4MechanicsofMaterials

Chapter 4 Mechanics of MaterialsSection A Mechanics of Materials（材料力学（材料力学）（材料力学材料力学）材料力学是一门应用力学，能够对固体机构受到不同类型的负荷进行处材料力学是一门应用力学，能够对固体机构受到不同类型的负荷进行处理。理。Mechanics of materials is a branch of applied mechanics that deals with the behavior of solid bodies subjected to various types of loading.This field of study is known by several names,including“strength of materials”and“mechanics of deformable(dif:mbl adj.可变形的可变形的)bodies.”The solid bodies considered include axially(ksili adv.轴向地轴向地)loaded members,shafts in torsion(t:n n.扭转，扭力扭转，扭力),thin shells(el n.壳体，壳壳体，壳层，壳层，壳),beams,and columns,as well as structures that are assemblies of these components.这一领域的研究通过这么几个名字为大家所知，包括这一领域的研究通过这么几个名字为大家所知，包括“材料强度材料强度”和和“力力固体机构包括轴心受压体系，轴向扭转，薄壳，梁和柱以及固体机构包括轴心受压体系，轴向扭转，薄壳，梁和柱以及学变形体系。学变形体系。”类似这些构件的结构体系。类似这些构件的结构体系。In Mechanics of Engineering Materials the members have shapes that either exist in actual structures or are being considered for their suitability as parts of proposed engineering structures.The materials in the members have propertied that are characteristic of commonly used engineering materials such as steel,aluminum,concrete,and wood.在工程材料中的力学模型，或者是在实际结构中有的或正在工程材料中的力学模型，或者是在实际结构中有的或正在考虑其是否适合作为部分拟议工程结构。在考虑其是否适合作为部分拟议工程结构。该材料中的成员有该材料中的成员有财产的特点，常用的工程材料，如钢铁，铝，水泥和木材。财产的特点，常用的工程材料，如钢铁，铝，水泥和木材。As you can see already from the variety of materials,forces,and shapes mentioned,Mechanics of Engineering Materials is of interest to all fields of engineering.The engineer used the principles of Mechanics of Materials to determine if the material properties and the dimensions of a member are adequate to ensure that it can carry its loads safely and without excessive distortion(dist:n n.扭转，扭曲，翘曲，变形扭转，扭曲，翘曲，变形).正如你已经从各种不同的材料，应力，和提到模型中看到正如你已经从各种不同的材料，应力，和提到模型中看到的，工程材料力学涉及各个工程领域。的，工程材料力学涉及各个工程领域。工程师运用材料力学的工程师运用材料力学的原理，确定材料特性和构件尺寸以确保它能够安全负载而不过原理，确定材料特性和构件尺寸以确保它能够安全负载而不过度变形。度变形。In general,then,we are interested in both the safe load that a member can carry and the associated deformation.Engineering design would be a dimple process if the designer could take into consideration the loads and the mechanical properties of the materials,manipulate an equation,and arrive at suitable dimensions.Design is seldom that simple.一般情况下，我们感兴趣的不仅是安全负荷，还有其与一般情况下，我们感兴趣的不仅是安全负荷，还有其与荷载有关的变形。荷载有关的变形。如果设计师考虑荷载和材料的力学性能，如果设计师考虑荷载和材料的力学性能，求解方程，得出合适的尺寸，那么工程设计将是一个波纹似求解方程，得出合适的尺寸，那么工程设计将是一个波纹似的进程，设计很少这么简单。的进程，设计很少这么简单。Theoretical analyses and experimental results have equally important roles in the study of mechanics of materials.On many occasions,we will make logical derivations to obtain formulas(f:mjul n.公式，方程式，计算式准则，方案公式，方程式，计算式准则，方案)and equations for predicting mechanical behavior,but we must recognize that these formulas cannot be used in a realistic way unless certain properties of the material are known.These properties are available to us only after suitable experiments have been carried out in the laboratory.理论分析和实验结果对研究材料力学有同样重要的作用。理论分析和实验结果对研究材料力学有同样重要的作用。在许多情况下，我们将得出符合逻辑的推导公式和方程，并在许多情况下，我们将得出符合逻辑的推导公式和方程，并对力学行为进行预测，对力学行为进行预测，但我们必须认识到，这些公式在现实但我们必须认识到，这些公式在现实方法中不能被使用，除非材料的某些性能是已知的。这些属性方法中不能被使用，除非材料的某些性能是已知的。这些属性只有在实验室进行实验以后才能够被获得。只有在实验室进行实验以后才能够被获得。Also,because many practical problems of great importance in engineering cannot be handled efficiently by theoretical means,experimental measurements become a necessity.Usually,on the basis of experience,the designer selects a trial member and then does an analysis to see if that member meets the specified requirements.Frequently,it does not and then a new trial member is selected and the analysis repeated.This design cycle continues until a satisfactory solution is obtained.此外，在很重要的工程当中，很多实际问题按理论的方法不此外，在很重要的工程当中，很多实际问题按理论的方法不能有效解决，因而，实验测量成为必要能有效解决，因而，实验测量成为必要.通常在经验基础通常在经验基础上，设计师选择一个试验构件，然后分析这个构件是否能够上，设计师选择一个试验构件，然后分析这个构件是否能够满足特定的要求。满足特定的要求。通常情况下，要是不满足，就会选一个新通常情况下，要是不满足，就会选一个新的试验构件并重新进行分析。这样的设计周期将持续到获得的试验构件并重新进行分析。这样的设计周期将持续到获得一个令人满意的解决办法。一个令人满意的解决办法。In general,the objectives of our analysis will be the determination of the stressed,strains（strein n.应变）应变）,and deflections（diflekn n.挠度，挠曲，偏离，偏差角）挠度，挠曲，偏离，偏差角）produced by the loads.If these quantities can be found for all values of load up to the failure（feilj n.失效，失败，破裂，故障）失效，失败，破裂，故障）load,then we will have a complete picture of the mechanical behavior of the body.一般情况下，我们分析的目标是确定应力、应变和荷载引起一般情况下，我们分析的目标是确定应力、应变和荷载引起的挠度。的挠度。如果可以找到导致破坏荷载的所有荷载值，那么我如果可以找到导致破坏荷载的所有荷载值，那么我们将有一个体系的力学行为的完整构图。们将有一个体系的力学行为的完整构图。An important consideration in engineering design is the capacity of the object being designed to support or transmit loads.Objects that must sustain loads include building structures,machines,aircraft,vehicles,ships,and a seemingly endless list of other man-made things.For simplicity,we will refer to all such objects as structures;thus,a structure is any object that must support or transmit loads.在工程设计中，一个很重要的问题是考虑物体支撑或传递荷在工程设计中，一个很重要的问题是考虑物体支撑或传递荷载的能力。负载物体包括建筑结构，机器，飞机，车辆，船载的能力。负载物体包括建筑结构，机器，飞机，车辆，船舶，以及似乎永无休止的其他人为的东西。舶，以及似乎永无休止的其他人为的东西。为了简便起见，为了简便起见，我们将提到所有这些物体视为结构我们将提到所有这些物体视为结构;因此，结构是必须支撑因此，结构是必须支撑或传递负荷的任何物体。或传递负荷的任何物体。If structural failure is to be avoided,the loads that a structure actually can support must be greater than the loads it will be required to sustain when in service.The ability of a structure to resist loads is called strength,hence the preceding criterion（kraitirin n.准则，判据，标准准则，判据，标准）can be restated as follows:The actual strength of a structure must exceed the required strength.如果结构的失效避免，结构的承载能力实际上可以比正常如果结构的失效避免，结构的承载能力实际上可以比正常使用时更大。使用时更大。结构抗负荷的能力称为强度，因此上述标准有如结构抗负荷的能力称为强度，因此上述标准有如下的表述：结构的实际应力必须超过所要求的应力。下的表述：结构的实际应力必须超过所要求的应力。The ration of the actual strength to the required strength is called the factor of safety（安全系数）（安全系数）n:实际应力与所需应力的比值称为安全系数实际应力与所需应力的比值称为安全系数n：Factor of safety n=actualstrengthrequiredstrength实际应力n=所需应力安全系数安全系数:Of course,the factor of safety must be greater than 1.0 if failure is to be avoided.Depending upon the circumstances,factors of safety from slightly above 1.0 are used.当然，如果失效避免，安全系数必须大于当然，如果失效避免，安全系数必须大于1.0。基于这种。基于这种情况，使用时安全系数从略高于情况，使用时安全系数从略高于1.0考虑。考虑。The incorporation of factors of safety into design is not a simple matter,because both strength and failure have many different meanings.Failure can mean the fracture（frkt n.破破裂，破碎，折断，断裂）裂，破碎，折断，断裂）or complete collapse（klps n.倒闭，坍；倒闭，坍；v.坍塌，陷落，倒塌，破坏）坍塌，陷落，倒塌，破坏）of a structure,or it can mean that the deformations have exceeded some limiting value so that the structure is no longer able to perform its intender functions.The latter kind of failure may occur at loads much smaller than those that cause actual collapse.把安全系数纳入设计不是一件简单的事，因为强度和失效把安全系数纳入设计不是一件简单的事，因为强度和失效有很多不同的含义。有很多不同的含义。失效可能意味着破裂或结构的彻底坍塌，失效可能意味着破裂或结构的彻底坍塌，也可能意味着一些变形已超过限定值以至于这样的结构已不再也可能意味着一些变形已超过限定值以至于这样的结构已不再后者的失效可能出现在负荷远低于引起后者的失效可能出现在负荷远低于引起能够履行既定的功能。能够履行既定的功能。实际破坏时的负荷值实际破坏时的负荷值 The determination of a factor of safety must also take into account such matters as the following:the probability of accidental overloading of the structure;the types of loads(static(sttik adj.静的，静力的，静电的静的，静力的，静电的),dynamic(dainmik adj.动态的，动力的，动力学的；电动的，冲击的动态的，动力的，动力学的；电动的，冲击的),or repeated)and how accurately they are known;the possibility of fatigue failure;inaccuracies in construction;quality of workmanship;variations in properties of materials;deterioration due to corrosion or other environmental effects;accuracy of the methods of analysis;whether failure is gradual(ample warning)or sudden(no warning);consequences of failure(minor damage or major catastrophe);and other such considerations.结构超载的可能性结构超载的可能性;负载负载的类型（静态，动态，或重复）的类型（静态，动态，或重复），以及如何准确地知道他们；疲劳破坏的可，以及如何准确地知道他们；疲劳破坏的可能性；施工时的不确性；工艺质量；材料性能的变化能性；施工时的不确性；工艺质量；材料性能的变化;确定一个安全系数也必须考虑到如下这些事项：确定一个安全系数也必须考虑到如下这些事项：由于腐蚀或其他环境影由于腐蚀或其他环境影响引起的恶化；分析方法的正确性；失败是否是渐进的（足够的预兆）或响引起的恶化；分析方法的正确性；失败是否是渐进的（足够的预兆）或突然的（没有预兆）；失效的后果（轻微损坏或重大灾难）；以及其他此突然的（没有预兆）；失效的后果（轻微损坏或重大灾难）；以及其他此类因素。类因素。If the factor of safety too low,the likelihood of failure will be high and hence the structure will be unacceptable;if the factor is too large,the structure will be wasteful of materials and perhaps unsuitable for its function(for instance,it may be too heavy).Because of these complexities,good engineering judgment is required when establishing factors of safety.They are usually determined by groups of experienced engineers who write the codes(kud n.规范，标准规范，标准)and specifications used by other designers.如果安全系数太低，失效的可能性将很高，因此，这样的如果安全系数太低，失效的可能性将很高，因此，这样的结构将是不能接受的；如果系数过大，结构将浪费材料，而且结构将是不能接受的；如果系数过大，结构将浪费材料，而且可能不适合它的功能（例如，它可能过重）。可能不适合它的功能（例如，它可能过重）。由于这些复杂由于这些复杂性，建立安全系数时需要良好的工程判断，它们通常是由经性，建立安全系数时需要良好的工程判断，它们通常是由经验丰富的编写规范的工程师决定的，而这些规范是设计师在验丰富的编写规范的工程师决定的，而这些规范是设计师在设计过程中使用的。设计过程中使用的。In actual practice,there are several ways in which factors of safety are defined and implemented.For many structures,it is important that the material remain within the linear elastic range(线弹性范围线弹性范围)in order to avoid permanent deformations when the loads are removed.Hence,a common method of design is to use a factor of safety with respect to yielding of the structure.The structure begins to yield when the yield stress,we obtain an allowable stress(允许应力允许应力),of working stress,that must not be exceeded anywhere in the structure.在实际工程中，有几种确定和实施安全系数的方法。对于在实际工程中，有几种确定和实施安全系数的方法。对于许多机构，重要的是，卸除载荷时这些材料仍在弹性线性范围许多机构，重要的是，卸除载荷时这些材料仍在弹性线性范围内，从而避免永久变形。内，从而避免永久变形。因此，通常的设计方法是使用与结构因此，通常的设计方法是使用与结构结构达到屈服应力时开始产生屈服，我结构达到屈服应力时开始产生屈服，我屈服对应的安全系数。屈服对应的安全系数。们会取得一个允许的工作应力，这个应力不能超过结构任何地们会取得一个允许的工作应力，这个应力不能超过结构任何地方所能承受的压应力方所能承受的压应力.Thus,Allowable stress=yieldstressfactorofstressOrnyallowin which we have introduced the notations and for the allowable and yield stresses,respectively.In building design,a typical factor of safety n with respect to yielding is 1.67;thus,a mild steel having a yield stress of 36 ksi has an allowable stress in tension of 21.6 ksi.因而因而：屈服应力允许应力=应力系数或者或者nyallow上式，我们引出了上式，我们引出了 和，分别表示允许应力和屈服应力。在建和，分别表示允许应力和屈服应力。在建筑设计中，一个典型的安全系数筑设计中，一个典型的安全系数n对应的屈服应力为对应的屈服应力为1.67；因；因此，低碳钢屈服应力为此，低碳钢屈服应力为36 ksi对应有一个允许拉应力对应有一个允许拉应力21.6 ksi。Another method of design is to establish the allowable stress by applying a factor of safety with respect to the ultimate stress(极限应力极限应力)instead of the yield stress.This method is suitable for brittle materials,such as concrete,and it also is used for wood.The allowable stress is obtained from the equation:另一种设计方法是通过应用与极限应力而不是屈服应力对应的另一种设计方法是通过应用与极限应力而不是屈服应力对应的安全系数。安全系数。nuallownuallow这种方法适用于脆性材料，如混凝土，也可用于木这种方法适用于脆性材料，如混凝土，也可用于木材。允许应力是从方程中获得材。允许应力是从方程中获得:The last method we will describe involves the application of factors of safety to loads rather than to stresses.We will use the term ultimate loads to mean the loads that produce failure or collapse of the structure.The loads that the structure must support in service are called service loads or working loads.The factor of safety is the ratio of the former to the latter:我们描述的后一种方法是关于荷载安全系数的应用而不是应力我们描述的后一种方法是关于荷载安全系数的应用而不是应力安全系数的应用。我们将使用的极限荷载会意味着结构的断裂安全系数的应用。我们将使用的极限荷载会意味着结构的断裂或倒塌。或倒塌。Factor of safety n=ultimateloadserviceload结构在使用期间需要支撑的载荷就是使用荷载或工作结构在使用期间需要支撑的载荷就是使用荷载或工作荷载。安全系数就是前者和后者的比值：荷载。安全系数就是前者和后者的比值：极限荷载安全系数 n=工作荷载 In as much as service loads are known quantities,the usual design procedure is to multiply them by the factor of safety to obtain the ultimate loads.Then the structure is designed so that it can just sustain the ultimate loads.Then the structure is designed so that it can just sustain the ultimate loads at failure.This method of design is known as strength design,or ultimate-load design,and the factor of safety is called the load factor because it is a multiplier of the service loads:在大家都知道的工作荷载中，通常的设计步骤是用安全系数在大家都知道的工作荷载中，通常的设计步骤是用安全系数乘以工作荷载得出极限荷载。这样的设计结构正好能够承担乘以工作荷载得出极限荷载。这样的设计结构正好能够承担其极限荷载。其极限荷载。Ultimate load=(service load)(load factor)极限荷载极限荷载=（工作荷载）（工作荷载）*（荷载系数）（荷载系数）然后，所设计的结构正好能够保证在破坏时能然后，所设计的结构正好能够保证在破坏时能够承担极限荷载。这种设计方法被称作强度设计或极限荷载够承担极限荷载。这种设计方法被称作强度设计或极限荷载设计，安全系数被称为荷载系数，因为它是工作荷载的乘数：设计，安全系数被称为荷载系数，因为它是工作荷载的乘数：Typical load factors used in the design of reinforced concrete structures are 1.4 for dead load,which is the weight of the structure itself,and 1.7 for live loads,which are loads applied to the structure,The strength-design method is used regularly for reinforced concrete structures and occasionally for steel structures.典型的荷载系数在设计钢筋混凝土中使用，恒载为典型的荷载系数在设计钢筋混凝土中使用，恒载为1.4，即，即是结构本身的重量，应用于结构中的活载为是结构本身的重量，应用于结构中的活载为1.7，这种强度设计，这种强度设计方法经常用于钢筋混凝土结构中，有时也用于钢结构中。方法经常用于钢筋混凝土结构中，有时也用于钢结构中。In aircraft design,it is customary to speak of the margin of safety rather than the factor of safety.The marginm:din n.边边缘部分，页面的空白，栏外缘部分，页面的空白，栏外 of safety is defined as the factor of safety minus one:Margin of safety=n-1 (4-6)Thus,a structure having an ultimate strength that is twice the required strength has a factor of safety of 2.0 and a margin of safety of 1.0.When the margin of safety is reduced to zero or less,the structure(presumably)will fail.在飞机设计中，习惯讲的是安全限度而不是安全系数。安全限在飞机设计中，习惯讲的是安全限度而不是安全系数。安全限度被定义为安全系数减去度被定义为安全系数减去1：安全限度安全限度=安全系数安全系数n-1 (4A-6)因此，结构所具有的极限强度安全系数为因此，结构所具有的极限强度安全系数为2.0，是安全限度为，是安全限度为1.0的强度的的强度的2.0倍。安全限度减小为倍。安全限度减小为0或更小，结构就垮了。或更小，结构就垮了。Exercises.Fill in the blanks with the information given in the text.1.Mechanics of materials is a _ of _ that deals_ the behavior of solid bodies subjected _various types of _.2.In general,the objectives of our analysis will be the determination _the _,_,and _produced _ the loads.3._ many structures,it is important that the material remain _the _ _ in order to avoid permanent deformations when the _ are removed.branch applied mechanics with to loading of stresses strains deflections by For within linear elastic range loads .Translate the following passages from English into Chinese.Superposition was presented as the preferred method for solving certain problems.However,becoming familiar with superposition was more important than finding solutions to the problems because superposition has application in many areas of stress analysis and will be used frequently in our future studies.对于解决一些特定的问题，叠加法被认为是更好的方法。对于解决一些特定的问题，叠加法被认为是更好的方法。然而，熟悉叠加法比解决这个问题本身更重要，因为叠加法可然而，熟悉叠加法比解决这个问题本身更重要，因为叠加法可应用在应力分析的很多领域，而且在我们今后的研究中还会经应用在应力分析的很多领域，而且在我们今后的研究中还会经常应用。常应用。When studying mechanics of materials,you will find that your efforts are divided naturally into two parts:first,understanding the logical development of the concepts,and second,applying those concepts to practical situations.The former is accomplished by studying the derivations,discussions,and examples,and latter by solving problems.Some of the examples and problems are numerical in character,and others are algebraic(or symbolic).当研究材料力学时，你会发现，你的努力自然分为两当研究材料力学时，你会发现，你的努力自然分为两部分：第一，理解概念的逻辑发展，第二，把这些概念用部分：第一，理解概念的逻辑发展，第二，把这些概念用于实际。于实际。前者是通过研究，推导，讨论和举例，后者是解前者是通过研究，推导，讨论和举例，后者是解决问题。一些例子和问题是数值的特点，其他是代数（或决问题。一些例子和问题是数值的特点，其他是代数（或符号的）性质的符号的）性质的。Section B Stress-strain Relationship of Materials（边坡上的基础（边坡上的基础）Every material undergoes deformation under the action of external forces or loads.Deformation,for example,change in dimension or in shape of the body or both simultaneously(simlteinisly adv.同时地同时地).While undergoing deformation,the particles of the material exert a resisting force.When this resisting force equals applied load,the equilibrium condition(平衡条件平衡条件)exists and hence deformation stops.This internal resistance is called the stress.The unit of stress is N/m2.任何材料在外力或荷载的作用下都要变形。例如，变形有尺寸任何材料在外力或荷载的作用下都要变形。例如，变形有尺寸的改变或形体的变化或二者同时进行。经历变形的同时，材料的改变或形体的变化或二者同时进行。经历变形的同时，材料各部分会产生抵抗力。各部分会产生抵抗力。当这种抗力等于载荷时，平衡条件就存当这种抗力等于载荷时，平衡条件就存在，而且变形就停止。这种内部抵抗叫做应力。该应力的单位在，而且变形就停止。这种内部抵抗叫做应力。该应力的单位是是N/m2。The satisfactory performance of a structure frequently is determined by the amount of deformation or distortion that can be permitted.A deflection of a few thousandths of an inch might make a boring machine useless,whereas the boom(bu:m n.悬臂，吊杆悬臂，吊杆)on a dragline(drlain n.拉牵，导索，拉牵，导索，拉铲挖土机拉铲挖土机)might deflect several inches without impairing(im p v.损害，损伤，断裂损害，损伤，断裂)its usefulness.It is often necessary to relate the loads on a structure,or on a member in a structure,to the deflection the loads will produce.结构的令人满意的表现通常是由其允许大的变形和扭曲结构的令人满意的表现通常是由其允许大的变形和扭曲决定的。变形几千分之一英寸就有可能使钻床毫无用处，决定的。变形几千分之一英寸就有可能使钻床毫无用处，而挖土机的悬臂可能偏移几英寸也不会损害其效用。关心结而挖土机的悬臂可能偏移几英寸也不会损害其效用。关心结构上或构件上的荷载以及荷载产生的挠度是必要的。构上或构件上的荷载以及荷载产生的挠度是必要的。Typical foundation types in Hong Kong are spread footings,caissons(keisn n.沉箱沉箱)(hand-dug and machine bored)and piles(percussion(p:kn n.冲击，撞击，碰击冲击，撞击，碰击),bored,precast(pri:k:st vt.现浇制；现浇制；adj.预制预制(的的)，预浇铸，预浇铸(的的)and cast-in-place(现浇现浇).Spread footings and hand-dug caissons are the most common because heavy machinery is not required for construction,the operation of which is difficult on steep hillsides.在香港，典型的基础形式包括扩展基础、沉箱（人工挖在香港，典型的基础形式包括扩展基础、沉箱（人工挖掘及机械钻挖）以及桩基础（冲击、钻孔、预制和现浇）。掘及机械钻挖）以及桩基础（冲击、钻孔、预制和现浇）。因为重型机械很难在陡坡上进行施工操作，所以扩展基础和因为重型机械很难在陡坡上进行施工操作，所以扩展基础和人工挖掘沉箱是最常见的基础形式。人工挖掘沉箱是最常见的基础形式。Such information can be obtained by plotting diagrams showing loads and deflections for each member and type of loading in a structure,but such diagrams(dairm n.图表，图图表，图解，立体图解，立体图)will vary with the dimensions of the members,and it would be necessary to draw new diagrams each time the dimensions were varied.A more useful diagram is one showing the relation between the stress and strain.Such diagrams are called stress-strain diagrams.这些信息的获得是通过绘制表格来表示构件的荷载和变形这些信息的获得是通过绘制表格来表示构件的荷载和变形以及在结构上的荷载类型。以及在结构上的荷载类型。但是这种图表随着构件尺寸的变化但是这种图表随着构件尺寸的变化而变化，所以每次尺寸变化的时候绘制新表格是有必要的。而变化，所以每次尺寸变化的时候绘制新表格是有必要的。显显示应力和应变关系的图更有用，这种图表被称为应力应变图。示应力和应变关系的图更有用，这种图表被称为应力应变图。Data for stress-strain diagrams are usually obtained by applying an axial load to a test specimen and measuring the load and deformation simultaneously.A testing machine is used to strain the specimen and to measure the load required to produce the strain.The stress is obtained by dividing the load by the initial cross-sectional(krssekn a.横截面的横截面的area of the specimen.The area will change somewhat during the loading,and the stress obtained using the initial area is obviously not the exact stress occurring at higher loads.通常应力应变图表的数据是根据轴向载荷作用到试件上，通常应力应变图表的数据是根据轴向载荷作用到试件上，测量荷载和同时发生的变形来获得的。测量荷载和同时发生的变形来获得的。测试机是用来测量测试机是用来测量产生应变的试样的荷载。应力是通过试样的荷载除以初始产生应变的试样的荷载。应力是通过试样的荷载除以初始在加载的过程中，这个面积是变化的，在加载的过程中，这个面积是变化的，横截面积得出的。横截面积得出的。使用初始面积获得应力是明显的，不是更高的荷载出现时使用初始面积获得应力是明显的，不是更高的荷载出现时的准确应力。的准确应力。It is the stress most commonly used,however,in designing structures.The stress obtained by dividing the load by the actual area is frequently called the true stress and is useful in explaining the fundamental behavior of materials.The stress being defined as:在结构设计中，最常用到的是应力。通过荷载除以实际面在结构设计中，最常用到的是应力。通过荷载除以实际面积而得到的应力通常叫做实际应力，这种应力对解释材料的基积而得到的应力通常叫做实际应力，这种应力对解释材料的基本行为很有用处。应力被定义为：本行为很有用处。应力被定义为：()loadPstressareaAPA载荷应力=面积Stress may thus be compressive or tensile depending on the nature of the load.When P is in Newtons and A is in square meters,stress,is in Newtons per square meter(N/m2),which is by definition Pascals(Pa).应力应力的压缩或拉伸取决于荷载的性质。荷载的压缩或拉伸取决于荷载的性质。荷载P的单位是牛顿，而面积的单位是牛顿，而面积A的单位的单位是平方米，应力的单位就是牛顿每平方米（是平方米，应力的单位就是牛顿每平方米（N/m2），这就是帕斯卡（帕）。），这就是帕斯卡（帕）。Strain is a measure of the deformation produced by the application of external forces.Strain is measured as the ratio of the change in length,to the original length.It is the linear(lini adj.线的，线形的线的，线形的)change in length per unit length.It is usually denoted by.The strain produced is defined as follows:应变是衡量应用外部力而产生变形的。应变是用长度的变应变是衡量应用外部力而产生变形的。应变是用长度的变化除以原始长度的比率来衡量的。每单位长度的变化是线性变化除以原始长度的比率来衡量的。每单位长度的变化是线性变化。它就是通常所指的化。它就是通常所指的。应变的产生的定义如下：。应变的产生的定义如下：()changeinlengthdlstrainoriginallengthldll长度的变化应变原始长度 True strain,like true stress,is computed on the basis of the actual length of the test specimen during the test and is used primarily to study the fundamental properties of materials.Strains are usually relatively small in materials used in engineering structures,often less than 0.1%,and their accurate determination require special measuring equipment.真正的应变，和实际应力一样，在实验当中试样的实际长度的真正的应变，和实际应力一样，在实验当中试样的实际长度的基础上计算出来的，而且主要用来研究材料的基本性能。基础上计算出来的，而且主要用来研究材料的基本性能。用于工程用于工程结构中的材料，应变相对较小，通常低于结构中的材料，应变相对较小，通常低于0.1 ，它的准确得出，它的准确得出需要特殊的测量设备。需