議的程序的近似計(jì)算來(lái)得到系統(tǒng)的整體能力曲線。</p><p>　　關(guān)鍵詞：近似非線性方法 連續(xù)模型 整體能力 非線性特性 框架和雙系統(tǒng)</p><p><b>　　1 介紹</b></p><p&

44、gt;　　結(jié)構(gòu)特性的可靠估計(jì)是抗震性能評(píng)估和設(shè)計(jì)必不可少，因?yàn)樗峁┲饕獢?shù)據(jù)在描述在強(qiáng)地震時(shí)結(jié)構(gòu)的整體能力。隨著計(jì)算機(jī)技術(shù)和先進(jìn)的結(jié)構(gòu)分析程序的出現(xiàn)，分析家現(xiàn)在能夠改進(jìn)其結(jié)構(gòu)模型來(lái)計(jì)算更準(zhǔn)確的結(jié)構(gòu)反應(yīng)。然而，在捕捉詳細(xì)的結(jié)構(gòu)性能為前提，模型參數(shù)未知的增加與地面運(yùn)動(dòng)相結(jié)合的不確定性，會(huì)使分析結(jié)果繁瑣與解釋費(fèi)時(shí)。復(fù)雜的結(jié)構(gòu)模型和反應(yīng)歷史分析，也可用于大型建筑群性能評(píng)估或新建筑物的初步設(shè)計(jì)的確定。連續(xù)模型，在這個(gè)意義上，是估計(jì)抗彎矩框架（MR

45、Fs）和剪力墻框架（dual）系統(tǒng)近似整體動(dòng)態(tài)反應(yīng)的工具。</p><p>　　連續(xù)模型，近似的作為一種復(fù)雜的離散模型，已被廣泛使用在文獻(xiàn)中。Westergaard（1933）是用于地震引起的沖擊下，高層建筑模型通過(guò)連續(xù)介質(zhì)傳播橫波方式的等效阻尼剪切梁的概念。后來(lái)，連續(xù)剪切梁模型由許多研究者實(shí)現(xiàn)了（如伊萬(wàn)1997年古坎和阿卡爾2002;阿卡爾等人，2005年。普拉和柴可珀達(dá)2001）模擬地震引起的變形對(duì)框架體系的

46、作用?？珊埠?貝冉斯 (1964)采用等效剪切梁的理念擴(kuò)展到連續(xù)剪切和彎曲梁的組合。黑布瑞去和斯塔福德史密斯（1973）所界定連續(xù)的結(jié)構(gòu)模型（以下簡(jiǎn)稱(chēng)HS73），是用一個(gè)四階偏微分方程（PDE）來(lái)解決高層剪力墻框架模型，</p><p>　　雖然連續(xù)介質(zhì)模型的理論應(yīng)用建立在簡(jiǎn)要討論上，其實(shí)際執(zhí)行情況是相當(dāng)有限，因?yàn)榈刃澢鷾y(cè)定和剪剛度測(cè)定，代表的實(shí)際離散系統(tǒng)橫向剛度變化在文獻(xiàn)里沒(méi)有得到充分處理。這一缺陷也限制了，

47、因?yàn)槌鰪椥詷O限的非線性行為的連續(xù)模型的有效利用，連續(xù)模型是取決于在后階段EI和GA的變化。</p><p>　　本文的重點(diǎn)是橫向剛度連續(xù)模型的定義。EI和GA在離散系統(tǒng)中的定義，是邊界條件下離散系統(tǒng)的變化模型的解析表達(dá)式。該HS73模型作為基礎(chǔ)連續(xù)模型，是因?yàn)樗憩F(xiàn)了純彎曲和剪切行為，能代表結(jié)構(gòu)反應(yīng)的能力。建議的解析表達(dá)式是通過(guò)比較在第一個(gè)模式兼容加載模式下的，連續(xù)模型和實(shí)際離散系統(tǒng)的變形模式。在EI和GA測(cè)定

48、的改善，在結(jié)合了第二個(gè)過(guò)程的極限狀態(tài)分析的基礎(chǔ)上，描述了結(jié)構(gòu)承載超出其彈性極限后的整體能力。說(shuō)明案例研究表明，連續(xù)模型，使用時(shí)與所建議的方法一起，可以成為線性和非線性靜力分析的有用工具。</p><p><b>　　2 連續(xù)模型的特點(diǎn)</b></p><p>　　該HS73模型是由彎曲和剪切梁組成，來(lái)定義彎曲（EI）及剪切（GA）剛度的，從而確定整體剛度橫向剛度。主要

49、的模型參數(shù)EI和GA有關(guān)，通過(guò)彼此的（公式1）系數(shù)α相互聯(lián)系。</p><p>　　以α趨于無(wú)窮模型將展出純剪切變形而α= 0表示純彎曲變形。注意的事，必須查明離散建筑物的結(jié)構(gòu)構(gòu)件的彎曲和剪切，因?yàn)檫B續(xù)模型的整體行為是受在EI和GA的變化而決定。公式2表示在HS73的一系列計(jì)算。變量Ic和H分別表示的慣性和層高。Ib1的慣性和由L1和L2，分別確定相對(duì)僵化的總長(zhǎng)度除以Ib2，梁毗鄰自頂柱（見(jiàn)圖。在3提到文件）。&

50、lt;/p><p>　　公式2表明，GA（占總數(shù)的橫向剛度剪切組件）是一個(gè)橫向載荷方向框架抗彎剛度的計(jì)算分?jǐn)?shù)。彎曲部分（EI）的總剛度計(jì)算或者考慮在剪力墻加載方向/或不成為一個(gè)框架中其它柱跨度方向的負(fù)荷載。這個(gè)假設(shè)對(duì)雙系統(tǒng)效果非常好。但是，它可能會(huì)失敗，因?yàn)樗鼤?huì)在抗彎矩框架上沿載荷方向，將柱并到GA橫向剛度。事實(shí)上，這種近似將減少整個(gè)抗彎矩框架到剪力梁，將會(huì)不準(zhǔn)確的描述抗彎矩框架反應(yīng)，除非所有的梁被認(rèn)為是剛性的。就作

51、者的所知，研究使用HS73模型不僅詳細(xì)描述了α的計(jì)算，而且把離散建筑系統(tǒng)作為連續(xù)模型。在大多數(shù)情況下，這些研究不同結(jié)構(gòu)分配過(guò)程，從純彎曲跨越到純剪通用的α值。這種方法被認(rèn)為是合理的，是代表不同結(jié)構(gòu)理論的行為。不過(guò)，以上強(qiáng)調(diào)的事實(shí)，即有關(guān)的橫向剛度計(jì)算需要進(jìn)一步調(diào)查，以提高模型的性能，同時(shí)簡(jiǎn)化HS73實(shí)際抗彎矩框架作為一個(gè)連續(xù)模型。在這個(gè)意義上說(shuō)，的關(guān)于框架側(cè)向剛度估計(jì)的一些重要研究是值得討論的。這可能是關(guān)于GA和EI有用的增強(qiáng)計(jì)算方法，

52、用于描述連續(xù)系統(tǒng)的總橫向剛度。</p><p>　　3 抗彎矩框架的近似橫向剛度</p><p>　　這里有很多研究關(guān)于抗彎矩框架橫向剛度的測(cè)定。Muto (1974) 和 Hosseini 和Imagh-e-Naiini (1999) 所提出的方法（以下分別簡(jiǎn)稱(chēng)M74和HI99）基于本文件和他們相對(duì)于HS73途徑提高了其在描述系統(tǒng)結(jié)構(gòu)的側(cè)向變形。公式3顯示總橫向剛度K的M74，是一根柱在

53、一個(gè)中間樓層的值。</p><p>　　參數(shù)lchIb1，Ib2，L1和L2在公式2中的具相同涵義。</p><p>　　公式（2）是在HS73提出的一個(gè)關(guān)于公式（3）的簡(jiǎn)化版本。前者表達(dá)假定頂部柱之間梁的跨度和底部柱之間梁的跨度相同。不過(guò)，公式（2）及（3）表現(xiàn)出一個(gè)重大的概念區(qū)別： M74 認(rèn)為它為總計(jì)的橫向剛度， HS73同樣地解釋為剪切作用的術(shù)語(yǔ)。</p><p

54、>　　該方法HI99通過(guò)一個(gè)簡(jiǎn)單的系統(tǒng)把抗彎框架的橫向剛度，定義為是由一層樓高的框架的子模板組成。每個(gè)子模塊表現(xiàn)為原結(jié)構(gòu)的一個(gè)樓層，而且子模塊的柱剛度，由最初的層所有柱的總計(jì)剛度的一半來(lái)計(jì)算。在一個(gè)子模塊的上面的 （ku ）、比較低的 （kl ）梁的相對(duì)剛度，由最初層的頂和底部梁的剛度計(jì)算而得來(lái)。樓層總的橫向剛度在公式5中由HI99給出。</p><p>　　參數(shù)架KC和h分別表示了柱在子模塊中的相對(duì)剛性和

55、長(zhǎng)度。第一層總橫向剛度的計(jì)算方法是用較大的那個(gè)剛度值，分配到kl來(lái)表示固定的基礎(chǔ)條件。具有類(lèi)似功能的公式（2）及公式（3）。由橫向剛度計(jì)算的總橫向剛度，它表現(xiàn)出一種更類(lèi)似于M74的理論框架。</p><p>　　上面介紹的討論表明，這兩個(gè)M74和HI99考慮橫向剛度從第一層到固定基地邊界的變化。但是，他們忽視了在頂層自由端的條件。由于事實(shí)上，舒爾茨（1992）指出，建筑物的橫向剛度沿高度變化可能發(fā)生在邊界層。根據(jù)

56、上述情況，舒爾茨（1992）的邊界層定義不僅包括地面和頂層也包括第二層。雖然舒爾茨（1992）為某些特定情況下提出了邊界層的修正系數(shù)。他不用一般表達(dá)式來(lái)計(jì)算邊界層上剛度的變化。</p><p><b>　　參 考 文 獻(xiàn)</b></p><p>　　1.Akkar S, Yazgan U, Gülkan P (2005) Drift estimates in

57、 frame buildings subjected to near-fault ground motions. J Struct Eng ASCE 131(7):1014–1024</p><p>　　2.American Society of Civil Engineers (ASCE) (2007) Seismic rehabilitation of existing buildings: ASCE sta

58、ndard, report no. ASCE/SEI 41-06. Reston, Virginia</p><p>　　3.Applied Technology Council (ATC) (2004) FEMA-440 Improvement of nonlinear static seismic analysis pro-cedures, ATC-55 project report. prepared by

59、 the Applied technology Council for the Federal Emergency Management Agency, Washington, DC.</p><p>　　4.Blume JA (1968) Dynamic characteristics of multi-story buildings. J Struct Div ASCE 94(2):377–402 </