PIPE STRESS ANALYSIS USING A COMPUTER MODEL OF THE PIPING SYSTEM
USING COMPUTER TO RUN A PIPE STRESS ANALYSIS Mathematical model of piping system built using Caesar II software.
BUILDING A MODEL WITH CAESAR II Engineers nowadays do not have to worry about solving higher degree, or differential equations to perform complicated calculations, because they can create complete models of the system they are trying to design and analyse and let the software perform the analysis for them. However as the saying goes, “garbage in; garbage out” the engineer still has to possess good engineering judgment to know what to expect from a computer analysis and how to interpret the output. Although there are various softwares available to do pipe stress analyses, Caesar II is one that is well known and frequently used for the oil and gas engineering analyses.
USING CAESAR II FOR PIPE ANALYSIS
CAESAR II is most often used for the mechanical design of new piping systems. Hot piping systems present a unique problem to the mechanical engineer—these irregular structures experience great thermal strain that must be absorbed by the piping, supports, and attached equipment. These “structures” must be stiff enough to support their own weight and also flexible enough to accept thermal growth. These loads, displacements, and stresses can be estimated through analysis of the piping model in CAESAR II. To aid in this design by analysis, CAESAR II incorporates many of the limitations placed on these systems and their attached equipment. These limits are typically specified by engineering bodies (such as the ASME B31 committees, ASME Section VIII, and the Welding Research Council) or by manufacturers of piping-related equipment (API, NEMA, or Expansion Joint Manufacturers‟ Association - EJMA).
CAESAR II is not limited to thermal analysis of piping systems. CAESAR II also has the capability of modeling and analyzing the full range of static and dynamic loads, which may be imposed on the system. Therefore, CAESAR II is not only a tool for new design but it is also valuable in troubleshooting or re-designing existing systems. Here, one can determine the cause of failure or evaluate the severity of un-anticipated operating conditions such as fluid/piping interaction or mechanical vibration caused by rotating equipment.
CONFIGURING CAESAR II Each time CAESAR II starts, the configuration file caesar.cfg is read from the current data directory. If this file is not found in the current data directory, eventually a fatal error will be generated and CAESAR II will terminate. To generate the caesar.cfg file select Tools/Configure/Setup (or the Configure button from the toolbar) from the CAESAR II Main Menu. Once finished users must click Exit w/Save at the bottom of the Configure/Setup window to create a new configuration file or to save changes to the existing configuration file. The configuration program produces the Computation Control window. Important: The caesar.cfg file may vary from machine to machine and many of the setup directives modify the analysis. The units' file, if modified by the user, would also need to be identical if the same results are to be produced.
See the next slide for an image of the Computational Control panel.
CAESAR II – COMPUTATIONAL CONTROL
CAESAR II – COMPUTATIONAL CONTROL CONFIGURATION SETTINGS
Use Pressure Stiffening on Bends- if used it will be the maximum of all psi Missing Mass ZPA- defaults to the last “extracted” mode Bend Axial Shape- if ignored the bend will be stiffer Rod Tolerance (degrees)- The default of CAESAR II is 1.0 degree Rod Increment (Degrees)- for difficult-to-converge problems, use 0.1 Alpha Tolerance- the default value is 0.05 Ambient Temperature- use the ambient temperature Friction Stiffness- default value is 1.0E6 lb./in (non-sliding) Friction Normal Force Variation- default value is 0.15, (15%) Friction Angle Variation- the default is 15 degrees Friction Slide Multiplier- should never be adjusted by the user Coefficient of Friction (Mu)- user defined (0 = no friction) WRC-107 Version / WRC-107 Interpolation Method- the default is to use the last value in the particular WRC table In-core Numerical Check- user enabled Decomposition Singularity Tolerance- the default value is 1.0 E10. Minimum Wall Mill Tolerance (%)- default value is 12.5, (12.5%) Bourdon Pressure- user choice except for FRP pipe; always considered Include / Ignore Spring Hanger Stiffness- user enabled Hanger Default Restraint Stiffness- default value is (1.0 E12 lb/in) Default Translational Restraint Stiffness- default value is (1.0 E12 lb/in) Default Rotational Restraint Stiffness- default value is (1.0 E12 in-lb/deg)
CAESAR II – STRESS INTENSIFICATION FACTORS (SIFS)
Default Code The piping code the user designs to most often should go here. This code will be used as the default if no code is specified in the problem input. The default piping code is B31.3, the chemical plant and petroleum refinery code. Valid entries are B31.1, B31.3, B31.4, B31.4 Chapter IX, B31.5, B31.8, B31.8 Chapter VIII, B31.11, ASME-NC(Class 2), ASME-ND(Class 3), NAVY505, Z662, Z662 Chapter 11, BS806, SWEDISH1, SWEDISH2, B31.1-1967, STOOMWEZEN, RCCM-C, RCCM-D, CODETI, Norwegian, FDBR, BS-7159, UKOOA, IGE/TD/12, DNV, EN-13480, and GPTC/192. Occasional Load Factor B31.3 states, “The sum of the longitudinal stresses due to pressure, weight, and other sustained loadings (S1) and of the stresses produced by occasional loads such as wind or earthquake may be as much as 1.33 times the allowable stress given in Appendix A…” The default for B31.3 applications is 33%. If this is too high for the material and temperature specified then a smaller occasional load factor could be input. Yield Stress Criterion: Von Mises Theory or the Maximum Shear Theory
CAESAR II – SIFS AND STRESS CONFIGURATION SETTINGS
CAESAR II – COMPUTATIONAL CONTROL CONFIGURATION SETTINGS (CONT’D.)
B31.3 Sustained SIF Multiplier - the default is 1.0 B31.3 Welding and Contour Tees Meet B16.9- the default setting for this directive is “NO”, which causes the program to use a flexibility characteristic of 3.1*T/r, as per the A01 addendum. Allow User's SIF at Bend- the default is off Use WRC 329- this activates the WRC329 guidelines for all intersections Use Schneider- activates the Schneider reduced intersection assumptions All Cases Corroded- if enabled, uses the corroded section modulus Liberal Expansion Stress Allowable- user choice to make it default Press. Variation in Expansion Case- user controlled Base Hoop Stress On ( ID/OD/Mean/Lamés )- The default is to use the ID of the pipe. If enabled, hoop stress value has the following options:
ID—Hoop stress is computed according to Pd/2t where “d” is the internal diameter of the pipe. OD—Hoop stress is computed according to Pd/2t where “d” is the outer diameter of the pipe. Mean—Hoop stress is computed according to Pd/2t where “d” is the average or mean diameter of the pipe. Lamés—Hoop stress is computed according to Lamés equation, = P ( Ri2 + Ri2 * Ro2 / R2 ) / ( Ro2 - Ri2 ) and varies through the wall as a function of R
CAESAR II – COMPUTATIONAL CONTROL CONFIGURATION SETTINGS (CONT’D.)
Use PD/4t- The more comprehensive calculation, i.e. the Default, is recommended Add F/A in Stresses- setting this to „Default‟ causes CAESAR II to use whatever the currently active piping code recommends. Add Torsion in SL Stress- setting to „Yes‟ will include the torsion term in those codes that don‟t include it already by default Reduced Intersection- options are B31.1(Pre 1980), B31.1(Post 1980), WRC329, ASME SEC III, and Schneider Class 1 Branch Flexibility- Activates the Class 1 flexibility calculations B31.1 Reduced Z Fix- if used in conjunction with B31.1, it makes the correction to the reduced branch stress calculation that existed in the 1980 through 1989 versions of B31.1 No RFT/WLT in Reduced Fitting SIFs- If enabled will use distinct in-plane and out-of-plane SIFs Implement B31.3 Appendix P- implements the alternate rules in B31.3 Appendix P.
Bends: IMPORTANT TOPICS IN MODEL BUILDING
Stiffened Bends 90-degree Bends Mitered Bends Elbows
Restraints:
Expansion Joints
Simple Bellows with Pressure Thrust
Anchors Guides Limit Stops Windows Double-Acting Restraints
Hangers:
Single Can
Tied Bellows
Liftoff Spring Can
Universal Joints
Bottom-out Spring Can
Hinged Joints
Constant Effort Hangers
Slip Joints
Gimbal Joints
Miscellaneous
Ball Joints
Reducers
Hanger w/ Sliding Movement Capability
Jacketed Pipe
MODELLING PIPE BENDS
Bends are defined by the element entering the bend and the element leaving the bend. The actual bend curvature is always physically at the “TO” end of the element entering the bend. (The element direction is defined from the first node to the second node.) The input for the element leaving the bend must follow the element entering the bend. The bend angle is defined by these two elements. Bend radius defaults to 1 1/2 times the pipe nominal diameter (long radius), but may be changed to any other value. Specifying a bend automatically generates two additional intermediate nodes, at the 0-degree location and at the bend midpoint (M). For stress and displacement output the TO node of the element entering the bend is located geometrically at the far-point on the bend. The far-point is at the weld line of the bend, and adjacent to the straight element leaving the bend. Nodes defined in the Angle and Node fields are placed at the given angle on the bend curvature. The angle starts with zero degrees at the near-point on the bend and goes to degrees at the far-point of the bend.
MODELLING PIPE BENDS (CONT’D.)
Nodes on the bend curvature cannot be placed closer together than specified by the Minimum Angle to Adjacent Bend parameter in the Configure-Setup—Geometry section. This includes the spacing between the nodes on the bend curvature and the near and far-points of the bend.
Entering the letter M as the angle designates the bend midpoints.
The minimum and maximum total bend angle is specified by the Minimum Bend Angle and Maximum Bend Angle parameters in the Configure Setup—Geometry section.
MODELLING PIPE BENDS (CONT’D.)
MODELLING PIPE SINGLE AND DOUBLE-FLANGED BENDS
Single and double flanged bend specifications only affect the stress intensification and flexibility of the bend. There is no automatic rigid element (or change in weight) generated for the end of the bend. Single and double-flanged bends are indicated by entering 1 or 2 (respectively) for the Type in the bend auxiliary input. Rigid elements defined before or after the bend will not alter the bend's stiffness or stress intensification factors. When specifying single flanged bends it does not matter which end of the bend the flange is on. If the user wishes to include the weight of the rigid flange(s) at the bend ends, then he/she should put rigid elements (whose total length is the length of a flange pair) at the bend ends where the flange pairs exist. As a guideline, British Standard 806 recommends stiffening the bends whenever a component that significantly stiffens the pipe cross section is found within two diameters of either bend end.
MODELLING PIPE SINGLE AND DOUBLEFLANGED BENDS
MODELLING PIPE 180º RETURN BENDS
The user is recommended to put nodes at the mid point of each bend comprising the 180 degree return. (See the example on this page)
Two 90-degree bends should be separated by twice the bend radius. The far-point of the first bend is the same as the near-point of the second (following) the bend.
MODELLING PIPE CLOSELY-SPACED MITER BENDS
Evenly spaced mitered bends, whether closely or widely spaced, are uniquely defined by two parameters: Number of cuts (changes in direction) Equivalent radius, or miter spacing. For closely spaced miters the equivalent radius is equal to the code defined “R1” for B31.3 and “R” for B31.1. The equation relating the equivalent radius to the spacing for evenly spaced miters is:
Req = S / [ 2 tan(Ɵ) ] Where: Req - equivalent miter bend radius S - spacing of the miter cuts along the centerline Ɵ - code defined half-angle between adjacent miter cuts: Ɵ = α / 2N And where: α - total bend angle N - number of cuts
MODELLING PIPE CLOSELY-SPACED MITER BENDS
An additional parameter „B‟ (length of miter segment at crotch) is checked for closely spaced miters when using B31.1. „B‟ may be found for evenly spaced miters from equation:
B = S [ 1 - ro / Req ] Where:
ro - outside radius of pipe cross-section Miter bends are closely spaced if:
S < r [ 1 + tan (Ɵ) ] Where:
S - miter spacing r - average pipe cross section radius: (ri+ro)/2 Ɵ - one-half the angle between adjacent miter cuts. ASME B31.1 has the additional requirements that: B > 6 tn Ɵ ≤ 22.5 deg. B - length of the miter segment at the crotch. tn - nominal wall thickness of pipe.
MODELLING PIPE CLOSELY-SPACED MITER BENDS
Closely spaced miters regardless of the number of miter cuts may be entered as a single bend. CAESAR II will always calculate the spacing from the bend radius. If the user has the miter spacing and not the bend radius, the radius must be calculated as shown below. The mitered bend shown 2 slides above has 4 cuts through 90 degrees and a spacing of 15.913 inches.
Req = S / [ 2 tan (Ɵ) ] Ɵ = α / 2N = 90 / [2(4)] = 11.25 deg. Req = 15.913 / [2 tan (11.25 deg.)] = 40
MODELLING PIPE WIDELY-SPACED MITERED BENDS Mitered bends are widely spaced if: S ≥ r * [1 + tan (Ɵ)] S - spacing between miter points along the miter segment centerline. r - average cross section radius (ri+ro)/2 Ɵ - one-half angle between adjacent miter cuts. B31.1 has the additional requirement that: Ɵ ≤ 22.5 deg. In CAESAR II, widely spaced miters must be entered as individual, single cut miters, each having a bend radius equal to: R = r [1 + cot (Ɵ)] / 2 R - reduced bend radius for widely spaced miters. During error checking, CAESAR II will produce a warning message for each mitered component, which does not pass the test for a closely spaced miter. These components should be re-entered as a group of single cut joints.
MODELLING PIPE WIDELY-SPACED MITER BENDS Pipe O. D. = 10.375 in Pipe Thk. = 0.500 in Bend Angle = 90 degrees Cuts = 2 Req = 45 in
Calculate the Δ coordinates to get from the tangent intersecting point of the single cut miter bend at node 10 to the single cut miter bend at node 15.
Note: The straight pipe section coming into and going out of the bend must be ≥ Req sin (Ɵ).
MODELLING ELBOWS WITH DIFFERENT WALL THICKNESSES
When the fitting thickness in the bend auxiliary field is entered, CAESAR II changes the thickness of the curved portion of the bend element only. The thickness of any preceding or following straight pipe is unaffected. The specified fitting thickness applies for the current elbow only and is not carried on to any subsequent elbows in the job. Stresses at the elbow are calculated based on the section modulus of the matching pipe as specified in the B31 codes. However, stress intensification factors and flexibility factors for the bend are based on the elbow wall thickness. The elbow at node 10 (in the next slide) has a thickness larger than the matching pipe wall. The matching pipe has a thickness of 0.5
MODELLING ELBOWS WITH DIFFERENT WALL THICKNESSES (CONT’D.)
RESTRAINTS
Anchors; Connecting nodes can be used with anchors to rigidly fix one point in the piping system to any other point in the piping system. Double-acting restraints; Double-acting restraints are those that act in both directions along the line of action. Most commonly used restraints are double-acting. A CNode is the connecting node. Single-directional restraints; Friction and gaps may be specified with single-directional restraints. A CNode is the connecting node. Guides; Guides are double-acting restraints with or without a specified gap. Connecting Nodes (CNodes) can be used with guides. Limit Stop; Limit stops are single- or double-acting restraint whose line of action is along the axis of the pipe. These can have gaps too. A gap is a length, and is always positive. Windows; Equal leg windows are modeled using two double-acting restraints with gaps orthogonal to the pipe axis. Unequal leg windows are modeled using four single-acting restraints with gaps orthogonal to the pipe axis.
RESTRAINTS (CONT’D.)
Vertical / Horizontal Dummy Legs; Dummy legs and/or any other elements attached to the bend curvature should be coded to the bend tangent intersection point. For each dummy leg/bend model a warning message is generated during error checking in CAESAR II. Large Rotation rods; Large rotation rods are used to model relatively short rods, where large orthogonal movement of the pipe causes shortening of the restraint along the original line of action. These can be entered in any direction. Large rotation is generally considered to become significant when the angle of swing becomes greater than 5 degrees. Static Snubbers; Translational restraints that provide resistance to displacement in static analysis of occasional loads only. Static snubbers may be directional, (i.e. may be preceded by a plus or minus sign). Plastic Hinges; Two bi-linear supports are used to model rigid resistance to bending until a breakaway force (yield force) is exceeded at which point bending is essentially free. Sway Brace assemblies; The sway brace is composed of a single compression spring enclosed between two movable plates. Manufacturers typically recommend a specific size sway brace for a given pipe nominal diameter.
SPRING HANGERS The hanger design algorithm will not design hangers that are completely predefined. Any other data can exist for the spring location but this data is not used. Entered spring rates and theoretical cold loads will be multiplied by the number of hangers at this location. CAESAR II requires the Theoretical Cold (Installation) Load to pre-define the spring. Theoretical Cold Load = Hot Load + Travel * Spring Rate where upward travel is positive.
NOTES ON CAESAR II HYDRODYNAMIC LOADING The basic parameters input into CAESAR II describe the wave height and period, and the current velocity. The most difficult to obtain, and also the most important parameters, are: the drag, Cd inertia, Cm and lift coefficients, Cl Based on the recommendations of API RP2A and DNV (Det Norske Veritas), values for Cd range from 0.6 to 1.2, values for Cm range from 1.5 to 2.0. Values for Cl show a wide range of scatter, but the approximate mean value is 0.7. The inertia coefficient Cm is equal to one plus the added mass coefficient Ca. This added mass value accounts for the mass of the fluid assumed to be entrained with the piping element. In actuality, these coefficients are a function of the fluid particle velocity, which varies over the water column. In general practice, two dimensionless parameters are computed which are used to obtain the Cd, Cm, and Cl values from published charts.
NOTES ON BOLT TIGHTENING STRESS This is a critical item for leakage determination and for computing stresses in the flange. The ASME code bases its stress calculations on a pre-specified, fixed equation for the bolt stress. The resulting value is however often not related to the actual tightening stress that appears in the flange when the bolts are tightened. For this reason, the initial bolt stress input field that appears in the first section of data input, Bolt Initial Tightening Stress, is used only for the flexibility/leakage determination. The value for the bolt tightening stress used in the ASME flange stress calculations is as defined by the ASME code: Bolt Load = Hydrostatic End Force + Force for Leak-tight Joint If the Bolt Initial Tightening Stress field is left blank, CAESAR II uses the value:
45000 / √(dbolt) where 45,000 psi is a constant and d is the nominal diameter of the bolt (correction is made for metric units).
NOTES ON BOLT TIGHTENING STRESS (CONT’D.) This is a rule of thumb tightening stress, that will typically be applied by field personnel tightening the bolts. This computed value is printed in the output from the flange program. It is interesting to compare this value to the bolt stress printed in the ASME stress report (also in the output). It is not unusual for the “rule-of-thumb” tightening stress to be larger than the ASME required stress. When the ASME required stress is entered into the Bolt Initial Tightening Stress data field, a comparison of the leakage safety factors can be made and the sensitivity of the joint to the tightening torque can be ascertained. Users are strongly encouraged to “play” with these numbers to get a feel for the relationship between all of the factors involved.
MODELLING EXPANSION JOINTS
To define an expansion joint, activate the Expansion Joint check box (see "Expansion Joints" on page 3-21 of the Caesar II manual) on the pipe element spreadsheet. The expansion joint will have a non-zero length if at least one of the element‟s spreadsheet Delta fields is non-blank and non-zero. This will usually result in a more accurate stiffness model in what is typically a very sensitive area of the piping system. Four stiffnesses define the expansion joint: Axial Stiffness Transverse Stiffness Bending Stiffness Torsional Stiffness
These stiffnesses are defined as shown in the figure shown in the next slide:
MODELLING EXPANSION JOINTS (CONT’D.)
Axial Stiffness
Torsional Stiffness
Transverse Stiffness
Bending Stiffness
MODELLING EXPANSION JOINTS (CONT’D.) The equation for estimating bellows‟ torsional stiffness is:
Where, π = 3.14159 Re = Expansion joint effective radius t = Bellows thickness E = Elastic Modulus ν = Poisson’s Ratio L = Flexible bellows length CAESAR II will calculate pressure thrust on the expansion joint if the bellows effective I.D. is given in the expansion joint auxiliary screen. The mathematical model for pressure thrust applies a force equal to the pressure times the effective area of the bellows at either end of the expansion joint. The force will tend to open the bellows if the pressure is positive, and close the bellows if the pressure is negative.
MODELLING EXPANSION JOINTS (CONT’D.) According to EJMA (Expansion Joint Manufacturers Association), the maximum permitted amount of axial movement per corrugation is defined as erated where, ex + ey + eq < erated The terms in the above equation are defined as: ex = The axial displacement per corrugation resulting from imposed axial movements. ey = The axial displacement per corrugation resulting from imposed lateral deflections. eq = The axial displacement per corrugation resulting from imposed angular rotation, i.e. bending. erated = The maximum permitted amount of axial movement per corrugation. This value should be obtained from the Expansion Joint Manufacturer‟s catalog.
MODELLING EXPANSION JOINTS (CONT’D.) The EJMA states: “Also, [as an expansion joint is rotated or deflected laterally] it should be noted that one side of the bellows attains a larger projected area than the opposite side. Under the action of the applied pressure, unbalanced forces are set up which tend to distort the expansion joint further. In order to control the effects of these two factors a second limit is established by the manufacturer upon the amount of angular rotation and/or lateral deflection which may be imposed upon the expansion joint. This limit may be less than the rated movement. Therefore, in the selection of an expansion joint, care must be exercised to avoid exceeding either of these manufacturer‟s limits.”
MODELLING EXPANSION JOINTS (CONT’D.) CAESAR II computes the terms defined in the erated equation and the movement of the joint ends relative to each other. These relative movements are reported in both the local joint coordinate system and the global coordinate system.
The expansion joint rating module can be entered by selecting Main Menu Analysis - Expansion Joint Rating option.
MODELLING PIPE SPRINGS Spring Design Requirements The smallest single spring that satisfies all design requirements is selected as the designed spring. The spring design requirements are:
Both the hot and the cold loads must be within the spring allowed working range.
If the user specified an allowed load variation then the absolute value of the product of the travel and the spring rate divided by the hot load must be less than the specified variation.
If the user specified some minimum available clearance then the spring selected must fit in this space.
If a single spring cannot be found that satisfies the design requirements, CAESAR II will try to find two identical springs that do satisfy the requirements. If satisfactory springs cannot be found, CAESAR II recommends a constant effort support for the location.
MODELLING PIPE SPRINGS (CONT’D.) Setting Up the Spring Load Cases The load cases that must exist for hanger design, as described above, are: Restrained Weight Operating Installed Weight ...if the user requested actual hanger installed loads.
After the hanger algorithm has run the load cases it needs to size the hangers. The newly selected springs are inserted into the piping system and included in the analysis of all remaining load cases. The spring rate becomes part of the global stiffness matrix, and is therefore added into all subsequent load cases.
MODELLING PIPE BRANCH FLEXIBILITIES When the Class 1 branch flexibilities are used, intersection models in the analysis will become stiffer when the reduced geometry requirements do not apply, and will become more flexible when the reduced geometry requirements do apply. Stiffer intersections typically carry more load, and thus have higher stresses (lowering the stress in other parts of the system that have been “unloaded”). More flexible intersections typically carry less load, and thus have lower stresses, (causing higher stresses in other parts of the system that have “picked up” the extra load).
MODELLING PIPE BRANCH FLEXIBILITIES When the reduced branch rules apply, the following equations are used for the local stiffnesses: TRANSLATIONAL:
ROTATIONAL:
AXIAL = RIGID AXIAL = RIGID CIRCUMFERENTIAL = CIRCUMFERENTIAL = (kx)d/EI RIGID LONGITUDINAL = (kz)d/EI LONGITUDINAL = RIGID where: RIGID = 1.0 E12 lb./in. or 1.0 E12 in.lb./deg. d = Branch diameter E = Young’s Modulus I = Cross Section Moment of Inertia D = Header diameter T = Header thickness Tb = Branch fitting thickness kx = 0.1(D/T)1.5[(T/t)(d/D)]0.5(Tb/T) kz = 0.2(D/T)[(T/t)(d/D)]0.5(Tb/T)
MODELLING PIPE BRANCH FLEXIBILITIES The Significance of the unbraced/unsupported span length “The significance of “k” depends upon the specifics of the piping system. Qualitatively, if “k” is small compared to the length of the piping system, including the effect of elbows and their k-factors, then the inclusion of “k” for branch connections will have only minor effects on the calculated moments. Conversely, if “k” is large compared to the piping system length, then the inclusion of “k” for branch connections will have major effects. The largest effect will be to greatly reduce the magnitude of the calculated moments acting on the branch connection. To illustrate the potential significance of “k’s” for branch connections, we use the equation [above] to calculate “k” for a branch connection with D=30 in., d=12.75 in. T=t=0.375 in.:
k = 0.1(80)1.5(0.425)0.5 * (1.0) = 46.6 This compares to the more typical rigid-joint interpretation that k=1, rather than k=46.6 !”
MODELLING PIPE FLANGES The following input parameters are required to get a leakage report. These parameters include: Flange Inside Diameter Flange Thickness Bolt Circle Diameter Number Of Bolts Bolt Diameter Effective Gasket Diameter Uncompressed Gasket Thickness Effective Gasket Width Leak Pressure Ratio Effective Gasket Modulus Externally Applied Moment Externally Applied Force Pressure
MODELLING PIPE FLANGES (CONT’D.) Leak Pressure Ratio This value is taken directly from Table 2-5.1 in the ASME Section VIII code. This table is reproduced in the help screens of the software. This value is more commonly recognized as “m”, and is termed the “Gasket Factor” in the ASME code. This is a very important number for leakage determination, as it represents the ratio of the pressure required to prevent leakage over the line pressure.
Effective Gasket Modulus Typical values are between 300,000 and 400,000 psi (20,684.27 and 27,579.03 bar) for spiral wound gaskets. The higher the modulus the greater the tendency for the program to predict leakage. Errors on the high side when estimating this value will lead to a more conservative design.
MODELLING PIPE FLANGES (CONT’D.) Flange Rating This is an optional input, but results in some very interesting output. As mentioned above, it has been a widely used practice in the industry to use the ANSI B16.5 and API 605 temperature/pressure rating tables as a gauge for leakage. Because these rating tables are based on allowable stresses, and were not intended for leakage prediction, the leakage predictions that resulted were a function of the allowable stress for the flange material, and not the flexibility, i.e. modulus of elasticity of the flange. To give the user a “feel” for this old practice, the minimum and maximum rating table values from ANSI and API were stored and are used to print minimum and maximum leakage safety factors that would be predicted from this method. Example output that the user will get upon entering the flange rating is shown as follows: EQUIVALENT PRESSURE MODEL ————————Equivalent Pressure (lb./sq.in.) 1639.85 ANSI/API Min Equivalent Pressure Allowed 1080.00 ANSI/API Max Equivalent Pressure Allowed 1815.00 This output shows that leakage, according to this older method, occurred if a carbon steel flange was used, and leakage did not occur if an alloy flange was used. (Of course both flanges would have essentially the same “flexibility” tendency to leak.)
MODELLING THE REMAINING STRENGTH OF CORRODED PIPES
The B31G criteria provides a methodology whereby corroded pipelines can be evaluated to determine when specific pipe segments must be replaced. The original B31G document incorporates a healthy dose of conservatism and as a result, additional work has been performed to modify the original criteria. This additional work can be found in project report PR-3805, by Battelle, Inc. The details of the original B31G criteria as well as the modified methods are discussed in detail in this report.
CAESAR II determines the following values according to the original B31G criteria and four modified methods. These values are: The hoop stress to cause failure The maximum allowed operating pressure The maximum allowed flaw length
MODELLING THE REMAINING STRENGTH OF CORRODED PIPES (CONT’D.) The four modified methods vary in the manner in which the corroded area is estimated. These methods are: .85dL—The corroded area is approximated as 0.85 times the maximum pit depth times the flaw length. Exact—The corroded area is determined numerically using the trapezoid method. Equivalent—The corroded area is determined by multiplying the average pit depth by the flaw length. Additionally, an equivalent flaw length (flaw length * average pit depth / maximum pit depth) is used in the computation of the Folias factor. Effective—This method also uses a numerical trapezoid summation, however, various sub lengths of the total flaw length are used to arrive at a worst case condition. Note that if the sub length which produces the worst case coincides with the total length, the Exact and Effective methods yield the same result.
ANALYSIS OPTIONS IN CAESAR II • Statics—Performs Static analysis of pipe and/or structure. This is available after error checking the input file. • Dynamics—Performs Dynamic analysis of pipe and/or structure. This is also available after error checking the input file. • SIFs—Displays scratch pads used to calculate stress intensification factors at intersections and bends. • WRC 107/297—Calculates stresses in vessels due to attached piping. • Flanges—Performs flange stress and leakage calculations. • B31.G—Estimates pipeline remaining life. • Expansion Joint Rating—Evaluates expansion joints using EJMA equations. • AISC—Performs AISC code check on structural steel elements. • NEMA SM23—Evaluates piping loads on steam turbine nozzles. • API 610—Evaluates piping loads on centrifugal pumps. • API 617—Evaluates piping loads on compressors. • API 661—Evaluates piping loads on air-cooled heat exchangers. • HEI Standard—Evaluates piping loads on feedwater heaters. • API 560—Evaluates piping loads on fired heaters.
ERROR CHECKING IN CAESAR II Static analysis cannot be performed until the error checking portion of the piping pre-processor has been successfully completed. Only after error checking is completed are the required analysis data files created. Similarly, any subsequent changes made to the model input are not reflected in the analysis unless error checking is rerun after those changes have been made. CAESAR II does not allow an analysis to take place if the input has been changed and not successfully error checked.
Error Checking can only be done from the input spreadsheet, and is initiated by executing the Error Check or Batch Run commands from the toolbar or menu. Error Check saves the input and starts the error checking procedure.
Batch Run causes the program to check the input data, analyze the system, and present the results without any user interaction. The assumptions
are that the loading cases to be analyzed do not need to change
Users may sort messages in the Message Grid by type, message number or element/node number by double-clicking the corresponding column header. Users can also print messages displayed in the Message Grid.
ERROR CHECKING IN CAESAR II
A fatal error would be if no length were defined for a piping element, for example.
ERROR CHECKING IN CAESAR II (CONT’D.) The software will give the user feedback when things are not right in the model. Three types of messages are possible with Caesar II:
Fatal Error Message - Errors are flagged when there is a problem with the model due to which analysis cannot continue.
Warning Message - Warnings are flagged whenever there is a problem with a model, which can be overcome using some assumptions.
Note Message - The third category of alert is the informational note. These messages simply inform the user of some noteworthy fact related to the model. An example of a note may be a message informing the user of the number of hangers to be designed by the software.
BUILDING STATIC LOAD CASES IN CAESAR II The first step in the analysis of an error-checked piping model is the specification of the static load cases. After entering the static load case editor, a screen appears which lists all of the available loads that are defined in the input, the available stress types, and the current load cases offered for analysis. If the job is entering static analysis for the first time, CAESAR II presents a list of recommended load cases. If the job has been run previously, the loads shown are those saved during the last session.
The load case input screen is shown on the next slide.
(CONT’D.)
BUILDING STATIC LOAD CASES
The user can define up to ninety-nine load cases. Load cases may be edited by clicking on a line in the Load List area.
BUILDING STATIC LOAD CASES IN CAESAR II The following commands are available to define load cases: .
Edit-Insert - Inserts a blank load case following the currently selected line in the load list. If no line is selected, the load case is added at the end of the list. Load cases are selected by clicking on the number to the left of the load case.
Edit-Delete - Deletes the currently selected load case.
File Analysis - Accepts the load cases and runs the job.
Recommend - Allows the user to replace the current load cases with the CAESAR II recommended load cases.
Load Cycles - Hides or displays the Load Cycles field in the Load Case list. Entries in these fields are only valid for load cases defined with the fatigue stress type.
ENTERING ENVIRONMENTAL DATA PARAMETERS The following environmental parameters can be added to the model: .
Wind Data: Up to four different wind load cases may be specified for any one job. The only wind load information that is specified in the piping input is the shape factor. It is this shape factor input that causes load cases WIN1, WIN2, WIN3, and WIN4 to be listed as an available load to be analyzed. More wind data is required, however, before an analysis can be made. There are three different methods that can be used to generate wind loads on piping systems: ASCE #7 Standard Edition, 1995 User entry of a pressure vs. elevation table User entry of a velocity vs. elevation table The appropriate method is selected by placing a value of 1.0 in one of the first three boxes.
ENTERING ENVIRONMENTAL DATA PARAMETERS (CONT’D.)
Hydrodynamic Parameters: Up to four different hydrodynamic load cases may be specified for any one job. Several hydrodynamic coefficients are defined on the element spreadsheet. The inclusion of hydrodynamic coefficients causes the loads WAV1, WAV2, WAV3, and WAV4 to be available in the load case editor. In the load case editor, four different wave load profiles can be specified. Current data and wave data may be specified and included together or either of them may be omitted so as to exclude the data from the analysis. CAESAR II supports three current models and six wave models.
List Input Format
RUNNING THE STATIC ANALYSIS The static analysis performed by CAESAR II follows the regular finite element solution routine. Element stiffnesses are combined to form a global system stiffness matrix. Each basic load case defines a set of loads for the ends of all the elements. These elemental load sets are combined into system load vectors. Using the relationship of force equals stiffness times displacement (F=K∙X), the unknown system deflections and rotations can be calculated. The known deflections however, may change during the analysis as hanger sizing, nonlinear supports, and friction all affect both the stiffness matrix and load vectors. The root solution from this equation, the system-wide deflections and rotations, is used with the elements‟ stiffness to determine the global (X,Y,Z) forces and moments at the end of each element. These forces and moments are translated into a local coordinate system for the element from which the code-defined stresses are calculated. Forces and moments on anchors, restraints, and fixed displacement points are summed to balance all global forces and moments entering the node. Algebraic combinations of the basic load cases pick up this process where appropriate - at the displacement, force & moment, or stress level. Once the setup for the solution is complete the calculation of the displacements and rotations is repeated for each of the basic load cases.
STRUCTURAL STEEL CHECKS (AISC) Allowable Stress Increase Factor The Allowable Stress Increase Factor is a multiplication factor applied to the computed values of the axial and bending allowable stresses. Typically this value is 1.0. However, in extreme events the AISC code permits the allowable stresses to be increased by a factor. Normally a 1/3 increase is applied to the computed allowables, making the Allowable Stress Increase Factor = 1.33. Examples of extreme events are earthquakes and 100 year storms. For more details see the AISC code, section 1.5.6.
Young’s Modulus The slope of the linear portion of the stress-strain diagram. For structural steel this value is usually 29,000,000 psi (199,948 MPa).
Material Yield Strength The specified minimum yield stress of the steel being used.
STRUCTURAL STEEL CHECKS (AISC) (CONT’D.) Stress Reduction Factors Cmy and Cmz Cmy and Cmz are interaction formula coefficients for the strong and weak axis of the elements (in-plane and out-of-plane). 0.85 for compression members in frames subject to joint translation (sidesway). For restrained compression members in frames braced against sidesway and not subject to transverse loading between supports in the plane of bending: 0.6 - 0.4(M1/M2); but not less than 0.4 where (M1/M2) is the ratio of the smaller to larger moments at the ends, of that portion of the member un-braced in the plane of bending under consideration. For compression members in frames braced against joint translation in the plane of loading and subject to transverse loading between supports, the value of Cmy may be determined by rational analysis. However, in lieu of such analysis, the following values are suggested per the AISC code: a. 0.85 for members whose ends are restrained against rotation in the plane of bending b. 1.0 for members whose ends are unrestrained against rotation in the plane of bending
STRUCTURAL STEEL CHECKS (AISC) (CONT’D.) Bending Coefficient The bending coefficient Cb shall be taken as 1.0 in computing the value of Fby and Fbz for use in Formula 1.6-1a. Cb shall also be unity when the bending moment at any point in an un-braced length is larger than the moment at either end of the same length. Otherwise, Cb shall be Cb = 1.75 + 1.05(M1/M2) + 0.3(M1/M2)2 but not more than 2.3 where (M1/M2) is the ratio of the smaller to larger moments at the ends. Form Factor Qa The form factor is an allowable axial stress reduction factor equal to the effective area divided by the actual area. (Consult the latest edition of the AISC code for the current computation methods for the effective area.) Allow Sidesway The ability of a frame or structure to experience sidesway (joint translation) affects the computation of several of the coefficients used in the unity check equations. Additionally, for frames braced against sidesway, moments at each end of the member are required. Normally sidesway is allowed (i.e., the box is checked).
RUNNING THE STATIC ANALYSIS (CONT’D.)
RUNNING THE STATIC ANALYSIS (CONT’D.) The stress categories: SUStained, EXPansion, OCCasional, OPErating, and FATigue These are specified at the end of the load case definition.
STATIC OUTPUT PROCESSOR
STATIC ANALYSIS OUTPUT User defined retained output data Report Options:
Displacements Restraints Restraint summary Global element forces Local element forces Stresses Stress summary Code compliance report Cumulative usage report
The next slide shows the on-screen static output processor.
STRESS INTENSIFICATION FACTORS OUTPUT
DYNAMIC ANALYSIS OF PIPING SYSTEMS Four types of dynamic analysis are possible: Natural Frequency calculations Harmonic analysis Response Spectrum analysis Earthquake [Valve] Relief loads Water Hammer/Slug Flow Time History analysis
DYNAMIC ANALYSIS OF PIPING SYSTEMS Caesar II‟s dynamic analysis capabilities include: Natural Frequency calculations -
Natural frequency information can indicate the tendency of a piping system to respond to dynamic loads. A system‟s modal natural frequencies typically should not be too close to equipment operating frequencies and, as a general rule, higher natural frequencies usually cause less trouble than low natural frequencies. Harmonic analysis - These are „forcing frequencies‟ that include fluid pulsation in reciprocating pump lines or vibration due to rotating equipment. These loads are modeled as concentrated forces or displacements at one or more points in the system. To provide the proper phase relationship between multiple loads a phase angle can also be associated with these forces or displacements. Response Spectrum analysis - The response spectrum method allows an impulse type transient event to be characterized by a response vs. frequency spectra. Each mode of vibration of the piping system is related to one response on the spectrum. These modal responses are summed together to produce the total system response. And Time History analysis - This is one of the most accurate methods, in that it uses numeric integration of the dynamic equation of motion to simulate the system response throughout the load duration. requires more resources (memory, calculation speed and time) than other methods. spectrum method might be a viable substitute if it offers sufficient accuracy.
PREPARATION OF MODEL FOR DYNAMIC ANALYSIS The dynamic analysis techniques employed by many softwares like Caesar II require strict linearity in the piping and structural systems. Dynamic responses associated with nonlinear effects are not addressed. An example of a nonlinear effect is “slapping”, such as when a pipe lifts off the rack at one moment and impacts the rack the next. For the dynamic model the pipe must be either held down or allowed to move freely. The nonlinear restraints used in the static analysis must be set to be active or inactive for the dynamic analysis. A second “nonlinear” effect is friction. Friction effects must also be “linearized” for use in dynamic analysis. For example, if the normal force on the restraint from the static analysis is 350 lb., the friction coefficient (mu) is 0.3, and the user defined Stiffness Factor for Friction is 50.0, then springs having a stiffness of 350 * 0.3 * 50.0 = 5250 lb/in are inserted into the dynamic model in the two directions perpendicular to the friction restraint’s line of action.
PREPARATION OF MODEL FOR DYNAMIC ANALYSIS (CONT’D.) Developing dynamic input for CAESAR II comprises four basic steps: 1) Specifying the load(s) 2) Modifying the mass and stiffness model 3) Setting the parameters that control the analysis 4) Starting and error checking the analysis To enter the dynamics input, the proper job name must be current prior to selecting the Analysis-Dynamics file options of the Main Menu.
CODE – STRESS EQUATIONS below are the “code stress” equations for the actual and allowable stresses used by CAESAR II. For the listed codes, the left hand side of the equation defines the actual stress and the right hand side defines the allowable stress. The CAESAR II load case label is also listed after the equation.
US Code Stresses
Stress Cat.
CODE – STRESS EQUATIONS (CONT’D.)
CODE – STRESS EQUATIONS (CONT’D.)
CODE – STRESS EQUATIONS (CONT’D.)
CODE – STRESS EQUATIONS (CONT’D.)
CODE – STRESS EQUATIONS (CONT’D.)
CODE – STRESS EQUATIONS (CONT’D.)
CODE – STRESS EQUATIONS (CONT’D.)
CODE – STRESS EQUATIONS (CONT’D.)
CODE – STRESS EQUATIONS (CONT’D.) International Code Stresses
Stress Cat.
CODE – STRESS EQUATIONS (CONT’D.)
CODE – STRESS EQUATIONS (CONT’D.)
BS 7159 (cont‟d.)
CODE – STRESS EQUATIONS (CONT’D.)
CODE – STRESS EQUATIONS (CONT’D.)
CODE – STRESS EQUATIONS (CONT’D.)
CODE – STRESS EQUATIONS (CONT’D.)
AVAILABLE MATERIALS (CAESAR II) ELASTIC MODULUS (lb/in2)
POISSON’S RATIO
DENSITY (lb/in3)
Low Carbon Steel
29.5 E6
0.2920
0.28993
-325
1400
High Carbon Steel
29.3 E6
0.2890
0.28009
-325
1400
Carbon Moly Steel
29.2 E6
0.2890
0.28935
-325
1400
Low Chrome Moly Steel
29.7 E6
0.2890
0.28935
-325
1400
Med Chrome Moly Steel
30.9 E6
0.2890
0.28935
-325
1400
Austenitic Stainless
28.3 E6
0.2920
0.28930
-325
1400
Straight Chromium
29.2 E6
0.3050
0.28010
-325
1400
Type 310 Stainless
28.3 E6
0.3050
0.28990
-325
1400
Wrought Iron
29.5 E6
0.3000
0.28070
-325
1400
Grey Cast Iron
13.4 E6
0.2110
0.25580
70
1000
Monel 67% Ni/30% Cu
26.0 E6
0.3150
0.31870
-325
1400
K-Monel
26.0 E6
0.3150
0.30610
-325
1400
Copper Nickel
22.0 E6
0.3300
0.33850
-325
1400
Aluminum
10.2 E6
0.3300
0.10130
-325
600
Copper 99.8% Cu
16.0 E6
0.3550
0.32270
70
400
Commercial Brass
17.0 E6
0.3310
0.30610
-325
1200
Leaded Tin Bronze 1
14.0 E6
0.3300
0.31890
-325
1200
MATERIAL NAME
TEMPERATURE RANGE (F)
PIPING CODE
PUBLICATION DATE
REVISION DATE
ANSI B31.1
2004
16-Aug-04
ANSI B31.3
2004
29-Apr-05
ANSI B31.4
2002
4-Oct-02
ANSI B31.4 Chapter IX
2002
4-Oct-02
ANSI B31.5
2001
30-May-05
ANSI B31.8
2003
6-Feb-04
ANSI B31.8 Chapter VIII
2003
6-Feb-04
ANSI B31.11
2002
30-May-03
ASME SECT III CLASS 2
2004
1-Jul-05
ASME SECT III CLASS 3
2004
1-Jul-05
U.S. NAVY 505
1984
N/A
CANADIAN Z662
(9/95)
N/A
CANADIAN Z662
Ch 11 (9/95)
N/A
BS 806, ISSUE 1
Sept. 1993
N/A
SWEDISH METHOD 1 2ND EDITION
STOCKHOLM, 1979
N/A
SWEDISH METHOD 2 2ND EDITION
STOCKHOLM 1979
N/A
ANSI B31.1
1967
N/A
STOOMWEZEN
1989
N/A
RCC-M C
1988
N/A
RCC-M D
1988
N/A
CODETI
2001
Jun-04
NORWEGIAN
1999
N/A
FDBR
1995
N/A
BS7159
1989
N/A
UKOOA
1994
N/A
IGE/TD/12
2003
N/A
DnV
1996
N/A
EN-13480
(3/2002)
N/A
GPTC/192
1998
N/A
CODES AND STANDARDS AVAILABLE IN CAESAR II FOR CODE-CHECKING A PIPE MODEL
REFERENCES 1.
2. 3.
4.
COADE, “Version 5.00 CAESAR II Applications Guide” Caesar II Pipe Analysis software, www.coade.com (Email at
[email protected]) British Standard, BS 806, Pipe Bends Water Resources Council (WRC) Specification 329 Caesar II enhancements and reference topics, http://www.intergraph.com/products/ppm/
END OF PRESENTATION
