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1、Translation The concepts of stress and strain can be illustrated in an elementary way by considering the extension of a prismatic bar.As shown in Fig.1,a prismatic bar is one that has constant cross section throughout its length and a straight axis.In this illustration the bar is assumed to be loade
2、d at its ends by axial forces P that produce a uniform stretching,or tension,of the bar.,应力和应变的概念可以通过考虑一根矩形梁的拉伸的简单方法来举例说明。如图1所示，这根矩形梁可以看作是由遍及长度方向的连续横截面所组成，这些横截面垂直于它的轴向。在这个例子中，这根矩形梁被假定在它两端施加了一对使它发生均匀拉伸的轴向力P。,By making an artificial cut(section mm)through the bar at right angles to its axis,we can iso
3、late part of the bar as a free body see Fig.1(b).At the left-hand end the tensile force P is applied,and at the other end there are forces representing the action of the removed portion of the bar upon the part that remains.These forces will be continuously distributed over the part cross section,an
4、alogous to the continuous distribution of hydrostatic pressure over a submerged surface.,假设在梁的轴向上做一个垂直截面（截面mm），可以分离出一部分自由的梁见图1(b)。在该梁的左端，有拉力P，而在另一端有相应的力可以替代梁的分离部分对它的作用。这些力连续分布在横截面上，类似于在水平面下的静水压力的连续分布。,The intensity of force,that is,the force per unit area,is called the stress and is commonly denoted
5、 by the Greek letter.Assuming that the stress has a uniform distribution over the cross section see Fig.1(b),we can readily see that its resultant is equal to the intensity times the cross-sectional area A of the bar.Furthermore,from the equilibrium of the body shown in Fig.1(b),we can also see that
6、 this resultant must be equal in magnitude and opposite in direction to the force P.Hence,we obtain=P/A.(1),力的强度，也就是说单位面积上的力，被称为应力，通常用希腊字母来表示。假定应力在横截面上均匀分布见图1(b)，那么我们可以很容易的看出它的合力等于强度乘以梁的横截面积A。而且，从图1上显示的物体的平衡来看，我们可以发现这个合力是跟拉力P在数值上相等，方向相反的。因此，我们得到方程（1）=P/A。,Eq.(1)can be regarded as the equation for th
7、e uniform stress in a prismatic bar.This equation shown that stress has units of force divided by area.When the bar is being stretched by the force P,as shown in the figure,the resulting stress is a tensile stress;if the forces are reversed in direction,causing the bar to be compressed,they are call
8、ed compressive stress.,方程(1)用于求解在梁中均匀分布的应力问题。它表示了应力的单位是力除以面积。正如我们在图1中所看到的，当梁被力P拉伸的时候，生成的应力是拉应力；如果力的方向被颠倒，导致梁被压缩时，产生的应力被称为压应力。,A necessary condition for Eq.(1)to be valid is that the stress must be uniform over the cross section of the bar.This condition will be realized if the axial force P acts thr
9、ough the centroid of the cross section.When the load P does not act at the centroid,bending of the bar will result,and a more complicated analysis is necessary.At present,however,it is assumed that all axial forces are applied at the centroid of the cross section unless specifically stated to the co
10、ntrary.Also,unless stated otherwise,it is generally assumed that the weight of the object itself is neglected,as was done when discussing the bar in Fig.1.,方程(1)成立的必要条件是应力在梁的横截面上是均匀分布的。如果轴向力P通过横截面的形心，那么这个条件是可以实现的。如果轴向力P不通过横截面的形心，则会导致梁的弯曲，必须经过更复杂的分析。然而，目前除非特定说明，都假定所有的轴向力都通过横截面的形心。同样，除非是另外说明，一般我们不考虑物体
11、自重，正如我们在图1中讨论的梁一样。,The total elongation of a bar carrying an axial force will be denoted by the Greek letter see Fig.1(a),and the elongation per unit length,or strain,is then determined by the equation=/L(2).Where L is the total length of the bar.Note that the strain is a non-dimensional quantity.It
12、 can be obtained accurately from Eq.(2)as long as the strain is uniform throughout the length of the bar.If the bar is in tension,the strain is a tensile strain,representing an elongation or stretching of the material;if the bar is in compression,the strain is a compressive strain,which means that a
13、djacent cross section of the bar move closer to one another.,在轴向力作用下，梁的总伸长用希腊字母来表示见图1(a)，单位伸长量或者说应变将由方程(2)决定，这里L是指梁的总长度。注意，这里应变是一个无量纲量，只要应变在梁的长度上各处是均匀的，那么它可以通过方程(2)精确获得。如果梁被拉伸，那么得到拉应变，表现为材料的延长或者拉伸；如果梁被压缩，那么得到压应变，意味着梁的横截面将彼此更加靠近。,When a material exhibits a linear relationship between stress and strai
14、n,it is said to be linear elastic.This is an extremely important property of many solid materials,including most metals,plastics,wood,concrete,and ceramics.The linear relationship between stress and strain for a bar in tension can be expressed by the simple equation=E(3)in which E is a constant of p
15、roportionality known as the modulus of elasticity for the material.,当一种材料的应力与应变表现出线性关系时，我们称这种材料为线弹性材料。这是许多固体材料的一个极其重要的性质，这些材料包括大多数金属，塑料，木材，混凝土和陶瓷。对于被拉伸的梁来说，这种应力与应变之间的线性关系可以用简单方程(3)=E 来表示，这里E是一个已知的比例常数，即该材料的弹性模量。,Note that E has the same units as stress.The modulus of elasticity is sometimes called Y
16、oungs modulus,after the English scientist Thomas Young(1773-1829)who studied the elastic behavior of bars.For most materials the modulus of elasticity in compression is the same as in tension.,注意，弹性模量的单位跟应力的单位相同。在研究梁的弹性行为的英国科学家Thomas Young(1773-1829)出现之后，弹性模量有时也被称为杨氏模量。对大多数材料而言，压缩和拉伸时的弹性模量是一样的。,Tran
17、slation,The relationship between stress and strain in a particular material is determined by means of a tensile test.A specimen of the material,usually in the form of a round bar,is placed in a testing machine and subjected to tension.The force on the bar and the elongation of the bar are measured a
18、s the load is increased.The stress in the bar is found by dividing the force by the cross-sectional area,and the strain is found by dividing the elongation by the length along which the elongation occurs.In this manner a complete stress-strain diagram can be obtained for the material.,一种材料的应力-应变关系可以
19、通过一个拉伸测试来确定。材料的样品通常做成圆棒状，放置在测试仪器上然后施加拉力。随着载荷的增加，圆棒受的力和伸长量可以被测定。圆棒的应力可以通过力除以横截面积得到，应变则通过伸长量除以圆棒的长度得到。这样，我们就得到了这种材料完整的应力-应变图表。,The typical shape of the stress-strain diagram for structural steel is shown in Fig.1,where the axial strains are plotted on the horizontal axis and the corresponding stresses
20、 are given by the ordinates to the curve OABCDE.From O to A the stress and the strain are directly proportional to one another and the diagram is linear.Beyond point A the linear relationship between stress and strain no longer exists,hence the stress at A is called the proportional limit.,图1是结构钢的经典
21、应力-应变图，图中横坐标表示轴向的应变，跟通过纵坐标表示的相应的应力一起形成曲线OABCDE。从O到A这一段，应力和应变彼此成正比关系，图形是成线性的。超过A点以后，应力和应变的线性关系不再存在，因此A点的应力被称为比例极限。,With an increase in loading,the strain increases more rapidly than the stress,until at point B a considerable elongation begins to occur with no appreciable increase in the tensile force
22、.This phenomenon is known as yielding of the material,and the stress at point B is called the yield point or yield stress.In the region BC the material is said to have become plastic,and the bar may actually elongate plastically by an amount which is 10 or 15 times the elongation which occurs up to
23、the proportional limit.,随着载荷的增加，应变的增长比应力更快，直到B点一个显著的伸长开始出现，而拉力的增加并不明显。这就是众所周知的材料的屈服现象，B点的应力被称为屈服点或者屈服应力。在区域BC中，材料被认为是塑性的，事实上杆的塑性伸长是达到比例极限时伸长的10到15倍。,At point C the material begins to strain harden and to offer additional resistance to increase in load.Thus,with further elongation the stress increase
24、s,and it reaches its maximum value,or ultimate stress,at point D.Beyond this point further stretching of the bar is accompanied by a reduction in the load,and fracture of the specimen finally occurs at point E on the diagram.,材料在C点出现应变强化，对载荷的增加产生了额外的阻力。这样，随着进一步的伸长，应力随之增加，直到D点，应力达到最大值即极限应力。超过D点以后，进一步
25、的伸长伴随着载荷的减少，最后在图表的E点处，样品发生断裂。,During elongation of the bar a lateral contraction occurs,resulting in a decrease in the cross-sectional area of the bar.This phenomenon has no effect on the stress-strain diagram up to about point C,but beyond that point the decease in area will have a noticeable effec
26、t upon the calculated value of stress.A pronounced necking of the bar occurs(see Fig.2),and if the actual cross-sectional area at the narrow part of the neck is used in calculating,it will be found that the true stress-strain curve follows the dashed line CE.Whereas the total load the bar can carry
27、does indeed diminish after the ultimate stress is reached(line DE),this reduction is due to the decrease in area and not to a loss in strength of the material itself.,在伸长过程中，圆棒发生了一个横向的收缩，导致了圆棒横截面积的减少。直到C点为止，这个现象对应力-应变图都没有影响，但是超出C点以后，面积的减少对应力的计算有着显著的影响。圆棒发生了一个明显的颈缩(见图2)，如果在计算时使用颈缩处狭窄的真实横截面积，我们发现真实应力-
28、应变曲线将沿着虚线CE进行。然而，当达到极限应力时(线段DE)，圆棒的总载荷可能真正的减少，这个减少归功于面积的减少而不是材料本身强度的损失。,The material actually withstands an increase in stress up to the point of failure.For most practical purposes,however,the conventional stress-strain curve OABCDE,based upon the original cross-sectional area of the specimen,provi
29、des satisfactory information for design purposes.,直到失效点为止，材料一直承受应力的增加。然而，对大多数实际目的而言，建立在样品的原始横截面积上的传统应力-应变曲线OABCDE给设计用途提供了令人满意的信息。,The diagram in Fig.1 has been drawn to show the general characteristics of the stress-strain curve.There is an initial region on the stress-strain curve in which the mate
30、rial behaves both elastically and linearly.The region from O to A on the stress-strain diagram for steel is an example.The presence of a pronounced yield point followed by large plastic strains is somewhat unique to steel,which is the most common structural metal in use today.Aluminium alloys exhibi
31、t a more gradual transition from the linear to the nonlinear region.,图1显示了应力-应变曲线的一般特征，在这个曲线上有一个体现材料的弹性和线性的初始区域。钢的应力-应变曲线上从O点到A点的这个区域就是一个例子。紧随大塑性应变之后的显著的屈服点现象是目前最常用的结构金属钢的一点独特的性质。铝合金则展示出了从线性到非线性区域的更平缓的转变。,Both steel and many aluminium alloys will undergo large strain before failure and are therefore
32、 classified as ductile.On the other hand,materials that are brittle fail at relatively low values of strain.Examples include ceramics,cast iron,concrete,certain metallic alloys,and glass.,钢和许多铝合金在失效之前都会出现大的应变，因此可以被分类为韧性材料。另一方面，许多材料在相当小的应变时也会出现破裂失效，例如陶瓷，铸铁，混凝土，某些金属合金和玻璃。,Translation When a structure
33、is subjected to dynamic loading,the whole or part of it is accelerated with the result that inertia forces are introduced.Due to the influence of inertia forces,the stresses vary during and after loading so that a particular state of stress exists only at a corresponding instant during the process.I
34、n many cases,however,when the loads are gradually applied or change slowly,the dynamic effect is insignificant and can be neglected.With suddenly applied loads the effect of inertia forces must be taken into account and in extreme cases such as impact or resonance vibration,the dynamic effect predom
35、inates.,当一个结构被施加动载荷时，它的整体或者部分会由于惯性力的引入而被加速。由于惯性力的影响，在加载过程中和加载后的应力变化很大，以至于在过程中每一个瞬间只对应一个特别的应力状态。然而，在许多情况下，当载荷是缓慢增加或者变化很小时，动态影响是无关紧要的或者是可以被忽略的。但是在突然加载时，惯性力的影响必须被考虑，而且在一些特殊的情况下例如冲击或者共振时，动态作用是主要的影响因素。,As mentioned previously,the dynamic effect,i.e.,the influence of inertia forces on the process of stres
36、s development in a body,depends on the dynamic loading conditions.Three groups of typical phenomena can be distinguished.There are(1)quasi-static states of stress,(2)vibrations,and(3)stress waves.The limits between these groups are not clearly defined,however,and frequently the phenomena associated
37、with more than one groups can occur in the same dynamic event.,正如前面所提到的一样，动力学的影响也就是在一个物体中，根据动态加载的条件，惯性力对应力发展过程的影响。这些影响可以区分为三种典型的现象。它们是应力的准静态状态，振动和应力波。然而，三种现象的界限并没有被清楚的说明，因此常常在同一个动力学事件中有超过一种以上的现象发生。,The dynamic response of a body depends not only on the magnitude of the forces acting but also,to a de
38、cisive extent,on their rate of change.Thus,while stress waves are produced by the change of forces,the frequency of these waves is determined by their rate of change.If the change of forces is due to the impact of a striking body,this means that the response of the body struck depends on the time of
39、 contact between the two bodies.,一个物体的动态响应不但跟作用力的数值有关，起决定因素的还是这些力变化的频率。因此，当力的变化产生应力波时，这些波的频率已经由产生它们的力的变化率所确定了。如果这些力的变化是由于一个物体的冲击，那就意味着这个被撞击物体的响应决定于这两个物体的接触时间。,When the forces acting on a body change slowly so that the frequency is very low,the length of the wave is usually great compared with the di
40、mensions of the body.In such extreme cases,the stress distribution is independent of the rate of the forces.Although the stresses vary in magnitude during the process,their distribution remains the same throughout and is identical with that under corresponding static loading.The external forces acti
41、ng on the body are in equilibrium throughout the event and all stresses vanish when these forces cease to act.Problems in which the behavior follows this pattern are called quasi-static.,当作用在物体上的力变化很慢导致频率很低时，波长通常要大于物体本身的尺寸。在这样极端的情况下，应力的分布与力的变化率无关。尽管在加载过程中，应力大小有变化，但是在整个过程中它们的分布和在相应静载荷作用下的情况相同。作用在物体上的
42、外力在过程中保持均衡，而且当外力停止作用时，应力消失。我们把变化过程遵循上述形式的问题称为准静态问题。,When the frequency of the loading cycle is of the same order as the resonance frequency of the body,the stress waves and their reflections cause vibrations,e.g.,longitudinal or flexural vibrations.Due to inertia forces the stress distribution will
43、differ to some extent from that in comparable static or quasi-static cases and the external forces are not in equilibrium throughout the event.,当循环加载的频率与物体本身的共振频率一致时，应力波和它们的反射波可以引起振动，例如，纵向的或者横向的振动。由于惯性力的存在，应力的分布在一定程度上不同于静态或者准静态的情况，外力在加载过程中也不是均衡的。,If the rate of change of the forces acting on a body
44、corresponds with a high frequency,i.e.,with the generation of waves which are short compared with the dimensions of the body,the effect of stress waves predominates.In such cases the stress distribution differs greatly from that produced under static or quasi-static conditions.,如果作用在物体上的外力的变化率，对应于一个
45、高的频率，也就是说，产生的波长小于物体本身的尺寸时，那么应力波的效果就很明显。在这样的情况下，应力的分布在很大程度上不同于在静态或者准静态条件下的分布。,一个经常遇到的问题是，在动态条件下，包括带有一个缺口或者别的不规则形状的物体的应力波或者振动，应力集中因子的确定。在这样的情况下，问题的解决方法取决于波长和缺口的相关尺寸。如果缺口的尺寸小于波长，那么在缺口附近应力的分布类似于相对应静载下的分布。因此，这样加载在物体相应的一小部分的模型上也会产生同样的应力分布。,A problem frequently encountered is that of determining the stress
46、 concentration factor under dynamic conditions involving stress waves or vibrations at a notch or other irregularity in the shape of a body.In such cases the procedure to be adopted depends on the relative dimensions of the wavelength and the notch.If the dimensions of the notch are small compared w
47、ith the wavelength,the stress distribution in the neighborhood of the notch will be similar to that under comparable static loading.Such loading applied to a model of the relevant small part of the body will therefore produce the same stress distribution.,When the length of a stress wave is of the s
48、ame order or smaller than the dimensions of a body or,for instance,of a notch in it,dynamic methods must be applied.This is also true in the case of vibrations.Since the stress concentration factor depends on the length of the stress wave involved,it is obvious that there is no generally applicable
49、dynamic factor of stress concentration.,当一个应力波的波长等于或者小于一个物体的本身尺寸，或者具体来说它等于或者小于物体上的一个缺口的尺寸时候，我们必须采用动力学方法。在振动情况下，同样如此。由于应力集中因子与应力波本身的波长有关，因此很明显，没有普遍适用的应力集中动态因子。,The modern digital computer can be defined as an electronic device for high speed automatic information processing.This powerful computationa
50、l device can receive the information provided by the user,operate upon it,and produce new information.For a better understanding of this process of acquisition,processing,and delivering of information,we should identify the basic components of a computer,and analyze their functions.These components
