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1、Reading material 3Theories of strength1. Principal stresses The state of the stress at a point in a structural member under a complex system of loading is described by the magnitude and direction of the principal stresses. The principal stresses are the maximum values of the normal stresses at the p
2、oint; which act on the planes on which the shear stress is zero. In a two-dimensional stress system, Fig.1.11, the principal stresses at any point are related to the normal stress in the x and y directions x and y and the shear stress xy at the point by the following equation:Principal stresses,The
3、maximum shear stress at the point is equal to half the algebraic difference between the principal stresses.stresses:Maximum shear stress,Compressive stresses are conventionally taken as negative; tensile as positive. 2. Classification of pressure vesselsFor the purpose of design and analysis, pressu
4、re vessels are sub-divided into two classes depending on the ratio of the wall thickness to vessel diameter: thin-wall vessels, with a thickness ratio of less than 1/10, and thick-walled above this ratio. The principal stresses acting at a point in the wall of a vessel, due to a pressure load, are s
5、hown in Fig.1.12. If the wall is thin, the radial stress 3 will be small and can be neglected in comparison with the other stresses , and the longitudinal and circumferential stresses 1 and 2 can be taken as constant over the wall thickness. In a thick wall, the magnitude of the radial stress will b
6、e significant, and the circumferential stress will vary across the wall. The majority of the vessels used in the chemical and allied industries are classified as thin-walled vessels. Thick-walled vessels are used for high pressures.3. Allowable stressIn the first two sections of this unit equations
7、were developed for finding the normal stress and average shear stress in a structural member. These equations can also be used to select the size of a member if the members strength is known. The strength of a material can be defined in several ways, depending on the material and the environment in
8、which it is to be used. One definition is the ultimate strength or stress. Ultimate strength of a material will rupture when subjected to a purely axial load. This property is determined from a tensile test of the material. This is a laboratory test of an accurately prepared specimen, which usually
9、is conducted on a universal testing machine. The load is applied slowly and is continuously monitored. The ultimate stress or strength is the maximum load divided by the original cross-sectional area. The ultimate strength for most engineering materials has been accurately determined and is readily
10、availableIf a member is loaded beyond its ultimate strength it will fail-rupture. In the most engineering structures it is desirable that the structure not fail. Thus design is based on some lower value called allowable stress or design stress. If, for example, a certain steel is known to have an ul
11、timate strength of 110000 psi, a lower allowable stress would be used for design, say 55000 psi. this allowable stress would allow only half the load the ultimate strength would allow. The ratio of the ultimate strength to the allowable stress is known as the factor of safety:We use S for strength o
12、r allowable and for the actual stress in material. In a design:This so-called factor of safety covers a multitude of sins. It includes such factors as the uncertainty of the load, the uncertainty of the material properties and the inaccuracy of the stress analysis. It could more accurately be called
13、 a factor of ignorance! In general, the more accurate, extensive, and expensive the analysis, the lower the factor of safety necessary.4. Theories of failureThe failure of a simple structural element under unidirectional stress (tensile or compressive) is easy to relate to the tensile strength of th
14、e material, as determined in a standard tensile test, but for components subjected to combined stresses (normal and shear stress) the position is not so simple, and several theories of failure have been proposed. The three theories most commonly used are described below:Maximum principal stress theo
15、ry: which postulates that a member will fail when one of the principal stresses reaches the failure value in simple tension, e. The failure point in a simple tension is taken as the yield-point stress, or the tensile strength of the material divided by a suitable factor of safety. Maximum shear stre
16、ss theory: which postulates that failure will occur in a complex stress system when the maximum shear stresses reaches the value of the shear stress at failure in simple tension.For a system of combined stresses there are three shear stresses maxima:In the tensile test, The maximum shear stress will
17、 depend on the sign of the principal stresses as well as their magnitude, and in a two-dimensional stress system, such as that in the wall of a thin-walled pressure vessel, the maximum value of the shear stress may be given by putting 3 =0 in equations 1.10. The maximum shear stresses theory is ofte
18、n called Trescas, or Guests theory. Maximum strain energy theory: which postulates the failure will occur in a complex stress system when the total strain energy per unit volume reaches the value at which failure occurs in simple tensile.The maximum shear-stress theory has been found to be suitable
19、for predicting the failure of ductile material under complex loading and is the criterion normally used in the pressure-vessel design.阅读材料3强度理论1、 主应力作用在受复杂负载的结构部件的一点上的应力用主应力的大小和方向来描述。主应力是作用在该点上的最大的正应力；在该面上作用的切应力为0。在如图1.11所示的二维应力系统中，主应力通过下面的方程和x、y方向上的正应力x、y及该点的切应力xy产生联系：主应力，1、2=（y+x） 切应力的最大值在数值上等于主应力
20、差值的一半：最大切应力，max=(12)通常规定压应力为正，拉应力为负。2、 压力容器分类为了设计和分析方便，通常根据容器厚度和直径的比值把容器分为两类：比值小于1/10的成为薄壁容器，大于1/10的成为厚壁容器。在容器壁上由压力产生的主应力如图1.12所示。若为薄壁，则径向应力3很小，与其他作用力相比可忽略不计，在厚度方向上的纵向和圆周向应力1和2是为常数。在厚壁中，径向应力非常明显，周围应力随着壁面变化。化学和应用工业上应用的主要是薄壁容器。厚壁容器用于高压力领域。3、 许用应力该单元方程的前两部分是为了求出结构部件的正应力和平均切应力。该方程也可用来在组件的强度确定时求其尺寸。材料的强度
21、可通过多种方法来定义，取决于材料本身和其使用的环境。一种定义是最终强度或应力。最终应力指的是材料受纯轴向负载破裂时的应力。该特性是通过对材料的拉伸实验测出的。这是用一个在通用测试机器上常用的精心准备的样本来做的实验室实验。负载缓慢增加并受到实时监测。最终应力或强度是跨界区域分开的最大负载。大多数工程材料的最终应力均已得到精确值并且简单实用。如果构件承受的负载超过其最终强度它将会失效-断裂。大多数情况下我们不希望工程构件失效。因此需要根据许用应力或称作“设计应力”来设计。举个例子，某种钢材的最终强度为110000帕，其许用应力会被设计得比该值低，如55000帕。许用应力是最终强度的一半。最终应力
22、和许用应力的比值称为“安全系数”：安全系数= 或 n= 我们用S表示许用应力，用代表实际应力。在设计时：SA这个所谓的安全系数包含了大多数的不确定因素。包括负载的不确定、材料属性的不确定、还有应力分析的不精确性。称其作忽略系数更贴切些。一般来说，分析得越精确、对象越多、消耗越多，安全系数的必要性越差。4、 失效理论在单向应力下（拉伸或压缩），简单构件的失效很容易和材料的拉伸强度关联起来，正如在标准拉伸实验中确定，但对于部件的连接应力（正应力或切应力），这个位置就不是那么容易确定的了，至今提出多种失效理论。下面是使用的最多的三种理论：最大主应力理论：假设主应力在简单拉伸作用下达到失效值，e。失效
23、点称为“屈服点应力”，或材料的拉伸强度，用一定的安全系数值分开。 最大切应力理论：假设在复杂受力系统中，失效发生在当最大切应力达到简单拉伸情况下的切应力值时。 对一个系统的连接应力来说有三个最大值：1=,2=,3=在拉伸实验中， e= 切应力的最大值取决于主应力和它的大小，在二维应力系统如在一薄壁容器的壁上，切应力的最大值通过将方程1.10的3定为0求得。最大切应力理论常被称作特雷斯卡理论或杰斯特理论。 最大拉伸能量理论：假设在一复杂受力系统中当单位体积内的总拉伸能量达到简单拉伸失效式的值时失效。最大切应力理论已被证实适用于计算在复杂负载下延展性良好的材料的失效值，并且被作为设计压力容器的标准。 （注：素材和资料部分来自网络，供参考。请预览后才下载，期待你的好评与关注！）