1、2022-6-9Basic Stress Theory & CAESAR II 管道应力分析培训管道应力分析培训王大辉北京艾思弗软件公司2022-6-9Basic Stress Theory & 2022-6-9Basic Stress Theory & 介介 绍绍 培训的目的在于让您了解和掌握 应力分析的基础概念 模型和边界条件的建立 结果的分析和评判 往复压缩机的分析专题 日常遇到的问题和解决方法2022-6-9Basic Stress Theory & 介介 绍绍3D梁单元的特征梁单元的特征无限细的杆单元全部行为靠端点位移决定弯曲变形是主要的2022-6-9Basic Stress Th
2、eory & 介介 绍绍3D Beam Element Characteristics3D梁单元的特征 仅说明整体行为 无局部作用（表面没有碰撞） 忽略二次影响（小转动） 遵循胡克定律2022-6-9Basic Stress Theory & Stress Basics应力基础应力基础局部坐标系下管道应力分类（引发应力的载荷）局部坐标系下管道应力分类（引发应力的载荷）轴向应力轴向应力Longitudinal Stress - SL环向应力Hoop Stress - SH径向应力Radial Stress - SR1. 剪切应力Shear Stress - 2022-6-9Basic Stres
3、s Theory & 轴向应力轴向应力 沿管道轴向Along axis of pipe 轴向力引起Axial Force 轴向力/面积 (F/A) 内压引起Pressure Pd / 4t or P*di / ( do2 - di2 ) 弯矩引起Bending Moment Mc/I 最大应力环向的外表面某点处 I/radius Z (截面模量); use M/Z2022-6-9Basic Stress Theory & 压力引起的环向应力压力引起的环向应力 环向（垂直于半径） Pd / 2t 和壁厚紧密相关 环向应力十分重要，但规范应力不考虑它。Hoop is very important,
4、 its just not part of the “code stress” 环向应力用来确定壁厚：依据直径、许用应力、腐蚀裕量、加工偏差、压力确定管道壁厚。2022-6-9Basic Stress Theory & 压力引发的径向应力压力引发的径向应力 沿半径方向向内 内壁的径向应力大小是： -P 外壁的径向应力大小为 0 最大弯曲应力发生在管道的外表面，故该项忽略2022-6-9Basic Stress Theory & 剪切应力剪切应力Shear Stresses 平面内垂直半径 Shear Force剪力 在外表面剪力很小，应力计算忽略 支架设计有时需要考虑 Torque扭矩 最大应
5、力在外表面 MT/2Z2022-6-9Basic Stress Theory & 3-D 应力评定应力评定 A loaded, 3-D pipe contains a representative infinitesimal stress cube add graphic (Fig 1-13) This stress cube is in equilibrium and can be rotated in space add graphic (rotated cube with loads) This cube can be rotated so that shear stresses are
6、 zero. This results in the Principal Stresses.2022-6-9Basic Stress Theory & Simplifying to a 2-D Stress This plane can be rotated to either eliminate or maximize shear stress by using Mohrs Circle: Since we use the outside surface where radial stress is zero; lets move to a plane element:2022-6-9Bas
7、ic Stress Theory & Using Mohrs Circle Cut the square at to calculate S1 Cut the square at +90 to calculate S2 Cut the square at +45 to calculate max2022-6-9Basic Stress Theory & Using Mohrs Circle Brittle material (failure by fracture) - max principal stress Ductile material (failure by general yiel
8、ding) - max principal stress is used to set wall thickness Maximum shear stress is a good prediction and errs on the conservative side see p84&85 of Adv. Mech. Of Matls2022-6-9Basic Stress Theory & 基本应力基本应力 “Code Stress规范应力规范应力”应力评定应力评定Evaluating a 3-D Stress S = F / A + Pd / 4t + M / Z 轴向力、轴向压力，轴向弯
9、矩一起的分量加和 规范不同，上面的算式也不同 那些应力没有包含进来？2022-6-9Basic Stress Theory & 基本应力基本应力 “Code Stress规范应力规范应力”几个实效理论几个实效理论A Few Failure Theories 变形能或八面体剪切应力 (根据米赛斯理论和其它的理论）。 最大剪应力理论 （Columb理论） 。 大多数理论都根据这个理论。 由于剪切影响而限制最大主应力 (Rankine理论) 。 CAESAR II 132列输出应力报告中显示了米赛斯或最大剪应力强度理论。 应力报告由configuration设置来决定。2022-6-9Basic S
10、tress Theory & 基本应力基本应力 “Code Stress规范应力规范应力”基于最大剪应力实效理论，ASME规范委员会颁布了规范应力方程Based on the maximum shear failure theory, the Code Committee developed the “code equations” 目的在于避免管道系统实效Purpose was to reduce system failures这种解决办法很实用，但仍然有问题存在This approach worked well, but there were still problems, even as
11、 late as post World War II.研究表明直管道比较符合理论Studies showed systems of straight pipe matched theory研究表明元件失效比理论发生的早Studies showed systems with fittings failed earlier than theory predicted.ASME规范委员会委托Markl来研究这个问题Code Committee commissioned Markl to study this .2022-6-9Basic Stress Theory & 基本应力基本应力 “Code
12、Stress规范应力规范应力”Markls 试验和结果试验和结果将试验用的管道充满水，按某个方向和位移反复摇晃管道。Test configurations filled with water and cycled through a predetermined displacement预测失效循环次数Theory should be able to predict “cycles to failure”发现最先失效的管件及其原因Fittings caused early failure because 对管件引入应力集中Stresses concentrations are introduce
13、d by fittings分析试验数据，修正轴向应力弯曲项Test data analyzed and a modification to the bending term of the code stress equation was introduced:Sbending = i M / z2022-6-9Basic Stress Theory & 基本应力基本应力 “Code Stress规范应力规范应力”Markls 试验和结果试验和结果 应力增强系数i 和元件的形式有关 对于弯头 “i” 的计算需要如下: 我们需要弯头的几何参数 计算弯头柔性“h” 计算应力增大系数Stress In
14、tensification Factor “i”, 石化规范对平面内、外的SIF取值不同，电力取相同的sif2022-6-9Basic Stress Theory & 基本应力基本应力 “Code Stress规范应力规范应力”Markls 试验和结果试验和结果 A load “in the plane” of the fitting causes “in-plane” bending 平面内 A load “out of the plane” of the fitting causes “out-of-plane” bending 平面外2022-6-9Basic Stress Theory
15、 & 基本应力基本应力 “Code Stress规范应力规范应力”Markls 试验和结果试验和结果 规范上的附注十分重要 PetroChem codes modify SIF (and flexibility factor) based on pressure stiffening in a note石化规范规定压力硬化影响和柔性系数 应力算式变化如下S = F / A + Pd / 4t + i M / z 应力增大系数不能小于2022-6-9Basic Stress Theory & Basis for “Code Stress Equations”Markls 试验和结果试验和结果Th
16、e SIF is a “fudge” factorSIF 是个近似的参数The SIF attempts to increase the bending stress computed at the node point, to match the actual higher stress due to the stress concentration caused by the fitting.引入SIF 在于改变特殊管件应力集中，让他们的应力根实际大小更接近。Markl only tested 4x4 Std fittings !但Markl 仅测试了Additional work is
17、still being done today in the field of SIFs. Results are published in: PVP, WRC, Journal of Pressure Vessel Technology.其余的工作人们仍然在继续进行。2022-6-9Basic Stress Theory & 规范效验的工况规范效验的工况两种失效： Primary failure一次失效 Secondary failure二次失效 (A third failure mode addressed is Occasional, which is similar to Primary
18、.)2022-6-9Basic Stress Theory & 规范效验的工况规范效验的工况Primary Failure Case一次失效 力的作用Force Driven 非自限性Not Self-Limiting 重量、压力、集中力Weight, Pressure, Concentrated Forces2022-6-9Basic Stress Theory & 规范效验的工况规范效验的工况Primary Failure Case一次失效 力的作用Force Driven 非自限性Not Self-Limiting 重量、压力、集中力, Weight、Pressure, Concentr
19、ated Forces2022-6-9Basic Stress Theory & 规范效验的工况规范效验的工况Secondary Failure Case二次失效 位移作用Displacement Driven 自限性Is Self-Limiting 温度、位移和其他变化载荷引起的 Temperature, Displacement, plus other varying loads - i.e. weight2022-6-9Basic Stress Theory & 规范效验的工况规范效验的工况 (1) = W + T1 + P1 (OPE) (2) = W + P1 (SUS) (3) =
20、 DS1 - DS2 (EXP) Operating case, used for:热态restraint & equipment loads推力和弯矩maximum displacements最大位移computation of EXP case计算二次应力 Sustained case for PRIMARY loads and stress compliance计算一次应力 Expansion case for “extreme displacement stress range”膨胀工况，计算二次应力displacements for case 3 are displacements
21、from case 1 minus displacements from case 22022-6-9Basic Stress Theory & 规范效验的工况规范效验的工况膨胀工况的解释膨胀工况的解释Expansion Case Explained What does “DS1 - DS2 (EXP)” mean? Is a load case with “T1 (EXP) the same thing?2022-6-9Basic Stress Theory & Load Cases for Code Compliance膨胀工况的解释膨胀工况的解释Expansion Case Explai
22、ned The code states that the expansion stresses are to be computed from the extreme displacement stress range. These are all very important words. Consider their meaning EXTREME极端极端: In this sense it means the most, or the largest. RANGE范围范围: Typically a difference. What difference? The difference b
23、etween the extremes. What extremes? DISPLACEMENT位移位移: This defines what extremes to take the difference of. STRESS应力应力: What we are eventually after.2022-6-9Basic Stress Theory & Load Cases for Code Compliance膨胀工况的解释膨胀工况的解释Expansion Case Explained Putting everything back together, we are told to com
24、pute stresses from the extreme displacement range. How can we do this?计算最大位移范围的应力 Consider the equation being solved; K x = f. In this equation, we know K and f, and we are solving for x, the displacement vector. In CAESAR II, when we setup an expansion case, we define it as DS1 - DS2, where the 1 a
25、nd 2 refer to the displacement vector (x) of load cases 1 and 2 respectively.2022-6-9Basic Stress Theory & Load Cases for Code Compliance膨胀工况的解释膨胀工况的解释Expansion Case Explained (Obviously the load case numbers are subject to change on a job by job basis.) What do you get when you take DS1 - DS2? Well
26、 x1 - x2 yields x, a pseudo displacement vector. x is not a real set of displacements that you can go out and measure with a ruler, rather it is the difference between two positions of the pipe. Once we have x, we can use the same routines used in the OPE or SUS cases to compute element forces, and
27、finally element stresses.2022-6-9Basic Stress Theory & Load Cases for Code Compliance膨胀工况的解释膨胀工况的解释Expansion Case Explained However, these element forces are also pseudo forces, i.e the difference in forces between two positions of the pipe.力的大小是两个工况力的差值 Similarly, the stresses computed are not real
28、 stresses, but stress differences.应力不是真实应力，是应力的差值 This is exactly what the code wants, the stress difference, which was computed from a displacement range.二次应力是位移变化量导致的 As to whether or not this stress difference is the extreme, well that depends on the job.2022-6-9Basic Stress Theory & Load Cases f
29、or Code Compliance膨胀工况的解释膨胀工况的解释Expansion Case Explained DS1-DS2 和 T1“一样吗？. 有可能. 如果是线性系统，答案是一样的。 如果是非线性系统 (如你有 +Ys, or gaps, or friction), 答案是不一样的。 原因是两个工况应用K x = f。 The reason for this can be found by examining the equation K x = f for the two different methods.2022-6-9Basic Stress Theory & Load Ca
30、ses for Code ComplianceExpansion Case Explained For this discussion, rearrange the equation to x = f / K, where we know we dont really divide by K, we multiply by its inverse. OPE: xope = fope / Kope = W + T1 + P1 / Kope SUS: xsus = fsus / Ksus = W + P1 / Ksus EXP: xexp = xope - xsus = W + T1 + P1 /
31、 Kope - W + P1 / Ksus Can we simplify the above equation as follows? EXP: xexp = W + T1 + P1 / K - W + P1 / K2022-6-9Basic Stress Theory & Load Cases for Code Compliance膨胀工况解释膨胀工况解释Expansion Case Explained Can we simplify the above equation as follows? EXP: xexp = W + T1 + P1 / K - W + P1 / K Cancel
32、ing like terms (the ones in red) yields: xexp = T1 / K 问题在于Kope 和 Ksus是否相等. 线性系统相等. 非线性系统不相等2022-6-9Basic Stress Theory & Load Cases for Code Compliance膨胀工况解释膨胀工况解释Expansion Case Explained 如果一个系统有两个操作温度。Another proof that the DS1-DS2 method is the correct way to go is to consider a job with two oper
33、ating temperatures, one above ambient and one below ambient. 如 T1 = +300, and T2 = -50. CAESAR II 软件自动建立如下工况: (1) W + T1 + P1 (OPE) (2) W + T2 + P1 (OPE) (3) W + P1 (SUS) (4) DS1 - DS3 (EXP) (5) DS2 - DS3 (EXP)2022-6-9Basic Stress Theory & Load Cases for Code Compliance膨胀工况解释膨胀工况解释Expansion Case Exp
34、lained 上述工况正确，但没能说明规范要求的最大应力范围因为CII并不能判断荷载所代表的具体含义 为满足规范的要求，用户必须自己定义: (6) DS1 - DS2 (EXP) 这个工况是最大位移膨胀应力，正是规范所要求的。 您根本不能考虑使用T1来计算膨胀应力.2022-6-9Basic Stress Theory & Load Cases for Code ComplianceExpansion Case Explained膨胀工况的解释膨胀工况的解释To summarize:概括如下 We take the difference between two load cases to de
35、termine a displacement range.两个工况确定位移范围 From this range we compute a force range and then a stress range.由此我们确定力的范围和应力范围 The code requires the extreme displacement stress range.规范要求极端的应力范围 The user only has to worry about whether or not the “extreme” case has been addressed.用户仅考虑最大应力范围即可2022-6-9Basi
36、c Stress Theory & Linear vs Non-Linear线性和非线性 Terminology applies to boundary conditions.边界条件的类型 Recall the equation being solved: Kx = f This is the equation of a spring. The piping system boundary conditions (i.e. the restraints) are represented as stiffnesses, or springs.管道边界条件代表刚度或弹簧 More complex
37、 boundary conditions can be defined, invalidating the “linear spring” assumption.2022-6-9Basic Stress Theory & Linear vs Non-Linear线性和非线性线性约束 boundary condition is a double acting restraint, such as a “Y” support.一种是上下约束 Another example of a linear boundary condition is a spring hanger.一种是弹簧 The for
38、ce versus displacement curve for these restraints is a straight line 力和位移是线性关系 Therefore these restraints are linear.约束是线性的 The slope of the line is the stiffness.斜率是刚度2022-6-9Basic Stress Theory & Linear vs Non-Linear线性和非线性非线性约束 A “+Y” support is a non-linear support.支架 Its force vs displacement cu
39、rve is not a straight line.力和位移不是直线关系 Stiffness only exists for negative displacements.向下的位移是刚度是存在的 For positive displacements, the stiffness is zero.向上的位移，刚度变为2022-6-9Basic Stress Theory & Linear vs Non-Linear线性和非线性 A “gap” is also a non-linear support.间隙的引进 The force vs displacement curve is not a
40、 straight line.力和位移不是线性关系 There is no stiffness in the gap.间隙部分没有刚度2022-6-9Basic Stress Theory & Linear vs Non-Linear线性和非线性 Friction makes a restraint non-linear摩擦让约束非线性 Large rotation rods are also non-linear restraints大的转动吊杆让约束非线性 Non-linear restraints in a job mean that Kope is not equal to Ksus.
41、 非线性后，热态管道刚度和冷态刚度不一致 (EXP) and (OCC) load cases must be constructed using the difference between two other load cases to account for non-linear restraints.2022-6-9Basic Stress Theory & 偶然工况的建立 Occasional loads are considered “primary”, since they are force driven.偶然荷载是主要载荷，力引起的。 Occasional loads occ
42、ur infrequently.不经常发生 The codes employ an “allowable increase” factor based on the frequency of occurrence in the determination of the allowable, i.e. k * Sh.基于发生的频率，确定值的大小 Examples of occasional loads are wind and earthquake.偶然载荷是风载荷和地震载荷2022-6-9Basic Stress Theory & 偶然工况的建立 The code equation for t
43、he OCCasional load case is:MA / Z + MB / Z kSh Here, MA is the moment term from the SUStained loads,冷态荷载引发力矩 and MB is the moment from the OCCasional loads.偶然荷载引发力矩 This equation states that the OCCasional case is the sum of the SUStained stresses and the OCCasional stresses.偶然工况是冷态和偶然的叠加 So we cant
44、 run a load case with just a “WIND” load and satisfy this code requirement. What about “W + P1 + WIND” as a load case?2022-6-9Basic Stress Theory & Occasional Load Case Setup The “W + P1 + WIND” case will work for “linear” systems only. For “non-linear” systems, this is not sufficient, for the same
45、reason “T1” is not sufficient for the EXPansion load case. The best way to setup OCCasional load cases is:(1) W + P1 + T1 (OPE)(2) W + P1 + T1 + WIND (OPE)(3) W + P1 (SUS)(4) DS1 - DS3 (EXP)(5) DS2 - DS1 (OPE)(6) ST5 + ST3 (OCC)2022-6-9Basic Stress Theory & Occasional Load Case Setup (1) W + P1 + T1
46、 (OPE) (2) W + P1 + T1 + WIND (OPE) (3) W + P1 (SUS) (4) DS1 - DS3 (EXP) (5) DS2 - DS1 (OPE) (6) ST5 + ST3 (OCC) This is the normal OPErating case This is a combined OPErating case which includes the OCC loads This is the standard SUStained case This is the standard EXPansion case This difference yi
47、elds the effects of the OCCasional load on the system. This is not a code case, only a construction case, therefore (OPE). This handles non-linearities. This is our OCCasional code compliance case, stresses from Primary plus Occasional loads.2022-6-9Basic Stress Theory & 工况的定义和维护 CAESAR II will reco
48、mmend load cases for “new” jobs. By “new” jobs, we mean jobs that do not have a “._J” file. For “old” jobs, having a “._J” file, CAESAR II reads in the defined load cases and presents them to the user. The load case editing screen is shown at the right.2022-6-9Basic Stress Theory & 工况的定义和维护 On this
49、dialog, available load types are listed in the upper left list box.载荷类型 Available load case types are listed in the lower left list box.工况类型 Load cases (recommended or previously defined) are shown in the grid at the right.推荐生成的工况 Recommended load cases can always be obtained by clicking on the Reco
50、mmend button. The analysis commences by clicking on “the running man”.2022-6-9Basic Stress Theory & Load Case Generation & Maintenance Say for a “new” job, the load cases at the right are recommended. Say you accept and run these load cases. Upon reviewing the output you discover that pre-defined di
