土木工程专业英语上册_翻译苏小卒_同济大学(考试手机专业版)(10)

当Marxwell提出力法分析时，他也发表了使弹性结构上任意两点的柔度系数相关的定理-无论是桁架、梁或框架。该定理称为位移互等定理，可以陈述如下：由作用在结构上A点的单位力引起B点的位移等于当单位力作用在B点时引起的A点的位移，即fBA = fAB。该定理也适用于转角互等。而且，将单位力和单位力偶矩施加在结构上不同的点，我们也可以陈述为：由作用在结构上A点的单位力引起B点的转角（单位为弧度）等于当单位力偶矩作用在B点时引起的A点的位移。

The displacement / stiffness method of analysis is based on first writing force-displacement relations（关系式）for the members and then satisfying the equilibrium requirements for the structure. In this case the unknowns（未知量）in the equations are displacements and their coefficients are called stiffness coefficients. Once the displacements are obtained, the forces are determined from the compatibility and force-displacement equations.

位移法或刚度法的分析是基于最初写出的构件的力-位移关系式，并且要满足结构的平衡要求。在这种情况下，方程式中的未知量是位移，而它们的系数称为刚度系数。一旦求得位移，就可从协调方程和力-位移方程中确定力。

Early in the 20th century slope deflection（转角位移法）was the most popular（流行的）method in use for analyzing statically indeterminate frames. It was developed by Professor G.A. Maney and began its reign of popularity（开始盛行）almost immediately after its publication（发表）in 1915. Fifteen years later the moment distribution method（弯矩分配法）was introduced and there began a period of spirited professional competition （激烈的专业竞争）over the merits（优势）of the two methods, with moment distribution eventually emerging as the “winner”, primarily because of its speed and simplicity. But the competition has not ended. Today, although moment distribution continues as（依然作为）the more popular method, there remain many contemporary（同时代的）engineers who prefer slope deflection.

早在20世纪，转角位移法是用以分析超静定框架最流行的方法。它由G.A. Maney教授提出，并在1915年发表后几乎迅速开始盛行。15年后弯矩分配法被采用，并在一段时期内开始了对两种方法的优势展开的激烈的专业竞争，弯矩分配法最终以胜者出现，主要是由于它的速度和简单。但是竞争没有结束。今天，尽管弯矩分配法依然作为较流行的方法，仍有很多同时代的工程师较喜欢用转角位移法。

They contend（辩解）that in performing a slope deflection analysis the engineer can acquire a better “intuitive feel”（直觉）for the structure than the use of any other method. More significant（重要的）, though, slope deflection has gained renewed（重新）importance（重要地位）with the advent（到来）of the computer, serving as（作为）the central method（重要方法） used for structural analysis software. Slope deflection focuses on（着重于）individual members, their loads, and certain conditions at their ends.

他们辩解在进行转角位移分析时能比在使用任何其它的方法中获得对结构更好的直觉。然而更重要的是，转角位移法由于计算机的到来已经重新获得了重要地位，作为用于结构分析软件的重要方法。转角位移法着重于单个构件、作用于它们的荷载和端部的某些条件。

In using this method, simultaneous equations（联立方程）are written and solved that have displacements, rather than forces or moments, as unknowns. It employs a simple sign convention（符号约定）: all variables（变量）related to a member are positive（正的）if they are clockwise（顺时针的）. The complete slope deflection equations for MAB and MBA are the superpositions of four parts: A, B, , and loads. Thus

MAB = 4EI/L A +2EI/L B -6EI/L2 +FEMAB （5-3） MBA = 2EI/L A +4EI/L B -6EI/L2 +FEMBA （5-4）

在采用该法时，写出联立方程并求解位移的未知量，而不是力或弯矩作为未知量。它采用了简单的符号约定：所有与构件有关的变量如果是顺时针则为正。对MAB和MBA ,完整的转角位移方程为四个部分的叠加： A, B , 和荷载。因此

MAB = 4EI/L A +2EI/L B -6EI/L2 +FEMAB （5-3）

MBA = 2EI/L A +4EI/L B -6EI/L2 +FEMBA （5-4）

Where MAB and MBA are clockwise end moments

Aand B are clockwise end rotations is a relative linear displacement of ends A and

B that matches（符合）a clockwise rotation

of AB

FEM is referred to as fixed end moment. A和 B为顺时针的端部转角； 是端部A相对于B的线位移，符合 AB的 FEM 称为固定端弯矩。 这里， MAB和MBA为顺时针的端部弯矩； 顺时针转动；

Analysis by slope deflection begins with use of above equations to write separate expressions for the end moments at each end of each member. Equilibrium is then imposed（利用）using moment equilibrium at joints rotated an unknown and transverse force equilibrium on members with an unknown . A system of equations（方程组）is produced that has the end displacements as unknowns. When solved simultaneously（联立求解）, the resulting displacements（得到的位移）are substituted in（代入）the slope deflection equations, giving the end moments.

转角位移法的分析从采用上述方程分别写出每个构件在每一端的端部弯矩表达式着手。然后利用平衡，即采用节点转动未知量 时的弯矩平衡和构件有未知量 时的横向力平衡。形成以端部位移为未知量的方程组。当联立求解时，将求解得到的位移代入转角位移方程，得到端部弯矩。

The method of analyzing beams and frames using moment distribution was developed by Hardy Cross, a professor of civil engineering at the University of Illinois. At the time this method was first published（公布）in 1932, it attracted immediate attention, and it has been recognized as one of the most notable（显著的） advances in structural analysis during the twentieth century. Moment distribution is a method of successive approximations（逐次近似计算法）that may be carried out （实现）any desired degree of accuracy（精度）. Essentially（本质上）, the method begins by（首先）assuming each joint of structure is fixed. Then, by unlocking and locking（解开与锁住）each joint in succession（连续地）, the internal moments at the joints are “distributed”（分配）and balanced until the joints have rotated to their final or nearly final positions. 采用弯矩分 …… 此处隐藏：4580字，全部文档内容请下载后查看。喜欢就下载吧 ……