1、Unit 4 第四单元Mechanics of Materials 材料力学,教学目标,了解构件（主要为梁）的设计过程了解单轴应力与多轴应力对失效理论的影响熟悉材料力学中涉及的专业词汇熟悉科技类文献常用句型熟悉in general、usually、frequently的不同含义与 be referred to as、be known as、that is、be defined as、in other words 等的用法,Introduction 介绍,Mechanics of Materials deals with（研究）the response of various bodies, us
2、ually called members（构件）, to applied forces（施加力）. In Mechanics of Engineering Materials the members have shapes that either exist in actual structures or are being considered for their suitability（根据其需要）as parts of proposed（拟建的）engineering structures. The materials in the members have properties tha
3、t are characteristic of commonly used（常用的）engineering materials such as steel, aluminum, concrete, and wood. 材料力学用以研究不同物体（通常称为构件）对施加力的响应。在工程材料力学中，构件的形状可以是实际结构中存在的，也可以根据其需要而进行考虑（设计），作为拟建工程结构的部件。构件中材料的性能即是常用的工程材料如钢材、铝材、混凝土和木材的特性。,As you can see already from the variety of materials, forces, and shapes
4、 mentioned, Mechanics of Engineering Materials is of interest to（对.有价值）all fields of engineering. The engineer uses the principles of Mechanics of Materials to determine if the material properties and the dimensions of a member are adequate to（足以）ensure that it can carry its loads safely and without
5、 excessive distortion. In general（通常）, then, we are interested in both the safe load that a member can carry and the associated（相关的）deformation. Engineering design would be a simple process if the designer could take into consideration（考虑）the loads and the mechanical properties of the materials, man
6、ipulate（利用）an equation, and arrive at（得到）suitable dimensions.,Design is seldom that simple. Usually（通常）, on the basis of（根据）experience, the designer selects a trial（试算） member and then does an analysis to see if that member meets the specified requirements. Frequently（常常）, it does not and then a new
7、 trial member is selected and the analysis repeated. This design cycle（设计周期） continues until a satisfactory solution is obtained. The number of cycles（循环次数） required to find an acceptable design diminishes as the designer gains experience.,正如你已经从提到的各种各样的材料、力和形状所看到的，工程材料力学对所有的工程领域都有价值。工程师利用材料力学的原理来确定
8、是否该材料的性能和构件尺寸足以保证它能安全地承受荷载且没有过多的变形。通常，我们关心的是构件能承受的安全荷载及其相应的变形。如果设计者能通过考虑荷载和材料的力学性能，并利用公式得到合适的构件尺寸，那么工程设计将是一个简单的过程。然而设计很少那么简单。通常，根据经验，设计者选择一个试算构件，然后进行分析，看它是否满足规定的要求。它常常不会满足要求，则再选择一个新的试算构件，再进行分析。这样的设计不断重复，直至得到一个满意的结果。当设计师拥有一定的经验后，为得到一个可接受的设计所需要的循环次数会减少。,Design of Axially Loaded Members 轴向力构件的设计 To giv
9、e you some insight into （使.有一些了解）the design cycle, an extremely simple member will be dealt with first. That member is a prismatic bar with a force, P, acting along its longitudinal axis in the direction（纵轴向）such that it tends to elongate the bar. Such a force is referred to as（称为）an axial tensile l
10、oad（轴向拉力）, and we can readily imagine it trying to（努力.）pull the fibers apart and to cause failure on a transverse plane（横向平面）. It is safe to assume that all fibers of the bar, in regions remote from（远离）the point of application of the load, are being pulled apart with the same load intensity（荷载强度）. W
11、ith this assumption, the load intensity or stress is uniform on a transverse plane and is given by,(4-1),when P is in（以.为单位）Newtons and A is in square metres, stress, ,is in Newtons per square metre (N/m2), which is by definition（根据定义）Pascals (Pa).,为了使你对设计周期有一些了解，首先研究一个非常简单的构件。构件是个棱形的杆件，其上沿着它的纵轴向作用一
12、个力P，这样往往使杆件在该方向上伸长。这样的力称为轴向拉力，我们能容易地想象它在努力地将纤维拉开，导致横向平面的破坏。安全地假定杆件的所有纤维在远离荷载施加点的区域以相同的荷载强度被拉开。在此假定下，荷载强度或应力在横向平面上是均匀的，为,当P的单位为牛顿、A的单位为平方米时，应力的单位为牛顿每平方米（N/m2），根据定义为帕斯卡（Pa）。,(4-1),For a given axial load and given dimensions, the stress can be calculated from (4-1) and compared with（与.相比）the stress tha
13、t can be safely carried by the material. The safe stress, known as（称为）the design stress or allowable stress（许用应力）, is determined by tests performed on material made to（按照） the same specifications as the part being considered. A safety factor（安全系数）, frequently imposed by a legally established code（法规
14、）, is applied to the strength, as determined by tests, to give the allowable stress. The allowable stress, a , is given by,where f is the stress at which the material fails (failure to be defined later) and n is the safety factor.,（4-2）,对已知的轴向力和（构件）尺寸，可根据公式（4-1）计算出应力，并与材料能安全承受的应力作比较。安全应力，称为设计应力或许用应力
15、，它是通过对材料的试验来确定的，该（试验）材料按照与所考虑（验算）的杆件相同的规范制作。根据法规规定，通常对试验所确定的强度考虑安全系数后得到许用应力。许用应力 a 为,（4-2）,这里，f 为材料失效（失效在下文有定义）时的应力，而n为安全系数。,Before approving（核准）trial dimensions, the designer makes certain（确信）that the design is safe by determining that the inequality（不等式）,is satisfied. The inequality is usually mor
16、e convenient in the form,（4-3）,不等式常常以更合适的形式出现，即,（4-4）,在核准试算的尺寸之前，设计者通过确定不等式成立而确信设计的安全，即,（4-3）,（4-4）,It might at first（起先）seem that the designer would always dimension（选定.的尺寸）the cross section（横截面） so that the stress would exactly equal the allowable stress. However, it may be very costly to produce
17、parts that have nonstandard sizes, so it is usually more economical to waste some material by selecting the next（接近的）larger standard size above that required by the allowable stress. Departure from（背离）standard sizes is justified（合理的） in cases where the penalty（不利后果）for excess weight is very severe,
18、as in aircraft（航天器）or space-ship（宇宙飞船）design. 起先似乎设计者总是在选定横截面的尺寸，以使应力恰好等于许用应力。但是，生产非标准尺寸部件的成本可能很高，因此，通常人们会选择比按许用应力要求的尺寸大一些的标准尺寸部件，这样尽管浪费了一些材料，但总体上更经济。但不选择标准尺寸的做法在诸如航天器和宇宙飞船的设计中证明是合理的，因为多余重量产生的不利后果是很严重的。,Design of Beams 梁的设计,Up to this point（至此）we have looked at（考虑）the beam problem as a problem in an
19、alysis; that is（即）, for a given set of loads, span, and cross section we have been calculating the stress. The more commonly encountered problem is to select a standard section, or design a member, for a given span and loads without exceeding a certain allowable stress. Under some conditions the all
20、owable stress may be dependent upon the dimensions and shape of the cross section, in which case the selection of the member becomes more difficult. For the present（暂时）we will take the allowable stress as though（似乎）it depends only on the strength of the material and the safety factor.,至此，我们已经考虑了梁的问题
21、而进行了（问题）分析，即对给定的一组荷载、跨度和横截面，我们已经计算了应力。更常遇到的问题是在不超过某个许用应力下对一个给定的跨度和荷载选择一个（构件的）标准截面，或设计一个构件。在某些条件下，许用应力可能依赖于横截面的尺寸和形状，这种情况下的构件选择会变得比较困难。暂时我们将采用许用应力法，似乎它只取决于材料的强度和安全系数。,A trial member will be acceptable（合格）when the stress is equal to, or less than, the allowable stress, that is, if,For design purposes
22、this inequality is more useful in the form,（4-5）,（4-6）,In the usual design process the maximum bending moment is taken from（取自于）the bending moment diagram（弯矩图） and the allowable stress is determined (quite frequently in accordance with（根据）the rules of some legally constituted code) from standard str
23、ength tests in combination with（与.结合）a safety factor. The right-hand side of (4-6) is then known, and it remains（仍然是） to select or design a member that will satisfy the inequality. When a standard section is to be used, the tables（表格）could be searched until a member is found such that the combinatio
24、n of I and c satisfies (4-6). This takes more time than is really necessary, since the tables also provide the value of I/c for each member under the heading（标题）S, the section modulus（截面模量）.,当试算构件的应力等于或小于许用应力时，也就是说，如果,在通常的设计过程中，最大的弯距从弯距图上取得，而许用应力通过标准强度试验并考虑安全系数后确定（往往是根据一些法规的规则）。这样，已知式（4-6）右手边的值，则仍然是
25、选择或设计构件以满足该不等式。当使用标准截面时可以查找表格，直至找到的构件其I和c值的组合能满足式（4-6）。这样花费的时间比实际需要的多，因为表格中在截面模量S的标题下也提供了每一个构件的I/c的值。,试算构件即为合格。根据设计的需要，（上述）不等式以下列形式出现更有用，即,（4-5）,（4-6）,That is, the section modulus is defined as（定义为）,To select a member, the S column（列） is consulted（查阅） and any member that satisfies (4-8) could be use
26、d. The members with very high values of S will obviously be understressed（应力不足的）and wasteful of material. The best design, if there are no other constraints, will be that which satisfies (4-8) with the minimum amount of material.,（4-7）,With tabulated values of S available it is much more convenient
27、to use (4-6) in the form,（4-8）,The smallest acceptable S does not necessarily coincide with（符合）the most economical member. To select the lightest and most economical standard section, the listed values of mass should be examined to find the lightest member with an acceptable S. The problem becomes m
28、uch more complex if built-up（组合）member is being designed because its cost will depend upon the combined costs of web plate, angles and cover plates as well as fabrication（装配）costs so that the lightest member is not necessarily the most economical.,截面模量定义为,为选择构件而查阅S这一列，则任何满足式（4-8）的构件都可采用。显而易见，对S值很高的构
29、件，其应力是不足的，并浪费了材料。如果没有其他的限制，最好的设计将是以最少的材料满足式（4-8）。能接受的最小的S值不必是最经济的构件。为了选择最轻和最经济的标准截面，应检查列出的质量值，以找到能接受的S值下的最轻构件。如果在设计一个组合构件时，则问题变得复杂得多，因为它的费用将依赖于腹板、角钢和盖板的费用以及装配的费用，因此，最轻的构件未必是最经济的构件。,根据表格中得到的值S，将式（4-6）以下列形式使用要方便得多，即,（4-7）,（4-8）,Deflections Due to Bending 弯曲挠度,The main purpose of this chapter（本节） was t
30、o develop（提出）the flexure（屈曲）formulas, and to provide some experience in applying them. Statically indeterminate（超静定）cases were encountered and some insight（认识） gained as to（就.）the difficulty and importance of this category of problem. 本节的主要目的是提出屈曲公式，并在运用公式时提供一些经验。当遇到超静定的情况时，就此类问题的难点和重点获得一些认识。,Superp
31、osition（叠加法）was presented（提出） as the preferred（优先的）method for solving certain problems. However, becoming familiar with（熟悉）superposition was more important than finding solutions to the problems（问题的答案） because superposition has application in many areas of stress analysis and will be used frequently
32、 in our future studies. 为解决某些问题，叠加法作为优先的方法被提出。但是，熟悉叠加法远比找到问题的答案重要，因为叠加法已经用于应力分析的很多领域，而且，在我们今后的研究中还会经常使用。,Moment-area（弯距图面积法）was found to be a convenient method for solving various problems. It is a method that becomes quite complicated and requires further development（展开） when more advanced structur
33、es are encountered. At the present stage it is sufficient for you to be acquainted with（了解）the fundamentals（基本原理）of the method. Deflection of long-radius（长半径） curved beams was introduced（引入）to illustrate the power of the principles underlying（构成.的基础）the moment-area method and so that you would appre
34、ciate（知道）the differences between straight and curved beams. 为解决不同的问题，发现弯距图面积法是一种很便利的方法。但当遇到更先进的结构时，此法会变得非常复杂，需要进一步地展开。对你来说在目前阶段了解此法的基本原理已经足够了。引入长半径曲梁的挠度来举例说明构成弯距图面积法基础的原理的功效，使你能知道直梁与曲梁之间的区别。,This chapter afforded an opportunity to become familiar with singularity functions （奇异函数）, and you have seen
35、that certain problems can be greatly simplified by their use. It must be appreciated（意识到）that merely an introduction to the topic has been given; there is much more to learned by those who have a special interest. To illustrate a serious limitation（缺陷） at our present stage, we can express distribute
36、d loads （分布荷载） that are variable and are intermittent, but we cannot write a load function for concentrated loads. If we had taken the next step and dealt with the concentrated load, we would have encountered the source of the expression（表达式）“singularity function”, but having regard for（考虑）the scope
37、 of this book we have stopped short of（达不到）that step.,本节使你熟悉了奇异函数，并发现通过利用它们能大大地简化某些问题。但必须意识到仅仅是介绍了题目，对那些有特殊兴趣的人还有很多要学。我们可以表示变化的、间断的分布荷载，但不能写出集中荷载的荷载函数，说明了在我们目前阶段（该函数）还存在着严重的缺陷。如果我们进入下一步去研究集中荷载，便会遇到奇异函数表达式的来源，但是考虑到本书的范围，我们不再进入那一步。,Failure Theories 失效理论,In the design of a member subjected to a uniaxia
38、l（单轴的） load, the stress was compared with the stress to cause failure in test specimens（试件）that had also been subjected to uniaxial load. This is the simplest of all design problems; the method is quite adequate（合适的）, since the nature（性能）of the loads and the stresses in the test and in the part bein
39、g designed are identical. However, we soon encounter cases where the member being designed is not so simple and the stresses are not uniaxial; consider, for example, the stresses in the web of a beam or in a pressure vessel（压力容器）. In these cases we know that the stress is two-dimensional（两向的）or biax
40、ial and it may, in other cases, be three-dimensional, or triaxial.,For a structure having biaxial or triaxial stresses, how should we check the safety of the design? The most obvious way would be to conduct tests（进行） in which specimens are stressed（受力）to failure in the same multiaxial（多轴的）manner as
41、in the structure; the allowable multiaxial stress then be determined by the application of an adequate safety factor. However, this would require a group of tests for every new set of multiaxial stresses that occurred in design. Such tests are difficult to perform, and the cost of performing them in
42、 the required numbers would be prohibitive. Consequently, we need a theory by which the results of the standard uniaxial test can be used to predict（预测）the failure of a part made of the same material when the stresses are multiaxial. In other words（换句话说）, we need a failure theory.,在设计承受轴向力的构件时，将其应力与
43、导致同样承受轴向力的试验样本（试件）失效的应力相比。这是所有设计问题中最简单的；该法是非常合适的，因为试验和设计中的荷载和应力性质是完全相同的。但是，不久我们便会遇到正在设计的构件不是那么简单，其应力也不是单轴向的；例如，考虑梁的腹板应力或压力容器中的应力。在这些情况下，我们知道其应力是两向的或两轴的，而在其他情况下可能是三向或三轴的。对一个有着两轴或三轴应力的结构，我们应该如何检查它的设计安全性？最显然的办法是进行试验，即试件以与结构相同的多轴受力方式失效；然后运用适当的安全系数确定许用的多轴应力。但是，对设计中出现的每组新的多轴应力都将需要一组试验。这样的试验很难进行，而且以需要的数量进行
44、试验的费用也是禁止的。因此，我们需要一个理论，根据它可以通过利用标准单轴试验的结果来预测同样材料制作的构件在承受多轴应力时的失效。换句话说，我们需要一个失效理论。,To illustrate the need for a failure theory, let us consider a cylindrical pressure vessel. To avoid unnecessary complications, we will consider that all welds（焊缝）are 100% efficient and that the walls（容器壁）are thin. Und
45、er internal pressure the main stresses（主应力） are circumferential and longitudinal, and it was implied（认为）in an earlier case that only the circumferential stress, because it is larger than the longitudinal stress, needs to be considered in judging the adequacy of the design. In this approach we tacitl
46、y（默认）assumed that the maximum stress could be treated as（看作为）a uniaxial stress and that it alone determined the safety of the design. The longitudinal stress was not considered although it may, without our knowledge（在我们的知识之外）, have had an influence on strength. It happens that our approach in this c
47、ase is acceptable, but, in a biaxial state of stress, the second stress is not always inconsequential（不重要）and an understanding of failure theory is necessary in order to avoid making some serious errors.,为了举例说明需要一个失效理论，让我们考虑一个圆柱形的压力容器。为避免不必要的复杂，我们认为焊缝完全有效，容器壁是薄的。在内部压力下，主应力是环向和纵向的，由于环向应力比纵向应力大，因此，在一个
48、较早的例子中认为只有环向应力需要在判断设计的适用性时加以考虑。在这个方法中，我们默认地假定最大的应力（即环向应力）可看作为单轴应力，并由它单独地确定设计的安全性。尽管在我们的知识以外，纵向应力可能会对强度有影响，但不被考虑。正巧，在这种情况下我们的方法能被接受，但是，在两轴应力状态下，第二种应力不总是不重要的，为了避免造成一些严重的错误，对失效理论的理解是必要的。,Unfortunately, as we will discover, no single theory（单一理论） will be found to apply in all cases; for example, theorie
49、s that are satisfactory for ductile materials are not acceptable for brittle materials. We will also find that one of the best theories is too complex for everyday use and that most designers prefer（更喜欢）a simpler theory that introduces（产生）a small but safeside（安全的）error. 很不幸，正如我们将发现的，没有找到一个单一的理论能运用于所
50、有的状况，例如，满足延性材料的理论，脆性材料不能接受。我们也将发现每天在使用一个最好的理论太复杂了，多数设计者更喜欢用一个会产生小而安全的错误但较简单的理论。,In developing（提出）the various failure theories, we cannot avoid three-dimensional effects, but we will treat（讨论）only those cases in which one of the stresses is zero, thus avoiding complications that would tend to obscure
51、（使.模糊不清）the important part of the theories. This is not a serious limitation, since in engineering practice（工程实践） most problems are reduced to（简化为）the biaxial stress state for design. When shear stresses（剪应力）occur along with（与.一起）normal stresses（正应力）, the principal stresses（主应力）are determined. Thus,
52、 for practical（实用的）purposes, we need to consider failure in a material subjected to two nonzero（非零）normal stresses while the third normal stress is zero. For ease in（为了便于.）designating （称呼）those principal stresses we will use numerical subscripts（数字下标）; 1 and 2 being the nonzero stresses and 3 being zero.,
