Study on nonlinear analysis of a highly redundant
cable-stayed bridge
1．Abstract
A comparison on nonlinear analysis of a highly redundant cable-stayed bridge is performed in the study. The initial shapes including geometry and prestress distribution of the bridge are determined by using a two-loop iteration method, i.e., an equilibrium iteration loop and a shape iteration loop. For the initial shape analysis a linear and a nonlinear computation procedure are set up. In the former all nonlinearities of cable-stayed bridges are disregarded, and the shape iteration is carried out without considering equilibrium. In the latter all nonlinearities of the bridges are taken into consideration and both the equilibrium and the shape iteration are carried out. Based on the convergent initial shapes determined by the different procedures, the natural frequencies and vibration modes are then examined in details. Numerical results show that a convergent initial shape can be found rapidly by the two-loop iteration method, a reasonable initial shape can be determined by using the linear computation procedure, and a lot of computation efforts can thus be saved. There are only small differences in geometry and prestress distribution between the results determined by linear and nonlinear computation procedures. However, for the analysis of natural frequency and vibration modes, significant differences in the fundamental frequencies and vibration modes will occur, and the nonlinearities of the cable-stayed bridge response appear only in the modes determined on basis of the initial shape found by the nonlinear computation.
2. Introduction
Rapid progress in the analysis and construction of cable-stayed bridges has been made over the last three decades. The progress is mainly due to developments in the fields of computer technology, high strength steel cables, orthotropic steel decks and construction technology. Since the first modern cable-stayed bridge was built in Sweden in 1955, their popularity has rapidly been increasing all over the world. Because of its aesthetic appeal, economic grounds and ease of erection, the
cable-stayed bridge is considered as the most suitable construction type for spans ranging from 200 to about 1000 m. The world’s longest cable-stayed bridge today is the Tatara bridge across the Seto Inland Sea, linking the main islands Honshu and Shikoku in Japan. The Tatara cable-stayed bridge was opened in 1 May, 1999 and has a center span of 890m and a total length of 1480m. A cable-stayed bridge consists of three principal components, namely girders, towers and inclined cable stays. The girder is supported elastically at points along its length by inclined cable stays so that the girder can span a much longer distance without intermediate piers. The dead load and traffic load on the girders are transmitted to the towers by inclined cables. High tensile forces exist in cable-stays which induce high compression forces in towers and part of girders. The sources of nonlinearity in cable-stayed bridges mainly include the cable sag, beam-column and large deflection effects. Since high pretension force exists in inclined cables before live loads are applied, the initial geometry and the
prestress of cable-stayed bridges depend on each other. They cannot be specified independently as for conventional steel or reinforced concrete bridges. Therefore the initial shape has to be determined correctly prior to analyzing the bridge. Only based on the correct initial shape a correct deflection and vibration analysis can be achieved. The purpose of this paper is to present a comparison on the nonlinear analysis of a highly redundant stiff cable-stayed bridge, in which the initial shape of the bridge will be determined iteratively by using both linear and nonlinear computation procedures. Based on the initial shapes evaluated, the vibration frequencies and modes of the bridge are examined.
3. System equations
3.1. General system equation
When only nonlinearities in stiffness are taken into account, and the system mass and damping matrices are considered as constant, the general system equation of a finite element model of structures in nonlinear dynamics can be derived from the Lagrange’s virtual work principle and written as follows:
K j bαj-∑S j a jα= Mαβqβ”+ Dαβqβ’
3.2. Linearized system equation
In order to incrementally solve the large deflection problem, the linearized system equations has to be derived. By taking the first order terms of the Taylor’s expansion of the general system equation, the linearized equation for a small time (or load) interval is obtained as follows:
MαβΔqβ”+ΔDαβqβ’ +2KαβΔqβ=Δpα- u pα
3.3. Linearized system equation in statics
In nonlinear statics, the linearized system equation becomes
2KαβΔqβ=Δpα- u pα
4. Nonlinear analysis
4.1. Initial shape analysis
The initial shape of a cable-stayed bridge provides the geometric configuration as well as the prestress distribution of the bridge under action of dead loads of girders and towers and under pretension force in inclined cable stays. The relations for the equilibrium conditions, the specified boundary conditions, and the requirements of architectural design should be satisfied. For shape finding computations, only the dead load of girders and towers is taken into account, and the dead load of cables is neglected, but cable sag nonlinearity is included. The computation for shape finding is performed by using the two-loop iteration method, i.e., equilibrium iteration and shape iteration loop. This can start with an arbitrary small tension force in inclined cables. Based on a reference configuration (the architectural designed form), having no deflection and zero prestress in girders and towers, the equilibrium position of the cable-stayed bridges under dead load is first determined iteratively (equilibrium iteration). Although this first determined configuration satisfies the equilibrium conditions and the boundary conditions, the requirements of architectural design are, in general, not fulfilled. Since the bridge span is large and no pretension forces exist in inclined cables, quite large deflections and very large bending moments may appear in the girders and towers. Another iteration then has to be carried out in order
to reduce the deflection and to smooth the bending moments in the girder and finally to find the correct initial shape. Such an iteration procedure is named here the ‘shape iteration ’. For shape iteration, the element axial forces determined in the previous step will be taken as initial element forces for the next iteration, and a new
equilibrium configuration under the action of dead load and such initial forces will be determined again. During shape iteration, several control points (nodes intersected by the girder and the cable) will be chosen for checking the convergence tolerance. In each shape iteration the ratio of the vertical displacement at control points to the main span length will be checked, i.e.,
ε<|span
main points control at nt displaceme vertical | The shape iteration will be repeated until the convergence tolerance ε, say 10-4, is
achieved. When the convergence tolerance is reached, the computation will stop and the initial shape of the cable-stayed bridges is found. Numerical experiments show that the iteration converges monotonously and that all three nonlinearities have less influence on the final geometry of the initial shape. Only the cable sag effect is significant for cable forces determined in the initial shape analysis, and the
beam-column and large deflection effects become insignificant.
The initial analysis can be performed in two different ways: a linear and a
nonlinear computation procedure. 1. Linear computation procedure: To find the equilibrium configuration of the bridge, all nonlinearities of cable stayed bridges are neglected and only the linear elastic cable, beam-column elements and linear constant coordinate transformation coefficients are used. The shape iteration is carried out without considering the equilibrium iteration. A reasonable convergent initial shape is found, and a lot of computation efforts can be saved.
2. Nonlinear computation procedure: All nonlinearities of cable-stayed bridges are taken into consideration during the whole computation process. The nonlinear cable element with sag effect and the beam-column element including stability coefficients and nonlinear coordinate transformation coefficients are used. Both the shape iteration and the equilibrium iteration are carried out in the nonlinear
computation. Newton –Raphson method is utilized here for equilibrium iteration.
4.2. Static deflection analysis
Based on the determined initial shape, the nonlinear static deflection analysis of cable-stayed bridges under live load can be performed incrementwise or iterationwise. It is well known that the load increment method leads to large numerical errors. The iteration method would be preferred for the nonlinear computation and a desired convergence tolerance can be achieved. Newton – Raphson iteration procedure is employed. For nonlinear analysis of large or complex structural systems, a ‘full ’iteration procedure (iteration performed for a single full load step) will often fail. An increment –iteration procedure is highly recommended, in which the load will be incremented, and the iteration will be carried out in each load step. The static deflection analysis of the cable stayed bridge will start from the initial shape
determined by the shape finding procedure using a linear or nonlinear computation.
The algorithm of the static deflection analysis of cable-stayed bridges is summarized in Section 4.4.2.
4.3. Linearized vibration analysis
When a structural system is stiff enough and the external excitation is not too intensive, the system may vibrate with small amplitude around a certain nonlinear static state, where the change of the nonlinear static state induced by the vibration is very small and negligible. Such vibration with small amplitude around a certain nonlinear static state is termed linearized vibration. The linearized vibration is different from the linear vibration, where the system vibrates with small amplitude around a linear static state. The nonlinear static state qαa can be statically determined by nonlinear deflection analysis. After determining qαa , the system matrices may be established with respect to such a nonlinear static state, and the linearized system equation has the form as follows:
MαβA qβ”+ DαβA qβ’+ 2KαβA qβ=pα(t)- TαA
where the superscript ‘A’denotes the quantity calculated at the nonlinear static state a . This equation represents a set of linear ordinary differential equations of second q
α
order with constant coefficient matrices MαβA, DαβA and 2KαβA. The equation can be solved by the modal superposition method, the integral transformation methods or the direct integration methods.
When damping effect and load terms are neglected, the system equation becomes
MαβA qβ” + 2KαβA qβ=0
This equation represents the natural vibrations of an undamped system based on the nonlinear static state qαa The natural vibration frequencies and modes can be obtained from the above equation by using eigensolution procedures, e.g., subspace iteration methods. For the cable-stayed bridge, its initial shape is the nonlinear static state qαa . When the cable-stayed bridge vibrates with small amplitude based on the initial shape, the natural frequencies and modes can be found by solving the above equation.
4.4. Computation algorithms of cable-stayed bridge analysis
The algorithms for shape finding computation, static deflection analysis and vibration analysis of cable-stayed bridges are briefly summarized in the following. 4.4.1. Initial shape analysis
1. Input of the geometric and physical data of the bridge.
2. Input of the dead load of girders and towers and suitably estimated initial forces in cable stays.
3. Find equilibrium position
(i) Linear procedure
?Linear cable and beam-column stiffness elements are used.
?Linear constant coordinate transformation coefficients a j
αare used.
by assembling element stiffness ?Establish the linear system stiffness matrix K
αβ
matrices.
?Solve the linear system equation for q
α(equilibrium position).
?No equilibrium iteration is carried out.
(ii) Nonlinear procedure
?Nonlinear cables with sag effect and beam-column elements are used. ?Nonlinear coordinate transformation coeffi- cients a j
α; a jα，βare used.
.
?Establish the tangent system stiffness matrix 2K
αβ
?Solve the incremental system equation for △q
α.
?Equilibrium iteration is performed by using the Newton–Raphson method.
4. Shape iteration
5. Output of the initial shape including geometric shape and element forces.
6. For linear static deflection analysis, only linear stiff-ness elements and transformation coefficients are used and no equilibrium iteration is carried out.
4.4.3. Vibration analysis
1. Input of the geometric and physical data of the bridge.
2. Input of the initial shape data including initial geometry and initial element forces.
3. Set up the linearized system equation of free vibrations based on the initial shape.
4. Find vibration frequencies and modes by sub-space iteration methods, such as the Rutishauser Method.
5. Estimation of the trial initial cable forces
In the recent study of Wang and Lin, the shape finding of small cable-stayed bridges has been performed by using arbitrary small or large trial initial cable forces. There the iteration converges monotonously, and the convergent solutions have similar results, if different trial values of initial cable forces are used. However for large cable-stayed bridges, shape finding computations become more difficult to converge. In nonlinear analysis, the Newton-type iterative computation can converge, only when the estimated values of the solution is locate in the neighborhood of the true values. Difficulties in convergence may appear, when the shape finding analysis of cable-stayed bridges is started by use of arbitrary small initial cable forces suggested in the papers of Wang et al. Therefore, to estimate a suitable trial initial cable forces in order to get a convergent solution becomes important for the shape finding analysis. In the following, several methods to estimate trial initial cable forces will be discussed.
5.1. Balance of vertical loads
5.2. Zero moment control
5.3. Zero displacement control
5.4. Concept of cable equivalent modulus ratio
5.5. Consideration of the unsymmetry
If the estimated initial cable forces are determined independently for each cable stay by the methods mentioned above, there may exist unbalanced horizontal forces on the tower in unsymmetric cable-stayed bridges. Forsymmetric arrangements of the cable-stays on the central (main) span and the side span with respect to the tower, the resultant of the horizontal components of the cable-stays acting on the tower is zero, i.e., no unbalanced horizontal forces exist on the tower. For unsymmetric cable-stayed bridges, in which the arrangement of cable-stays on the central (main) span and the side span is unsymmetric, and if the forces of cable stays on the central span and the side span are determined independently, evidently unbalanced horizontal forces will
exist on the tower and will induce large bending moments and deflections therein. Therefore, for unsymmetric cable-stayed bridges, this problem can be overcome as follows. The force of cable stays on the central (main) span T i m can be determined by the methods mentioned above independently, where the superscript m denotes the main span, the subscript I denotes the ith cable stay. Then the force of cable stays on the side span is found by taking the equilibrium of horizontal force components at the node on the tower attached with the cable stays, i.e., T i m cosαi= T i s cosβi, and T i s = T i m cosαi/ cosβi, where αi is the angle between the ith cable stay and the girder on the main span, andβi, angle between the ith cable stay and the girder on the side span.
6. Examples
In this study, two different types of small cable-stayed bridges are taken from literature, and their initial shapes will be determined by the previously described shape finding method using linear and nonlinear procedures. Finally, a highly redundant stiff cable-stayed bridge will be examined. A convergence tolerance e =10-4 is used for both the equilibrium iteration and the shape iteration. The maximum number of iteration cycles is set as 20. The computation is considered as not convergent, if the number of the iteration cycles exceeds 20.
The initial shapes of the following two small cable stayed bridges in Sections 6.1 and 6.2 are first determined by using arbitrary trial initial cable forces. The iteration converges monotonously in these two examples. Their convergent initial shapes can be obtained easily without difficulties. There are only small differences between the initial shapes determined by the linear and the nonlinear computation. Convergent solutions offer similar results, and they are independent of the trial initial cable forces.
7. Conclusion
The two-loop iteration with linear and nonlinear computation is established for finding the initial shapes of cable-stayed bridges. This method can achieve the architecturally designed form having uniform prestress distribution, and satisfies all equilibrium and boundary conditions. The determination of the initial shape is the most important work in the analysis of cable-stayed bridges. Only with a correct initial shape, a meaningful and accurate deflection and/or vibration analysis can be achieved. Based on numerical experiments in the study, some conclusions are summarized as follows:
(1). No great difficulties appear in convergence of the shape finding of small cable-stayed bridges, where arbitrary initial trial cable forces can be used to start the computation. However for large scale cable-stayed bridges, serious difficulties occurred in convergence of iterations.
(2). Difficulties often occur in convergence of the shape finding computation of large cable-stayed bridge, when trial initial cable forces are given by the methods of balance of vertical loads, zero moment control and zero displacement control. (3). A converged initial shape can be found rapidly by the two-loop iteration method, if the cable stress corresponding to about 80% of E eq=E value is used for the trial initial force of each cable stay in the main span, and the trial force of the cables in side spans is determined by taking horizontal equilibrium of the cable forces acting
on the tower.
(4). There are only small differences in geometry and prestress distributionforces. The iteration converges monotonously in these two examples. Their convergent initial shapes can be obtained easily without difficulties. There are only small differences between the initial shapes determined by the linear and the nonlinear computation. Convergent solutions offer similar results, and they are independent of the trial initial cable forces.
7. Conclusion
The two-loop iteration with linear and nonlinear computation is established for finding the initial shapes of cable-stayed bridges. This method can achieve the architecturally designed form having uniform prestress distribution, and satisfies all equilibrium and boundary conditions. The determination of the initial shape is the most important work in the analysis of cable-stayed bridges. Only with a correct initial shape, a meaningful and accurate deflection and/or vibration analysis can be achieved. Based on numerical experiments in the study, some conclusions are summarized as follows:
(1). No great difficulties appear in convergence of the shape finding of small
cable-stayed bridges, where arbitrary initial trial cable forces can be used to start the computation. However for large scale cable-stayed bridges, serious difficulties occurred in convergence of iterations.
(2). Difficulties often occur in convergence of the shape finding computation of large cable-stayed bridge, when trial initial cable forces are given by the methods of balance of vertical loads, zero moment control and zero displacement control. (3). A converged initial shape can be found rapidly by the two-loop iteration method, if the cable stress corresponding to about 80% of E eq=E value is used for the trial initial force of each cable stay in the main span, and the trial force of the cables
in side spans is determined by taking horizontal equilibrium of the cable forces acting on the tower.
(4). There are only small differences in geometry and prestress distribution between the results of initial shapes determined by linear and nonlinear procedures.
(5). The shape finding using linear computation offers a reasonable initial shape and saves a lot of computation efforts, so that it is highly recommended from the point of view of engineering practices.
(6). In small cable-stayed bridges, there are only small difference in the natural frequencies based on initial shapes determined by linear and nonlinear computation procedures, and the mode shapes are the same in both cases.
(7). Significant differences in the fundamental frequency and in the mode shapes of highly redundant stiff cable stayed bridges is shown in the study. Only the vibration modes determined by the initial shape based on nonlinear procedures exhibit the nonlinear cable sag and beam-column effects of cable-stayed bridges, e.g., the first and third modes of the bridge are dominated by the transversal motion of the tower, not of the girder. The difference of the fundamental frequency in both cases is about 12%. Hence a correct analysis of vibration frequencies and modes of cable-stayed bridges can be obtained only when the ‘correct’initial shape is determined by
nonlinear computation, not by the linear computation.
高度超静定斜拉桥的非线性分析研究
1.摘要
一个拉索高度超静定的斜拉桥的非线性分析比较在研究中被实行。包括桥的几何学和预应力分配的初始形状是使用双重迭代的方法决定的,也就是,一个平衡迭代和一个形状迭代。对于开始的形状分析，一个线性和一个非线性计算程序被建立。以前斜拉桥所有非线性被忽视，而且形状迭代是不考虑平衡而实行的。后来桥的所有非线性被考虑到，而且平衡和形状的重复都实行了。基于收敛于一点的起始形状由不同的程序决定,自振频率和震动模态也被详细地研究。数字的结果表明收敛于一点的起始形状能由二个环的重复方法快速地得到,合理的起始形状能由线性的计算程序决定，而且那样许多计算工作将被节省。在由线性的和非线性计算程序决定的结果之间的几何学和预应力分配中只有很小的不同。然而，对于自振频率和震动模态的分析来说，基本的频率和震动模态将会有显著的不同，而且斜拉桥反应的非线性只出现在由非线性计算得到的初始形状的基础之上的模态中。
2.序言
在过去的三十年中斜拉桥分析和建筑中取得了飞速的进步。进步主要是由于计算机技术的领域发展,高强度的钢拉索,正交异性钢板和建筑技术产生的。既然第一座现代的斜拉桥1955年在瑞典被建造，他们的名声在全世界得到快速地增长。因为它的直立美学的外观，经济原因和便于直立，斜拉桥被认为是跨径范围从200m到大约1000m的最合适的建筑类型。世界上现在最长的斜拉桥是日本的横跨岛海、连接本州四国的多多罗桥。多多罗斜拉桥在1999年5月1日被开通，它有890m的一个中央跨径和1480m的总跨度。一座斜拉桥由三个主要的成分所组成，也就是主梁、索塔和斜拉索。主梁在沿纵向方向由拉索弹性支撑以使主梁能跨越一个更长的距离而不需要中间桥墩。主梁的永久荷载和车辆荷载通过拉索传递给索塔。很大的拉力存在于拉索中减小了索塔中大部分和梁的一部分压力。斜拉桥的非线性的来源主要地包括拉索下垂,梁柱的偏压和大的偏转效应。因为在未施加活载前拉索中存在高度预应力，斜拉桥的初始形状和预应力由每条拉索决定。他们不能够被独立地看成是传统的钢或者是高强混凝土桥。因此开始的形状必须被在桥的分析之前正确的决定。只有基于正确的起始形状才能得到一个正确的偏转和震动分析。这篇论文的目的要提供一个高度冗余的斜拉桥的非线性分析的比较，桥的开始形状将会由线性和非线性计算程序迭代来决定。基于开始的形状计算,桥的震动频率和模态被确定。
3. 系统方程
3.1 一般的系统方程
当只有非线性在刚体中被考虑到，而且系统的衰减矩阵被认为是恒定的时候,在非线性动力学中结构的一个有限元模型才能从虚工作原则中得到，如下:
K j bαj-∑S j a jα= Mαβqβ”+ Dαβqβ’
3.2 线性化系统方程
为了要不断的解决更大的偏转问题,线性化系统的方程必需用到。通过泰勒的一般方程的扩展的最早的条目，对于一个小的时间（或荷载）间隔的线性化的方程便得到，如下：
MαβΔqβ”+ΔDαβqβ’ +2KαβΔqβ=Δpα- u pα
3.3 在静力学中的线性化系统方程
在非线性静力学中，线性化系统方程变成：
2KαβΔqβ=Δpα- u pα
4．非线性分析
4.1. 起始形状分析
斜拉桥的初始形状提供了几何学的结构和桥在主梁和索塔的恒载、斜拉索的拉力作用下的预应力分配。作用的平衡条件，指定的边界条件和建筑的设计需求应该被满足。因为计算的形状,主梁和索塔的永久荷载必须被考虑，拉索的自重被疏忽，而且拉索下垂的非线性应包括在内。形状的计算通过使用二重迭代的方法运行,也就是,平衡重复和形状重复循环。这能用拉索中的任意小的张力开始。基于参考结构 (建筑设计形式)，没有歪斜和零的预应力在主梁和索塔中,斜拉桥平衡位置在恒载作用下是由迭代首先确定的(平衡迭代)。虽然首先决定结构的是使平衡情况和边界情况得到满足，但是建筑的设计需求大体上没有得到实现。因为桥的跨径是很大的而没有预应力存在斜拉索中,相当大的偏转和非常大的弯矩可能在主梁和索塔中出现。那么另外的一个迭代有必要执行来减少偏转和使主梁的弯矩平滑并最后找出正确的初始形状。如此的一个迭代程序在这里命名为‘形状迭代’。对于形状迭代,在先前步骤中确定的基本的轴线力将会被作为下个重复采取的初始基本力,这样一个新的平衡结构在恒载和这个初始力下再次被确定。在形状迭代的时候，一些控制点(主梁和拉索连接的点)将会被选择检验应力集中。在每次形状迭代过程中，主跨的控制点的垂直位移比率将会被检验。也就是,
控制点的垂直位移
ε
|
<|
主跨
形状迭代将会重复直到应变可以达到所说的10-4。当应变达到的时候, 计算将会停止而斜拉桥的初始形状就找到了。数字的实验表明重复收敛于一点是没什么作用的，并且所有的三个非线性对最后的几何初始形状有比较少的影响。只有拉索下垂作用在确定初始形状分析中有显著作用，而偏压柱和大的偏转效应变则无关重要。
开始的分析能以二种不同的方式被实行: 一个线性和一个非线性计算程序。
(1) 线性的计算程序:为了要找到桥的平衡结构,斜拉桥的所有非线性因素被疏忽，而只是线性的弹性拉索、梁单元、同等的线形的变形系数被使用。形状迭代是不考虑平衡迭代而实行的。合理的收敛于一点的起始形状被得到，而且许多计算的工作能被节省。
(2) 非线性计算程序:斜拉桥所有的非线性因素在整个的计算程序中被考虑。非线性拉索元素的下沉作用、主梁元素的稳定系数和非线性变形调整系数被应用。形状的迭代和平衡迭代都在非线性计算中实行。牛顿-瑞普生方法在这里被用于平衡迭代。
4.2 静态偏转分析
基于确定的起始形状,斜拉桥在活载作用下的非线性静态偏转分析可通过模数或迭代运行。荷载模数方法导致很大的数字错误是广为人知的。迭代方法比较适于非线性计算，而且需要的应变应能被达到。牛顿- 瑞普生的迭代程序将被
使用。因为非线性分析较大或复杂的结构系统,一个‘完整’的迭代程序(重复为一个单一全部荷载运行步骤)将会时常失败。一个模数-迭代程序高度地被推荐,荷载将会被增加，而且重复将会在每个荷载步骤中实行。斜拉桥的静态偏转分析将会从使用线性或非线性计算程序决定的初始形状开始。斜拉桥静态的偏转分析的运算法则在第4.4.2节中被概述。
4.3. 线性振动分析
当一个结构系统是足够稳固而且外部的刺激不是太强烈,系统可能以一个确定的非线性的静态系数作一个小振幅振动，由振动引起的非线性静态系数的变化是很小的和可以忽略的。这种以一个非线性静态系数以一个小振幅的振动被称作线性化振动。线性化振动不同于线性振动，系统用很小的振幅以一个线性静态系
数振动。非线性静态系数q
αa能由非线性偏转分析决定。在决定q
α
a之后，系统
矩阵可能被建立有关于如此的一个非线性静态系数，线性化系统的等式如下所示：
MαβA qβ”+ DαβA qβ’+ 2KαβA qβ=pα(t)- TαA
上面的上标字母‘A' 代表在非线性静态系数q
α
a被计算的数量。这个等式用恒
定系数矩阵M
αβA、D
αβ
A、2K
αβ
A表现第二的次序一组线性的一般差别的等式。
这个等式能被模型的重叠方法，整体的变形方法或直接的整合方法解答。
当减幅效应和荷载限制被忽略的时候,系统等式变成：
MαβA qβ” + 2KαβA qβ=0
这个等式表现基于非线性静态系数qαa的不减幅的系统天然振动。天然振动的频率和模态可以从上面的等式运用程序，举例来说子空间重复方法来得到。对于斜拉桥,它的起始形状是非线性静态系数q
α
a。斜拉桥由于以开始的形状为基础小振幅振动的时候,天然的频率和模态能被找到来解决上述的等式。
4.4. 斜拉桥计算运算法则分析
斜拉桥的形状的确定计算、静态偏转分析和振动分析的计算法则简短的概述如下。
4.4.1 起始形状分析
1. 桥的几何和实际的数据输入。
2. 主梁和索塔的恒载的输入而且适当地估计了起始拉索中的受力。
3. 确定平衡位置
(i)线性的程序
o 运用线性的拉索和主梁刚性单元。
o 运用线性的恒定变形调整系数a j
α。
o 建立线性系统刚度矩阵K
αβ
通过排列元素的刚度矩阵。
o 求解线性等式得到q
α。(平衡位置)
o 没有平衡的迭代被实行。
(ii)非线性程序
o 非线性下垂效应的拉索和主梁单元被使用。
o 非线性变形调整系数a j
α; a jα，β被使用。
o 建立接触的系统刚度矩阵2K
αβ
。
o 求解增量系统的等式以得到△q
α。
o 平衡迭代使用牛顿-瑞普生方法运行△q
α。
4. 变形迭代。
5. 包括几何形状和基本力的初始的形状输出。
6. 对于线性偏转分析，只有线性刚度单元和变形系数被采用且没有平衡迭代的实行。
4.4.3. 振动分析
1. 桥的几何的和物理的数据输入。
2. 包括开始的几何和开始单元常受力的初始形状数据的输入。
3. 建立以初始形状的自由振动的线性化系统等式。
4. 运用子空间重复方法得到振动频率和模态,例如Rutishauser方法。
5. 初始拉索受力估算：
在王教授和林教授的最近研究中,小型的斜拉桥的通过任意小或任意大试验初始拉索应力来实现。如果不同的初始拉索受力试验评价被采用，在那里重复单调的迭代，而最后的结论有相似的结果。然而对于大型斜拉桥，确定形状的计算变得更困难以达到一致。在非线性分析中，牛顿-瑞普生类型迭代计算能收敛到一点,只有当解决的被估计的价值是在真正的价值附近时才能实现。当斜拉桥分析的形状在王的论文中建议用任意小的初始拉索应力开始时，收敛到一点的困难可能会出现。因此,估计适当的试验开始的拉索应力来得到一致的结论对于形状确定分析变得重要起来。接下来,一些估计试验初始拉索应力的方法将会被讨论。
5.1. 垂直荷载的平衡
5.2. 零力矩的控制
5.3. 零位移的控制
5.4. 拉索等价系数比的概念
5.5. 不对称的考虑
如果估计的初始拉索应力是用上面介绍的方法对每条拉索独立地确定的，非对称的斜拉桥索塔中可能会存在不平衡的水平受力。因为中间跨(主跨)和边跨的对称的拉索布置对索塔的水平分力的合力为零，也就是没有不平衡的水平力。而对于非对称的斜拉桥，拉索在中间跨和边跨分布是不对称的，拉索在索塔上产生的分力分别独立计算，很明显的索塔中的不平衡的水平力将会引起很大的弯矩和偏移。因此，非对称的斜拉桥的这个问题可以按如下解决。中间跨(主要部份)的拉索受力可以通过上面独立介绍的方法确定，其中上标m代表主跨，上标i代表第i条拉索。然后边跨上拉索受力通过与索塔连接的拉索的水平平衡方程确定，即T i m cosαi= T i s cosβi, and T i s = T i m cosαi/ cosβi, αi是指斜拉索与主跨梁的夹角，βi是指斜拉索与边跨梁的夹角。
6. 例子
在这项研究中，二座不同的类型小型斜拉桥从文学中取得,而且他们的起始形状将会用先前描述的形状确定方法使用线性和非线性程序来确定。最后，一座高度冗余的斜拉桥将会被研究。对于平衡迭代和形状迭代都采用应变10-4。重复的最大周期定为20。如果重复的循环数超过20则计算被认为是不收敛于一点的。
接着的二个小型斜拉桥的开始形状在第6.1节和6.2首先采用任意小的试验拉索应力决定的。在这二个例子中收敛于一点是重复单调的。他们的收敛于一点的起始形状可以很容易地获得。由线性和非线性计算决定的开始形状之间只有很小的不同。收敛于一点的结论显示同样的结果，而且他们与试验的拉索应力无关。
7. 结论
通过线性和非线性计算二重循环的建立而得到斜拉桥的初始形状。这个方法
能达到建筑的设计形式有统一的预应力分配,而且使所有的平衡和边界情况满足。初始的形状确定是斜拉桥分析中最重要的工作。只有一个正确的起始形状，才能得到一个有意义的和正确的偏转及震动分析。基于研究的数字实验,一些结论概述如下:
(1).对于小型斜拉桥初始形状的确定不会出现现在的困难，任意的初始试验拉索应力都能用来计算。然而对于大跨度的斜拉桥，循环的收敛于一点会产生很大问题。
(2).在跨度的斜拉桥的形状确定的收敛于一点通常会产生困难，当拉索的试验应力通过垂直荷载平衡、零弯矩控制、零位移控制的方法给出时。
(3). 如果主跨的每条拉索的预应力符合到约E eq的80%，通过两重循环的方法可以很快的找到收敛于一点的初始形状，而且边跨拉索的初始应力是由作用于索塔上的水平等式决定的。
(4). 由线性程序和非线性的程序得到的初始形状的结果对于几何和预应力的分配的结果只有很小的不同。
(5).使用线性的计算能提供一个合理的起始形状而且节省很多的计算工作, 所以在工程实践中它高度的被推荐。
(6).在小型的斜拉桥中,由线性和非线性计算程序确定的初始形状为基础得到的自振频率只有很小的差别，而模态情形在两种情况中是一样的。
(7). 基本频率和高度冗余刚性斜拉桥的显著不同在研究中被展示。只有基于非线性程序的初始形状确定的模态展示非线性拉索下沉和主梁的偏转效应。举例来说，桥的第一和第三的模态被索塔的横向运动支配,而不是主梁。两个情形的基本频率的差别约为12%。只有通过非线性的计算而不是线性的计算确定的正确的初始形状才能得到斜拉桥的振动频率和模态的正确分析。
出师表(原文) 先帝创业未半而中道崩殂，今天下三分，益州疲弊，此诚危急存亡之秋也。然侍卫 之臣不懈于内，忠志之士忘身于外者，盖追先帝之殊遇，欲报之于陛下也。诚宜开张圣听，以光先帝遗德，恢弘志士之气，不宜妄自菲薄，引喻失义，以塞忠谏之路也宫中府中，俱为一体，陟罚臧否，不宜异同。若有作奸犯科及为忠善者，宜付有司 论其刑赏，以昭陛下平明之理，不宜偏私，使内外异法也。 侍中侍郎郭攸之、费祎、董允等，此皆良实，志虑忠纯，是以先帝简拔以遗陛下。愚以为宫中之事，事无大小，悉以咨之，然后施行，必能裨补阙漏，有所广益。 将军向宠，性行淑均，晓畅军事，试用于昔日，先帝称之曰能，是以众议举宠为督。愚以为营中之事，悉以咨之，必能使行阵和睦，优劣得所。 亲贤臣，远小人，此先汉所以兴隆也；亲小人，远贤臣，此后汉所以倾颓也。先帝在时，每与臣论此事，未尝不叹息痛恨于桓、灵也。侍中、尚书、长史、参军，此悉贞良 死节之臣，愿陛下亲之信之，则汉室之隆，可计日而待也。 臣本布衣，躬耕于南阳，苟全性命于乱世，不求闻达于诸侯。先帝不以臣卑鄙，猥自枉屈，三顾臣于草庐之中，咨臣以当世之事，由是感激，遂许先帝以驱驰。后值倾覆， 受任于败军之际，奉命于危难之间，尔来二十有一年矣。 先帝知臣谨慎，故临崩寄臣以大事也。受命以来，夙夜忧叹，恐托付不效，以伤先帝之明，故五月渡泸，深入不毛。今南方已定，兵甲已足，当奖率三军，北定中原，庶竭 驽钝，攘除奸凶，兴复汉室，还于旧都。此臣所以报先帝而忠陛下之职分也。至于斟酌损益，进尽忠言，则攸之、祎、允之任也。 愿陛下托臣以讨贼兴复之效，不效则治臣之罪，以告先帝之灵。若无兴德之言，则责攸之、祎、允等之慢，以彰其咎；陛下亦宜自谋，以咨诹善道，察纳雅言，深追先帝遗诏。臣不胜受恩感激。 今当远离，临表涕零，不知所言. 译文： 先帝创立帝业还没有完成一半，就中途去世了。现在，天下已分成魏、蜀、吴三国，我们蜀国人力疲惫，物力又很缺乏，这确实是国家危急存亡的关键时刻。然而，侍卫大 臣们在宫廷内毫不懈怠，忠诚有志的将士在疆场上舍身作战，这都是因为追念先帝在世 时对他们的特殊待遇，想报效给陛下啊。陛下确实应该广泛地听取群臣的意见，发扬光 大先帝留下的美德，弘扬志士们的气概；不应该随随便便地看轻自己，言谈中称引譬喻 不合大义（说话不恰当），以致堵塞忠臣进谏劝告的道路。 皇宫的侍臣和丞相府的宫吏都是一个整体，对他们的提升、处分、表扬、批评，不应该因人而有什么差别。如果有营私舞弊、违犯法律和尽忠行害的人，陛下应交给主管 的官吏，由他们评定应得的处罚或奖赏，用来表明陛下公正严明的治理方针。不应偏袒 徇私，使得宫内和宫外有不同的法则。 侍中郭攸之、费祎、侍郎董允等人，他们都是忠良诚实的人，他们的志向和心思忠 诚无二，因此先帝把他们选拔出来留给陛下。我认为宫中的事情，无论大小，陛下都应 征询他们，然后再去实施，这样一定能补求欠缺疏漏的地方，获得更好的效果。 将军向宠，性格和善，品德公正，精通军事，从前经过试用，先帝称赞他有才能， 因此大家商议推举他做中部督。我认为军营中的事务，都应与他商量，这样一定能使军 队团结协作，将士才干高的差的、队伍强的，都能够得到合理的安排。
陶瓷 ceramics 合成纤维 synthetic fibre 电化学腐蚀 electrochemical corrosion 车架 automotive chassis 悬架 suspension 转向器 redirector 变速器 speed changer 板料冲压 sheet metal parts 孔加工 spot facing machining 车间 workshop 工程技术人员 engineer 气动夹紧 pneuma lock 数学模型 mathematical model 画法几何 descriptive geometry 机械制图 Mechanical drawing 投影 projection 视图 view 剖视图 profile chart 标准件 standard component 零件图 part drawing 装配图 assembly drawing 尺寸标注 size marking
技术要求 technical requirements 刚度 rigidity 内力 internal force 位移 displacement 截面 section 疲劳极限 fatigue limit 断裂 fracture 塑性变形 plastic distortion 脆性材料 brittleness material 刚度准则 rigidity criterion 垫圈 washer 垫片 spacer 直齿圆柱齿轮 straight toothed spur gear 斜齿圆柱齿轮 helical-spur gear 直齿锥齿轮 straight bevel gear 运动简图 kinematic sketch 齿轮齿条 pinion and rack 蜗杆蜗轮 worm and worm gear 虚约束 passive constraint 曲柄 crank 摇杆 racker 凸轮 cams
桥梁专业外文翻译--欧洲桥梁研究
附录 Bridge research in Europe A brief outline is given of the development of the European Union, together with the research platform in Europe. The special case of post-tensioned bridges in the UK is discussed. In order to illustrate the type of European research being undertaken, an example is given from the University of Edinburgh portfolio: relating to the identification of voids in post-tensioned concrete bridges using digital impulse radar. Introduction The challenge in any research arena is to harness the findings of different research groups to identify a coherent mass of data, which enables research and practice to be better focused. A particular challenge exists with respect to Europe where language barriers are inevitably very significant. The European Community was formed in the 1960s based upon a political will within continental Europe to avoid the European civil wars, which developed into World War 2 from 1939 to 1945. The strong political motivation formed the original community of which Britain was not a member. Many of the continental countries saw Britain’s interest as being purely economic. The 1970s saw Britain joining what was then the European Economic Community (EEC) and the 1990s has seen the widening of the community to a European Union, EU, with certain political goals together with the objective of a common European currency. Notwithstanding these financial and political developments, civil engineering and bridge engineering in particular have found great difficulty in forming any kind of common thread. Indeed the educational systems for University training are quite different between Britain and the European continental countries. The formation of the EU funding schemes —e.g. Socrates, Brite Euram and other programs have helped significantly. The Socrates scheme is based upon the exchange of students between Universities in different member states. The Brite Euram scheme has involved technical research grants given to
出师表原文及翻译 先帝创业未半而中道崩殂(cú)，今天下三分，先帝：指蜀昭烈帝刘备。 先，尊称死去的人。 创：开创，创立。业：统一天下的大业。 中道：中途。 崩殂（cú）:死。崩，古时指皇帝死亡。殂，死亡。 今：现在。 三分：天下分为孙权，曹操，刘备三大势力。翻译：先帝开创的事业没有完成一半，却中途去世了。现在天下分裂成三个国家。 益州疲(pí)弊，此诚危急存亡之秋也。 益州疲弊：困乏，疲弱，处境艰难；益州：汉代行政区域十三刺史部之一，包括今四川省和陕西省一带。这里指蜀汉。疲弊：人力缺乏，物力缺无，民生凋敝。此：这；诚：的确，实在；之：的；秋：时，时候。这里指关键时期；一般多指不好的。 翻译：蜀汉民力困乏，这实在是危急存亡的时
候啊。 然侍卫之臣不懈(xiè)于内，忠志之士忘身于外者，盖追先帝之殊遇，欲报之于陛下也。然：然而；侍：侍奉；卫：护卫；懈：松懈，懈怠；于：在；内：皇宫中。忘身：舍身忘死，奋不顾身。盖：原来；追：追念；殊遇：优待，厚遇。 翻译：然而朝中官员在首都毫不懈怠，忠诚有志的将士在外面舍生忘死，是因为追念先帝对他们的特殊厚待，想要在陛下身上报恩啊。诚宜开张圣听，以光先帝遗(yí)德，恢弘志士之气， 诚：的确，确实；宜：应该。开张圣听：扩大圣明的听闻，意思是要后主广泛地听取别人的意见。开张，扩大。光：发扬光大，用作动词；遗德：留下的美德。恢弘：发扬扩大，用作动词。恢，大。弘，大，宽。这里是动词，也做“恢宏”；气：志气。 翻译：实在应该广泛地听取意见，发扬先帝遗留下来的美德，振奋有抱负的人们的志气，
不宜妄自菲薄，引喻失义，以塞(sè)忠谏之路也. 妄自菲薄：过于看轻自己；妄：过分；菲薄：小看，轻视。引喻失义：讲话不恰当。引喻：称引、譬喻；喻：比如；义：适宜、恰当。以：以致（与以伤先帝之明的以用法相同：以致）；塞：阻塞；谏：劝谏。 翻译：不应该随便看轻自己，说一些不恰当的话，以致堵塞人们忠言劝谏的道路啊! 宫中府中，俱为一体， 宫：指皇宫；府：指丞相府；俱：通“具”；全，都。 翻译：皇宫中和丞相府中的人，都是国家的官员； 陟(zhì)罚臧(zāng)否(pǐ)，不宜异同。 陟（zhì）：提升，奖励；罚：惩罚；臧否(pǐ）：善恶，这里用作动词，意思是评论人物好坏。翻译：升降官吏，评论人物，不应该因在宫中或在府中而异。 若有作奸犯科及为忠善者，宜付有司论其刑
机械专业英语词汇 陶瓷ceramics 合成纤维synthetic fibre 电化学腐蚀electrochemical corrosion 车架automotive chassis 悬架suspension 转向器redirector 变速器speed changer 板料冲压sheet metal parts 孔加工spot facing machining 车间workshop 工程技术人员engineer 气动夹紧pneuma lock 数学模型mathematical model 画法几何descriptive geometry 机械制图Mechanical drawing 投影projection 视图view 剖视图profile chart 标准件standard component 零件图part drawing 装配图assembly drawing 尺寸标注size marking 技术要求technical requirements 刚度rigidity 内力internal force 位移displacement 截面section 疲劳极限fatigue limit 断裂fracture 塑性变形plastic distortion 脆性材料brittleness material 刚度准则rigidity criterion 垫圈washer 垫片spacer 直齿圆柱齿轮straight toothed spur gear 斜齿圆柱齿轮helical-spur gear 直齿锥齿轮straight bevel gear 运动简图kinematic sketch 齿轮齿条pinion and rack 蜗杆蜗轮worm and worm gear 虚约束passive constraint 曲柄crank 摇杆racker 凸轮cams 共轭曲线conjugate curve 范成法generation method 定义域definitional domain 值域range 导数\\微分differential coefficient 求导derivation 定积分definite integral 不定积分indefinite integral 曲率curvature 偏微分partial differential 毛坯rough 游标卡尺slide caliper 千分尺micrometer calipers 攻丝tap 二阶行列式second order determinant 逆矩阵inverse matrix 线性方程组linear equations 概率probability 随机变量random variable 排列组合permutation and combination 气体状态方程equation of state of gas 动能kinetic energy 势能potential energy 机械能守恒conservation of mechanical energy 动量momentum 桁架truss 轴线axes 余子式cofactor 逻辑电路logic circuit 触发器flip-flop 脉冲波形pulse shape 数模digital analogy 液压传动机构fluid drive mechanism 机械零件mechanical parts 淬火冷却quench 淬火hardening 回火tempering 调质hardening and tempering 磨粒abrasive grain 结合剂bonding agent 砂轮grinding wheel 后角clearance angle 龙门刨削planing 主轴spindle
附录一：中文翻译 土木工程师 桥梁工程156 2003年3月发表于BEI 31~37页 2002年1月31日收到 C.詹姆斯 2002年12月9日通过高级土木工程师佩尔 Frischmann ，埃克塞特 关键词：桥梁；河堤；土工布；膜与土工格栅 英国锁城大桥 锁城大桥是横跨住宅发展区的铁路桥梁。由于工程施工受到周围建筑与地形的限制，该工程采取加固桥台、桥墩与桥面的刚构结构，以及预制栏杆等方法提高了大桥的使用安全程度，并降低了大桥建造与维护的费用。因此，城堡大桥科学的设计方案使工程成本降到最低。 一、引言 本文描述的是在受限制地区用最小的费用修建一座铁路桥梁使之成为开放的住宅发展区。锁城地区是位于住宅发展十分紧张的韦斯顿超 图1 锁城大桥位置远景
马雷的东部。监督桥梁建设的客户是城堡建设有限公司，它由二大房建者组成。该区的规划局是北盛捷区议会（NSDC）。该发展地区被分为布里斯托尔和埃克塞特。规划条件规定，直到建成这条横跨的铁路大桥为止，该地区南部区域不可能适应居住。可见锁城大桥的建成对该地区发展的重要性。 发展地区位于萨默塞特的边缘，这个地区地形十分的恶劣，该范围位于韦斯顿以北和A321飞机双程双线分隔线的南面。现在只有一条乡下公路，是南部区域的唯一通道。该地区是交通预期不适合住宅增加的区域。 由于盛捷地区水平高程的限制，新的铁路线在桥台两边必须设有高程差。并且该地区地形限制，允许正常横跨的区域较小，这导致在结构的布局上的一定数量的妥协。为了整个城堡地区的发展，全 图2 锁城大桥地图上位置 桥限速20公里/时，并考虑区域范围内的速度制约。这样在得到客户和NSDC的同意后，桥梁采取了最小半径的方法，这使得桥梁采用了比正常梯度更加陡峭地方法实现高程的跨越。 客户的工程师、工程顾问、一般设计原则和初步认同原则下(AIP)与NSDC发出投标文件。 该合同在2000年7月1授予安迪。投标价值1.31亿美元，合同期定为34周，到2001年4月完成。
前出师表 先帝创业未半而中道崩殂[cú]，今天下三分，益州疲弊，此诚危急存亡之秋也。然侍卫之臣不懈于内，忠志之士忘身于外者，盖追先帝之殊遇，欲报之于陛下也。诚宜开张圣听，以光先帝遗德，恢弘志士之气，不宜妄自菲薄，引喻失义，以塞忠谏之路也。 宫中府中，俱为一体，陟[zhì]罚臧[zāng]否[pǐ]，不宜异同。若有作奸犯科及为忠善者，宜付有司论其刑赏，以昭陛下平明之理，不宜偏私，使内外异法也。 侍中侍郎郭彼之、费、董允等，此皆良实，志虑忠纯，是以先帝简拔以遗[wèi]陛下。愚以为官中之事，事无大小，悉以咨之，然后施行，必能裨补阙漏，有所广益。 将军向宠，性行[xíng]淑均，晓畅军事，试用于昔日，先帝称之曰能，是以众议举宠为督。愚以为营中之事，悉以咨之，必能使行[h áng]阵和睦，优劣得所。 亲贤臣，远小人，此先汉所以兴隆也；亲小人，远贤臣，此后汉所以倾颓也。先帝在时，每与臣论此事，未尝不叹息痛恨于桓、灵也。侍中、尚书、长史、参军，此悉贞良死节之臣，愿陛下亲之信之，则汉室之隆，可计日而待也。 臣本布衣，躬耕于南阳，苟全性命于乱世，不求闻达于诸侯。先帝不以臣卑鄙，猥[wěi]自枉屈，三顾臣于草庐之中，咨臣以当世之事，由是感激，遂许先帝以驱驰。后值倾覆，受任于败军之际，奉命于危难之间，尔来二十有一年矣。 先帝知臣谨慎，故临崩寄臣以大事也。受命以来，夙夜忧叹，恐托付不效，以伤先帝之明，故五月渡沪，深入不毛。今南方已定，兵
甲已足，当奖率三军，北定中原，庶竭驽[nú]钝，攘[rǎng]除奸凶，兴复汉室，还于旧都。此臣所以报先帝而忠陛下之职分也。至于斟酌损益，进尽忠言，则攸之、韦、允之任也。 愿陛下托臣以讨贼兴复之效，不效则治臣之罪，以告先帝之灵。若无兴德之言，则责攸之、韦、允等之慢，以彰其咎；陛下亦宜自谋，以咨诹[zōu]善道，察纳雅言，深追先帝遗诏。臣不胜受恩感激。 今当远离，临表涕零，不知所言。 《前出师表》译文 先帝创立帝业还没有完成一半，就中途去世了。现在，天下已分成魏、蜀、吴三国，我们蜀国人力疲惫，物力又很缺乏，这确实是国家危急存亡的关键时刻。然而，侍卫大臣们在宫廷内毫不懈怠，忠诚有志的将士在疆场上舍身作战，这都是因为追念先帝在世时对他们的特殊待遇，想报效给陛下啊。陛下确实应该广泛地听取群臣的意见，发扬光大先帝留下的美德，弘扬志士们的气概；不应该随随便便地看轻自己，言谈中称引譬喻不合大义（说话不恰当），以致堵塞忠臣进谏劝告的道路。 宫里身边的近臣和丞相府统领的官吏，本都是一个整体，升赏惩罚，扬善除恶，不应标准不同。如果有营私舞弊、违犯法律和尽忠行害的人，陛下应交给主管的官吏，由他们评定应得的处罚或奖赏，用来表明陛下公正严明的治理方针。不应偏袒徇私，使得宫内和宫外有
英文翻译 机械设计 一台完整机器的设计是一个复杂的过程。机械设计是一项创造性的工作。设计工程师不仅在工作上要有创造性，还必须在机械制图、运动学、工程材料、材料力学和机械制造工艺学等方面具有深厚的基础知识。 Machine Design The complete design of a machine is a complex process. The machine design is a creative work. Project engineer not only must have the creativity in the work, but also must in aspect and so on mechanical drawing, kinematics, engineerig material, materials mechanics and machine manufacture technology has the deep elementary knowledge. 任何产品在设计时第一步就是选择产品每个部分的构成材料。许多的材料被今天的设计师所使用。对产品的功能，它的外观、材料的成本、制造的成本作出必要的选择是十分重要的。对材料的特性必须事先作出仔细的评估。 One of the first steps in the design of any product is to select the material from which each part is to be made. Numerous materials are available to today's designers. The function of the product, its appearance, the cost of the material, and the cost of fabrication are important in making a selection. A careful evaluation of the properties of a. material must be made prior to any calculations. 仔细精确的计算是必要的，以确保设计的有效性。在任何失败的情况下，最好知道在最初设计中有有缺陷的部件。计算（图纸尺寸）检查是非常重要的。一个小数点的位置放错，就可以导致一个本可以完成的项目失败。设计工作的各个方面都应该检查和复查。 Careful calculations are necessary to ensure the validity of a design. In case of any part failures, it is desirable to know what was done in originally designing the defective components. The checking of calculations (and drawing dimensions) is of utmost importance. The misplacement of one decimal point can ruin an otherwise acceptable project. All aspects of design work should be checked and rechecked. 计算机是一种工具，它能够帮助机械设计师减轻繁琐的计算，并对现有数据提供进一步的分析。互动系统基于计算机的能力，已经使计算机辅助设计（CAD）和计算机辅助制造（CAM）成为了可能。心理学家经常谈论如何使人们适应他们所操作的机器。设计人员的基本职责是努力使机器来适应人们。这并不是一项容易的工作，因为实际上并不存在着一个对所有人来说都是最优的操作范围和操作
桥梁结构 桥梁起源 第一座人工桥梁是由横架在河流上的树干或者平石而形成的。毫无疑问，它比基督的诞生还要早几千年建成。甚至在此之前，古人一定惊讶于，在Ardeche 会有跨度为194英尺、高度为111英尺的Pont d’Arc这样的天然拱桥横跨河流。但是随着时间的流逝，一些先驱者将两块石头横跨狭窄的小溪并堵在一起形成倒置的“V”形，从而建成了第一座拱桥。 据degrand所言，有所记载的最早的桥是在大约公元前2650年，由埃及的第一任国王Menes在尼罗河上修建的，但是没有更多的细节描述。Diodorus Siculus提供了另外一座5个世纪后建成的桥梁的详细资料，它是由巴比伦皇后Semiramis在幼发拉底河上建成的。Herodotus将这座桥视为女王统治Nitocris5个世纪的原因。首先，河流在经过城市时转向流入一个人工湖，使桥墩可以修建在干燥的河床上。桥墩的石头采用铁条焊接在一起。甲板是由不低于30英尺宽的木材、雪松、松柏、棕榈修建的，部分甲板是可移动的，每晚拿掉用来防止土匪。当桥建成后，河水再被引回到原来的河道。因此今天还存在一些记录，多少是真实的，多少是随着时间的流逝使我们永远不知道的，但毫无疑问，在4000年前的巴比伦有一座不同寻常的桥。 桥梁类型 我们只能推测这些起源。我们知道古代的吊桥是用扭曲的藤蔓绑在峡谷两侧的树干上形成的，就像一张充满危险的悬挂着的蜘蛛网。但是桥梁型式什么时候得到发展，或者第一座桥是什么型式的，我们都不能肯定。我们只知道三种桥梁类型：板梁桥（在河流上架设一根树干）、拱桥、吊桥，它们在有所记载的早期就开始被建造了。最常见的板梁桥被称为跨桥，如果两个或者更多的梁相连修建在桥墩上就会连在一起形成跨桥，或者是修建成悬臂桥。然而，他们仅是不同类型的板梁桥而已，并不是其他类型的桥梁。改变梁、拱、悬架这三种型式并使其相互结合来共同适应建筑物结构的受力要求，数年来，建筑材料已经越来越普及，涉及到木材、石头，人工材料如砖、水泥、铁和钢材。 板梁桥 一个简单的单跨桥可能是钢结构（可能是板梁），钢筋混凝土或预应力钢筋混凝土。一个钢结构简支桥梁的最大跨度通常约为100英尺（虽然更成长跨度的桥梁已经建成）。然而，当跨度很大时，通常采用连续梁。在德国有一个中央跨度为354英尺、边跨为295英尺的板梁桥。 对于约150英尺的支墩之间的梁，通常采用桁架，并且钢材是必不可少的。1917年，在伊利诺斯州的俄亥俄河上修建了一座跨度为720英尺的简支桥。 无论有没有悬跨，悬臂桥的布置原则就是在桥墩建成后，在桥墩上架设桥梁。两个桥墩之间的部分称为悬跨，通常是先放在一个预制单元，再架在适当位置。因此，这种型式的桥梁是从悬臂的两端用两条锚固的悬臂来支撑桥梁的。桥墩中间的弯矩和剪力最大，在这些位置通常要求桥墩埋设的更深。 当桥的跨度很大时，就要求桥要有更好的强度，悬臂桥通常采用钢桁架结构（桁梁）。这种型式可以使桥墩间的跨度达到约1800英尺。尽管这座桥看起来像是拱桥，事实上它是双悬臂桁架梁。我们会注意到悬臂桥上的最高强度设计在主墩处，因为这些地方可能有最大应力产生。
中文1850字 附录 Bridge research in Europe A brief outline is given of the development of the European Union, together with the research platform in Europe. The special case of post-tensioned bridges in the UK is discussed. In order to illustrate the type of European research being undertaken, an example is given from the University of Edinburgh portfolio: relating to the identification of voids in post-tensioned concrete bridges using digital impulse radar. Introduction The challenge in any research arena is to harness the findings of different research groups to identify a coherent mass of data, which enables research and practice to be better focused. A particular challenge exists with respect to Europe where language barriers are inevitably very significant. The European Community was formed in the 1960s based upon a political will within continental Europe to avoid the European civil wars, which developed into World War 2 from 1939 to 1945. The strong political motivation formed the original community of which Britain was not a member. Many of the continental countries saw Britain’s interest as being purely economic. The 1970s saw Britain joining what was then the European Economic Community (EEC) and the 1990s has seen the widening of the community to a European Union, EU, with certain political goals together with the objective of a common European currency. Notwithstanding these financial and political developments, civil engineering and bridge engineering in particular have found great difficulty in forming any kind of common thread. Indeed the educational systems for University training are quite different between Britain and the European continental countries. The formation of the EU funding schemes —e.g. Socrates, Brite Euram and other programs have helped significantly. The Socrates scheme is based upon the exchange of students between Universities in different member states. The Brite Euram scheme has involved technical research grants given to consortia of academics and industrial
《出师表》原文及翻译 出师表(原文) 先帝创业未半而中道崩殂，今天下三分，益州疲弊，此诚危急存亡之秋也。然侍卫之臣不懈于内，忠志之士忘身于外者，盖追先帝之殊遇，欲报之于陛下也。诚宜开张圣听，以光先帝遗德，恢弘志士之气，不宜妄自菲薄，引喻失义，以塞忠谏之路也 宫中府中，俱为一体，陟罚臧否，不宜异同。若有作奸犯科及为忠善者，宜付有司论其刑赏，以昭陛下平明之理，不宜偏私，使内外异法也。 侍中侍郎郭攸之、费祎、董允等，此皆良实，志虑忠纯，是以先帝简拔以遗陛下。愚以为宫中之事，事无大小，悉以咨之，然后施行，必能裨补阙漏，有所广益。 将军向宠，性行淑均，晓畅军事，试用于昔日，先帝称之曰能，是以众议举宠为督。愚以为营中之事，悉以咨之，必能使行阵和睦，优劣得所。 亲贤臣，远小人，此先汉所以兴隆也；亲小人，远贤臣，此后汉所以倾颓也。先帝在时，每与臣论此事，未尝不叹息痛恨于桓、灵也。侍中、尚书、长史、参军，此悉贞良死节之臣，愿陛下亲之信之，则汉室之隆，可计日而待也。 臣本布衣，躬耕于南阳，苟全性命于乱世，不求闻达于诸侯。先帝不以臣卑鄙，猥自枉屈，三顾臣于草庐之中，咨臣以当世之事，由是感激，遂许先帝以驱驰。后值倾覆，受任于败军之际，奉命于危难之间，尔来二十有一年矣。 先帝知臣谨慎，故临崩寄臣以大事也。受命以来，夙夜忧叹，恐托付不效，以伤先帝之明，故五月渡泸，深入不毛。今南方已定，兵甲已足，当奖率三军，北定中原，庶竭驽钝，攘除奸凶，兴复汉室，还于旧都。此臣所以报先帝而忠陛下之职分也。至于斟酌损益，进尽忠言，则攸之、棉、允之任也。 愿陛下托臣以讨贼兴复之效，不效则治臣之罪，以告先帝之灵。若无兴德之言，则责攸之、祎、允等之慢，以彰其咎；陛下亦宜自谋，以咨诹善道，察纳雅言，深追先帝遗诏。臣不胜受恩感激。 今当远离，临表涕零，不知所言。
外文翻译 英文原文 Belt Conveying Systems Development of driving system Among the methods of material conveying employed，belt conveyors play a very important part in the reliable carrying of material over long distances at competitive cost．Conveyor systems have become larger and more complex and drive systems have also been going through a process of evolution and will continue to do so．Nowadays，bigger belts require more power and have brought the need for larger individual drives as well as multiple drives such as 3 drives of 750 kW for one belt(this is the case for the conveyor drives in Chengzhuang Mine)．The ability to control drive acceleration torque is critical to belt conveyors’ performance．An efficient drive system should be able to provide smooth，soft starts while maintaining belt tensions within the specified safe limits．For load sharing on multiple drives．torque and speed control are also important consideratio ns in the drive system’s design. Due to the advances in conveyor drive control technology，at present many more reliable．Cost-effective and performance-driven conveyor drive systems cov ering a wide range of power are available for customers’ choices[1]. 1 Analysis on conveyor drive technologies 1．1 Direct drives Full-voltage starters．With a full-voltage starter design，the conveyor head shaft is direct-coupled to the motor through the gear drive．Direct full-voltage starters are adequate for relatively low-power, simple-profile conveyors．With direct fu11-voltage starters．no control is provided for various conveyor loads and．depending on the ratio between fu11- and no-1oad power requirements，empty starting times can be three or four times faster than full load．The maintenance-free starting system is simple，low-cost and very reliable．However, they cannot control starting torque and maximum stall torque；therefore．they are
本科毕业设计（论文） 专业外文翻译 专业名称：土木工程专业（道路与桥梁）年级班级：道桥08-5班 学生姓名： 指导教师： 二○一二年五月十八日
Geometric Design of Highways The road is one kind of linear construction used for travel. It is made of the roadbed, the road surface, the bridge, the culvert and the tunnel. In addition, it also has the crossing of lines, the protective project and the traffic engineering and the route facility. The roadbed is the base of road surface, road shoulder, side slope, side ditch foundations. It is stone material structure, which is designed according to route's plane position .The roadbed, as the base of travel, must guarantee that it has the enough intensity and the stability that can prevent the water and other natural disaster from corroding. The road surface is the surface of road. It is single or complex structure built with mixture. The road surface require being smooth, having enough intensity, good stability and anti-slippery function. The quality of road surface directly affects the safe, comfort and the traffic. Highway geometry designs to consider Highway Horizontal Alignment, Vertical Alignment two kinds of linear and cross-sectional composition of coordination, but also pay attention to the smooth flow of the line of sight, etc. Determine the road geometry, consider the topography, surface features, rational use of land and environmental protection factors, to make full use of the highway geometric components of reasonable size and the linear combination. 1.Alignment Design The alignment of a road is shown on the plane view and is a series of straight lines called tangents connected by circular. In modern practice it is common to interpose transition or spiral curves between tangents and circular curves. Alignment must be consistent. Sudden changes from flat to sharp curves and long tangents followed by sharp curves must be avoided; otherwise, accident hazards will be created. Likewise, placing circular curves of different radii end to end (compound curves) or having a short tangent between two curves is poor practice unless suitable transitions between them are provided. Long, flat curves are preferable at all times, as they are pleasing in appearance and decrease possibility of future