Lesson 2 Simple Stress and Strain
In any engineering structure the individual components or members will be subjected to external forces arising from the service conditions or environment in which the component works. If the component or member is in equilibrium, the resultant of the external forces will be zero but, nevertheless, they together place a load on the member which tends to deform that member and which must be reacted by internal forces set up within the material.
在任何工程结构中，单个部件或构件将受到部件工作条件或环境产生的外力。如果部件或构件处于平衡状态，则外力的合力将为零，但是，它们一起在构件上施加一个荷载，该荷载趋向于使该构件变形，并且必须受到材料内设置的内力的作用。
There are a number of different ways in which load can be applied to a member. Loads may be classified with respect to time:
有许多不同的方法可以将荷载施加到构件上。荷载可按时间分类：
(a) .A static load is a gradually applied load for which equilibrium is reached
in a relatively short time.
静载荷是在较短时间内达到平衡的逐渐施加的载荷。
(b.)A sustained load is a load that is constant over a long period of time, such as the weight of a structure. This type of load is treated in the same manner as a
static load; however, for some materials and conditions of temperature and stress, the resistance to failure may be different under short time loading and under sustained loading.
持续荷载是一种长期不变的荷载，如结构的重量。这种载荷的处理方式与静载荷相同；但是，对于某些材料和温度和应力条件，短期载荷和持续载荷下的抗破坏性可能不同。
(c).An impact load is a rapidly applied load (an energy load). Vibration normally
results from an impact load, and equilibrium is not established until the vibration is eliminated, usually by natural damping forces.
冲击载荷是一种快速施加的载荷（能量载荷）。振动通常是由冲击载荷引起的，通常是由自然阻尼力消除振动后才能建立平衡。
(d).A repeated load is a load that is applied and removed many thousands of times.
重复荷载是施加和移除数千次的荷载。
(e).A fatigue or alternating load is a load whose magnitude and sign are changed with time.
疲劳或交变载荷是指其大小和符号随时间变化的载荷。
It has been noted above that external force applied to a body in equilibrium is reacted by internal forces set up within the material. If, therefore, a bar is subjected to a uniform tension or compression, i.e. a force, which is uniformly applied across the cross-section, then the internal forces set up are also distributed uniformly and the bar is said to be subjected to a uniform normal stress, the stress being defined as:
如上所述，施加在平衡物体上的外力是由物质内部的内力产生的。因此，如果一根钢筋受到均匀的拉伸或压缩，即均匀地施加在横截面上的力，则所设置的内力也均匀地分布，并且钢筋被称为受到均匀的正应力，应力定义为
Stress σ may thus be compressive or tensile depending on the nature of the load and will be measured in units of Newtons per square meter(N/m²) or multiples of this.
因此，应力σ可以是压缩应力或拉伸应力，具体取决于荷载的性质，应力σ的测量单位为牛顿/平方米（N/m²）或其倍数。
If a bar is subjected to an axial load, and hence a stress, the bar will change in
length. If the bar has an original length L and changes in length by an amount δL, the strain produced is defined as follows:
如果一根钢筋受到轴向荷载，因此受到应力，则钢筋的长度将发生变化。如果钢筋的原始长度为l，长度变化量为δL，则产生的应变定义如下：
Strain is thus a measure of the deformation of the material and is non-dimensional, i.e. it has no units; it is simply a ratio of two quantities with the same unit.
因此，应变是对材料变形的一种测量，是无量纲的，也就是说，它没有单位；它只是两个量与相同单位之比。
Since, in practice, the extensions of material under load are very small, it is often convenient to measure the strains in the form of strain ×10-6, i.e. microstrain, when the symbol used becomes με.
由于在实际应用中，材料在荷载作用下的延伸量很小，当符号变为με时，通常可以方便地以应变×10-6的形式测量应变，即微应变。
Tensile stresses and strains are considered positive in sense. Compressive stress and strains are considered negative in sense. Thus a negative strain produces a decrease in length.
拉伸应力和应变在意义上被认为是正的。压应力和应变在意义上被认为是负的。因此，负应变会使长度减小。
Figure 2. 1 shows a typical stress-strain curve for a material such as ductile low-carbon significant
steel.
Ductility refers to the ability of a material to withstand a
stretching before it breaks.
Structural
amount
steels and some aluminum alloys are examples of ductile metals, and they are often used in machine components because when they become overloaded, they tend to noticeably stretch or bend before they break. On the other end, so-called brittle materials such as iron, engineering ceramics, and glass break suddenly and without much prior warning when they are overloaded.
图2.1显示a材料如韧性低碳钢的典型应力-应变曲线。延性是指A材料在断裂前承受大量拉伸的能力。结构钢和一些铝合金是韧性金属的例子，它们经常用于机器部件，因为当它们超载时，在断裂前往往会明显拉伸或弯曲。另一方面，所谓的易碎材料，如铁、工程陶瓷和玻璃，在超载时会突然破碎，而不会事先发出任何警告。
A stress-strain curve for a ductile material is broken down into two regions: the
low-strain
elastic
region(
where no permanent
deformation remains after a load has been applied and removed ) and the high-strain plastic region( where the load is large enough that, upon removal, the
materila is permanently elongated). For strains below the proportional limit A in Fig.2.1, stress is proportional to strain. Hooke’s law applies, it has been shown that
A延性材料的应力-应变曲线被分解成两个区域:低应变弹性区（施加和移除荷载后无永久变形依然存在）和高应变塑性区（其中荷载足够大，移除后，材料永久拉长）。对于图2.1中比例极限A以下的应变，应力与应变成比例。胡克定律适用，已经证明
Elastic modulus E is generally assumed to be the same in tension or compression and for most engineering materials has a high numerical value. Typically, E=200×109N/m² for steel, so it will be observed from equation that strains are normally very small.
弹性模量E一般假定在拉伸或压缩时是相同的，对于大多数工程材料来说具有较高的数值。一般来说，钢的E=200×109N/m²，因此从方程中可以看出应变通常非常小。
In most common engineering applications strains rarely exceed 0.1%. The actual value of Young’s modulus for any material is normally determined by carrying out a standard test on a specimen of the material.
在最常见的工程应用中，菌株很少超过0.1%。任何材料杨氏模量的实际值通常通过对材料样品进行标准试验来确定。
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