薄壁容器的应力分析

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,第四章 压力容器设计,CHAPTER 4,Design of Pressure Vessel,Mechanical Design of Process Equipment,1,Mechanical Design of Process Equipment,Our topic covers those aspects of the mechanical design of chemical plant,that,are of particular interest to chemical engineers. The main topic considered is the design of pressure vessels. The design of storage tanks，centrifuges and heat-exchanger tube sheets are also discussed briefly.,The chemical engineer will not usually be called on to undertake the detailed mechanical design of a pressure vessel. Vessel design is a speciafised subject，and will be carried out by mechanical engineers who are conversant with the current design codes and practices，and methods of stress analysis. However，the chemical engineer will be responsible for developing and specifying the basic design information for a particular vessel，and needs to have a general appreciation of pressure vessel design to work effectively with the specialist designer.,2,The basic data needed,The basic data needed by the specialist designer will be：,1.Vessel function.,2.Process materials and services.,3.Operating and design temperature and pressure.,4.Materials of construction.,5. Vessel dimensions and orientation.,6. Type of vessel heads to be used.,7. Openings and connections required.,8. Specification of heating and cooling jackets or coils.,9. Type of agitator.,10. Specification of internal fittings.,3,Them is no strict definition of what constitutes a pressure vessel，but it is generally accepted that any closed vessel over 150 mm diameter subject to a pressure difference of more than 1 bar should be designed as a pressure vessel.,It is not possible to give a completely comprehensive account of vessel design in one chapter. The design methods and data given should be sufficient for the preliminary design of conventional vessels. Sufficient for the chemical engineer to check the feasibility of a proposed equipment design；to estimate the vessel cost for an economic analysis；and to determine the vessels general proportions and weight for plant layout purposes. For a more detailed account of pressure vessel design the reader should refer to other useful books on the mechanical design of process equipment.,4,An elementary understanding of the principles of the “Strength of Materials”（Mechanics of Solids）will be needed to follow this chapter. Readers who are not familiar with the subject should consult one of the many textbooks available；such as those by Faupel and Fisher（1981）. The book by Faupel and Fisher is particularly recommended as a general introduction to mechanical design for chemical engineers.,5,Classification of pressure vessels,For the purposes of design and analysis，pressure vessels are sub-divided into two classes depending on the ratio of the wall thickness to vessel diameter：thin-walled vessels，with a thickness ratio of less than 1：10；and thick-walled above this ratio.,6,7,The principal stresses acting at a point in the wall of a vessel，to a pressure load，are shown in Figure 3.1.,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 be 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.,8,Membrane stresses in shells of revolution,A shell of revolution is the form swept out by a line or curve rotated about an axis.（A solid of revolution is formed by rotating an area about an axis.）Most process vessels are made up from shells of revolution：cylindrical and conical sections；and hemispherical，ellipsoidal and torispherical heads.,The walls of thin vessels can be considered to be“membranes”；supporting loads without significant bending or shear stresses；similar to the walls of a balloon.,9,The analysis of the membrane stresses induced in shells of revolution by internal pressure gives a basis for determining the minimum wall thickness required for vessel shells. The actual thickness required will also depend on the stresses arising from the other loads to which the vessel is subjected.,Consider the shell of revolution of general shape shown in Figure ，under a loading that is rotationally symmetric；that is，the load per unit area（pressure）on the shell is constant round the circumference，but not necessarily the same from top to bottom.,10,11,第一、第二曲率半径,Let P = pressure，,t = thickness of shell，,= the meridional（longitudinal）stress，the stress acting along a meridian，,= the circumferential or tangential stress，the stress acting along parallel circles（often called the hoop stress），,R,1,= the meridional radius of curvature，,R,2,= circumferential radius of curvature.,12,13,14,15,或,当角度（弧度）很小时，,sin,x,x,（拉力的一个分量）,16,两个分量，平衡力大小相互抵消,微元近似一个平面，,这是微积分的思想,17,两个分量，平衡力大小相互抵消,微元近似一个平面，,这是微积分的思想,18,19,Equations 13.5 and 13.6 are completely general for any shell of revolution.,13.5,13.6,20,Cylinder （,圆筒形壳体,）,A cylinder is swept out by the rotation of a line parallel to the axis of revolution,so:,where,D,is the cylinder diameter.,Substitution in equations 13.5 and 13.6 gives:,21,带有椭圆孔的 薄板上的应力集中,22,Sphere,（,球形壳体,）,hence:,23,Cone,（,锥形壳体,）,A cone is swept out by a straight line inclined an angle to the axis:,Substitution in equations 13.5 and 13.6 gives:,The maximum values will occur at,24,Ellipsoid,（,椭圆形壳体，封头,）,For a ellipse with major axis,2a,and minor axis,2b,，it can be shown that（see any,standard geometry text,）：,From equations 13.5 and 13.6,25,At the crown（top）,At the equator（bottom） ，so,26,It should be noted that if,1， will be negative（compressive）and the shell could fail by buckling. This consideration places a limited on the practical proportions of ellipsoidal head.,27,Torispherical,heads,（,准球形封头，碟形封头，折边封头,）,A torispherical shape，which is often used as the end closure of cylindrical vessels，is formed from part of a torus and part of a sphere. The shape is close to that of an ellipse but is easier and cheaper to fabricate,.,is the knuckle radius（the radius of the torus）and,the crown radius （the radius of the torus）.For the spherical portion：,28,29,For the torus ：,depends on the location，and is function of and ；,it can be calculated as well.,The ratio of the knuckle radius to crown radius should be made not less than 6/100 to avoid buckling. The stress will be higher in the torus than the spherical section. and the crown radius should not be greater than the diameter of the cylindrical section.,30,Secondary stresses,（,二次应力,）,1,In the stress analysis of pressure vessels and pressure vessel components stresses are classified as primary or secondary. Primary stresses can be defined as those stresses that are necessary to satisfy the conditions of static equilibrium. The membrane stresses induced by the applied pressure and the bending stresses due to wind loads are examples of primary stresses. Primary stresses are not self-limiting；if they exceed the yield point of the material，gross distortion，and in the extreme situation，failure of the vessel will occur.,31,Secondary stresses,（,二次应力,）,2,Secondary stresses are those stresses that arise from the constraint of adjacent parts of the vessel. Secondary stresses are self-limiting；local yielding or slight distortion will satisfy the conditions causing the stress，and failure would not be expected to occur in one application of the loading. The“thermal stress”set up by the differential expansion of parts of the vessel，due to different temperatures or the use of different materials，is an example of a secondary stress.,32,Secondary stresses,（,二次应力,）,3,Other sources of secondary stresses are the constraints arising at flanges，supports，and the change of section due to reinforcement at a nozzle or opening.,Though secondary stresses do not affect the“bursting strength”of the vessel，they are an important consideration when the vessel is subject to repeated pressure loading. If local yielding has occurred，residual stress will remain when the pressure load is removed，and repeated pressure cycling can lead to fatigue failure.,33,一次应力与二次应力,一次应力,又叫基本应力，它是由外载荷引起的。这类应力的出现是为了抵抗外载对容器的破坏作用，它们随外载的增大而增大，当外载增大到使这些应力达到材料的屈服极限时，容器筒壁就屈服。当外载继续增加时，这类应力也会因材料的强化而继续上升，直至达到材料的强度极限，容器发生破裂为止。,二次应力,是由于容器部件的自身约束或相邻部件的相互约束而产生的正应力或剪应力。这类应力不是为平衡外载而产生，而是由于受到自身或外部的约束而引起。如果限制增大到使应力达到了材料的屈服极限，使器壁金属在这些受限制的区域发生了塑性变形，那么这里的限制将被突破，相互的约束得到缓解，应力便会自动地限制在一定范围之内。所以二次应力有时被称为“自限性”应力。,34,取一段单位长度圆环,35,