shear lag in box girders
中英文对照英文版
Structural Systems to resist lateral loads Commonly Used structural SystemsWith loads measured in tens of thousands kips, there is little room in the design of high-rise buildings for excessively complex thoughts. Indeed, the better high-rise buildings carry the universal traits of simplicity of thought and clarity of expression.It does not follow that there is no room for grand thoughts. Indeed, it is with such grand 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.Omitting some concepts 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:1.Moment-resisting frames.2.Braced frames, including eccentrically braced frames.3.Shear walls, including steel plate shear walls.4.Tube-in-tube structures.5.Tube-in-tube structures.6.Core-interactive structures.7.Cellular or bundled-tube systems.Particularly with the recent trend toward more complex forms, but in response 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. Further, for the taller buildings, the majorities are composed of interactive elements in three-dimensional arrays.The method of combining these elements is the very essence of the design process 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. This 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 structural engineer, while only fine structure, not great architecture, can be developed without the genius and the leadership of a talented architect. In any event, the best of both isneeded to formulate a truly extraordinary design of a high-rise building.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.Moment-Resisting FramesPerhaps the most commonly used system in low-to medium-rise buildings, the moment-resisting frame, is characterized by linear horizontal and vertical members 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 buildings, the system is likely to be found inappropriate for a stand-alone system, this because of the difficulty in mobilizing sufficient stiffness under lateral forces.Analysis can be accomplished by STRESS, STRUDL, or a host of other appropriate computer programs; analysis by the so-called portal method of the cantilever method has no place in today’s technology.Because of the intrinsic flexibility of the column/girder intersection, and 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 realistic appraisal in-joint deformation is essential.Braced Frame sThe braced frame, intrinsically stiffer than the moment –resisting frame, finds also greater application to higher-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 buildings and as a stand-alone system in low-to medium-rise buildings.While the use of structural steel in braced frames is common, concrete frames are more likely to be of the larger-scale variety.Of special interest in areas of high seismicity is the use of the eccentric braced frame.Again, analysis can be by STRESS, STRUDL, or any one of a series of two –or three dimensional analysis computer programs. And again, center-to-center dimensions are used commonly in the preliminary analysis.Shear wallsThe shear wall is yet another step forward along 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 functions.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 system, 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 system, which does have the needed width, is in the exterior walls of building, where the requirement for windows is kept small.Structural steel shear walls, generally stiffened against buckling by a concrete overlay, have found application 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 sys tem has the further advantage of having high ductility a feature of particular importance in areas of high seismicity.The analysis of shear wall systems is made complex because of the inevitable 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 coupling, of shear walls.Framed or Braced TubesThe concept of the framed or braced or braced tube erupted into the technology with the IBM Building in Pittsburgh, but was followed 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 surface more or less cylindrical in nature, but of nearly any plan configuration. Because those columns that resist lateral forces are placed as far as possible from the cancroids of the system, the overall moment of inertia is increased and stiffness is very high.The analysis of tubular structures is done using 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.The presence of shear lag, detected 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 techniques 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 trusses interfere with nearly every building function associated with the outside wall; the trusses are placed often at mechanical floors, mush to the disapproval of the designers of the mechanical systems. Nevertheless, as a cost-effective structural system, the belt truss works well and will likely find continued approval from designers. Numerous studies have sought to optimize the location of these trusses, with the optimum location very dependent on the number of trusses provided. Experience would indicate, however, that the location of these trusses is provided by the optimization of mechanical systems and by aesthetic considerations, as the economics of the structural system is not highly sensitive to belt truss location.Tube-in-Tube StructuresThe tubular framing system mobilizes every column in the exterior wall in resisting over-turning and shearing forces. The term‘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 to 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, while the other could be braced.In considering this system, is important 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 bending 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 tube, the shear component of deflection is associated with the axial deformation of diagonals while the flexural component of deflection is associated with the axial shortening and lengthening of columns.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 substantiallylarger 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 in the outer ring. This seeming anomaly is associated with differences in the shearing component of stiffness between the two systems. This is easiest to under-stand where the inner tube is conceived as a braced (i.e, shear-stiff) tube while the outer tube is conceived as a framed (i.e, shear-flexible) tube.Core Interactive StructuresCore interactive structures are a special case 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 Steel 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 straight line from the “hat”structure. Note that the exterior columns would be improperly modeled if they were considered as systems passing in a straight line from the “hat”to the foundations; these columns are perhaps 15% stiffer as they follow the elastic curve of the braced core. Note also that the axial forces associated with the lateral forces in the inner columns change from tension to compression over the height of the tube, with the inflection point at about 5/8 of the height of the tube. The outer columns, of course, carry the same axial force under lateral load for the full height of the columns because the columns because the shear stiffness of the system is close to zero.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 is an example of an astonishing array of interactive elements:1.The structural system is 94 ft (28.6m) wide, 196ft(59.7m) long, and 601ft (183.3m) high.2.Two inner tubes are provided, each 31ft(9.4m) by 40 ft (12.2m), centered 90 ft (27.4m) apart in the long direction of the building.3.The inner tubes are braced in the short direction, but with zero shear stiffness in the long direction.4. A single outer tube is supplied, which encircles the building perimeter.5.The outer tube is a moment-resisting frame, but with zero shear stiffness for the center50ft (15.2m) of each of the long sides.6. A space-truss hat structure is provided at the top of the building.7. A similar space truss is located near the bottom of the building8.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.Cellular structuresA 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 basic 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 the weaknesses of the system.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 is given by the expression△=ΣfL/EFor buildings of 12 ft (3.66m) floor-to-floor distances and an average compressive stress of 15 ksi (138MPa), the shortening 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, say, 50stories high and an adjacent cell is, say, 100stories high, those columns near the boundary between .the two systems need to have this differential deflection reconciled.Major structural work has been found to 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 deflections of columns in close proximity with the post-tensioning of the shorter column simulating the weight to be added on to adjacent, higher columns。
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波形钢腹板PC箱梁桥应用综述
波形钢腹板PC箱梁桥应用综述一、本文概述Overview of this article随着桥梁工程技术的不断发展与创新，波形钢腹板PC箱梁桥作为一种新型桥梁结构形式，其独特的优点在近年来逐渐受到了国内外桥梁工程界的广泛关注和应用。
波形钢腹板PC箱梁桥结合了预应力混凝土（PC）与波形钢腹板的优点，既提高了桥梁的承载能力，又增强了结构的耐久性。
本文旨在综述波形钢腹板PC箱梁桥的设计原理、施工技术、工程应用以及未来发展趋势，以期为该类型桥梁在我国桥梁建设中的推广应用提供有益的参考和借鉴。
通过总结和分析波形钢腹板PC箱梁桥的应用经验和成果，本文将探讨其在我国桥梁工程领域中的优势和潜力，以期为桥梁工程技术的进步和创新贡献力量。
With the continuous development and innovation of bridge engineering technology, the corrugated steel web PC box girder bridge, as a new type of bridge structure, has gradually attracted widespread attention and application from the bridge engineering community at home and abroad in recent years due to its unique advantages. The corrugated steel web PC box girderbridge combines the advantages of prestressed concrete (PC) and corrugated steel web, which not only improves the bearing capacity of the bridge but also enhances the durability of the structure. This article aims to summarize the design principles, construction techniques, engineering applications, and future development trends of PC box girder bridges with corrugated steel web plates, in order to provide useful reference and inspiration for the promotion and application of this type of bridge in bridge construction in China. By summarizing and analyzing the application experience and achievements of corrugated steel web PC box girder bridges, this article will explore their advantages and potential in the field of bridge engineering in China, in order to contribute to the progress and innovation of bridge engineering technology.二、波形钢腹板PC箱梁桥的结构特点Structural characteristics of PC box girder bridges with corrugated steel web plates波形钢腹板PC箱梁桥是一种新型的桥梁结构形式，其结构特点主要体现在以下几个方面。
波形钢腹板箱梁桥面板横向内力计算的框架分析法
波形钢腹板箱梁桥面板横向内力计算的框架分析法赵品;叶见曙【摘要】Based on the basic principles of the frame analysis method and structural characteristics and mechanical properties of box girders with corrugated steel webs, a model which can be applied to the calculation of the transverse internal force of bridge deck is established. This calculation model can reflect the influence of the transverse frame effect and the distortion effect of box girders on the transverse internal force of bridge deck. By comparing with indoor model test results and data of finite element analysis, it is shown that the calculated value of the frame analysis method is consistent with the finite element results and experimental values, and both the errors are both less than 10% , which verifies the correctness of the calculation model. Furthermore, the model is adopted to analyze the influence of linear stiffness change of corrugated steel webs on the transverse internal force of bridge deck. Results demonstrate that the linear stiffness ratio of steel web and bridge deck is the important influence factor when the web spacing in the cross section is certain.%基于框架分析法的基本原理,结合波形钢腹板箱梁的结构特点和力学特性,建立了适用于其桥面板横向内力的计算模型.该计算模型能够反映横向框架作用和箱梁畸变效应对桥面板横向内力的影响.通过与相关室内模型试验数据和有限元分析结果的对比可知,框架分析法计算值与有限元结果、试验值吻合,误差均在10％以内,验证了此计算模型的正确性.并采用上述模型分析了钢腹板线刚度变化对桥面板横向内力的影响,结果表明在波形钢腹板箱梁截面上的腹板间距确定的条件下,波形钢腹板与混凝土顶板的线刚度比是影响桥面板横向内力的重要因素.【期刊名称】《东南大学学报（自然科学版）》【年(卷),期】2012(042)005【总页数】5页(P940-944)【关键词】波形钢腹板箱梁;框架分析法;桥面板;横向内力;畸变效应;线刚度比【作者】赵品;叶见曙【作者单位】东南大学交通学院,南京210096;东南大学交通学院,南京210096【正文语种】中文【中图分类】U448.36波形钢腹板箱梁的混凝土顶板与两侧波形钢腹板及混凝土底板形成闭合截面来抵抗纵向内力，同时箱梁顶板又作为桥面板直接承受车辆局部轮载作用产生的横向内力［1］.混凝土箱梁桥面板的横向内力分析与计算一般采用板理论，但是板理论不能计入箱梁截面变形对桥面板受力的影响.在箱梁中顶板作为箱梁整体的一部分，在车辆荷载作用下其内力会受到箱梁的畸变、扭转变形等的影响;且波形钢腹板箱梁的抗扭及纵横向抗弯刚度相比混凝土箱梁有不同程度的降低［1］，其桥面板横向内力与混凝土箱梁必然有所差异.从波形钢腹板箱梁这种结构形式受力特点和分析方法的研究现状来看，目前对结构纵向弯曲、扭转和畸变的受力特性研究较多，而对桥面板局部荷载作用下的受力特性和横向内力分析方法的研究较少.混凝土箱梁的框架分析法是将箱梁空间三维问题转化为平面框架问题的一种方法，该方法既能考虑腹板及底板对面板横向挠曲的影响，又能反映构件纵向挠曲与畸变等因素对面板横向内力分布的影响.因此，本文拟根据框架分析法［2］的基本原理，并结合波形钢腹板箱梁的结构特点和力学特性，对这种结构的横向内力分析方法［3-4］进行研究.1 波形钢腹板箱梁桥面板横向内力的力学分析模型在竖向偏心荷载作用下，波形钢腹板箱梁产生弯曲、扭转和畸变效应［2，5］;与混凝土腹板箱梁相比，由于钢腹板厚度较薄，其面内挠曲刚度与箱梁顶、底混凝土板相比小很多，使得限制截面畸变的横向框架作用有所降低.考虑波形钢腹板箱梁的结构特点，本文将建立基于框架分析法的力学模型，并给出主要计算公式.1.1 基本假定［6-7］首先对波形钢腹板箱梁受力模式作以下基本假定:1)波形钢腹板箱梁截面周边不可压缩;2)组成波形钢腹板箱梁的各板沿自身平面的挠曲满足平截面假定;3)翘曲正应力及剪应力沿壁厚均匀分布;4)波形钢腹板的纵向抗弯刚度很小，但不为零.1.2 加支撑的框架分析模型以波形钢腹板简支梁为例，在桥跨某一截面作用单个集中偏载P(见图1(a))，沿纵向取箱梁单位长(1 m)节段作为平面框架结构进行分析，其中纵向单位长度框架上的线荷载集度为q(z)=P/A(见图1(b))，其中A为箱梁顶板的有效分布宽度，与普通混凝土腹板箱梁的有效分布宽度相同.1.3 支撑释放后反对称荷载作用下箱梁剪力差箱梁在反对称荷载作用下产生畸变，由于波形钢腹板的纵向抗弯刚度小，且畸变翘曲刚度很低即在纵向不抵抗翘曲，截面畸变变形几乎全由箱梁顶、底混凝土板来协调［8］，如图 2所示.图中σA，σB，σC和σD为波形钢腹板箱梁的角隅点的翘曲正应力;M0，Mu分别为箱梁顶、底板对y轴的畸变内力矩;Mhy为钢腹板畸变翘曲应力对y轴的力矩;a，b，b0，c，h 为箱梁截面尺寸.图1 波形钢腹板加支承的框架分析图图2 畸变翘曲正应力示意图由于钢腹板的畸变翘曲应力值很小，只是在与顶、底板相交部位存在部分畸变翘曲应力值;腹板其余位置的畸变翘曲应力值接近于0，故省略.假定h'为波形钢腹板分布畸变翘曲应力的高度，h'=φh，其中h为腹板高度.根据文献［9］中的试验数据，φ可取值为20%.对y轴的自平衡关系为Mu－M0－Mhy=0，而Mu，M0，Mhy的表达式为式中，t0，tu，tc分别为波形钢腹板箱梁顶、底板及腹板的厚度;β为畸变翘曲系数;α0=b0/b;Lc=由箱梁各板的畸变内力矩，根据弯矩与剪力的关系可推导出畸变剪力差为式中，T's，T'x，T'h分别为箱梁顶、底板及腹板的畸变剪力差.1.4 支撑释放后反对称荷载作用下箱梁的框架相对侧移值畸变引起波形钢腹板箱梁的横向内力，其位移与内力的关系在畸变理论中用畸变角表示.由于框架取自箱梁，故按框架计算求得的位移不但应与箱梁的畸变位移协调，与框架剪力也存在一定关系［10］.框架剪力及框架畸变位移如图3所示.图3 框架剪力及畸变位移图由图3可得到用框架内剪力Qh表示的框架相对侧移值为图3(a)中所示系数ηm为式(6)和式(7)中n=Es/E，其中Es，E分别为钢与混凝土的弹性模量;I0，Iu和Ic分别为沿纵向单位长度的顶、底板及波形钢腹板横向抗弯惯矩，其中单位波长的波形钢腹板节段如图4所示.将式(1)～(10)代入框架分析法中，即可计算得到偏心集中荷载作用下波形钢腹板箱梁截面的横向内力值.图4 波形钢腹板形状2 试验验证为验证上述方法的准确性，本文以集中荷载作用下的波形钢腹板箱梁为例，分别采用框架分析法和空间有限元方法计算顶板的横向应力值，并同文献［11］中的试验数据进行对比.模型梁的试验资料取自文献［11］，室内波形钢腹板试验简支梁全长4.8 m(见图5).截面形式、尺寸及加载工况见图6(a)，其中工况Ⅰ为梁截面的对称加载，而工况Ⅱ为梁截面的偏载;跨中截面的应变片横向布置见图6(b).试验时施加的荷载P=5 kN，作用于跨中截面.图5 试验梁的纵向布置图(单位:mm)表1为2个加载工况作用下，波形钢腹板箱梁顶板横向正应力实测值与计算值的比较.图6 试验梁的横向布置图(单位:mm)表1 桥面板横向应力比较 MPa位置0.65 D －1.22 －1.09 －1.01 －2.80 －2.90 －2.75 E －4.05 －4.29 －4.20 －1.69 －1.90 －1.80 F －1.22 －1.09 －1.01 －0.40 －0.68 －0.55 G 0.78 0.89 0.81 0.69 0.62实测值C 0.78 0.88 0.83 0.62 0.79对称加载框架分析法有限元法实测值偏载框架分析法有限元法0.56图7 工况Ⅰ和工况Ⅱ作用下跨中位置桥面板横向应力图由图7可看出，2种加载工况下，框架分析法计算值、有限元计算值与试验值沿波形钢腹板箱梁顶板的总体分布规律是一致的.由表1可知，针对2种加载工况下的桥面板横向应力值，框架分析法计算值与有限元值、实测值的误差均在10%以内，符合精度要求.说明波形钢腹板箱梁采用框架分析法计算横向内力是可行的.3 波形钢腹板线刚度变化对桥面板横向内力的影响箱梁桥面板的横向受力与腹板的间距及腹板的约束程度有关，如实际工程中的变截面箱形梁，其跨中与支座处截面的腹板线刚度存在很大差异，此种差异会形成对桥面板不同程度的约束，从而使其横向内力值随之变化［12］.针对对称荷载作用下的波形钢腹板箱梁框架分析法，取出纵向单位长度的箱梁框架(见图8)，可得到对称荷载下顶板跨中位置处的横向内力值.图8 对称荷载下波形钢腹板加支承的框架分析图取波形钢腹板箱梁顶板和腹板的线刚度分别为i1=EIc/a，i2=EI0/b0，则由力学基本方程，可求得顶板中点横向弯矩的表达式为式中，m=i1/i2.由式(11)可知M与m成反比，即波形钢腹板的线刚度越大，其分担的内力值越大，顶板所承担的弯矩值M越小.下面进一步以文献［11］的试验梁尺寸为基础，变换腹板高度即改变腹板的线刚度来研究波形钢腹板与顶板线刚度比值m的变化对桥面板横向内力的影响.分别采用框架分析法及有限元法进行参数分析，得出不同顶、腹板线刚度比m条件下顶板跨中的横向内力值(见表2).表2中，线刚度比是指腹板线刚度与顶板线刚度的比值;应力值是指不同加载方式下荷载作用处的横向应力值，图6(a)中的对称加载、偏载分别取图6(b)中E点和F点的数值;误差指本文公式值相对有限元值的误差.表2 工况Ⅰ、Ⅱ作用下在不同腹板与顶板线刚度比值条件下顶板的横向应力值MPa梁高H/m 线刚度比m/%0.20 0.31 －3.95 －4.17 －5.3 －2.66 －2.72对称加载框架分析法有限元法误差/%偏载框架分析法有限元法误差－2.2 0.270.24 －4.05 －4.29 －5.6 －2.80 －2.90 －3.4 0.43 0.18 －4.16 －4.36 －4.6 －2.91 －3.03 －4.0 0.63 0.12 －4.22 －4.44 －5.0 －3.00 －3.11 －3.5 0.32 0.06 －4.30 －4.53 －5.1 －3.12 －3.20－2.5从图9可看出，顶板横向应力值随腹板线刚度变化基本呈直线变化;随着顶板与腹板线刚度比值m的增加，顶板的横向应力值随之减小.图9 不同线刚度比条件下桥面板横向应力变化图4 结论1)基于框架分析法的基本原理，在充分考虑波形钢腹板箱梁结构特点的基础上，建立了适用于波形钢腹板箱梁横向内力分析的计算模型.该计算模型能够反映由钢腹板和顶、底板构成的横向框架作用和箱梁畸变效应对桥面板横向内力的影响.2)框架分析法计算值与有限元结果、试验值吻合，误差均在10%以内.表明框架分析法可用于波形钢腹板箱梁腹板之间的桥面板横向内力计算.3)在波形钢腹板箱梁截面上的腹板间距确定的条件下，波形钢腹板与混凝土顶板的线刚度比是影响桥面板(箱梁顶板)横向内力的重要因素.参考文献(References)［1］陈宜言.波形钢腹板预应力混凝土桥设计与施工［M］.北京:人民交通出版社，2009.［2］郭金琼，房贞政，郑振.箱形梁设计理论［M］.2版.北京:人民交通出版社，2008.［3］郑震，郭金琼.箱形梁桥横向内力计算的计算机方法［J］.福州大学学报，1995，23(1):60-66.Zheng Zhen，Guo Jinqiong.A computer method of calculating the transversal internal force in box girder bridge ［J］.Journal of Fuzhou University，1995，23(1):60-66.(in Chinese)［4］程翔云.单室箱梁的横向内力分析与荷载分布宽度［J］.重庆交通学院学报，1987，20(1):83-90.Cheng Xiangyun.Analysis of transverse internal force of single-cell box girder and its effective width of load-distribution load-distribution［J］.Journal of Chongqing Jiaotong University，1987，20(1):83-90.(in Chinese)［5］Elgaaly M，Seshadri A.Girders with corrugated webs under partial compressive edge loading［J］.Journal of Structural Engineering，ASCE，1997，123(4):783-791.［6］刘玉擎.组合结构桥梁［M］.北京:人民交通出版社，2005.［7］吴文清，叶见曙，万水，等.波形钢腹板-混凝土组合箱梁截面变形的拟平截面假定及其应用研究［J］.工程力学，2005，22(5):177-180.Wu Wenqing，Ye Jianshu，Wan Shui，et al.Quasi plane assumption and its application in steel-concrete composite box girders with corrugated steel webs ［J］.Engineering Mechanics，2005，22(5):177-180.(in Chinese)［8］周绪红，孔祥福，侯健，等.波纹钢腹板组合箱梁的抗剪受力性能［J］.中国公路学报，2007，20(2):77-82.Zhou Xuhong，Kong Xiangfu，Hou Jian，et al.Shear mechanical property of composite box girder with corrugated steel webs［J］.China Journal of Highway and Transport，2007，20(2):77-82.(in Chinese)［9］李宏江.波形钢腹板箱梁扭转与畸变的试验研究与分析［D］.南京:东南大学交通学院，2003.［10］Kristek V.Theory of box girders［M］.New York:John Wiley and Sons Ltd，1979.［11］刘清.波形钢腹板组合箱梁横向内力理论及试验研究［D］.长沙:湖南大学土木工程学院，2009.［12］方志，张志田.钢筋混凝土变截面箱梁横向受力有效分布宽度分析［J］.湖南大学学报，2003，30(6):82-85.Fang Zhi，Zhang Zhitian.The effective distribution width of the transverse internal force in R-C box girders with varied section［J］.Journal of Hunan University，2003，30(6):82-85.(in Chinese)。
基于矩阵求逆理论的曲梁单元刚度矩阵解析解
基于矩阵求逆理论的曲梁单元刚度矩阵解析解宋郁民;吴定俊【摘要】基于矩阵求逆理论,提出矩阵求逆的综合法.弹性核法求解曲梁单元的刚度矩阵时,由于柔度矩阵的每个元素表达式繁琐,难以直接求逆得到曲梁单元的刚度矩阵.既有相关文献均指出采用数值方法求逆可得出曲梁单元的刚度矩阵.应用矩阵求逆的综合法,推导出曲梁单元刚度矩阵的解析解,并通过算例分析比较,证明了公式的正确性.由此,在编制曲梁杆系梁段有限元的计算程序时,解析解的应用不但简化了程序的编写,而且节约了计算机工作单元,提高了计算精度.【期刊名称】《结构工程师》【年(卷),期】2010(026)004【总页数】6页(P57-62)【关键词】矩阵求逆;综合法;曲梁单元;刚度矩阵;解析解【作者】宋郁民;吴定俊【作者单位】同济大学桥梁工程系,上海,200092;同济大学桥梁工程系,上海,200092【正文语种】中文1 引言曲线梁桥能很好地适应地形、地物的限制,且线形流畅、视觉明快,桥梁美感好,因而在国内外的桥梁建设中广泛应用。
自 20世纪 80年代初曲线梁桥在我国修建以来,众多科技工作者对曲梁结构做了大量的理论与试验研究,取得了丰硕成果[1-4]。
曲线梁的有限元分析方法因其可处理各种形式的曲线梁(如连续、变截面、变曲率、不同支承等情况),便成为诸多学者热衷研究的内容。
较之壳单元、折板单元和条单元,梁单元的应用更为广泛,因而曲线梁的梁段有限元理论研究成果相对丰富。
最早是Ferguson于1979年提出的将空间曲壳单元作退化处理而建立的曲梁单元[5]。
Kapania则于2003年基于刚周边假定而建立了每节点4自由度的三维曲梁单元[6]。
Kim对曲梁结构做了大量的研究,先后给出了非对称薄壁曲梁精确的静态单元刚度矩阵、轴力作用下非对称薄壁曲梁的动力刚度矩阵[7]。
国内学者黄剑源、张罗溪较早做了曲梁结构的矩阵分析研究[8-10]。
赵会东、周世军从薄壁曲梁控制微分方程的闭合解出发,导出了适合于开口薄壁梁具有显式表达式的薄壁曲梁单元刚度矩阵[11]。
波形钢腹板箱梁剪力滞效应的变分法求解_冀伟
( 14)
3 分析验证
为分析验证计算结果的可靠性 , 对有限元模型 进行加载计算 , 加载工况按四级加载 , 分别为 5 , 10 , 15 , 20 kN 作用于跨中截面 . 表 1 中比较了有限元模 型计算值与本文所推导的变分法的理论值 .
当集中力作用在跨中时 , 则 hi σ x = Is M( x )-14P (1 -y 3 )× sh kx 3k 4 kl ch 2 ( 15)
冀 伟, 蔺鹏臻 , 刘世忠 , 王 玲
( 兰州交通大学 甘肃省道路桥梁与地下工程重点实验室 , 甘肃 兰州 730070)
＊
摘 要 : 变分原理通常适用于箱形截面梁剪力滞效应弹性 分析 . 基于波形钢腹板组合 箱梁在弯曲 荷载作用 下的“ 拟 平截 面假定” , 运用变分原理推导了波形钢腹板箱梁在集中荷载作用下翼板的正应 力和剪力滞 系数计算 公式 , 并 与 有限 元分析结果进行了对比 . 分析结果表明 : 变分法算得的翼板正应力和剪力滞系 数和有限元 法结果吻 合 , 该法 可 为今后波形钢腹板组合梁桥的设计计算提供参考 . 关键词 : 组合箱梁 ; 变分原理 ; 剪力滞效应 ; 波形钢腹板 ; 拟平截面假 定 中图分类号 : U448 . 213 文献标志码 : A
当 a ≤ x ≤l 时 , 2 28 η P u″ 2 -k u2 =3EI s u2 = 28 P c3 sh kx +c4 ch kx + η 2 3 EI s k ( 12)
边界条件 : u′ 1 | x =0 = 0 , u ′ 2 | x =l = 0 在 x = a 点的变形连续条件 u 1 = u 2 , 以及变分 要求在 x = a 点 : 28M u′ 1 3EI s
＊ 收稿日期 : 2010 - 09 -13
桥梁工程中英文对照外文翻译文献
桥梁工程中英文对照外文翻译文献(文档含英文原文和中文翻译)BRIDGE ENGINEERING AND AESTHETICSEvolvement of bridge Engineering,brief reviewAmong the early documented reviews of construction materials and structu re types are the books of Marcus Vitruvios Pollio in the first century B.C.The basic principles of statics were developed by the Greeks , and were exemplifi ed in works and applications by Leonardo da Vinci,Cardeno,and Galileo.In the fifteenth and sixteenth century, engineers seemed to be unaware of this record , and relied solely on experience and tradition for building bridges and aqueduc ts .The state of the art changed rapidly toward the end of the seventeenth cent ury when Leibnitz, Newton, and Bernoulli introduced mathematical formulatio ns. Published works by Lahire (1695)and Belidor (1792) about the theoretical a nalysis of structures provided the basis in the field of mechanics of materials .Kuzmanovic(1977) focuses on stone and wood as the first bridge-building materials. Iron was introduced during the transitional period from wood to steel .According to recent records , concrete was used in France as early as 1840 for a bridge 39 feet (12 m) long to span the Garoyne Canal at Grisoles, but r einforced concrete was not introduced in bridge construction until the beginnin g of this century . Prestressed concrete was first used in 1927.Stone bridges of the arch type (integrated superstructure and substructure) were constructed in Rome and other European cities in the middle ages . Thes e arches were half-circular , with flat arches beginning to dominate bridge wor k during the Renaissance period. This concept was markedly improved at the e nd of the eighteenth century and found structurally adequate to accommodate f uture railroad loads . In terms of analysis and use of materials , stone bridges have not changed much ,but the theoretical treatment was improved by introd ucing the pressure-line concept in the early 1670s(Lahire, 1695) . The arch the ory was documented in model tests where typical failure modes were considered (Frezier,1739).Culmann(1851) introduced the elastic center method for fixed-e nd arches, and showed that three redundant parameters can be found by the us e of three equations of coMPatibility.Wooden trusses were used in bridges during the sixteenth century when P alladio built triangular frames for bridge spans 10 feet long . This effort also f ocused on the three basic principles og bridge design : convenience(serviceabili ty) ,appearance , and endurance(strength) . several timber truss bridges were co nstructed in western Europe beginning in the 1750s with spans up to 200 feet (61m) supported on stone substructures .Significant progress was possible in t he United States and Russia during the nineteenth century ,prompted by the ne ed to cross major rivers and by an abundance of suitable timber . Favorable e conomic considerations included initial low cost and fast construction .The transition from wooden bridges to steel types probably did not begin until about 1840 ,although the first documented use of iron in bridges was the chain bridge built in 1734 across the Oder River in Prussia . The first truss completely made of iron was in 1840 in the United States , followed by Eng land in 1845 , Germany in 1853 , and Russia in 1857 . In 1840 , the first ir on arch truss bridge was built across the Erie Canal at Utica .The Impetus of AnalysisThe theory of structures ,developed mainly in the ninetheenth century,foc used on truss analysis, with the first book on bridges written in 1811. The Wa rren triangular truss was introduced in 1846 , supplemented by a method for c alculating the correcet forces .I-beams fabricated from plates became popular in England and were used in short-span bridges.In 1866, Culmann explained the principles of cantilever truss bridges, an d one year later the first cantilever bridge was built across the Main River in Hassfurt, Germany, with a center span of 425 feet (130m) . The first cantileve r bridge in the United States was built in 1875 across the Kentucky River.A most impressive railway cantilever bridge in the nineteenth century was the Fir st of Forth bridge , built between 1883 and 1893 , with span magnitudes of 1711 feet (521.5m).At about the same time , structural steel was introduced as a prime mater ial in bridge work , although its quality was often poor . Several early exampl es are the Eads bridge in St.Louis ; the Brooklyn bridge in New York ; and t he Glasgow bridge in Missouri , all completed between 1874 and 1883.Among the analytical and design progress to be mentioned are the contrib utions of Maxwell , particularly for certain statically indeterminate trusses ; the books by Cremona (1872) on graphical statics; the force method redefined by Mohr; and the works by Clapeyron who introduced the three-moment equation s.The Impetus of New MaterialsSince the beginning of the twentieth century , concrete has taken its place as one of the most useful and important structural materials . Because of the coMParative ease with which it can be molded into any desired shape , its st ructural uses are almost unlimited . Wherever Portland cement and suitable agg regates are available , it can replace other materials for certain types of structu res, such as bridge substructure and foundation elements .In addition , the introduction of reinforced concrete in multispan frames at the beginning of this century imposed new analytical requirements . Structures of a high order of redundancy could not be analyzed with the classical metho ds of the nineteenth century .The importance of joint rotation was already dem onstrated by Manderla (1880) and Bendixen (1914) , who developed relationshi ps between joint moments and angular rotations from which the unknown mom ents can be obtained ,the so called slope-deflection method .More simplification s in frame analysis were made possible by the work of Calisev (1923) , who used successive approximations to reduce the system of equations to one simpl e expression for each iteration step . This approach was further refined and int egrated by Cross (1930) in what is known as the method of moment distributi on .One of the most import important recent developments in the area of analytical procedures is the extension of design to cover the elastic-plastic range , also known as load factor or ultimate design. Plastic analysis was introduced with some practical observations by Tresca (1846) ; and was formulated by Sa int-Venant (1870) , The concept of plasticity attracted researchers and engineers after World War Ⅰ, mainly in Germany , with the center of activity shifting to England and the United States after World War Ⅱ.The probabilistic approa ch is a new design concept that is expected to replace the classical determinist ic methodology.A main step forward was the 1969 addition of the Federal Highway Adim inistration (F HWA)”Criteria for Reinforced Concrete Bridge Members “ that co vers strength and serviceability at ultimate design . This was prepared for use in conjunction with the 1969 American Association of State Highway Offficials (AASHO) Standard Specification, and was presented in a format that is readil y adaptable to the development of ultimate design specifications .According to this document , the proportioning of reinforced concrete members ( including c olumns ) may be limited by various stages of behavior : elastic , cracked , an d ultimate . Design axial loads , or design shears . Structural capacity is the r eaction phase , and all calculated modified strength values derived from theoret ical strengths are the capacity values , such as moment capacity ,axial load ca pacity ,or shear capacity .At serviceability states , investigations may also be n ecessary for deflections , maximum crack width , and fatigue .Bridge TypesA notable bridge type is the suspension bridge , with the first example bu ilt in the United States in 1796. Problems of dynamic stability were investigate d after the Tacoma bridge collapse , and this work led to significant theoretica l contributions Steinman ( 1929 ) summarizes about 250 suspension bridges bu ilt throughout the world between 1741 and 1928 .With the introduction of the interstate system and the need to provide stru ctures at grade separations , certain bridge types have taken a strong place in bridge practice. These include concrete superstructures (slab ,T-beams,concrete box girders ), steel beam and plate girders , steel box girders , composite const ruction , orthotropic plates , segmental construction , curved girders ,and cable-stayed bridges . Prefabricated members are given serious consideration , while interest in box sections remains strong .Bridge Appearance and AestheticsGrimm ( 1975 ) documents the first recorded legislative effort to control t he appearance of the built environment . This occurred in 1647 when the Cou ncil of New Amsterdam appointed three officials . In 1954 , the Supreme Cou rt of the United States held that it is within the power of the legislature to de termine that communities should be attractive as well as healthy , spacious as well as clean , and balanced as well as patrolled . The Environmental Policy Act of 1969 directs all agencies of the federal government to identify and dev elop methods and procedures to ensure that presently unquantified environmenta l amentities and values are given appropriate consideration in decision making along with economic and technical aspects .Although in many civil engineering works aesthetics has been practiced al most intuitively , particularly in the past , bridge engineers have not ignored o r neglected the aesthetic disciplines .Recent research on the subject appears to lead to a rationalized aesthetic design methodology (Grimm and Preiser , 1976 ) .Work has been done on the aesthetics of color ,light ,texture , shape , and proportions , as well as other perceptual modalities , and this direction is bot h theoretically and empirically oriented .Aesthetic control mechanisms are commonly integrated into the land-use re gulations and design standards . In addition to concern for aesthetics at the sta te level , federal concern focuses also on the effects of man-constructed enviro nment on human life , with guidelines and criteria directed toward improving quality and appearance in the design process . Good potential for the upgradin g of aesthetic quality in bridge superstructures and substructures can be seen in the evaluation structure types aimed at improving overall appearance .Lords and lording groupsThe loads to be considered in the design of substructures and bridge foun dations include loads and forces transmitted from the superstructure, and those acting directly on the substructure and foundation .AASHTO loads . Section 3 of AASHTO specifications summarizes the loa ds and forces to be considered in the design of bridges (superstructure and sub structure ) . Briefly , these are dead load ,live load , iMPact or dynamic effec t of live load , wind load , and other forces such as longitudinal forces , cent rifugal force ,thermal forces , earth pressure , buoyancy , shrinkage and long t erm creep , rib shortening , erection stresses , ice and current pressure , collisi on force , and earthquake stresses .Besides these conventional loads that are ge nerally quantified , AASHTO also recognizes indirect load effects such as fricti on at expansion bearings and stresses associated with differential settlement of bridge components .The LRFD specifications divide loads into two distinct cate gories : permanent and transient .Permanent loadsDead Load : this includes the weight DC of all bridge components , appu rtenances and utilities, wearing surface DW nd future overlays , and earth fill EV. Both AASHTO and LRFD specifications give tables summarizing the unit weights of materials commonly used in bridge work .Transient LoadsVehicular Live Load (LL) Vehicle loading for short-span bridges :considera ble effort has been made in the United States and Canada to develop a live lo ad model that can represent the highway loading more realistically than the H or the HS AASHTO models . The current AASHTO model is still the applica ble loading.桥梁工程和桥梁美学桥梁工程的发展概况早在公元前1世纪，Marcus Vitrucios Pollio 的著作中就有关于建筑材料和结构类型的记载和评述。
中英文翻译
Talling building and Steel constructionAlthough there have been many advancements in building construction technology in general.Spectacular archievements have been made in the design and construction of ultrahigh-risebuildings.The early development of high-rise buildings began with structural steel framing. Reinforced concrete and stressed-skin tube systems have since been economically and competitively used in a number of structures for both residential and commercial purposes. The high-rise buildings ranging from 50 to 110 stories that are being built all over the United States are the result ofinnovations and development of new structual systems.Greater height entails increased column and beam sizes to make buildings more rigid so that under wind load they will not sway beyond an acceptable limit. Excessive lateral sway may cause serious recurring damage to partitions, ceilings. and other architectural details. In addition, excessive sway may cause discomfort to the occupants of the building because their perception of such motion. Structural systems of reinforced concrete, as well as steel, take full advantage of inherent potential stiffness of the total building and therefore require additional stiffening to limitthe sway.In a steel structure, for example, the economy can be defined in terms of the total average quantity of steel per square foot of floor area of the building. Curve A in Fig .1 represents the average unit weight of a conventional frame with increasing numbers of stories. Curve B represents the average steel weight if the frame is protected from all lateral loads. The gap between the upper boundary and the lower boundary represents the premium for height for the traditional column-and-beam frame. Structural engineers have developed structural systems with aview to eliminating this premium.Systems in steel. Tall buildings in steel developed as a result of several types of structural innovations. The innovations have been applied to the construction of both office and apartmentbuildings.Frame with rigid belt trusses. In order to tie the exterior columns of a frame structure to the interior vertical trusses, a system of rigid belt trusses at mid-height and at the top of the building may be used. A good example of this system is the First Wisconsin Bank Building(1974) inMilwaukee.Framed tube. The maximum efficiency of the total structure of a tall building, for both strength and stiffness, to resist wind load can be achieved only if all column element can be connected to each other in such a way that the entire building acts as a hollow tube or rigid box in projecting out of the ground. This particular structural system was probably used for the first time in the 43-story reinforced concrete DeWitt Chestnut Apartment Building in Chicago. The most significant use of this system is in the twin structural steel towers of the 110-story World TradeCenter building in New YorkColumn-diagonal truss tube. The exterior columns of a building can be spaced reasonably far apart and yet be made to work together as a tube by connecting them with diagonal members interesting at the centre line of the columns and beams. This simple yet extremely efficient system was used for the first time on the John Hancock Centre in Chicago, using as much steel as isnormally needed for a traditional 40-story building.Bundled tube. With the continuing need for larger and taller buildings, the framed tube or thecolumn-diagonal truss tube may be used in a bundled form to create larger tube envelopes while maintaining high efficiency. The 110-story Sears Roebuck Headquarters Building in Chicago has nine tube, bundled at the base of the building in three rows. Some of these individual tubes terminate at different heights of the building, demonstrating the unlimited architectural possibilities of this latest structural concept. The Sears tower, at a height of 1450 ft(442m), is theworld’s tallest building.Stressed-skin tube system. The tube structural system was developed for improving the resistance to lateral forces (wind and earthquake) and the control of drift (lateral building movement ) in high-rise building. The stressed-skin tube takes the tube system a step further. The development of the stressed-skin tube utilizes the façade of the building as a structural element which acts with the framed tube, thus providing an efficient way of resisting lateral loads in high-rise buildings, and resulting in cost-effective column-free interior space with a high ratio ofnet to gross floor area.Because of the contribution of the stressed-skin façade, the framed members of the tube require less mass, and are thus lighter and less expensive. All the typical columns and spandrel beams are standard rolled shapes, minimizing the use and cost of special built-up members. The depth requirement for the perimeter spandrel beams is also reduced, and the need for upset beams above floors, which would encroach on valuable space, is minimized. The structural system has been used on the 54-story One Mellon Bank Center in Pittburgh.Systems in concrete. While tall buildings constructed of steel had an early start, development of tall buildings of reinforced concrete progressed at a fast enough rate to provide a competitive chanllenge to structural steel systems for both office and apartment buildings.Framed tube. As discussed above, the first framed tube concept for tall buildings was used for the 43-story DeWitt Chestnut Apartment Building. In this building ,exterior columns were spaced at 5.5ft (1.68m) centers, and interior columns were used as needed to support the 8-in . -thick(20-m) flat-plate concrete slabs.Tube in tube. Another system in reinforced concrete for office buildings combines the traditional shear wall construction with an exterior framed tube. The system consists of an outer framed tube of very closely spaced columns and an interior rigid shear wall tube enclosing the central service area. The system (Fig .2), known as the tube-in-tube system , made it possible to design the world’s present tallest (714ft or 218m)lightweight concrete building ( the 52-story One Shell Plaza Building in Houston) for the unit price of a traditional shear wall structure of only 35stories.Systems combining both concrete and steel have also been developed, an examle of which is the composite system developed by skidmore, Owings &Merril in which an exterior closely spaced framed tube in concrete envelops an interior steel framing, thereby combining the advantages of both reinforced concrete and structural steel systems. The 52-story One Shell Square Building in New Orleans is based on this system.Steel construction refers to a broad range of building construction in which steel plays the leading role. Most steel construction consists of large-scale buildings or engineering works, with the steel generally in the form of beams, girders, bars, plates, and other members shaped through the hot-rolled process. Despite the increased use of other materials, steel construction remained a major outlet for the steel industries of the U.S, U.K, U.S.S.R, Japan, West German, France, andother steel producers in the 1970s.Early history. The history of steel construction begins paradoxically several decades before the introduction of the Bessemer and the Siemens-Martin (openj-hearth) processes made it possible to produce steel in quantities sufficient for structure use. Many of problems of steel construction were studied earlier in connection with iron construction, which began with the Coalbrookdale Bridge, built in cast iron over the Severn River in England in 1777. This and subsequent iron bridge work, in addition to the construction of steam boilers and iron ship hulls , spurred the development of techniques for fabricating, designing, and jioning. The advantages of iron over masonry lay in the much smaller amounts of material required. The truss form, based on the resistance of the triangle to deformation, long used in timber, was translated effectively into iron, with cast iron being used for compression members-i.e, those bearing the weight of direct loading-and wrought iron being used for tension members-i.e, those bearing the pull of suspendedloading.The technique for passing iron, heated to the plastic state, between rolls to form flat and rounded bars, was developed as early as 1800;by 1819 angle irons were rolled; and in 1849 the first I beams, 17.7 feet (5.4m) long , were fabricated as roof girders for a Paris railroad station.Two years later Joseph Paxton of England built the Crystal Palace for the London Exposition of 1851. He is said to have conceived the idea of cage construction-using relatively slender iron beams as a skeleton for the glass walls of a large, open structure. Resistance to wind forces in the Crystal palace was provided by diagonal iron rods. Two feature are particularly important in the history of metal construction; first, the use of latticed girder, which are small trusses, a form first developed in timber bridges and other structures and translated into metal by Paxton ; and second, the joining of wrought-iron tension members and cast-iron compression members by means ofrivets inserted while hot.In 1853 the first metal floor beams were rolled for the Cooper Union Building in New York. In the light of the principal market demand for iron beams at the time, it is not surprising that the Cooper Union beams closely resembled railroad rails.The development of the Bessemer and Siemens-Martin processes in the 1850s and 1860s suddenly open the way to the use of steel for structural purpose. Stronger than iron in both tension and compression ,the newly available metal was seized on by imaginative engineers, notably by those involved in building the great number of heavy railroad bridges then in demand in Britain,Europe, and the U.S.A notable example was the Eads Bridge, also known as the St. Louis Bridge, in St. Louis (1867-1874), in which tubular steel ribs were used to form arches with a span of more than 500ft (152.5m). In Britain, the Firth of Forth cantilever bridge (1883-90) employed tubular struts, some12 ft (3.66m) in diameter and 350 ft (107m) long. Such bridges and other structures wereimportant in leading to the development and enforcement of standards and codification of permissible design stresses. The lack of adequate theoretical knowledge, and even of an adequate basis for theoretical studies, limited the value of stress analysis during the early years of the 20th century, as iccasionally failures, such as that of a cantilever bridge in Quebec in 1907,revealed.But failures were rare in the metal-skeleton office buildings; the simplicity of their design proved highly practical even in the absence of sophisticated analysis techniques. Throughout the first third of the century, ordinary carbon steel, without any special alloy strengthening or hardening, wasuniversally used.The possibilities inherent in metal construction for high-rise building was demonstrated to theworld by the Paris Exposition of 1889.for which Alexandre-Gustave Eiffel, a leading French bridge engineer, erected an openwork metal tower 300m (984 ft) high. Not only was the height-more than double that of the Great Pyramid-remarkable, but the speed of erection and low cost were even more so, a small crew completed the work in a few months.The first skyscrapers. Meantime, in the United States another important development was taking place. In 1884-85 Maj. William Le Baron Jenney, a Chicago engineer , had designed the Home Insurance Building, ten stories high, with a metal skeleton. Jenney’s beams wer e of Bessemer steel, though his columns were cast iron. Cast iron lintels supporting masonry over window openings were, in turn, supported on the cast iron columns. Soild masonry court and party walls provided lateral support against wind loading. Within a decade the same type of construction had been used in more than 30 office buildings in Chicago and New York. Steel played a larger and larger role in these , with riveted connections for beams and columns, sometimes strengthened for wind bracing by overlaying gusset plates at the junction of vertical and horizontal members. Light masonry curtain walls, supported at each floor level, replaced the old heavy masonry curtain walls, supported at each floor level , replaced the old heavy masonry.Though the new construction form was to remain centred almost entirely in America for several decade, its impact on the steel industry was worldwide. By the last years of the 19th century, the basic structural shapes-I beams up to 20 in. ( 0.508m) in depth and Z and T shapes of lesser proportions were readily available, to combine with plates of several widths and thicknesses to make efficient members of any required size and strength. In 1885 the heaviest structural shape produced through hot-rolling weighed less than 100 pounds (45 kilograms) per foot; decade by decade this figure rose until in the 1960s it exceeded 700 pounds (320 kilograms) per foot.Coincident with the introduction of structural steel came the introduction of the Otis electric elevator in 1889. The demonstration of a safe passenger elevator, together with that of a safe and economical steel construction method, sent building heights soaring. In New York the 286-ft (87.2-m) Flatiron Building of 1902 was surpassed in 1904 by the 375-ft (115-m) Times Building ( renamed the Allied Chemical Building) , the 468-ft (143-m) City Investing Company Building in Wall Street, the 612-ft (187-m) Singer Building (1908), the 700-ft (214-m) Metropolitan Tower (1909) and, in 1913, the 780-ft (232-m) Woolworth Building.The rapid increase in height and the height-to-width ratio brought problems. To limit street congestion, building setback design was prescribed. On the technical side, the problem of lateral support was studied. A diagonal bracing system, such as that used in the Eiffel Tower, was not architecturally desirable in offices relying on sunlight for illumination. The answer was found in greater reliance on the bending resistance of certain individual beams and columns strategically designed into the skeletn frame, together with a high degree of rigidity sought at the junction of the beams and columns. With today’s modern interior lighting systems, however, diagonal bracing against wind loads has returned; one notable example is the John Hancock Center in Chicago, where the external X-braces form a dramatic part of the structure’s façade.World War I brought an interruption to the boom in what had come to be called skyscrapers (the origin of the word is uncertain), but in the 1920s New York saw a resumption of the height race, culminating in the Empire State Building in the 1931. The Empire State’s 102 stories (1,250ft. [381m]) were to keep it established as the hightest building in the world for the next 40 years. Its speed of the erection demonstrated how thoroughly the new construction technique had been mastered. A depot across the bay at Bayonne, N.J., supplied the girders by lighter and truck on aschedule operated with millitary precision; nine derricks powerde by electric hoists lifted the girders to position; an industrial-railway setup moved steel and other material on each floor. Initial connections were made by bolting , closely followed by riveting, followed by masonry and finishing. The entire job was completed in one year and 45 days.The worldwide depression of the 1930s and World War II provided another interruption to steel construction development, but at the same time the introduction of welding to replaceriveting provided an important advance.Joining of steel parts by metal are welding had been successfully achieved by the end of the 19th century and was used in emergency ship repairs during World War I, but its application to construction was limited until after World War II. Another advance in the same area had been the introduction of high-strength bolts to replace rivets in field connections.Since the close of World War II, research in Europe, the U.S., and Japan has greatly extended knowledge of the behavior of different types of structural steel under varying stresses, including those exceeding the yield point, making possible more refined and systematic analysis. This in turn has led to the adoption of more liberal design codes in most countries, more imaginative design made possible by so-called plastic design ?The introduction of the computer byshort-cutting tedious paperwork, made further ad高层建筑和钢结构尽管一般的建筑结构设计取得了很大的进步，取得显著成绩的还要属超高层建筑结构设计。
小箱梁抗剪及抗弯加固措施及效果分析
小箱梁抗剪及抗弯加固措施及效果分析陈敏武汉光谷建设投资有限公司 湖北武汉 430070摘要：改扩建工程往往面临着既有桥梁的加固，以浙江某高速改扩建项目为案例，首先分析了抗弯承载能力、抗剪承载能力、局部承压承载能力不足的原因；其次结合各自承载能力基本原理，结合规范要求，分析了加固常用方法，并对每种加固方法的原理进行了介绍；最后结合项目实际特点，介绍了所采用的方法以及加固的效果。
结果表明，采用合适的加固方法可以有效解决城市高速公路桥梁的结构问题，确保了其长期安全运营。
这一研究为城市基础设施的可持续发展提供了有力支持。
关键词：小箱梁 抗弯承载能力 抗剪承载能力 桥梁工程 加固原理中图分类号：X913.4;U448.23文献标识码：A 文章编号：1672-3791(2024)03-0098-03 Analysis of Shear and Flexural Strengthening Measures and TheirEffects for Small Box GirdersCHEN MinWuhan Optics Valley Construction Investment Co., Ltd., Wuhan, Hubei Province, 430070 China Abstract:Renovation and expansion projects often face the reinforcement of existing bridges. Taking a high-speed renovation and expansion project in Zhejiang as a case, this paper first analyzes the reasons for the insufficient bend‐ing bearing capacity, shear bearing capacity and local loading and bearing capacity. Then, based on the basic prin‐ciples of their respective bearing capacity and the requirements of specifications, it analyzes common reinforcement methods and introduces the principles of each reinforcement method. Finally, combined with the actual character‐istics of the project, it introduces the used methods and reinforcement effects. The results indicate that adopting ap‐propriate reinforcement methods can effectively solve the structural problems of urban highway bridges and ensure their long-term safe operation. This study provides strong support for the sustainable development of urban infra‐structure.Key Words: Small box girder; Flexural bearing capacity; Shear bearing capacity; Bridge engineering; Reinforce‐ment principle近年来城市汽车保有量逐步提升，随着电动化的发展，未来一段时间内城市汽车数量将会迎来快速发展期。
预应力活性粉末混凝土箱梁抗弯性能试验
预应力活性粉末混凝土箱梁抗弯性能试验方志;刘明;郑辉【摘要】In order to study the mechanical behavior of prestressed reactive powder concrete (RPC) box girders ,the flexural behavior tests of two prestressed RPC box girders were carried out .T he force characteristic of RPC box girders and the influence of transverse prestressing force to its flexural performance were studied .The results show that the prestressed RPC box girders display a good deformation capacity ,with a maximal deflection of 1/50 of its span .The crack width a nd the short‐time stiffness of the RPC box girders can be calculated according to the formula in Technical Specif ication for Fiber Reinforced Concrete Structures (CECS38 :2004) , with a coefficient of 0 .4 and 0 .2 considering influence from steel fiber , respectively . The transverse prestressing force in the top plate of RPC box girders has little influence on the flexural bearing capacity , but the force can make a more uniform strain distribution of the compressive concrete so as to reduce the shear‐l ag effect and increase the ductility of the specimen .By applying a transverse prestressing force of 2 .95 M Pa (only 3 .1% of the RPC prism compressive strength of 94 MPa) at the top plate ,the effective distribution width of box girder increases by 10% ,and ductility index of specimen increases by 3% .The calculated formula to evaluate the cracking moment and the ultimate moment of a prestressed RPC box girders is proposed and verified by the experimental results .%为研究预应力活性粉末混凝土（RPC ）箱梁的正截面受力性能，进行了2片预应力RPC箱梁的抗弯性能试验，研究了RPC箱梁的受力变形特征以及顶板横向预应力对其抗弯性能的影响。
梁桥外文翻译
英文翻译:BEAMBRIDGEIn designing a bridge, preference is often given to beam structure, unless it has a very long span. Simple in structure, convenient to fabricate and erect, easy to maintain, and with less construction time and low cost, beam structure has found wide application in bridgework. In 1937, over the Qiantang River, in the city of Hangzhou, was erected a railway-highway bi-purpose bridge, with a total length of 1453m, the longest span being 67m. Whencompleted, it was a remarkable milestone of the beambridges designed and built by Chinese engineers themselves before liberation. Since 1949, this kind of bridge has made giant strides.Reinforced concrete beam structure is the most commonly used for short- and medium-span bridges. A representative masterpiece is the RongJiangBridge completed in 1964 in the city of Nanning, the provincial capital of Guangxi Zhuangzu Autonomous Region. The bridge, with a main span of 55m and its cross section of a thin-walled box with continuous cells, was designed in accordance with closedthin-walled membertheory, the first of its kind in China.Pre-stressed concrete girder bridges cover a wide range of spans and types. In the short span range, pre-cast AASHTO beams with a composite cast-in-place non pre-stressed concrete slab are frequently used for simple spans. A similar form of construction is used for partially continuous spans using I-girders and box girder in the medium span range .In the medium to long span range, continuous pre-cast segmental box girders are common, while the longest spans are generally cast-in-place segmental box girders.For cost-in-place construction, the girders and slab are generally formed together and both cast before formwork and supports are removed. This construction is fully composite for dead load and live load. The usual cross sections are T-beams and box girders. Spans are usually continuous, and transverse post-tensioning of the slab is frequently prescribed to allow the use of thinner slabs or a reduced number of longitudinal girders at a larger spacing. Since longitudinal post-tensioning is required on site, transverse post-tensioning is usually economical and normally used.The design and analysis items given for reinforced concrete girder bridges also apply to pre-stressed girder bridges. For the box girder section, a detailed transverse live load analysis of the section should be carried out. Temperature effects are important for box girder, due to the possibility of large differential temperatures between the top and bottom slabs.For cast-in-place segmental construction built by the balanced cantilever method, a knowledge of the exact construction loads is necessary, in order to calculate stresses and deformations at each stage. A knowledge of the creep characteristics of the concrete is essential for calculating deformations after the addition of each segment,and also to calculate the redistribution of moments after completion and final stressing.Standard pre-cast, pre-stressed beamscover spans up to the 140ft (43m) range. After the beamsare erected, forms for the slabs are placed between the beamsand a reinforced concrete slab cast in place. The slab and beams act compositely for superimposed dead load and live load. Intermediate diaphragms are not normally used , and the design and analysis items given for reinforced concrete girder bridges, also apply to pre-stressed multi-beam type bridges.Pre-cast pre-stressed beams can be made partially continuous for multi-span bridges. This system is not only structurally efficient, but has the advantage of reducing the number of deck joints. Support moments are developed due to superimposed dead load, live load, differential temperature, shrinkage and creep. Continuity for superimposed dead load and for live load can be achieved by casting diaphragms at the time the deck concrete is placed. Reinforced steel placed longitudinally in the deck slab across the intermediate pier will resist the tension from negative moment at the supports. At the diaphragms, the bottom flanges of adjacent beams should be connected to resist the tensile stress due to positive momentsgenerated by differential temperature, shrinkage and creep. Continuous spans , beyond the range of the type pre-cast girder, temporarily supported on bends, with joints near points of minimummoment, are post-tensioned for continuity after placement of the deck slab. The maximumlengths of segments are usually determined by shipping length and weight restriction.Pre-cast segmental construction employs single or multiple cell boxes with transverse segments post-tensioned together longitudinally. For medium sans, the segments may be erected for the full span on falsework before post-tensioning. Longer spans are usually erected by the balanced cantilever method, where each segment is successively stressed after erection. The design and analysis considerations given for cast-in-place segmental construction also apply to pre-cast segmental construction. The deformation of the structure during cantilever erection is dependent upon the time difference between segment pre-casting and erection. The design calculations mayneed to be repeated if the construction schedule differ from that assumed at the design stages.Pre-stressed con crete beam bridge is a new type of structure.Chi na bega n to makeresearches and develop its con struct ion in the fifties.In early 1956, a simply-supported prestressed con crete beam bridge with a main spa n of 23.9m -a railway bridge -was erected over the Xiny iRiver along the Longhai Railway line. Completed at the sametime, the first P.C. highway bridge was the Jin gzhouHighwayBridge. The Ion gest simply-supported P.C. beam which reaches 62m bel ongs to theFeiy un RiverBridge in Ruan'an, Zhejia ngPro vin ce, built in 1988. Ano ther example is the 4475.09mYellow RiverBridge, built in the city of Kaifeng, HenanProvince in 1989.77 of its spa ns are 50msimply-supported P.C. beams and its continuous deck extends to 450m. It is also noticeable that the bridge is designed on the basis of partially prestressed concrete theory.Elastic an alysis and beam theory are usually used in the desig n of segme ntalbox girder structures. For box girders of unu sual proporti on, other methods of an alysis which con sider shear lag should be used to determ ine the porti on of the cross secti on effective in resist ing Iongitudinal bending. Possible reserve shearing stress in the shear keysshould be investigated, particularly in segments near a pier. At time oferecti on, the shear stress carried by the key should not exceedThe prestressed concrete rigid T-frame bridge was primarily developed and built in China in the sixties. This kind of structure is most suitable to be erected by bala need can tilever con struct ion process, either by can tilever segme ntal con creti ng with suspe nded formwork, or by can tilevererecti on with segme nts of precast con crete. The first example of can tilever erect ion is the WeiRiverBridge (completed in 1964) in Wuli ng, Henan Provi nee, while the Liujia ngBridge (completed in 1967) in Liuzhou in Guan gxi Zhua ngzu Aut onom ous Regi on is the first by can tilever casti ng. Nevertheless, the Yan gtze RiverBridge at Chongqing (completed in 1980), hav ing a main spa n of 174m, is regarded as the largest of this kind at prese nt.On the basis of the desig n and con structi on of P.C. rigid T-frame bridges, was developed multi P.C. continuous beam and continuous rigid frame bridges, which can have Ion ger spa ns and offer better traffic con diti ons. Among the others, the LuoxiBridge in Guan gzhou, Guangdong Province (completed in 1988) features a180m main span. And the Huan gshiBridge cross ing the Yan gtze River in HubeiPro vin ce, which is still un der con struct ion, has a spa n of 245 meters. The represe ntive of P.C. continu ous girder railway bridge, the sec ond bridge over the QiantangRiver (finished in 1991), boasts its large span and its great len gth, its main spa n being 80m long and con tin uity over 18 spa ns. Its erecti on is an arduous task as the structure was subjected to a wave height of 1.96m and a tidal pressure of 32kPa whe n un der con struct ion. The exte nsive con struct ion of continu ous beam bridges has led to theapplication of incremental launching method especially to straight and plane curved bridges. Besides, large capacity (500t) floating crane installation and movable slip forms as well as span by span erection scheme have also attained remarkable advancement.In order to optimize the bridge configuration, to cut off the peak moment value at supports, and to diminish the constructional height, V-shaped or Y-shaped piers are developed for P.C. continuous beam, cantilever or rigid frame bridges. The prominent examples are the medium or the short Bridge (1981) in TaiwanProvince and the LijiangBridge (1987) at Zhishan in the city of Guilin.Steel structure is employed primarily for railway-highway bi-purpose bridges. The longest steel highway bridge is the BeizhenYellow RiverBridge in ShandongProvince (1972), its main span being 113m long. It has a rivet-connected continuous truss. The foundation is composedof f1.5m concrete boring piles, whose penetration depth into subsoil reaches 107m, the deepest pile ever drilled in our country. A new structure of field bolting welded box girder paved with orthotropic steel deck was first introduced in the North RiverHighwayBridge at Mafang, Guangdong Province, which was completedin 1980. In 1957, in the city of Wuhan, over the Yangtze River waserected arailway-highway bi-purpose superstructure, another milestone in China's bridge construction history. The bridge has a continuous steel truss with a 128mmain span. The rivet-connected truss is made of No. 3 steel. A newly developed cylinder shaft of 1.55m In diameter was initially used in the deep foundation. (Later in 1962, f5.8m cylinder shaft foundation was laid in the Ganijang South Bridge in Nanchang, Jiangxi Province.) In 1968, another wonder over the Yangtze River -the NanjingYangtze RiverBridge- cameinto being. The whole project, including its material, design and installation, was completed through the Chinese own efforts. It is a rivet-connected continuous truss with a 160m main span. The material used is high quality steel of 16 Mnq. In erection, deep water foundation was developed. Open caissons were submerged to a depth of 54.87m, and pretensioned concrete cylinder shafts 3.6m in diameter were laid, thus forming a newtype of compoundfoundation. And subwater cleaning was performed in a depth of 65m.Another attractive and gigantic structure standing over the Yangtze River is the JiujiangBridge completed in 1992. Chinese-made 15 MnVNqsteel was used andshop-welded steel plates 56mmthick were bolted on site. The main span reaches 216m. The continuous steel truss is enforced by flexible stiffening arch ribs. In laying the foundation, a double-walled sheet piling cofferdam was built, in which concrete bored pile cast-in-situ was set up. Whenerecting the steel beams, double suspended cable frame took the place of single one, which is another innovation.梁桥梁桥构造简单、施工方便、工期短、造价低、且维修容易，除特大跨度桥梁外，是设计中优先考虑的结构体系，应用甚广。
薄壁箱梁剪力滞效应研究
西南交通大学硕士学位论文薄壁箱梁剪力滞效应研究姓名：王子健申请学位级别：硕士专业：桥梁与隧道工程指导教师：强士中20040201西南交通大学硕士学位论文摘要剪力滞（应力分散）问题很早就有学者对其进行研究，最初是在航空工程上，后来应用到土建工程当中，经过２０多年的发展，对剪力滞的研究也取得了一些成果，解决了一些实际工程问题，但许多问题并没有得到完全的解决，随着我国交通事业的发展，有关剪力滞的新问题也在不断出现，需要进一步的研究，本文就剪力滞的问题进行了如下的一些工作：１．对于箱形截面主梁，本文考虑剪力滞效应的变形特点，根据箱梁纵向位移函数，采用基于能量变分法基础上的最小势能原理推导出系统的总势能表达式，然后通过变分法得到带有不同边界条件的一组微分方程，并写出轴向应力的解析表达式。
结合实际的算例研究了等截面简支梁的剪力滞效应。
采用截面当量法研究了变截面连续梁的剪力滞效应。
２．就悬臂梁的负剪力滞现象进行理论分析和推导，并结合实际算例来对悬臂梁负剪力滞现象进行参数分析。
３．阐述了宜宾中坝金沙江斜拉桥的模型试验，并结合该桥的模型试验数据，研究该斜拉桥的剪力滞效应。
通过本论文的工作，箱形截面梁桥的设计、分析提供更安全、合理的设计依据。
【关键词】剪力滞负剪力滞有限元最小势能原理能量变分法西南交通大学硕士学位论文１１ＡＢＳＴＲＣＴＳｈｅａｒｌａｇｐｈｅｎｏｍｅｎａｏｒｔｈｅｎｏｎｕｎｉｆｏｍｄｉｓｔｒｉｂｕｔｉｏｎｏｆｂｅｎｄｉｎｇｓｔｒｅｓｓａｃｒｏｓｓｗｉｄｅｆｌａｎｇｅｓｏｆｂｅａｍｃｒｏｓｓｓｅｃｔｉｏｎｈａｖｅ１０ｎｇｂｅｅｎｒｅｃｏｇｎｉｚｅｄａｎｄｓｔｕｄｉｅｄ。
ＦｉｒｓｔｓｔｕｄｉｅｓｗｅｒｅｗｉｔｈｓｔｉｆｆｅｎｂｅａｍｏｆＩｓｈａｐｅｉｎａｖｉａｔｉｏｎｅｎｇｉｎｅｅｒｉｎｇ．ｗｈｉｌｅ１ａｔｃｒｍａｉｎｌｙｃｏｎｃｅｒｎｅｄｃｏｎｃｅｒｎｅｄｗｉｔｈｃｉｖｉｌｅｎｇｉｎｅｅｒｉｎｇ．Ｓｏｍｅｒｅｓｅａｒｃｈｏｕｔｃｏｍｅｓａｂｏｕｔｓｈｅａｒｌａｇｐｒｏｂｌｅｍｓｗｅｒｅａａａｉｎｅｄａｎｄｐａｒｔｏｆｐｒｏｊｅｃｔｐｒｏｂｌｅｍｓｗｅｒｅｓｏｌｖｅｄｄ嘶ｎｇｔｈｅＰ．ｖｅｎｔｙｙｅａｒｓ．ｗ｛ｔｌｌｔｈｅｄｅｖｅｌｏｐｍｅｎｔｏｆｃｏｍｍｕｎｉｃａｔｉｏｎｔｈｅｒｅａｒｅｓｔｉｌｌｍａｎｙｐｒｏｂｌｅｍｓｗｈｉｃｈｎｅｅｄｆａｒｔｈｅｒｒｅｓｅａｒｃｈ．Ｉｎｔｈｉｓｄｉｓｓｅｒｔａｔｉｏｎ．ｓｈｅａｒｌａｇｅｆｆｅｅｔｉｓｓｔｕｄｉｅｄ．Ｔｈｅｍａｉｎｃｏｎｔｅｎｔｓａｒｅｔｈｅｆｏｌｌｏｗｉｎｇｓ．１．Ａｇｅｎｅｒａｌｐｏｔｅｎｔｉａｌｅｎｅｒｇｙｅｑｕａｔｉｏｎｉｓｄｅｒｉｖｅｄａｃｃｏｒｄｉｎｇｔｏｔｈｅｐｒｉｎｃｉｐｌｅｏｆｍｉｎｉｍｕｍｐｏｔｅｎｔｉａｌｅｎｅｒｇｙａｎｄａｓｅｔｏｆｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ、ｖｉｔｌｌｄｉｆｆｅｒｅｎｔｂｏｕｎｄａｒｙｃｏｎｄｉｔｉｏｎｓａｒｅｄｅｒｉｖｅｄａｃｃｏｒｄｉｎｇｔｏｖａｒｉａｔｉｏｎａｌｐｒｉｎｃｉｐｌｅｍｅｔｈｏｄｃｏｎｓｉｄｅｒｉｎｇｔｈｅｄｅｆｏｒｍｍｉｏｎｐｒｏｐｅｒｔｉｅｓａｎｄｌｏｎｇｉｔｕｄｉｎａｌｄｉｓｐｌａｃｅｍｅｎｔｆｕｎｃｔｉｏｎｓｏｆｃｏｎｓｔａｎｔｄｅｐｍｂｏｘｂｅａｍｗｉｌｌｂｅｓｔｕｄｉｅｄｗｉｔｈａｎｇｉｒｄｅｒｓ．Ｔｈｅｓｈｅａｒｌａｇｅｆｒｃｃｔｏｆｓｉｍｐｌｅｓｕｐｐｏｒｔｅｄｅｘａｍｐｌｅ．Ｔ１１ｅｍｅｔｈｏｄｏｆｓｕｂｓｔｉｔｕｔｅｖａｒｉａｂｌｅｉｓａｐｐｌｉｅｄｔｏｓｔｕｄｙｔｈｅｓｈｅａｒ１ａｇｅｆｆｅｃｔｏｆｃｏｎｔｉｎｕｏｕｓｂｏｘ２ｉｒｄｅｒｓｗｉｔｈｖａｒｉａｂｌｅｄｅｐｔｈ．２．Ｔｈｅｎｅｇａｔｉｖｅｓｈｅａｒｌａｇｅｆｆｅｃｔｏｆｔｈｅｃａｎｔｉｌｅｖｅｒａｎｄｃｏｎｔｉｎｕｏｕｓｇｉｒｄｅｒｓｉｓｓｔｕｄｉｅｄａｎｄｔｈｅｐａｒａｍｅｔｅｒｓｗｈｉｃｈｉｎｆｌｕｅｎｃｅｔｈｅｓｈｅａｒｌａｇｅｆｆｅｃｔｉｓａｎａｌｙｓｅｄ．３．ＣｏｍｂｉｎｉｎｇｗｉｔｈｔｈｅｅｘｐｅｒｉｍｅｎｔｏｆＹｉｂｉｎＺｈｏｎｇｂａＪｉｎｓｈａｊｉａｎｇｃａｂｌｅ・ｓｔａｙｅｄｂｒｉｄｇｅｃｏｎｃｒｅｔｅｍｏｄｅｌ，ｔｈｉｓｄｉｓｓｅｒｔａｔｉｏｎａｎａｌｙｓｅｓｔｈｅｓｈｅａｒｌａｇｅｆｆｅｃｔｏｆｔｈｅｃａｂｌｅ－ｓｔａｙｅｄｂｒｉｄｇｅ．Ｂｙｔｈｅｗｏｒｋｏｆｔｈｉｓｄｉｓｓｅｒｔａｔｉｏｎ，ｍｏｒｅｓａｆｅｒａｎｄｍｏｒｅｒｅａｓｏｎａｂｌｅｄｅｓｉｇｎａｎｄａｎａｌｙｓｉｓｍｅｔｈｏｄｆｏｒｂｏｘｇｅｒｄｅｒｈａｖｅｂｅｅｎｏｆｆｅｒｅｄ．［ｋｅｙｗｏｒｄｓ］ｓｈｅａｒｌａｇ，ｎｅｇａｔｉｖｅｓｈｅａｒｌａｇ，ｆｉｎｉｔｅｅｌｅｍｅｎｔｍｅｔｈｏｄ，ｈｅｐｒｉｎｃｉｐｌｅｏｆｍｉｎｉｍｕｍｐｏｔｅｎｔｉａｌｅｎｅｒｇｙ，ｅｎｅｒｇｙｖａｒｉａｔｉｏｎａｌｐｒｉｎｃｉｐｌｅｍｅｔｈｏｄ．＋第１章绪论１．１选题背景随着交通事业的发展以及城市化速度的加快，桥梁在日益繁忙的公路和城市交通中显得越来越来重要。
AISC_360
Section Classification
• Compact, non-compact or slender element sections • Section Classification is done as per section B4 and Table B4.1
Pr < 0.2 Pc
Design for Combined Forces
UNSYMMETRIC AND OTHER MEMBERS
Compression Members
• Chapter E addresses members subject to axial compression. • The Nominal Compressive Strength, Pn, shall be the minimum value obtained according to the Limit States of Flexural Buckling Torsional Buckling Flexural-Torsional Buckling
Changes
• Analysis
− changes in analysis methods − loading − combination rules
• Design
− new design equations − strength calculation rather than stress
Analysis Methods
Bending Members contd …
毕业设计商场中英文对照英文版
Structural Systems to resist lateral loads Commonly Used structural SystemsWith loads measured in tens of thousands kips, there is little room in the design of high-rise buildings for excessively complex thoughts. Indeed, the better high-rise buildings carry the universal traits of simplicity of thought and clarity of expression.It does not follow that there is no room for grand thoughts. Indeed, it is with such grand 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.Omitting some concepts 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:1.Moment-resisting frames.2.Braced frames, including eccentrically braced frames.3.Shear walls, including steel plate shear walls.4.Tube-in-tube structures.5.Tube-in-tube structures.6.Core-interactive structures.7.Cellular or bundled-tube systems.Particularly with the recent trend toward more complex forms, but in response 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. Further, for the taller buildings, the majorities are composed of interactive elements in three-dimensional arrays.The method of combining these elements is the very essence of the design process 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. This 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 structural engineer, while only fine structure, not great architecture, can be developed without the genius and the leadership of a talented architect. In any event, the best of both isneeded to formulate a truly extraordinary design of a high-rise building.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.Moment-Resisting FramesPerhaps the most commonly used system in low-to medium-rise buildings, the moment-resisting frame, is characterized by linear horizontal and vertical members 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 buildings, the system is likely to be found inappropriate for a stand-alone system, this because of the difficulty in mobilizing sufficient stiffness under lateral forces.Analysis can be accomplished by STRESS, STRUDL, or a host of other appropriate computer programs; analysis by the so-called portal method of the cantilever method has no place in today’s technology.Because of the intrinsic flexibility of the column/girder intersection, and 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 realistic appraisal in-joint deformation is essential.Braced Frame sThe braced frame, intrinsically stiffer than the moment –resisting frame, finds also greater application to higher-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 buildings and as a stand-alone system in low-to medium-rise buildings.While the use of structural steel in braced frames is common, concrete frames are more likely to be of the larger-scale variety.Of special interest in areas of high seismicity is the use of the eccentric braced frame.Again, analysis can be by STRESS, STRUDL, or any one of a series of two –or three dimensional analysis computer programs. And again, center-to-center dimensions are used commonly in the preliminary analysis.Shear wallsThe shear wall is yet another step forward along 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 functions.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 system, 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 system, which does have the needed width, is in the exterior walls of building, where the requirement for windows is kept small.Structural steel shear walls, generally stiffened against buckling by a concrete overlay, have found application 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 sys tem has the further advantage of having high ductility a feature of particular importance in areas of high seismicity.The analysis of shear wall systems is made complex because of the inevitable 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 coupling, of shear walls.Framed or Braced TubesThe concept of the framed or braced or braced tube erupted into the technology with the IBM Building in Pittsburgh, but was followed 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 surface more or less cylindrical in nature, but of nearly any plan configuration. Because those columns that resist lateral forces are placed as far as possible from the cancroids of the system, the overall moment of inertia is increased and stiffness is very high.The analysis of tubular structures is done using 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.The presence of shear lag, detected 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 techniques 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 trusses interfere with nearly every building function associated with the outside wall; the trusses are placed often at mechanical floors, mush to the disapproval of the designers of the mechanical systems. Nevertheless, as a cost-effective structural system, the belt truss works well and will likely find continued approval from designers. Numerous studies have sought to optimize the location of these trusses, with the optimum location very dependent on the number of trusses provided. Experience would indicate, however, that the location of these trusses is provided by the optimization of mechanical systems and by aesthetic considerations, as the economics of the structural system is not highly sensitive to belt truss location.Tube-in-Tube StructuresThe tubular framing system mobilizes every column in the exterior wall in resisting over-turning and shearing forces. The term‘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 to 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, while the other could be braced.In considering this system, is important 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 bending 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 tube, the shear component of deflection is associated with the axial deformation of diagonals while the flexural component of deflection is associated with the axial shortening and lengthening of columns.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 substantiallylarger 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 in the outer ring. This seeming anomaly is associated with differences in the shearing component of stiffness between the two systems. This is easiest to under-stand where the inner tube is conceived as a braced (i.e, shear-stiff) tube while the outer tube is conceived as a framed (i.e, shear-flexible) tube.Core Interactive StructuresCore interactive structures are a special case 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 Steel 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 straight line from the “hat”structure. Note that the exterior columns would be improperly modeled if they were considered as systems passing in a straight line from the “hat”to the foundations; these columns are perhaps 15% stiffer as they follow the elastic curve of the braced core. Note also that the axial forces associated with the lateral forces in the inner columns change from tension to compression over the height of the tube, with the inflection point at about 5/8 of the height of the tube. The outer columns, of course, carry the same axial force under lateral load for the full height of the columns because the columns because the shear stiffness of the system is close to zero.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 is an example of an astonishing array of interactive elements:1.The structural system is 94 ft (28.6m) wide, 196ft(59.7m) long, and 601ft (183.3m) high.2.Two inner tubes are provided, each 31ft(9.4m) by 40 ft (12.2m), centered 90 ft (27.4m) apart in the long direction of the building.3.The inner tubes are braced in the short direction, but with zero shear stiffness in the long direction.4. A single outer tube is supplied, which encircles the building perimeter.5.The outer tube is a moment-resisting frame, but with zero shear stiffness for the center50ft (15.2m) of each of the long sides.6. A space-truss hat structure is provided at the top of the building.7. A similar space truss is located near the bottom of the building8.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.Cellular structuresA 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 basic 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 the weaknesses of the system.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 is given by the expression△=ΣfL/EFor buildings of 12 ft (3.66m) floor-to-floor distances and an average compressive stress of 15 ksi (138MPa), the shortening 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, say, 50stories high and an adjacent cell is, say, 100stories high, those columns near the boundary between .the two systems need to have this differential deflection reconciled.Major structural work has been found to 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 deflections of columns in close proximity with the post-tensioning of the shorter column simulating the weight to be added on to adjacent, higher columns。
鱼腹式连续钢箱梁纵向剪力滞规律分析
简支薄壁箱梁自由振动的摄动法解析解
简支薄壁箱梁自由振动的摄动法解析解潘旦光;丁民涛;陈钒【摘要】为研究简支薄壁箱梁中剪力滞效应对结构动力特性的影响，基于模态摄动法提出了一种求解薄壁箱梁自由振动的新方法。
该方法以相同跨度等截面欧拉梁的频率和模态为Ritz基函数，将箱梁自由振动的微分方程组转化为一组非线性代数方程进行求解。
对于简支箱梁，可进一步将代数方程组简化为一元二次方程，从而得到精确的特征值和特征向量。
在此基础上，利用所得箱梁振动模态的解析表达式，提出了模态剪力滞系数的概念，从而建立了箱梁固有频率和剪力滞效应之间的关系。
随后研究了模态剪力滞系数随跨宽比、翼板抗弯刚度和截面抗弯刚度之比的变化规律。
计算结果表明：简支梁腹板处剪力滞系数最大且大于1，为正剪力滞效应；随着模态阶数的增加、跨宽比的减小和翼板抗弯刚度和截面抗弯刚度之比的增大，剪力滞效应呈现增大的趋势。
%To investigate the shear lag effect of thin⁃walled box girder on the dynamic characteristics, a new approach was developed to analyze the free vibration of box girders based on the modal perturbation method. The natural modes of vibration of the corresponding prismatic Euler beam with the same length and boundary conditions were used as Ritz base functions. Then, the new method can transform the set of partial differential equations governing the transverse vibration of the box girder into a set of nonlinear algebraic equations. For thesimply⁃supported beams, the algebraic equations were further simplified as quadratic equation with one unknown, so that the exact eigenvalues and eigenvectors could be obtained. The analytical vibration modes of the box girder were used to propose the shear lag coefficients of modes,which illustrates the relationship between the natural frequency and shear lag effect. Numerical examples were used to analyze the shear lag coefficients of modes varying with the ratio between span and width, the second moment of area ratio between flange slab and the full section. The numerical results show that the maximum shear lag coefficients of modes located at the web of the box girder are greater than 1, which are positive shear lag effect. As the increase of modes order, the reduction of the ratio between span and width and the increase of the second moment of area ratio between flange slab and the full section, the shear lag coefficientsand shear lag effect would be more remarkable.【期刊名称】《哈尔滨工业大学学报》【年(卷),期】2016(048)012【总页数】6页(P56-61)【关键词】箱梁;剪力滞;模态摄动法;动力特性;解析解【作者】潘旦光;丁民涛;陈钒【作者单位】北京科技大学土木工程系，北京100083;北京科技大学土木工程系，北京100083;北京科技大学土木工程系，北京100083; 中电建路桥集团有限公司，北京100048【正文语种】中文【中图分类】TU311.3;U448.21薄壁箱梁具有良好的抗弯和抗扭性能在现代桥梁中得到广泛应用.当箱梁发生竖向位移时，由于翼板中剪力滞后的影响引起翼板纵向应力沿横向分布不均匀，而存在剪力滞效应[1-5].对于箱梁自由振动而言，剪力滞效应引起箱梁的动力特性发生显著变化.对于不同的跨高比，可忽略箱梁部分影响因素而建立相应的自由振动方程.当跨高比较大时，甘亚南等[6]、吴有俊等[7]以欧拉梁为基础，忽略了剪力滞引起纵向位移的惯性影响，分别研究了剪力滞引起的弹性势能对梁动力特性的影响.对于跨高比小的箱梁，此时截面的剪切变形和转动惯量影响不可忽略.张永健等[8]分析了剪切变形和剪力滞效应对简支箱梁自振频率的影响.甘亚南等[9-10] 基于Timoshenko梁理论讨论了剪力滞效应对等截面箱梁自振频率的影响.周旺保等[11]研究了剪力滞、剪切变形、转动惯量、滑移效应对钢-混凝土组合箱型梁动力特性的影响.在上述箱梁自由振动的求解过程中，大部分是基于分离变量法得到箱梁自由振动的解析解.由于箱梁的自由振动控制方程是一个微分方程组，因此自振频率超越方程及模态函数很复杂.从梁的振动方程角度看，剪力滞效应对梁振动的影响可看作是欧拉梁振动方程修正后形成的系统，则可以利用摄动法求解箱梁自由振动.楼梦麟[12]首先利用模态摄动法，将变系数微分方程的求解问题转化为代数方程组进行求解，从而简化了特征方程的求解.随后，楼梦麟等[13]、潘旦光等[14]将模态摄动法应用于变截面梁的振动.潘旦光等[15-16]进一步将模态摄动法推广到变截面Timoshenko梁振动方程的求解.本文将利用模态摄动法的基本思想，研究箱梁的自振频率和振型的简化分析方法.在此基础上，根据箱梁位移和弯矩的关系，推导了箱梁自由振动的模态剪力滞系数，并分析跨宽比和翼缘板的刚度占梁总刚度百分比等对梁模态剪力滞系数的影响.图1所示的矩形薄壁箱型梁，若梁的竖向位移为w (x, t)，上下翼缘板的纵向位移函数为vi(x, y, t)，且假定vi(x, y, t)可表示为式中：u(x, t)为翼缘板剪切转角的最大差值，x、y和z分别表示顺梁方向、垂直于梁方向和竖向，b为箱室净宽的一半，hi截面形心到顶、底板的距离，i分别取顶、底板.基于欧拉梁理论，梁的动能T为梁的势能V为式中：ρ、E、G、A分别为箱梁的密度、弹性模量、剪切模量和截面面积.I为截面的转动惯量，Is为顶板和底板的转动惯量.根据Hamilton原理可得梁的自由振动方程为：若式(4)所对应的第j阶模态的特征值为，特征向量为和，则第j阶模态的特征方程为：忽略剪力滞效应后，具有相同跨度欧拉梁第j阶模态的控制方程为当梁为简支梁时，与式(6)特征方程相对应的特征值和模态为直接模态摄动法的基本思想是把式(5)考虑剪力滞效应薄壁箱梁的特征方程看成式(6)所表示的等截面欧拉梁经过参数修改所得到的新系统，这个新系统的主模态函数以及特征值可以用等截面欧拉梁的模态特征经过简单的摄动分析求解.则可以假设：从理论上来说，式(6)中梁有无穷多个主模态函数，即式(8)中n应该趋向于无穷.但是在实际计算时，通常只需要考虑有限个低阶模态进行近似的计算就可以满足要求.当解出Δλj，pkj，qkj这2n个未知数，即可计算箱梁的第j阶特征值及其对应的主模态函数.将(8)式代入(5)式可得：在方程(9)两边同时乘以，然后沿全长积分，根据欧拉梁的模态正交性，化简后可得：式(10)中：式中δij为Kronecker符号.依次取i为1, 2, …，n，重复利用式(10)可得2n个代数方程.将2n个代数方程写成矩阵形式：式中：C11、C12、C21、C22、D11、D22都为n阶方阵，p、q、M、N为n阶向量.各个方阵和向量的元素分别为：显然C11、C12、C21、C22、D11、D22都为对角矩阵，Mi=0，Ni=0(i≠j)，因此，p、q只有第j个元素不为零，则式(11)只剩下两个方程.由此可得：将式(12b)代入式(12a)可得式中为瑞纳斯常数.当Is=0，α=1，即梁不存在翼板而没有剪力滞效应，此时，梁的动力特性等于欧拉梁的动力特性.因此，式(13)中等式右边第二项为剪力滞效应所引起梁动力特性变化.当Is>0时，α>1，由此使j<λj，这表明剪力滞使梁的频率降低.对于等式右边第二项分母中的项是剪力滞所引起的惯性效应.若忽略剪力滞的惯性效应，即为吴有俊等[7]所得箱形简支梁动力特性的计算公式.由式(13)可得j的两个根，其数值小的根为式中.将式(14)代入式(12b)可得qjj的解为由式(14)可知，采用直接模态摄动法计算等截面箱梁振动特性式的计算结果与式(8)中n的选取无关.当n趋近于无穷时，式(8)中代表了全模态的展开，是精确的坐标变换.所以式(14)和式(15)所得的特征值和特征向量是简支箱梁动力特性的精确解. 由式(8)和(15)可知，箱形简支梁的模态为则第j阶模态翼板中的正应力为式(16)模态位移下，箱梁任意截面的弯矩为在式(18)弯矩作用下，按欧拉梁理论所得翼板的正应力为根据剪力滞系数的定义，由式(15)～(19)，可得到模态的剪力滞系数为由式(20)可知，对简支梁而言，剪力滞系数和x无关，即纵向各截面的剪力系数相同.箱梁翼板和腹板交角处的剪力滞系数为箱梁翼板和腹板交角处的剪力滞系数为最大剪力滞系数.最大剪力滞系数用于度量箱梁剪力滞影响的大小.式(21)表明单箱单室截面翼板和腹板交角处的剪力滞系数等于欧拉梁特征值和剪力滞影响下箱梁特征值的比.这表明对于箱梁自由振动而言，最大剪力滞系数既反映了箱梁剪力滞的大小，又反映了由于剪力滞引起梁自振频率的变化.最大剪力滞系数越大，梁的自振频率降低越多.式(14)所得的特征值和特征向量是在忽略剪切变形和转动惯量影响后所得的精确解.为验证本文方法计算结果的精度，下面对箱型截面梁分别进行欧拉梁理论，本文方法和有限元方法的自由振动计算.其中有限元方法是采用壳单元的分析结果.箱梁截面的材料参数为：E=35 GPa，G=15 GPa.箱梁截面形式和坐标如图(1)所示，各部位的尺寸为：t=0.25 m，b=3.55 m，h=2 m.当Is/I=0.88时，腹板宽度为tw=0.4 m；当Is/I=0.94时，腹板宽度为tw=0.2 m，同时选取梁的跨度为40、30和20 m.不同方法所得箱梁的前三阶的自振频率见表1.由计算结果可知本文的方法由于忽略了转动惯量、剪切变形以及翼缘板振动的影响而与有限元结果有一定差别，但是误差并不大，可满足工程需要.同时，本文方法所得各阶模态的频率都小于欧拉梁的频率，且模态阶数越高，两者的频率相差越大，这表明剪力滞对梁的自由振动有显著影响.以跨宽比(l/2b)和翼板相对转动惯量(Is/I)为参数讨论箱梁自由振动时，模态剪力滞系数和梁自振频率的变化规律.参数分析时箱梁截面的跨度和腹板厚度为变量，其余参数同前.5.1 模态剪力滞系数的横向分布箱梁顶板的剪力滞分布沿箱梁中轴线左右对称，因此只画出一半的剪力滞系数.取梁的跨度为40 m，前4阶模态箱梁上翼板的剪力滞系数见图2.由计算结果可知：1)腹板附近剪力滞系数最大，且≥1，这表明简支梁自由振动时，梁的剪力滞效应为正剪力滞效应.事实上，由式(13)可知，剪力滞使梁的特征值降低，因此，≥1是剪力滞使梁振动频率降低的必然结果；2) 前四阶模态的最大剪力滞系数分别为1.045、1.176、1.389和1.706.这表明随着振动阶数的增加，剪力滞后效应越来越明显.剪力滞使箱梁前四阶模态的频率分别降低了2.2%、7.8%、15.1%和23.4%.因此，对于有高阶模态参与振动的箱梁，必须考虑剪力滞效应的影响.5.2 不同参数对最大剪力滞系数的影响简支梁的最大剪力滞系数随l/2b和Is/I的变化曲线见图3、4.由图可知:1)l/2b越大，γe越小.因此相同截面情况下，梁跨度越大，剪力滞影响越小.对于第一阶模态，当l/2b >4时，γe<1.05.因此，对于仅需考虑第一阶模态振动的箱梁可忽略剪力滞效应的影响；2)Is/I反映翼缘板刚度占总刚度的百分比.Is/I显著地影响箱梁的剪力滞后效应，由此也显著影响箱梁自振频率.Is/I越大，γe越大.这说明Is/I比值越大，频率降低越多.但是，对于第一阶模态而言，Is/I<0.9时，γe<1.05，此时剪力滞影响很小，可以忽略不计.但是对于2阶以上模态，当Is/I >0.4时，则γe>1.05，此时，剪力滞影响不可忽略.本文基于欧拉梁的特征值和模态，利用模态摄动法将箱梁的自由振动方程组转化为非线性代数方程组来求解，从而简化计算.应用于等截面简支梁时，可得到箱梁主频率和模态的精确解.基于箱型梁的模态，进一步推导了模态剪力滞系数.由理论分析和数值计算可得如下结论：1)对于简支梁而言，模态剪力滞系数沿梁轴线方向不变.且单箱单室截面翼板和腹板交角处的剪力滞系数等于欧拉梁特征值和剪力滞影响下箱梁特征值的比.2) 腹板附近剪力滞系数最大，且≥1，这表明简支箱梁自由振动时，梁的剪力滞效应为正剪力滞效应.3)随着模态阶数的增加，剪力滞效应越来越大，由此导致箱梁高阶模态的自振频率显著降低.4) l/2b越小，Is/I越大，γe越大.当l/2b >4或Is/I <0.9时，γe <1.05.此时，对于仅需考虑第一阶模态振动的箱梁可忽略剪力滞效应的影响.除此以外，剪力滞效应对结构动力反应的影响不可忽略，因此，一旦激振荷载能激起箱梁高阶模态的振动，剪力滞效应将显著地影响结构的动力反应.【相关文献】[1] CHEN Jun, SHEN Shuilong, YIN Zhenyu, et al. Closed-form solution for shear lag with derived flange deformation function [J]. Journal of Constructional Steel Research, 2014, 102(11):104-110.[2] GARA F, LEONI G, DEZI L. A beam finite element including shear lag effect for thetime-dependent analysis of steel-concrete composite decks [J]. Engineering Structures, 2009, 31(8):1888-1902.[3] 郭健，孙炳楠. 型钢-混凝土箱形桥塔的剪力滞后效应分析[J]. 哈尔滨工业大学学报, 2003, 35(增刊):269-271,275. GUO Jian, SUN Bingnan. Analysis of shear lag effect of steel-concrete composite box tower in cable-stayed bridge[J]. Journal of Harbin Institute of Technology, 2003, 35(s): 269-271,275.[4] 王浩, 李爱群, 赵大亮, 等. 润扬悬索桥钢箱梁受力分析及实验研究[J]. 哈尔滨工业大学学报, 2006, 38(7):1062-1064. WANG Hao, LI Aiqun, ZHAO Daliang, et al. FE analysis and experimental study on local stress of steel box girder of runyang suspension bridge [J]. Journal of Harbin Institute of Technology, 2006, 38(7):1062-1064.[5] ZHANG Yuanhai, LIN Lixia. Shear lag analysis of thin-walled box girders based on anew generalized displacement [J]. Engineering Structures, 2014, 61(1):73-83.[6] 甘亚南, 吴亚平, 王根会, 等. 剪力滞效应对简支箱梁自振特性的影响研究[J]. 兰州铁道学院学报，2002, 21(3): 23-25. GAN Y N, WU Y P, WANG G H, et al. Influence of shear lag on the characteristic of free vibration to box girder under simply supported[J]. Journal of Lanzhou Railway Institute, 2002，21(3):23-25 [7] 吴有俊, 罗旗帜, 陈玉骥. 考虑剪力滞效应简支箱梁自振方程的求解[J]. 佛山科学技术学院学报(自然科学版), 2010, 28(2):12-17. WU Youjun, LUO Qizhi, CHEN Yuji. The Solution of free vibration equation to simply-supported box girder considering shear lag effect[J]. Journal of Foshan University (Natural Science Edition), 2010, 28(2): 12-17.[8] 张永健, 黄平明. 一种计入剪力滞及剪切变形效应的箱梁自振频率计算方法[J]. 郑州大学学报(工学版), 2007, 28(1): 51-55. ZHANG Yongjian, HUANG Pingming. A new method to calculate the natural frequencies of simply supported box girder including the effect of shear lag and shear deformation[J]. Journal of Zhengzhou University (Engineering Science), 2007, 28(1): 51-55.[9] 甘亚南, 周广春, 赫中营. 大悬臂板矩形截面箱梁动力反应的分析[J]. 振动与冲击, 2010, 29(11): 61-65. GAN Y N, ZHOU G C, HE Zhongying. Dynamic response analysis for a large cantilever rectangular box girder in consideration of shear lag effect[J]. Journal of Vibration & Shock, 2010, 29(11):61-65.[10]甘亚南, 周广春. 基于能量变分原理的薄壁箱梁自振特性分析[J]. 中国公路学报, 2007,20(1):73-78. GAN Yanan, ZHOU Guangchun. Analysis of free vibration characteristics of thin-walled box girder based on energy variation principle[J]. China Journal of Highway & Transport, 2007, 20(1):73-78.[11]ZHOU Wangbao, JIANG Lizhong, YU Zhiwu. Analysis of free vibration characteristic of steel-concrete composite box-girder considering shear lag and slip [J]. Journal of Central South University, 2013, 20: 2570-2577.[12]楼梦麟. 变参数土层的动力特性和地震反应分析[J]. 同济大学学报, 1997, 25(2)：155-160. LOU Menglin. Dynamic analysis for modal characteristics and seismic response of soil layer with variable properties[J]. Journal of Tongji University, 1997, 25(2)：155-160. [13]楼梦麟, 吴京宁. 复杂梁动力问题的近似分析方法[J]. 上海力学, 1997, 18(3)：234-240. LOU Menglin, WU Jingning. An approach to approximate analysis of dynamic problems of complicated beams [J]. Shanghai Journal of Mechanics, 1997, 18(3): 234～240.[14]张怀静, 潘旦光. 变截面连续梁动力特性的半解析解法[J]. 北京科技大学学报, 2008，30(6)：590-593. ZHANG Huaijing, PAN Danguang. Semi-analytic solution to dynamic characteristics of non-uniform continuous beams[J]. Journal of University of Science and Technology Beijing, 2008, 30(6): 590-593.[15]潘旦光, 楼梦麟. 变截面Timoshenko简支梁动力特性的半解析解[J]. 工程力学,2009, 26(8): 6-9. PAN D G, LOU M L. Semi-analytic solution of dynamic characteristics of non-prismatic timoshenko simply supported beams[J]. Engineering Mechanics, 2009, 26(8):6-9.[16]PAN Danguang, CHEN Genda, LOU Menglin. A modified modal perturbation method for vibration characteristics of non-prismatic Timoshenko beams [J]. Structural Engineering and Mechanics An international Journal, 2011, 40(5): 689-703.。
五层教学楼建筑的设计
五层教学楼建筑的设计内容摘要本设计主要进⾏了结构⽅案中横向框架A，B，C，D轴框架的设计。
在确定框架布局之后，先计算了恒载，活载，风载的等效荷载以及各杆端的内⼒，然后⽤分层法进⾏内⼒分配，然后各层叠加，进⽽求出在⽔平荷载作⽤下的结构内⼒（弯矩、剪⼒、轴⼒）。
接着内⼒组合找出最不利的⼀组或⼏组内⼒组合。
选取最安全的结果计算配筋并绘图。
还进⾏地基设计。
此外还进⾏了结构⽅案中的楼梯的设计。
完成了平台板，梯段板，平台梁等构件的内⼒和配筋计算及施⼯图绘制。
关键词：框架结构设计内⼒组合AbstractThe purpose of the design is to do the anti-seismic design in the longitudinal frames of axis A，B，C，D，E，F. When the directions of the frames is determined, firstly the weight of each floor is calculated .Then the vibrate cycle is calculated by utilizing the peak-displacement method, then making the amount of the horizontal seismic force can be got by way of the bottom-shear force method. The seismic force can be assigned according to the shearing stiffness of the frames of the different axis. Then the internal force in the structure under the horizontal loads can be easily calculated. After the determination of the internal force under the dead and live loads, the combination of internal force can be made by using the Excel software, whose purpose is to find one or several sets of the most adverse internal force of the wall limbs and the coterminous girders, which will be the basis of protracting the reinforcing drawings of the components. The design of the stairs is also be approached by calculating the internal force and reinforcing such components as landing slab, step board and landing girder whose shop drawings are completed in the end.Keywords : frames, structural design, Combine inside the dint⼀.⼯程概况1.建设项⽬名称：辅助教学楼本⼯程建筑功能为公共建筑，使⽤年限为50年；建筑平⾯的横轴轴距为8.1m，纵轴轴距为5.4m和4.5m；内、外墙体材料为陶粒混凝⼟空⼼砌块，外墙装修使⽤乳⽩⾊涂料仿⽯材外墙涂料，内墙装修喷涂乳胶漆，教室内地⾯房间采⽤⽔磨⽯地⾯，教室房间墙⾯主要采⽤⽯棉吸⾳板，门窗采⽤塑钢窗和装饰⽊门。