外文翻譯---抗側(cè)向荷載的結(jié)構(gòu)體系

1、<p>　　抗側(cè)向荷載的結(jié)構(gòu)體系</p><p><b>　　常用的結(jié)構(gòu)體系</b></p><p>　　若已測出荷載量達(dá)數(shù)千萬磅重，那么在高層建筑設(shè)計(jì)中就沒有多少可以進(jìn)行極其復(fù)雜的構(gòu)思余地了。確實(shí)，較好的高層建筑普遍具有構(gòu)思簡單、表現(xiàn)明晰的特點(diǎn)。</p><p>　　這并不是說沒有進(jìn)行宏觀構(gòu)思的余地。實(shí)際上，正是因?yàn)橛辛诉@種宏觀的構(gòu)

2、思，新奇的高層建筑體系才得以發(fā)展，可能更重要的是：幾年以前才出現(xiàn)的一些新概念在今天的技術(shù)中已經(jīng)變得平常了。</p><p>　　如果忽略一些與建筑材料密切相關(guān)的概念不談，高層建筑里最為常用的結(jié)構(gòu)體系便可分為如下幾類：</p><p><b>　　抗彎矩框架。</b></p><p>　　支撐框架，包括偏心支撐框架。</p><

3、;p>　　剪力墻，包括鋼板剪力墻。</p><p><b>　　筒中框架。</b></p><p><b>　　筒中筒結(jié)構(gòu)。</b></p><p><b>　　核心交互結(jié)構(gòu)。</b></p><p>　　框格體系或束筒體系。</p><p>　　

4、特別是由于最近趨向于更復(fù)雜的建筑形式，同時也需要增加剛度以抵抗幾力和地震力，大多數(shù)高層建筑都具有由框架、支撐構(gòu)架、剪力墻和相關(guān)體系相結(jié)合而構(gòu)成的體系。而且，就較高的建筑物而言，大多數(shù)都是由交互式構(gòu)件組成三維陳列。</p><p>　　將這些構(gòu)件結(jié)合起來的方法正是高層建筑設(shè)計(jì)方法的本質(zhì)。其結(jié)合方式需要在考慮環(huán)境、功能和費(fèi)用后再發(fā)展，以便提供促使建筑發(fā)展達(dá)到新高度的有效結(jié)構(gòu)。這并不是說富于想象力的結(jié)構(gòu)設(shè)計(jì)就能夠創(chuàng)造出

5、偉大建筑。正相反，有許多例優(yōu)美的建筑僅得到結(jié)構(gòu)工程師適當(dāng)?shù)闹С志捅粍?chuàng)造出來了，然而，如果沒有天賦甚厚的建筑師的創(chuàng)造力的指導(dǎo)，那么，得以發(fā)展的就只能是好的結(jié)構(gòu)，并非是偉大的建筑。無論如何，要想創(chuàng)造出高層建筑真正非凡的設(shè)計(jì)，兩者都需要最好的。</p><p>　　雖然在文獻(xiàn)中通常可以見到有關(guān)這七種體系的全面性討論，但是在這里還值得進(jìn)一步討論。設(shè)計(jì)方法的本質(zhì)貫穿于整個討論。設(shè)計(jì)方法的本質(zhì)貫穿于整個討論中。</p&

6、gt;<p><b>　　抗彎矩框架</b></p><p>　　抗彎矩框架也許是低，中高度的建筑中常用的體系，它具有線性水平構(gòu)件和垂直構(gòu)件在接頭處基本剛接之特點(diǎn)。這種框架用作獨(dú)立的體系，或者和其他體系結(jié)合起來使用，以便提供所需要水平荷載抵抗力。對于較高的高層建筑，可能會發(fā)現(xiàn)該本系不宜作為獨(dú)立體系，這是因?yàn)樵趥?cè)向力的作用下難以調(diào)動足夠的剛度。</p><p&

7、gt;　　我們可以利用STRESS，STRUDL 或者其他大量合適的計(jì)算機(jī)程序進(jìn)行結(jié)構(gòu)分析。所謂的門架法分析或懸臂法分析在當(dāng)今的技術(shù)中無一席之地，由于柱梁節(jié)點(diǎn)固有柔性，并且由于初步設(shè)計(jì)應(yīng)該力求突出體系的弱點(diǎn)，所以在初析中使用框架的中心距尺寸設(shè)計(jì)是司空慣的。當(dāng)然，在設(shè)計(jì)的后期階段，實(shí)際地評價(jià)結(jié)點(diǎn)的變形很有必要。</p><p><b>　　支撐框架</b></p><p&g

8、t;　　支撐框架實(shí)際上剛度比抗彎矩框架強(qiáng)，在高層建筑中也得到更廣泛的應(yīng)用。這種體系以其結(jié)點(diǎn)處鉸接或則接的線性水平構(gòu)件、垂直構(gòu)件和斜撐構(gòu)件而具特色，它通常與其他體系共同用于較高的建筑，并且作為一種獨(dú)立的體系用在低、中高度的建筑中。</p><p>　　尤其引人關(guān)注的是，在強(qiáng)震區(qū)使用偏心支撐框架。</p><p>　　此外，可以利用STRESS，STRUDL，或一系列二維或三維計(jì)算機(jī)分析程序中

9、的任何一種進(jìn)行結(jié)構(gòu)分析。另外，初步分析中常用中心距尺寸。</p><p><b>　　剪力墻</b></p><p>　　剪力墻在加強(qiáng)結(jié)構(gòu)體系剛性的發(fā)展過程中又前進(jìn)了一步。該體系的特點(diǎn)是具有相當(dāng)薄的，通常是（而不總是）混凝土的構(gòu)件，這種構(gòu)件既可提供結(jié)構(gòu)強(qiáng)度，又可提供建筑物功能上的分隔。</p><p>　　在高層建筑中，剪力墻體系趨向于具有相對

10、大的高寬經(jīng)，即與寬度相比，其高度偏大。由于基礎(chǔ)體系缺少應(yīng)力，任何一種結(jié)構(gòu)構(gòu)件抗傾覆彎矩的能力都受到體系的寬度和構(gòu)件承受的重力荷載的限制。由于剪力墻寬度狹狹窄受限，所以需要以某種方式加以擴(kuò)大，以便提從所需的抗傾覆能力。在窗戶需要量小的建筑物外墻中明顯地使用了這種確有所需要寬度的體系。</p><p>　　鋼結(jié)構(gòu)剪力墻通常由混凝土覆蓋層來加強(qiáng)以抵抗失穩(wěn)，這在剪切荷載大的地方已得到應(yīng)用。這種體系實(shí)際上比鋼支撐經(jīng)濟(jì)，對于

11、使剪切荷載由位于地面正上方區(qū)域內(nèi)比較高的樓層向下移特別有效。這種體系還具有高延性之優(yōu)點(diǎn)，這種特性在強(qiáng)震區(qū)特別重要。</p><p>　　由于這些墻內(nèi)必然出同一些大孔，使得剪力墻體系分析變得錯綜復(fù)雜?？梢酝ㄟ^桁架模似法、有限元法，或者通過利用為考慮剪力墻的交互作用或扭轉(zhuǎn)功能設(shè)計(jì)的專門計(jì)處機(jī)程序進(jìn)行初步分析</p><p>　　框架或支撐式筒體結(jié)構(gòu)：</p><p>　

12、　框架或支撐式筒體最先應(yīng)用于IBM公司在Pittsburgh的一幢辦公樓，隨后立即被應(yīng)用于紐約雙子座的110層世界貿(mào)易中心摩天大樓和其他的建筑中。這種系統(tǒng)有以下幾個顯著的特征：三維結(jié)構(gòu)、支撐式結(jié)構(gòu)、或由剪力墻形成的一個性質(zhì)上差不多是圓柱體的閉合曲面，但又有任意的平面構(gòu)成。由于這些抵抗側(cè)向荷載的柱子差不多都被設(shè)置在整個系統(tǒng)的中心，所以整體的慣性得到提高，剛度也是很大的。</p><p>　　在可能的情況下，通過三維

13、概念的應(yīng)用、二維的類比，我們可以進(jìn)行筒體結(jié)構(gòu)的分析。不管應(yīng)用那種方法，都必須考慮剪力滯后的影響。</p><p>　　這種最先在航天器結(jié)構(gòu)中研究的剪力滯后出現(xiàn)后，對筒體結(jié)構(gòu)的剛度是一個很大的限制。這種觀念已經(jīng)影響了筒體結(jié)構(gòu)在60層以上建筑中的應(yīng)用。設(shè)計(jì)者已經(jīng)開發(fā)出了很多的技術(shù)，用以減小剪力滯后的影響，這其中最有名的是桁架的應(yīng)用?？蚣芑蛑问酵搀w在40層或稍高的建筑中找到了自己的用武之地。除了一些美觀的考慮外，桁架

14、幾乎很少涉及與外墻聯(lián)系的每個建筑功能，而懸索一般設(shè)置在機(jī)械的地板上，這就令機(jī)械體系設(shè)計(jì)師們很不贊成。但是，作為一個性價(jià)比較好的結(jié)構(gòu)體系，桁架能充分發(fā)揮它的性能，所以它會得到設(shè)計(jì)師們持續(xù)的支持。由于其最佳位置正取決于所提供的桁架的數(shù)量，因此很多研究已經(jīng)試圖完善這些構(gòu)件的位置。實(shí)驗(yàn)表明：由于這種結(jié)構(gòu)體系的經(jīng)濟(jì)性并不十分受桁架位置的影響，所以這些桁架的位置主要取決于機(jī)械系統(tǒng)的完善，審美的要求，</p><p><

15、b>　　筒中筒結(jié)構(gòu)：</b></p><p>　　筒體結(jié)構(gòu)系統(tǒng)能使外墻中的柱具有靈活性，用以抵抗顛覆和剪切力?！巴仓型病边@個名字顧名思義就是在建筑物的核心承重部分又被包圍了第二層的一系列柱子，它們被當(dāng)作是框架和支撐筒來使用。配置第二層柱的目的是增強(qiáng)抗顛覆能力和增大側(cè)移剛度。這些筒體不是同樣的功能，也就是說，有些筒體是結(jié)構(gòu)的，而有些筒體是用來支撐的。</p><p>　　在

16、考慮這種筒體時，清楚的認(rèn)識和區(qū)別變形的剪切和彎曲分量是很重要的，這源于對梁的對比分析。在結(jié)構(gòu)筒中，剪切構(gòu)件的偏角和柱、縱梁（例如：結(jié)構(gòu)筒中的網(wǎng)等）的彎曲有關(guān)，同時，彎曲構(gòu)件的偏角取決于柱子的軸心壓縮和延伸（例如：結(jié)構(gòu)筒的邊緣等）。在支撐筒中，剪切構(gòu)件的偏角和對角線的軸心變形有關(guān)，而彎曲構(gòu)件的偏角則與柱子的軸心壓縮和延伸有關(guān)。</p><p>　　根據(jù)梁的對比分析，如果平面保持原形（例如：厚樓板），那么外層筒中柱的

17、軸心壓力就會與中心筒柱的軸心壓力相差甚遠(yuǎn)，而且穩(wěn)定的大于中心筒。但是在筒中筒結(jié)構(gòu)的設(shè)計(jì)中，當(dāng)發(fā)展到極限時，內(nèi)部軸心壓力會很高的，甚至遠(yuǎn)遠(yuǎn)大于外部的柱子。這種反常的現(xiàn)象是由于兩種體系中的剪切構(gòu)件的剛度不同。這很容易去理解，內(nèi)筒可以看成是一個支撐（或者說是剪切剛性的）筒，而外筒可以看成是一個結(jié)構(gòu)（或者說是剪切彈性的）筒。</p><p><b>　　核心交互式結(jié)構(gòu)：</b></p>

18、<p>　　核心交互式結(jié)構(gòu)屬于兩個筒與某些形式的三維空間框架相配合的筒中筒特殊情況。事實(shí)上，這種體系常用于那種外筒剪切剛度為零的結(jié)構(gòu)。位于Pittsburgh的美國鋼鐵大樓證實(shí)了這種體系是能很好的工作的。在核心交互式結(jié)構(gòu)中，內(nèi)筒是一個支撐結(jié)構(gòu)，外筒沒有任何剪切剛度，而且兩種結(jié)構(gòu)體系能通過一個空間結(jié)構(gòu)或“帽”式結(jié)構(gòu)共同起作用。需要指出的是，如果把外部的柱子看成是一種從“帽”到基礎(chǔ)的直線體系，這將是不合適的；根據(jù)支撐核心的彈性曲

19、線，這些柱子只發(fā)揮了剛度的15%。同樣需要指出的是，內(nèi)柱中與側(cè)向力有關(guān)的軸向力沿筒高度由拉力變?yōu)閴毫Γ瑫r變化點(diǎn)位于筒高度的約5/8處。當(dāng)然，外柱也傳遞相同的軸向力，這種軸向力低于作用在整個柱子高度的側(cè)向荷載，因?yàn)檫@個體系的剪切剛度接近于零。</p><p>　　把內(nèi)外筒相連接的空間結(jié)構(gòu)、懸臂梁或桁架經(jīng)常遵照一些規(guī)范來布置。美國電話電報(bào)總局就是一個布置交互式構(gòu)件的生動例子。</p><p>

20、;　　結(jié)構(gòu)體系長59.7米，寬28.6米，高183.3米。</p><p>　　布置了兩個筒，每個筒的尺寸是9.4米×12.2米，在長方向上有27.4米的間隔。</p><p>　　在短方向上內(nèi)筒被支撐起來，但是在長方向上沒有剪切剛度。</p><p>　　環(huán)繞著建筑物布置了一個外筒。</p><p>　　外筒是一個瞬時抵抗結(jié)構(gòu)，但

21、是在每個長方向的中心15.2米都沒有剪切剛度。</p><p>　　在建筑的頂部布置了一個空間桁架構(gòu)成的“帽式”結(jié)構(gòu)。</p><p>　　在建筑的底部布置了一個相似的空間桁架結(jié)構(gòu)。</p><p>　　由于外筒的剪切剛度在建筑的底部接近零，整個建筑基本上由兩個鋼板筒來支持。</p><p>　　框格體系或束筒體系結(jié)構(gòu)：</p>

22、<p>　　位于美國芝加哥的西爾斯大廈是箱式結(jié)構(gòu)的經(jīng)典之作，它由九個相互獨(dú)立的筒組成的一個集中筒。由于西爾斯大廈包括九個幾乎垂直的筒，而且筒在平面上無須相似，基本的結(jié)構(gòu)體系在不規(guī)則形狀的建筑中得到特別的應(yīng)用。一些單個的筒高于建筑一點(diǎn)或很多是很常見的。事實(shí)上，這種體系的重要特征就在于它既有堅(jiān)固的一面，也有脆弱的一面。</p><p>　　這種體系的脆弱，特別是在結(jié)構(gòu)筒中，與柱子的壓縮變形有很大的關(guān)系，柱

23、子的壓縮變形有下式計(jì)算：</p><p><b>　　△=ΣfL/E</b></p><p>　　對于那些層高為3.66米左右和平均壓力為138MPa的建筑，在荷載作用下每層柱子的壓縮變形為15（12）/29000或1.9毫米。在第50層柱子會壓縮94毫米，小于它未受壓的長度。這些柱子在50層的時候和100層的時候的變形是不一樣的，位于這兩種體系之間接近于邊緣的那些柱

24、需要使這種不均勻的變形得以調(diào)解。</p><p>　　主要的結(jié)構(gòu)工作都集中在布置中。在Melbourne的Rialto項(xiàng)目中，結(jié)構(gòu)工程師發(fā)現(xiàn)至少有一幢建筑，很有必要垂直預(yù)壓低高度的柱子，以便使柱不均勻的變形差得以調(diào)解，調(diào)解的方法近似于后拉伸法，即較短的柱轉(zhuǎn)移重量到較高的鄰柱上。</p><p>　　Structural Systems to resist lateral loads<

25、/p><p>　　Commonly Used structural Systems</p><p>　　With loads measured in tens of thousands kips,there is little room in the design of high-rise buildings for excessively complex thoughts. Indeed,

26、the better high-rise buildings carry the universal traits of simplicity of thought and clarity of expression.</p><p>　　It does not follow that there is no room for grand thoughts. Indeed, it is with such gra

27、nd thoughts that the new family of high-rise buildings has evolved. Perhaps more important, the new concepts of but a few years ago have become commonplace in today’ s technology.</p><p>　　Omitting some conc

28、epts that are related strictly to the materials of construction, the most commonly used structural systems used in high-rise buildings can be categorized as follows:</p><p>　　Moment-resisting frames.</p&g

29、t;<p>　　Braced frames, including eccentrically braced frames.</p><p>　　Shear walls, including steel plate shear walls.</p><p>　　Tube-in-tube structures.</p><p>　　Tube-in-tube

30、 structures.</p><p>　　Core-interactive structures.</p><p>　　Cellular or bundled-tube systems.</p><p>　　Particularly with the recent trend toward more complex forms, but in response

31、also to the need for increased stiffness to resist the forces from wind and earthquake, most high-rise buildings have structural systems built up of combinations of frames, braced bents, shear walls, and related systems.

32、 Further, for the taller buildings, the majorities are composed of interactive elements in three-dimensional arrays.</p><p>　　The method of combining these elements is the very essence of the design process

33、for high-rise buildings. These combinations need evolve in response to environmental, functional, and cost considerations so as to provide efficient structures that provoke the architectural development to new heights. T

34、his is not to say that imaginative structural design can create great architecture. To the contrary, many examples of fine architecture have been created with only moderate support from the structura</p><p>

35、　　While comprehensive discussions of these seven systems are generally available in the literature, further discussion is warranted here .The essence of the design process is distributed throughout the discussion.</p&

36、gt;<p>　　Moment-Resisting Frames</p><p>　　Perhaps the most commonly used system in low-to medium-rise buildings, the moment-resisting frame, is characterized by linear horizontal and vertical members

37、connected essentially rigidly at their joints. Such frames are used as a stand-alone system or in combination with other systems so as to provide the needed resistance to horizontal loads. In the taller of high-rise buil

38、dings, the system is likely to be found inappropriate for a stand-alone system, this because of the difficulty in mobilizi</p><p>　　Analysis can be accomplished by STRESS, STRUDL, or a host of other appropri

39、ate computer programs; analysis by the so-called portal method of the cantilever method has no place in today’s technology.</p><p>　　Because of the intrinsic flexibility of the column/girder intersection, an

40、d because preliminary designs should aim to highlight weaknesses of systems, it is not unusual to use center-to-center dimensions for the frame in the preliminary analysis. Of course, in the latter phases of design, a re

41、alistic appraisal in-joint deformation is essential.</p><p>　　Braced Frames</p><p>　　The braced frame, intrinsically stiffer than the moment –resisting frame, finds also greater application to h

42、igher-rise buildings. The system is characterized by linear horizontal, vertical, and diagonal members, connected simply or rigidly at their joints. It is used commonly in conjunction with other systems for taller buildi

43、ngs and as a stand-alone system in low-to medium-rise buildings.</p><p>　　While the use of structural steel in braced frames is common, concrete frames are more likely to be of the larger-scale variety.</

44、p><p>　　Of special interest in areas of high seismicity is the use of the eccentric braced frame.</p><p>　　Again, analysis can be by STRESS, STRUDL, or any one of a series of two –or three dimensio

45、nal analysis computer programs. And again, center-to-center dimensions are used commonly in the preliminary analysis.</p><p>　　Shear walls</p><p>　　The shear wall is yet another step forward alo

46、ng a progression of ever-stiffer structural systems. The system is characterized by relatively thin, generally (but not always) concrete elements that provide both structural strength and separation between building func

47、tions.</p><p>　　In high-rise buildings, shear wall systems tend to have a relatively high aspect ratio, that is, their height tends to be large compared to their width. Lacking tension in the foundation syst

48、em, any structural element is limited in its ability to resist overturning moment by the width of the system and by the gravity load supported by the element. Limited to a narrow overturning, One obvious use of the syste

49、m, which does have the needed width, is in the exterior walls of building, where the requ</p><p>　　Structural steel shear walls, generally stiffened against buckling by a concrete overlay, have found applica

50、tion where shear loads are high. The system, intrinsically more economical than steel bracing, is particularly effective in carrying shear loads down through the taller floors in the areas immediately above grade. The sy

51、s tem has the further advantage of having high ductility a feature of particular importance in areas of high seismicity.</p><p>　　The analysis of shear wall systems is made complex because of the inevitable

52、presence of large openings through these walls. Preliminary analysis can be by truss-analogy, by the finite element method, or by making use of a proprietary computer program designed to consider the interaction, or coup

53、ling, of shear walls.</p><p>　　Framed or Braced Tubes</p><p>　　The concept of the framed or braced or braced tube erupted into the technology with the IBM Building in Pittsburgh, but was followe

54、d immediately with the twin 110-story towers of the World Trade Center, New York and a number of other buildings .The system is characterized by three –dimensional frames, braced frames, or shear walls, forming a closed

55、surface more or less cylindrical in nature, but of nearly any plan configuration. Because those columns that resist lateral forces are placed as far </p><p>　　The analysis of tubular structures is done using

56、 three-dimensional concepts, or by two- dimensional analogy, where possible, whichever method is used, it must be capable of accounting for the effects of shear lag.</p><p>　　The presence of shear lag, detec

57、ted first in aircraft structures, is a serious limitation in the stiffness of framed tubes. The concept has limited recent applications of framed tubes to the shear of 60 stories. Designers have developed various techniq

58、ues for reducing the effects of shear lag, most noticeably the use of belt trusses. This system finds application in buildings perhaps 40stories and higher. However, except for possible aesthetic considerations, belt tru

59、sses interfere with nearly e</p><p>　　Tube-in-Tube Structures</p><p>　　The tubular framing system mobilizes every column in the exterior wall in resisting over-turning and shearing forces. The t

60、erm‘tube-in-tube’is largely self-explanatory in that a second ring of columns, the ring surrounding the central service core of the building, is used as an inner framed or braced tube. The purpose of the second tube is t

61、o increase resistance to over turning and to increase lateral stiffness. The tubes need not be of the same character; that is, one tube could be framed, whil</p><p>　　In considering this system, is important

62、 to understand clearly the difference between the shear and the flexural components of deflection, the terms being taken from beam analogy. In a framed tube, the shear component of deflection is associated with the bendi

63、ng deformation of columns and girders (i.e, the webs of the framed tube) while the flexural component is associated with the axial shortening and lengthening of columns (i.e, the flanges of the framed tube). In a braced

64、tube, the shear comp</p><p>　　Following beam analogy, if plane surfaces remain plane (i.e, the floor slabs),then axial stresses in the columns of the outer tube, being farther form the neutral axis, will be

65、substantially larger than the axial stresses in the inner tube. However, in the tube-in-tube design, when optimized, the axial stresses in the inner ring of columns may be as high, or even higher, than the axial stresses

66、 in the outer ring. This seeming anomaly is associated with differences in the shearing component of st</p><p>　　Core Interactive Structures</p><p>　　Core interactive structures are a special ca

67、se of a tube-in-tube wherein the two tubes are coupled together with some form of three-dimensional space frame. Indeed, the system is used often wherein the shear stiffness of the outer tube is zero. The United States S

68、teel Building, Pittsburgh, illustrates the system very well. Here, the inner tube is a braced frame, the outer tube has no shear stiffness, and the two systems are coupled if they were considered as systems passing in a

69、straight line fr</p><p>　　The space structures of outrigger girders or trusses, that connect the inner tube to the outer tube, are located often at several levels in the building. The AT&T headquarters i

70、s an example of an astonishing array of interactive elements:</p><p>　　The structural system is 94 ft (28.6m) wide, 196ft(59.7m) long, and 601ft (183.3m) high.</p><p>　　Two inner tubes are prov

71、ided, each 31ft(9.4m) by 40 ft (12.2m), centered 90 ft (27.4m) apart in the long direction of the building.</p><p>　　The inner tubes are braced in the short direction, but with zero shear stiffness in the lo

72、ng direction.</p><p>　　A single outer tube is supplied, which encircles the building perimeter.</p><p>　　The outer tube is a moment-resisting frame, but with zero shear stiffness for the center5

73、0ft (15.2m) of each of the long sides.</p><p>　　A space-truss hat structure is provided at the top of the building.</p><p>　　A similar space truss is located near the bottom of the building</

74、p><p>　　The entire assembly is laterally supported at the base on twin steel-plate tubes, because the shear stiffness of the outer tube goes to zero at the base of the building.</p><p>　　Cellular s

75、tructures</p><p>　　A classic example of a cellular structure is the Sears Tower, Chicago, a bundled tube structure of nine separate tubes. While the Sears Tower contains nine nearly identical tubes, the basi

76、c structural system has special application for buildings of irregular shape, as the several tubes need not be similar in plan shape, It is not uncommon that some of the individual tubes one of the strengths and one of t

77、he weaknesses of the system.</p><p>　　This special weakness of this system, particularly in framed tubes, has to do with the concept of differential column shortening. The shortening of a column under load i

78、s given by the expression</p><p><b>　　△=ΣfL/E</b></p><p>　　For buildings of 12 ft (3.66m) floor-to-floor distances and an average compressive stress of 15 ksi (138MPa), the shortenin

79、g of a column under load is 15 (12)(12)/29,000 or 0.074in (1.9mm) per story. At 50 stories, the column will have shortened to 3.7 in. (94mm) less than its unstressed length. Where one cell of a bundled tube system is, sa

80、y, 50stories high and an adjacent cell is, say, 100stories high, those columns near the boundary between .the two systems need to have this differential defl</p><p>　　Major structural work has been found to

81、be needed at such locations. In at least one building, the Rialto Project, Melbourne, the structural engineer found it necessary to vertically pre-stress the lower height columns so as to reconcile the differential defle