建筑專業(yè)畢業(yè)設(shè)計(jì)外文翻譯--世界第一高樓的地震分析

1、<p><b>　　外文資料翻譯</b></p><p>　　Contents lists available at ScienceDirect</p><p>　　Journal of Constructional Steel Research</p><p>　　Seismic analysis of the world’s ta

2、llest building</p><p>　　Hong Fana,b, Q.S. Lia,?, Alex Y. Tuanc, Lihua Xud</p><p>　　a Department of Building and Construction, City University of Hong kong, Hong kong</p><p>　　b Chin

3、a Nuclear Power Design Company, Shenzhen 518026, China</p><p>　　c Department of Civil Engineering, Tam kang University, Taipei, Taiwan</p><p>　　d School of Civil Engineering, Wuhan University, H

4、ubei Wuhan 430072, China</p><p>　　a r t i c l ei n f o</p><p>　　Article history: Received 13 March 2008 Accepted 8 October 2008</p><p>　　keywords: Super-tall building Mega-frame

5、 structure Finite element modeling Seismic analysis Dynamics response</p><p>　　Shaking table test</p><p>　　a b s t r a c t</p><p>　　Taipei 101 (officially known as the Tai

6、pei Financial Center) with 101 stories and 508 m height, located in Taipei where earthquakes and str o -ng typhoons are common occurrences, is currently the tallest bui lding in the world. The great height of the buildin

7、g, the special geog- raphic an -d environmental conditions, not surprisingly, presented one of the gre -atest challenges for structural engineers. In particular, its dynamic pe -rformance under earthquake or wind actions

8、 requires inte- nsive</p><p>　　1. Introduction</p><p>　　Owing to the growing use of high-strength materials and advanced co- nstruction techniques, building structures have become more and more

9、flexible and taller. The increasing height of modern tall buildings po- sed a series of challenges for structural engineers. In the design of such a tall building, the structural system must meet three major require- men

10、ts: strength, rigidity, and stability [1].As is well known, the stre- ngth requirement is the dominant factorin the design of low-rise structu</p><p>　　Taipei 101, rising 508 m above the city of Taipei, earn

11、s the title of the tallest building in the world. Its dynamic responses due to wind, ea- rthquake and other extraordinary loads are of great concern. As Taiwan is located in one of the most active seismic regions in the

12、world, this supertall building may be susceptible to damage caused by strong eart- hquakes. These features make a detailed study on the structural perf- ormance of the world’s highest tall building under earthquake excit

13、- ati</p><p>　　Numerous investigations on seismic behavior of tall buildings Have been carried out in the past; in particular shaking table tests play an im- portant role in earthquake-resistant design of st

14、ructures, analysis of se- ismic responses and failure mechanisms [3–5]. On the other hand, the finite element method (FEM) is a powerful tool for structural analysis of tall buildings. Fan and Long [6] adopted spline ele

15、ments in the ana- lysis of tall buildings. In their method, the element displacements ar</p><p>　　With consideration of the effect of bending, transverse shear defor- mation, shear-lag and torsion. Li et al.

16、 [8,9] proposed finite segment a- pproaches for estimating the dynamic characteristics of tall buildings. Recently, Li and Wu [10] established seven 3-D FE models for a 78-st- ory super-tall building, and numerical resul

17、ts of the structural dynamic characteristics were compared with their field measurements to identify the FEM modeling errors for the purpose of updating the FEM models. Ve</p><p>　　dynamic characteristic of

18、a 30-storey RC building. A reducedorder con- tinuum model was proposed by Chajes et al. [12] to conduct dynamic analysis of a 47-storey steel-framed building and correlate the numeri- cal results with those from measured

19、 responses during an earthquake. Pan et al. [13] and Brownjohn et al. [14] presented numerical studies on dynamic responses of the tallest building in Singapore with correlation with their field measurements. Qi et al. [

20、15] employed the finite elem- ent </p><p>　　2. The structural system of Taipei 101</p><p>　　Taipei 101, a 508-m high office tower, is located at the east district of downtown Taipei City, and th

21、e elevation view of the building is shown in Fig. 1. The structure is symmetrical with a 62.4 m by 62.4 m square footprint [17]. Two sloping rectangular mega-columns with a maximum cross-sectional dimension of 2400 mm &#

22、215; 3000 mm, are positioned one at each side of the building extending to the 90th floor, and finally the cross-sectional dimension of the mega-column is reduced to 1600 mm×2000 mm. </p><p>　　Belt-trus

23、ses, one or two-stories high, are placed every 8-story interval at the perimeter frame, and the brace core is connected to mega-columns via belt-trusses consisting of in-floor braces and vertical trusses. The locations o

24、f the belt-trusses in the 8th floor are shown in Fig. 3 [17]. When the space of the column is 10.5 m, the shape of the steel braces are ‘‘V’’ or reverse ‘‘V’’, and when the space is 6 m, the shape of steel braces are acc

25、livitous braces Fig. 4 presents an elevation view a</p><p>　　A FE model was established in this study based on the design drawings of the super-tall building. The dead loads for building elements were determ

26、ined by a commercial FE program ANSYS 10.0 [18] and the design live loads were calculated according to the data found from the design documents [17].</p><p>　　3. Structural analysis</p><p>　　3.1

27、. Finite element modeling</p><p>　　With rapid development in computer technology and computational mechanics algor- ithms, three-dimensional finite element analysis has become a routine design tool of tall b

28、uildings. Four kinds of elements are emp- loyed in establishing the FE model of Taipei 101 structure: 3-D beam elements, suitable for nonlinear large rotations and large strains, are employed to model the columns and bea

29、ms. Li- nk elements are used to mo- del the brace. Mass elements are employed to model the live loads and no</p><p>　　3.2. Constitutive relationships of rectangular CFT columns</p><p>　　Concrete

30、-filled steel tube (CFT) columns are widely used due to their good earthquake resistant behavior such as improved strength and high ductility capacity. When a short CFT column is under an axial load, as shown inFig. 4(b

31、), there is a basicassumption that steel and concrete have the same longitudinal strain ε3, then the hoop stains of steel ε1s and concrete ε1ccan be calculated by:</p><p>　　ε1s=µsε3, ε1c=µc

32、ε3 (1)</p><p>　　whereµs,µcare the Poisson’s ratio of steel and concrete, respectively.</p><p>　　Generally, at low stress conditions, concrete has a lower value of Po

33、isson’s ratio than steel, which may result in occurrence of separation between the two materials in a CFT column. At high compressive stresses, internal micro-cracking in concrete causes it to swell. Its outwards movemen

34、t is restrained by steel, and the strength of concrete is increased due to this lateral restraint. Thus the concrete and steel are stressed triaxially, as shown in Fig.5 (a).</p><p>　　Zhong [19,20] proposed

35、a unified theory to model CFT columns based on extensive expe- rimental and FE analysis results of CFT columns under axial loading. According to the theory, a CFT column is regarded as a new composite column or material

36、instead of Sep- arate components of concrete and steel. The properties of the composite column depend on those of steel and concrete and their dimensions (e.g., tube diameter and steel wall thickness).The u- ltmate stre

37、ngth and other property parameters of</p><p>　　The yield strength of the composite column is</p><p>　　fscy= (1.212 + Bξ + Cξ2)fck (2)</p><p>　　where, B and C are coefficients. They

38、 depend on the cross-sectiongeometry. For a rectangular cross-section, one has:</p><p>　　B = 0.1381(fy/235) + 0.7646,</p><p>　　C= ?0.0727(fck/20) + 0.2016,where ξ is the confining factor which

39、is expressed as</p><p>　　in whichfy,fck,AsandAcare the yield strength of steel, theunconfined strength of concrete and the areas of steel and concretecomponents in the column, respectively.The elastic mo

40、dulusEscof the composite column can beexpressed as</p><p>　　Esc= fscp/εscp (3)</p><p>　　wherefscp,εscpare the proportional stress and strain of the composite column, respective

41、ly.For a rectangular CFT column, one has</p><p>　　fscp= [0.192(fy/235) + 0.488]fscy (4)</p><p>　　εscp= 0.67fy/ Es. (5)</p><p>　　The tangent mo

42、dule of the composite column can be calculated as</p><p>　　(fscy? ¯σ)σ¯ (6)</p><p>　　where σ¯= N/Asc, N is the axial load on the column and Ascis the total a

43、rea of the column section. The hardening modulus of the composite column can be determined by </p><p>　　E0sc=400ξ ? 150. (7)</p><p>　　In this paper, the load–deformation (stress–stra

44、in) relation of a CFT column was determined based on experimental measure- ments from CFT columns under axial compressions [19], which was simplified as a tri-linear stress–strain model including proportional, yield and

45、hardening stages, as shown in Fig. 6(a). The tangent module is substituted by the module of a straight line connected the proportional point and the yield point. According to Eqs. (2)–(5) and (7), the related parameters

46、for a CFT co</p><p>　　For structural analysis of the steel beams and brace members in Taipei 101 building, a bilinear stress–strain curve with 2% post- yield hardening (see Fig. 6(b)) was adopted to model th

47、e inelastic behavior of these structural members, with Young’s modulus of 420 MPa and Poisson’s ratio of 0.3, respectively. Von Mises yield criterion with kinematic hardening rule was employed in the numerical analysis.&

48、lt;/p><p>　　3.3. Verification of the constitutive relationships of CFT columns</p><p>　　For verification of the adequacy of the constitutive relationships of CFT columns and steel members discussed

49、 above as well as the selected finite element types for modeling the structural members of Taipei 101 structural system, a shaking table test and the associated FEM analysis were conducted in this study for a frame struc

50、ture model composed of rectangular CFT columns and steel members by comparing the numer- ical results with the experimental data. The test model and its finite element mod</p><p>　　Table 3 lists the first fo

51、ur natural frequencies of the model</p><p>　　obtained from the test and the numerical analysis of the FE model.</p><p>　　Furthermore, acceleration dynamic amplification factors of the </p>

52、<p>　　modeling strategies presented above in the establishment of the FE model of Taipei 101 structural system.</p><p>　　4. Dynamic characteristics of the super-tall building</p><p>　　A t

53、hree-dimensional FE model of Taipei 101 structural system</p><p>　　was established for numerical analysis of the super-tall building, as shown in Fig. 10, based on the constitutive relationships for rectangu

54、lar CFT columns and steel members as well as the selected finite element types which were verified above. The FE model of the super-tall bu- ilding contains 20 532 beam elements, 24 048 shell elements, and 3496 link elem

55、ents. In addition to the main structural elements, nonstructural components were modeled with mass elements. Fig. 11 shows the first six mod</p><p>　　, which shows the modes that contribute most to the dynam

56、ic response, where TMU is the mass matrices, TuU is the vi- bration mode vector of the structure, and TEU is the uniform matrix. The model participation ratio in every direction for each mode is defined as (c D x, y, z

57、), while the cumulative modal participation mass ratios is defined as tD1 mct(c D x, y, z), where m is the effective mass participating the dy- namic response of each mode. Table 4 shows the modal participation ratios an

58、d t</p><p>　　5. Response spectrum analysis</p><p>　　For earthquake-resistant designs, a structure should meet perfo- rma- nce requirements at two different levels, depending upon the magnitude o

59、f earthquake actions. The first level of performance esse- ntially requ- ires structural response in the elastic range without sign- ificant structural damage under a moderate earthquake action, and the second level of p

60、erformance requires that the structure does not colla- pse under a severe earthquake event with rare occurrence. Taipei 101 is located in </p><p>　　目錄列出了有用的科學(xué)指南 </p><p><b>　　建筑鋼材研究雜志 </

61、b></p><p><b>　　建筑學(xué)報(bào)鋼鐵研究</b></p><p>　　世界第一高樓的地震分析</p><p><b>　　洪帆 </b></p><p>　　a建筑系，香港城市大學(xué)，香港大學(xué)b中國核電設(shè)計(jì)公司，深圳518026，中國c土木工程系，淡江大學(xué)，臺(tái)北，臺(tái)灣</p&

62、gt;<p>　　d土木工程學(xué)院，武漢大學(xué)，湖北武漢430072，中國</p><p>　　文章信息： </p><p>　　文章歷史：收到2008年3月13日二零零八年十月八日關(guān)鍵詞：超高層建筑，巨型框架結(jié)構(gòu)，有限元模擬，地震分析，動(dòng)力響應(yīng)，振動(dòng)臺(tái)試驗(yàn)</p><p>　　臺(tái)北101大廈（官方稱呼為臺(tái)北金融中心

63、）有101層樓、高508m，位于地震和強(qiáng)臺(tái)風(fēng)屢見不鮮的臺(tái)北，是目前世界上最高的建筑物。建筑的巨大高度，特殊的地理環(huán)境條件，毫無疑問，目前它是對(duì)結(jié)構(gòu)工程師的最大的挑戰(zhàn)之一。特別是，需要深入研究其在地震或風(fēng)作用下的動(dòng)態(tài)表現(xiàn)。此建筑是由鋼管混凝土柱（CFT）和鋼筋支撐核心及由抵抗豎向和橫向荷載相聯(lián)合的桁架帶組成的一個(gè)巨型框架結(jié)構(gòu)體系。在此研究中，振動(dòng)臺(tái)試驗(yàn)的進(jìn)行是用來確定本構(gòu)關(guān)系和鋼管混凝土柱的有限元素類型并建立有限元（FE）的高層建筑鋼構(gòu)件

64、模型。然后，對(duì)超高層建筑的地震反應(yīng)進(jìn)行數(shù)值研究。臺(tái)北盆地產(chǎn)生的地震頻譜被搜集起來用來計(jì)算建筑的側(cè)向位移和柱子內(nèi)力的分布。另外，彈性和非彈性地震反應(yīng)的時(shí)程分析被進(jìn)行用縮放加速度分別代表重現(xiàn)期為50年、950年和100年的地震活動(dòng)。計(jì)算結(jié)果表明，超高型建筑和巨型框架體系具有大量的儲(chǔ)備強(qiáng)度，高層結(jié)構(gòu)將滿足惡劣地震情況下的設(shè)計(jì)要求。本研究的結(jié)果預(yù)計(jì)對(duì)超高層建筑設(shè)計(jì)工作的研究人員和專業(yè)人士會(huì)有很大興趣并且很實(shí)用。</p><p

65、><b>　　1、介紹</b></p><p>　　由于高強(qiáng)度材料和先進(jìn)的施工技術(shù)越來越多的使用，建筑結(jié)構(gòu)變得越來越靈活越來越高?，F(xiàn)代高層建筑高度的不斷增加對(duì)結(jié)構(gòu)工程師構(gòu)成一系列的挑戰(zhàn)。在這樣的高層建筑設(shè)計(jì)中，結(jié)構(gòu)體系必須滿足三大要求：強(qiáng)度、剛度和穩(wěn)定性[1]。眾所周知，在低層結(jié)構(gòu)設(shè)計(jì)中，強(qiáng)度要求是主導(dǎo)因素。然而，隨著建筑物高度的增加，剛度和穩(wěn)定性的要求變的越來越重要，他們才常常是結(jié)構(gòu)

66、設(shè)計(jì)的主導(dǎo)因素。尤其是在橫向荷載下，內(nèi)力是整體可變因素，其隨著高度的增加而迅速增加，并且作為一個(gè)建筑高度的第四要素可能會(huì)發(fā)生變化。故在現(xiàn)代高層建筑設(shè)計(jì)中結(jié)構(gòu)的動(dòng)態(tài)行為是最重要的考慮因素之一。</p><p>　　臺(tái)北101大廈，臺(tái)北市以上508米，被譽(yù)為世界上最高建筑，由于風(fēng)、地震和其他的不一般的荷載作用下的動(dòng)力反應(yīng)所以被高度關(guān)注。由于臺(tái)灣是世界上地震最活躍的地區(qū)之一，這種超高型建筑可能容易感覺到地震引起的損害。

67、這些特性體現(xiàn)了做一個(gè)地震作用下世界上最高建筑的結(jié)構(gòu)性能的詳細(xì)研究的重要性和必要性。</p><p>　　在過去對(duì)高層建筑抗震性能的調(diào)查已進(jìn)行了許多，特別是振動(dòng)臺(tái)試驗(yàn)在地震響應(yīng)和實(shí)效機(jī)制的分析【3-5】抗震結(jié)構(gòu)設(shè)計(jì)中發(fā)揮了重要作用。另一方面，有限元法（FEM）是一種用于高層建筑結(jié)構(gòu)分析的有力工具，在高層建筑分析中fan和長通過祥條單元分析。在這種方法中，該單元的位移被插入到樣條函數(shù)中并計(jì)算出準(zhǔn)確的結(jié)果可以得到低階函

68、數(shù)和極少的自由度，提出了初步設(shè)計(jì)的簡(jiǎn)單分析方法的雙對(duì)稱單和通過在高層結(jié)構(gòu)中取代具有等效桿的管的雙幀管，同時(shí)考慮彎曲效應(yīng)，橫向剪切變形，剪切和扭轉(zhuǎn)滯后。李等人提出了估算高層建筑動(dòng)力特征的有限元方法。最近，李和吳建立了7個(gè)78層超高型建筑的三維有限元模型，結(jié)構(gòu)動(dòng)態(tài)特征的數(shù)值結(jié)果和他們場(chǎng)地測(cè)量相比較從而鑒定有限元建模誤差已達(dá)到有限元模型更新的目的。Ventura和Schuster提出了一個(gè)關(guān)于一個(gè)30層鋼筋混凝土動(dòng)態(tài)特性估計(jì)的數(shù)值研究。Cha

69、jes等人提出了一個(gè)連續(xù)降階模型來進(jìn)行一棟47層的鋼筋混凝土結(jié)構(gòu)的建筑與在地震當(dāng)中測(cè)量相應(yīng)的數(shù)值結(jié)果進(jìn)行關(guān)聯(lián)。潘等人。 [13]和布朗約翰等提出了關(guān)于在新加坡最高建筑的動(dòng)態(tài)響應(yīng)的數(shù)值研究并和她們實(shí)地測(cè)量進(jìn)行關(guān)聯(lián)。齊等人采用有限元分析的方法研究了一個(gè)</p><p>　　型建筑（建筑物高度>500m）綜合研究報(bào)告很少在文獻(xiàn)中報(bào)道。因此，一個(gè)詳細(xì)的分析提出了超高型建筑的動(dòng)態(tài)特性和地震反應(yīng)。這項(xiàng)研究的目的是探討世

70、界上最高建筑物所受到的地震影響，以便為將來設(shè)計(jì)和建設(shè)其他類似結(jié)構(gòu)提供寶貴的資料。</p><p>　　2、臺(tái)北101大廈的結(jié)構(gòu)體系</p><p>　　臺(tái)北101大廈，一個(gè)508m高的商業(yè)大廈，位于市中心的東部，建筑物的海拔如圖1所示，是對(duì)稱結(jié)構(gòu)有一個(gè)62.4m62.4m的方形基礎(chǔ)。兩個(gè)傾斜的長方形矩形柱，最大截面尺寸為2400mm3000mm,位置是建筑物延伸到第90層的每邊，最后的巨形

71、柱截面尺寸減小到1600mm2000mm。所有周邊柱子從地下傾斜至25層，傾斜角是4.4度。核心柱是方形和矩形的鋼管混凝土柱?；炷恋目箟簭?qiáng)度為70MPa，由鋼管提供額外的強(qiáng)度和剛度，從底層到62層。核心柱的截面積從1200mm1200mm減少至900mm900mm，小于巨形柱。在每層135mm的板基礎(chǔ)上建造一層復(fù)合金屬板，然而，這些機(jī)械層有200mm厚。主要的梁有H型鋼梁和抗彎鏈接在梁柱接頭處的鏈接。狗骨鏈接被放置在當(dāng)梁固定到主梁的困

72、難的地方。如圖2所示</p><p>　　帶式桁架，一或兩層高，被放置在外圍框架，間隔每八層，該支撐核心是連接到矩形柱通過帶式桁架包括地板支撐和垂直桁架。帶式桁架的位置在第八層如圖3所示。當(dāng)柱的空間是10.5m時(shí)，鋼支撐的形狀是“V”形或扭轉(zhuǎn)的“V”形，當(dāng)其空間是6m時(shí)，鋼支撐是大傾角支架，圖4指出了帶式桁架的高度和位置在M9和P1軸線上。該帶式桁架和矩形柱有助于穩(wěn)定建筑核心以相同的方式及支撐核心能幫助平衡外圍桁

73、架。這種矩形框架設(shè)計(jì)最大限度的提高了建筑內(nèi)部的空間并且在選定的柱周圍加豎向荷載。如果一些構(gòu)件被意外情況破壞則該支撐，支腿和帶式連接的柱能夠重新分布荷載。該結(jié)構(gòu)是個(gè)雙重體系：外部結(jié)構(gòu)由巨型柱組成并且外柱能提供側(cè)向剛度來應(yīng)對(duì)地震和風(fēng)荷載。其內(nèi)部結(jié)構(gòu)也被設(shè)計(jì)了子結(jié)構(gòu)，提供了可利用的空間并可以耗散大量能量。帶式桁架由一個(gè)每棟樓放在第八或第十層的轉(zhuǎn)換層體系構(gòu)成，因此，內(nèi)柱只能在有限的樓層傳遞豎向荷載。因此，他們的尺寸都大大小于傳統(tǒng)結(jié)構(gòu)體系，這樣他

74、們從基礎(chǔ)水平上升到樓頂。</p><p>　　在這項(xiàng)研究中，一個(gè)有限元模型的建立是基于超高型建筑的設(shè)計(jì)圖紙之上的。建筑單元的恒荷載是由一個(gè)商業(yè)軟件ANSYS 10.0確定的，活荷載則是由設(shè)計(jì)文件的數(shù)據(jù)中找到并計(jì)算出來的。</p><p><b>　　3、結(jié)構(gòu)分析</b></p><p>　　3.1 有限元建模</p><p

75、>　　隨著計(jì)算機(jī)技術(shù)和計(jì)算力學(xué)算法的快速發(fā)展，三維有限元分析已成為常規(guī)的建筑設(shè)計(jì)工具。建立臺(tái)北101大廈的有限元模型選擇了四種單元：三維梁?jiǎn)卧侠淼姆蔷€性大扭轉(zhuǎn)和大應(yīng)變，被選擇到的模型中的柱和梁。連接單元被用到了模型的支撐上。塊單元被用到模型的活荷載和非結(jié)構(gòu)組件上。地板則是由殼單元模擬。結(jié)構(gòu)和基礎(chǔ)之間的鏈接則被認(rèn)為固定的。</p><p>　　3.2矩形鋼管混凝土柱的本構(gòu)關(guān)系</p><

76、;p>　　由于其有良好的抗震性能鋼管混凝土管柱所以被廣泛的應(yīng)用由于其有良好的抗震性能例如可以提高強(qiáng)度和具有高韌性能力。當(dāng)一個(gè)短鋼管混凝土住在豎向軸心荷載下如圖4（b）所示，有一個(gè)基本假設(shè)是鋼筋和混凝土具有相同的應(yīng)變，則鋼箍的應(yīng)變和混凝土的應(yīng)變可以被下邊的公式計(jì)算出來：</p><p>　　= = （1）</p><p>　　

77、其中、分別是鋼和混凝土的泊松比。</p><p>　　通常在較低應(yīng)力的狀態(tài)下，混凝土相比于鋼有一個(gè)較低的泊松比值，這可能會(huì)導(dǎo)致鋼管混凝土柱的兩種材料的分離的發(fā)生。在高壓應(yīng)力狀態(tài)下，內(nèi)部微型混凝土開裂使其膨脹。其向外運(yùn)動(dòng)受制于鋼，混凝土的強(qiáng)度由于這個(gè)側(cè)向約束而提高。因此，鋼和混凝土都強(qiáng)調(diào)三軸，如圖5所示</p><p>　　鐘提出一個(gè)統(tǒng)一的鋼管混凝土柱理論模型基于鋼管混凝土柱受軸向荷載時(shí)廣泛

78、的實(shí)驗(yàn)和對(duì)其進(jìn)行有限元分析。通過這個(gè)理論，一個(gè)鋼管混凝土柱應(yīng)被視為是一個(gè)柱和其他材料的綜合體而不是獨(dú)立的混凝土和鋼筋元件。該綜合體的性能取決于鋼管和混凝土的尺寸（例如，管徑和鋼管壁厚）。一個(gè)鋼管混凝土柱的最終強(qiáng)度和其他性能參數(shù)能夠在復(fù)合材料的力學(xué)性能和幾何參數(shù)的基礎(chǔ)上求得。下面這個(gè) 矩形鋼管混凝土柱的公式通過在此基礎(chǔ)上研究的統(tǒng)一理論：</p><p>　　組合柱的屈服強(qiáng)度是：</p><p&

79、gt;<b>　?。?）</b></p><p>　　其中，B和C是系數(shù)，它們?nèi)Q于截面的幾何形狀。對(duì)于矩形截面，則有：</p><p>　　其中，是一個(gè)范圍因素，表示為：</p><p>　　其中，，，，是鋼的屈服強(qiáng)度，混凝土的無約束強(qiáng)度，鋼筋和混凝土組建的面積。</p><p>　　組合柱的彈性模量可以表示為：<

80、;/p><p><b>　?。?）</b></p><p>　　其中，，分別是組合柱的應(yīng)力和應(yīng)變比。</p><p>　　對(duì)于一個(gè)矩形鋼管混凝土柱，則有：</p><p>　　該組合柱的切線模塊可以按以下公式計(jì)算：</p><p>　　其中，=, N柱子的軸向荷載，是柱截面的總面積。</p>

81、;<p>　　組合柱的硬化模量可以由以下公式確定：</p><p>　　本文中，一根鋼管混凝土柱的位移-荷載（應(yīng)變-應(yīng)力）關(guān)系可以從鋼管混凝土柱軸向壓縮的實(shí)驗(yàn)測(cè)量的基礎(chǔ)上求得，這是簡(jiǎn)化為一個(gè)包括比例的三線應(yīng)力應(yīng)變模型，屈服和硬化階段如圖6（a）所示。其正切可以有比例點(diǎn)和屈服點(diǎn)的直線模量來取代。鋼管混凝土柱的相關(guān)參數(shù)可以根據(jù)公式（2）、（5）和（7）確定。對(duì)101大廈的鋼梁和構(gòu)件支撐的結(jié)構(gòu)分析 ，一條

82、2%屈服后硬化雙線性應(yīng)力應(yīng)變曲線（如圖6（b））是被取自這些結(jié)構(gòu)構(gòu)件的無彈性行為模量和420MPa的楊氏模量和0.3的泊松比。Von Mises屈服標(biāo)準(zhǔn)和運(yùn)動(dòng)學(xué)硬化規(guī)則被用于數(shù)值分析。</p><p>　　3.3 鋼管混凝土柱本構(gòu)關(guān)系的驗(yàn)證</p><p>　　為使鋼管混凝土柱的本構(gòu)關(guān)系和上面選定的101大廈結(jié)構(gòu)體系鋼構(gòu)件的有限元模型的討論得到充分的驗(yàn)證，一個(gè)由鋼管混凝土柱和鋼構(gòu)件組成的

83、框架結(jié)構(gòu)模型的振動(dòng)臺(tái)實(shí)驗(yàn)和有限元分析在這項(xiàng)研究中得以進(jìn)行并和實(shí)驗(yàn)數(shù)據(jù)的數(shù)值結(jié)果相比較。實(shí)驗(yàn)?zāi)Ｐ秃陀邢拊Ｐ头謩e如圖7和圖8所示。</p><p>　　該縮放模型在一個(gè)振動(dòng)臺(tái)上通過三個(gè)代表地震的力的記錄如下：（1）人工地震加速度記錄（根據(jù)中國設(shè)計(jì)規(guī)范提出）（2）El-Centro地震記錄（3）天津地震記錄。地面峰值加速度分別被調(diào)整為根據(jù)中國設(shè)計(jì)規(guī)范中規(guī)定的6到7度地震活動(dòng)設(shè)計(jì)值的0.05g到0.1g。設(shè)計(jì)規(guī)范根據(jù)地

84、震不同而劃分為不同地區(qū)這些地區(qū)地震強(qiáng)度通常被認(rèn)為共用一個(gè)峰值加速度。表1顯示了地震強(qiáng)度和地震峰值加速度的關(guān)系。每個(gè)幅值都被縮放為原來的五分之一通過表2中的縮放系數(shù)。</p><p>　　表3列出了從測(cè)試所得到的模型的自然頻率和模型的有限元數(shù)值分析。此外，結(jié)構(gòu)模型在PGA提供的0.1g的地震加速度下的動(dòng)態(tài)加速度擴(kuò)大因子即通過數(shù)值計(jì)算和實(shí)驗(yàn)所求得的值，如圖9所示。</p><p>　　表3中所

85、展示的與實(shí)驗(yàn)和數(shù)值分析得到的模型的基本自然頻率不謀而合。從圖9中可觀察到兩個(gè)在三個(gè)地震記錄下的動(dòng)態(tài)加速度擴(kuò)大因子基本吻合。因此，預(yù)計(jì)該矩形鋼管混凝土柱與鋼構(gòu)件以及選定的有限元模型的本構(gòu)關(guān)系是充分的，因?yàn)橛?jì)算結(jié)果與實(shí)驗(yàn)數(shù)據(jù)吻合的相當(dāng)良好。因此，決定采取數(shù)值模擬的策略來展現(xiàn)上述的臺(tái)北101大廈結(jié)構(gòu)體系的有限元模型的建立。</p><p>　　4、超高型建筑的動(dòng)力特性</p><p>　　一個(gè)臺(tái)

86、北101大廈的三維有限元模型被用超高型建筑的數(shù)值分析建立起來了，如圖10所示，在矩形鋼管混凝土柱和鋼構(gòu)件以及選定的有限元模型的本構(gòu)關(guān)系已經(jīng)被證實(shí)的基礎(chǔ)之上。超高型建筑的有限元模型包括20532根梁?jiǎn)卧?4048個(gè)殼單元以及3496個(gè)連接單元。除了主要的結(jié)構(gòu)單元，非結(jié)構(gòu)構(gòu)件也被用大量的單元建立了模型。圖11顯示的是有限元模型的頭六個(gè)模型包括在每個(gè)橫向上的平動(dòng)運(yùn)動(dòng)和豎直軸上的扭轉(zhuǎn)運(yùn)動(dòng)。模式1和2分別是X和Y方向上的平移模式，模式3則是基本

87、扭轉(zhuǎn)模式。建筑物在X方向上的基本周期是6.21s，在Y方向上是6.19s而扭</p><p>　　轉(zhuǎn)方向上則是3.62s。每個(gè)模式的振型系數(shù)定義為：</p><p>　　，這表明該模式有助于大部分的動(dòng)態(tài)響應(yīng)，其中為質(zhì)量矩陣，是該模式的振動(dòng)模態(tài)向量則是統(tǒng)一矩陣。每個(gè)模型在每個(gè)方向上的模型參與率定義為，累計(jì)模式參與質(zhì)量比則定義為</p><p>　　，其中m是每個(gè)模式的

88、動(dòng)態(tài)響應(yīng)的有效參與質(zhì)量。表4則表示了模型參與的比率和頭30個(gè)模型的累計(jì)參與的質(zhì)量的比率。X和Y方向上頭兩個(gè)模型的振動(dòng)參與比最后形成一個(gè)。隨著模型數(shù)的增加其他模型的這個(gè)比值減小。在橫向上模式累計(jì)質(zhì)量參與比頭30個(gè)模型達(dá)到1。因此，決定使用高層建筑反應(yīng)譜分析的頭30個(gè)模型，這些下面將會(huì)描述。</p><p><b>　　5、反應(yīng)譜分析</b></p><p>　　對(duì)于抗震

89、設(shè)計(jì)，一個(gè)結(jié)構(gòu)應(yīng)該滿足兩個(gè)級(jí)別的要求，這取決于地震活動(dòng)的震級(jí)。第一級(jí)性能上要求在中等地震作用下不發(fā)生重大結(jié)構(gòu)損壞并且結(jié)構(gòu)反應(yīng)在彈性范圍之內(nèi)，第二個(gè)級(jí)別則要求在罕遇的比較嚴(yán)重的地震作用下結(jié)構(gòu)不發(fā)生倒塌。臺(tái)北101大廈位于臺(tái)北盆地，在經(jīng)過長期的沉積所形成的深厚的軟土層。根據(jù)臺(tái)灣建筑技術(shù)標(biāo)準(zhǔn)，建筑地點(diǎn)是一個(gè)中等地震活動(dòng)地區(qū)。一個(gè)反應(yīng)譜，最初是由國立臺(tái)灣大學(xué)和其他一些研究機(jī)構(gòu)為臺(tái)北101大廈的設(shè)計(jì)所開發(fā)的。在當(dāng)?shù)氐卣鹨?guī)范所規(guī)定的反應(yīng)譜的基礎(chǔ)上被