大部分设备并不是静态的，这里提出的方法适用于动态，如果与动态有关的额外载荷被考虑进去。。任何时候只要动力与静态载荷有任何的关系，那么系统就被认为是静态的。
In engineering mechanics, we will appreciate欣赏到 the various各种各样 types of approximations近似法 that are inherent in固有的 any real problem:
在工程机械中，我们可以欣赏到各种各样形式的近似法来解决固有的问题。
Primarily首先, we will be discussing things which are in “equilibrium,” i.e., not accelerating加速的. However, if we look closely enough, everything is accelerating. We will consider many structural members结构部件 to be “weightless” — but they never are. We will deal with forces that act at a “point” — but all forces act over an area. We will consider some parts to be “rigid坚硬的” — but all bodies will deform under load.
首先，我们讨论处于平衡中的物体，也就是说没有加速的。然而，如果我们仔细观察，可以看到所有物体都是运动的，我们会认为构件是没有重量的，但是他们总有重量。我们会认为力作用在点上，但是力总是作用在面上的，我们认为一些部分是坚硬的，但是任何物体在力的作用下都会变形。
We will make many assumptions假定 that clearly are false. But these assumptions should always render the problem easier,
more tractable易处理的. You will discover that the goal is to make as many simplifying assumptions as possible without seriously degrading退化 the result.
我们会假定一些显然是错误的东西。但是这些假设会使问题变得简单，更易处理。你会发现我们的目的是找到尽量简单的假设，只要不使结果严重变形。
Generally there is no clear method to determine确定 how completely, or how precisely, to treat a problem: If our analysis is too simple, we may not get a pertinent相关的 answer; if our analysis is too detailed详细, we may not be able to obtain得到 any answer. It is usually preferable to start with a relatively simple analysis and then add more detail as required to obtain a practical solution.
During the past two decades, there has been a tremendous growth in the availability of computerized methods for solving problems that previously were beyond solution because the time required to solve them would have been prohibitive. At the same time the cost of computer capability and use has decreased by orders of magnitude. We are experiencing an influx of “personal computers” on campus, in the home, and in business.
Lesson 6 Shaft轴 Design
A shaft is a rotating旋转 or stationary固定的 member零件，构件, usually of circular圆形的 cross section横截面, having mounted安
装 upon it such elements as gears齿轮, pulleys滑轮, flywheels飞轮, and other power-transmission传动装置 elements.
轴类零件一般都是固定的或者是旋转体。截面一般都是圆形，并且有齿轮，滑轮，飞轮或者其他的传动装置安装在上面。
If a shaft carries安装 several gears or pulleys齿轮或者滑轮, different sections截面 of the shaft will be subjected to承受 different torques力矩, because the total power delivered to传递 the shaft is taken off piecemeal分散成片 at various points. Hence one must note记录 the amount of torque力矩 on each part of the shaft. Then study the distribution分布 of the bending moment弯矩, preferably较好的 sketching草图( freehand is all right) the shear force切应力 and bending moment diagrams弯矩图.
如果轴上安装了几个齿轮和滑轮，不同的截面将会承受不同的力矩。因为传递到轴上的总力被分散到了不同的点。因此我们必须分别记录不同部分的力矩，然后研究弯矩的分布，较好的画出切应力和弯矩的图。
From this preliminary examination预备考试，预先检查, which is a problem in mechanics, we note the section截面 where the bending moment弯矩 is a maximum and the section where the torque扭矩 is a maximum. If these maximums occur at the same section, the diameter直径 needed for that section is determined- and used for the entire整个的 shaft when the diameter is to be constant恒定. If the maximums do not
occur at the same section, determine the diameter for the section of maximum torque and also for the section of maximum bending moment, and use the larger value.
从之前的检查我们可以知道，我们在工程中注意弯矩和扭矩达到最大的截面。如果这些截面重合，那么我们就说当此直径恒定的时候，截面的的直径也就定了，当然此轴的尺寸也就定下来了。如果两个面没有重合，那么我们就取其中大的那个。
The diameter of shaft is often varied from point to point , sometimes for structure reasons. In this case, check the stress or determine the size needed for each section. The designer makes certain that all sections of the shaft are subjected to safe stresses, taking due note of holes, keyways, and other stress raisers应力集中装置.
轴各部分的直径常常是不同的。一些是结构的原因。这种时候，我们要检查上面的应力并且决定所需面的尺寸。设计师要特别注意孔，键槽和其他的应力集中装置，确保所有的截面所受的力都在允许范围内。
Hollow洞 round shafts园轴 sometimes serve a useful purpose, usually in large sizes, though they are more expensive than solid ones. They have the advantage of being stronger and stiffer更硬的, weight for weight, because the outer fibers外部纤维 are more effective in resisting the applied moments, and they respond better to heat treatment because quenching淬火 can proceed outward as well as
inward.
孔轴常常可以发挥重要的作用，它们的尺寸一般都比较大，而且比一般的实心轴更贵。它们的优点是等质量的情况下更加的硬，因为外部的纤维更有利于承受应力，而且由于它们可以内外同时进行热处理所以效果可以更好。
Deflection偏差 is a significant重大的 consideration in the design of shafts. Criteria标准条件 for the limiting torsional deflection扭转变形 vary from 0.25 degree per meter of length for machinery shafts to 1 degree per meter or 1 degree in a length of 20 diameters for transmission shafting传动轴. Even short shafts become special problems in rigidity硬度 when the load is applied in impulses脉冲, as on an automobile crankshaft汽车机轴. The impulses脉冲 produce a torsional vibration扭转变形, usually compensated by torsional-vibration dampers扭转减震器 in an automotive engine汽车发动机.
在轴的设计中，偏差将会被着重考虑。传动轴的标准扭转变形范围是每米0.25度到1度。就算是微小的偏差如果加载上脉冲负载都会严重影响轴的硬度。就比如汽车的机轴，就需要汽车发动机中的扭转减震器来消除脉冲造成的扭转变形。
Data on permissible values允许值 of deflections变形 are rare, probable because the range范围 of values would be large and each situation has its own peculiarities独特性. An old rule of thumb检验