The following document contains the intensive updates and features regarding the PRG June 2022 release.

Section 1 – General Features

PRG Integration with CEI

PRG is now acquired by and integrated with CEI and their suite of pressure vessel design and welding software solutions. DesignCalcs and Finglow customers can now enjoy native PRG integrations to their pressure vessel designs so they can access advanced features of the software without extensive FEA knowledge or training.

PRG User Documentation

New format conglomerated PRG “Help” documentation is now available.

Open

UI Changes and Entitlement Improvements

Open

The ASME degree of conservatism is now available from any PRG program and helps to evaluate system risk while allowing the user to adjust calculation conservative classifications from anywhere in the program.

The above data panel can be opened from FEPipe and NozzlePRO.

The user can complete the following actions:

• Compute a criticality factor for the condition, operation, dimensions, and content of the system under study. If the factor is above 15 then there are multiple items acting that suggest some greater conservatism might be warranted.

• If the user wishes to use additional conservatism, then the following settings should be selected:

Changing the above settings will potentially increase the calculated stress when any fillets in the model are larger than the attached pipe or plate thicknesses. It may also reduce the allowable stress by up to about two times. The actual adjustments cannot be predicted because any change depends on the distribution of the membrane and bending stress in the geometry.

Fig. Simultaneous Loads Thru the Run and Branch

Analyzing simultaneous loads is now a functionality in NozzlePRO Vessel Link and NozzlePRO. Vessel Link now calculates the load at the appropriate elevation in the beam model of the vessel.

Thru run loads tend to affect the nozzle allowable loads and code satisfaction when the orientation of the loads is such that loads at the nozzle in the shell are close to general allowables. When there are attached pipes on one significant side of the vessel introducing torsion and/or shear, increases in stresses due to nozzle loads can be more significant.

Note: When computing allowable loads in the nozzle the “use run loads” switch can be turned off and on. When the use run loads switch is on the nozzle, allowable loads should be influenced by simultaneously applied run loads. The user should recognize that the combination of the allowable loads represents an infinite five dimensional space (ax, in, out, tor, pre). When the run loads are added this, in theory, becomes a ten dimensional space. The computation approximates various points in this space. When first using this feature, the user is encouraged to verify the particular predicted combinations of branches and run loads.

Load Calculations

Stress Classification

The classification of loads and stresses can result in a doubling of allowable stresses (see schematic below). The user must make sure that associated assumptions are conservative. These switches are now available from the ASME data panel.

Allowables can vary by up to two times. It is important for the user to classify the stress appropriately. The chart below shows this.

Stress Calculations

The Degree of Conservatism

This panel is intended to crudely identify potentially high-risk systems, where high risk is a combination of the probability of failure and consequences of failure. Consequences (pressure and contents) have an approximately +20 rating, while the probability of failure has an approximately +10 rating. This panel only provides a crude “rule of thumb” and can be used with the piping criticality calculator. If the user is unsure about how to classify allowables or stresses please contact PRG for a PS engagement. Nonlinear analysis can also be used to resolve elastic classification issues.

Section 2 – NozzlePRO Integration Features

Introducing NozzlePRO Vessel Link

Vessel Link imports vessel models by XML & JSON files.

The Vessel Link will construct beam models of the vessels and FEA models of a given nozzle or lug on the vessel. Loads in the XML/JSON will be imported along with pressures and material properties.

The models will run through NozzlePRO and produce ASME VIII-2 results. The beam models include liquid levels, fluid sloshing, and all nozzle flexibilities. The models can be transported to Pipe Stress products such as PCLGold as well.

The Vessel Link beam models can also be run by NozzlePRO using 6 or 18dof beam elements. The 18dof beam models are important when natural frequencies should include breathing and shell modes. This would be important when someone is looking for potential modes that could be excited by a given compressor harmonic.

NozzlePRO Integrations with DesignCalcs and Finglow

DesignCalcs and Finglow customers can now enjoy native PRG integrations to their pressure vessel designs so they can access advanced features of the software without extensive FEA knowledge or training.

Key Uses/Attributes of Vessel Link

The following attributes are now available in the Vessel Link:

• Reads in pressures, loads, material, and geometry for nozzles and lugs/clips for pressure vessels and creates local FEA models and global 6/18 DOF beam model with sloshing and nozzle flexibilities.

• Local finite element models using NozzlePRO can be built for a given component.

• An ASME-styled report with comparisons to allowables is generated for the selected component.

• The engineer should visually inspect models to be sure anomalies do not exist. NozzlePRO has been used for countless models over decades but a cursory review of the input mesh and the output stresses and displacements is always recommended.

Each individual model can be further analyzed using NozzlePRO or the Drawing Tools (DT) and the beam model can be manipulated in Vessel Link and analyzed. The Vessel Link is a beam model that can be in Pipe Stress Programs such as PCLGold. It allows for the following functions:

• Allows the user to run one vessel nozzle.

• Allows the user to run one clip/lug

• Output is included separately or in a single file

• ASME VIII-2 Part 5 Output

Note: The Vessel Link does not import nozzles on other nozzles. This generally small connection can be analyzed separately in NozzlePRO.

New Documentation Format

All PRG documentation is available from a single source. This documentation is searchable such that the user can more easily access descriptions of features and engineering methods and recommendations.

Section 3 – ASME Section VIII, Div 2 Part 5 Compliance Features

Tools to Evaluate Stress States

The user is responsible for verifying/checking any or all calculations. As the need for checking, verification and report writing increases, parameters that control code compliance assumptions and their automated documentation helps to expedite this process. These parameters are printed in the Code Notes and should be checked by the user.

Where compressive stresses and high D/T (low pressure) vessels or pipes are present, there are a variety of new tools that are now available to help the user evaluate these stress states. The following tools are now available:

Option 55

Located in the drawing tools. This option allows the user to plot averaged (if requested) or not averaged (worst case) minimum principle membrane stress. When negative this compressive stress helps to evaluate the tendency for a geometry to become unstable and transfer high membrane energy associated with high loads and small displacements to bending energy associated with low loads and high displacements (dimples or undulations in pipe or pressure vessels). Option 55 can be compared to stresses on the order of 0.15 E t/R.

Note: Instability limits can be a function of the modulus of elasticity and t/R instead of the yield stress.

For smaller D/T geometries plastic collapse and elastic-plastic (combined) failures can occur. These guidelines are mainly used for large D/T pipes and vessels. For pipe, the D/T limit is perhaps 80, while for pressure vessels the (rough) rule of thumb limit can be taken as around 350. ASME VIII-2 Part 4 gives guidance for specific load combinations on cylinders. A calculator for this is available from the PCLGold main screen and some discussion is found in the Stability calculator.

Compressive Elastic Stress Report

The compressive elastic stress report is not a code report but is provided to give the user guidelines for evaluating membrane elastic compressive states. When the Compressive Stress summary shows a large number of compressive stresses in a region, the user should evaluate the model further for buckling. This can include running and checking the stability calculator and plotting minimal principle stresses for load cases of interest.

Compressive Stress Summary of a Longitudinal Plate Region

Shell Verifications and Structural Stress Calculation

“Mesh insensitive” structural stress calculations using the drawing tools can be used to verify membrane, bending, and equivalent stress calculations that are independent of stress singularities because the calculations are made from element forces. The curves:miscellaneous options for Option 14 are now available to help verify the shell types. Option 17 is usually executed first to help the user create a curve over typical pipe or beam cross sections.

Important: The structural stress calculation functionalities in FEPipe and NozzlePRO now determines the entire curves cross section properties to verify the net loads on the cross section like beam bending, membrane, and shear to name a few.

ASME Structural Stress Calculation

ASME structural stress calculation shells can be described in Table 5A.8, and these calculations are prepared in the form as described in Table 5A.8 along curves. For more instructions on how to perform the calculations and example output, see Drawing Tools Miscellaneous Curve Help.

For non-joining curves in single shells, the ASME equations must be adjusted to produce curve end stresses. Both recommended methods are included in the output report that is available. These end curve stresses can be used to confirm the stress at the end singularities of clips and lugs. This is a case where deviations from the ASME calculations shown in Table 5-A.8 are needed. Welding Research Bulletins provide theoretical support for the methods.

ASME Data Panel

The bottom half of the Degree of Conservatism panel contains what is considered the most important code classification determinations. These selections appear in the Stress Notes section of every shell model and can have an up to two times effect on the calculated allowable stress.

Fig. Degree of Conservatism Panel

Stress Calculations Guidelines with the New Criticality Evaluator

If membrane stresses are large and bending stresses are small, or l is small, then the characterization of the bending stress tends not to be so important, which includes the bending stress has a small influence on the acceptability of the pressure design. If the bending stresses are large and l is large, then including the bending stress can have a large influence on the acceptability of the pressure design.

ASME “by rule” pressure designs are intended to provide a suitable separation between the design pressure and the failure pressure. If the “suitable separation can be defined” and a test can be performed, then the acceptability of the nozzle can always be determined.

Allowing bending stresses due to pressure to be classified as secondary stresses will generally permit some small, local areas of plastic deformation surrounded by elastic stress zones. One-half to 75% of the twice elastic slope load (due to pressure) can be thought to define a separation between some permanent plastic deformation and linear returns to the original displaced shape. Varieties of elastic plastic calculations can be performed to evaluate this stress condition.

Generally, the M+B stresses control the fatigue life of a geometry. If t >> M+B then shallower sloped S-N curves may apply.

Analyzing operating (thermal) loads on nozzles as primary is addressed in VIII-2 Sect. 5.6 and is intended to apply to protect nozzles in pressure vessels at the boundary (high moment connection) in a piping system.

Important: For vertical vessels that are highly stressed, with large D/T and/or are controlled by vacuum, the loads in the shell from sources other than pressure are often not included in the nozzle analysis and so allowable nozzle loads should be smaller as a result. This is an engineering judgment determination that should be made by the owner/designer.

Fig. General Concerns by Selection Category

Model Verification

FEPipe and NozzlePRO continue to add the capability to help the user evaluate stress and load predictions to ensure that the model solution is appropriately accurate and to help the user produce reports demonstrating validation of the model and predictions. Further functionality to aid in model verification includes the following features:

• Compressive Stress Report

• Stability Processor Report

• Elevation to Lower Bound Limit Load or Elastic-Plastic Model Review

• Elastic/Plastic Analysis

• Elastic-Eigenvalue Buckling

• Elastic-Plastic Buckling with Perturbation

• A variety of model perturbation features in Drawing Tools.

The common model refinement/sensitivity checks include the following functions:

• Comparison to other known manual solutions (pressure and the SCF in WRC 335 in Stability for example), ASME pressure design, etc.

• Mesh refinement check and element side lengths thru stress gradients compared to ROOT(RT).

• Mesh refinement and stress not increasing or decreasing +/- tolerance. Reduced integration shells do not converge monotonically and so as the mesh is refined the stress can get higher and lower about the mean.

• Comparing averaged and not averaged stresses (same mesh). Usually, this will be done when the mesh has already been checked for ROOT(RT) in critical areas.

• When there are high compressive stresses look at Compressive stress output in FEPipe/NozzlePRO. For other software plot and review extents of minimum principle membrane stress.

• The twice elastic slope (TES) is codified in Section III as the definition for collapse and was in VIII-2 Art. 6 before being removed in the 2007 rewrite. The TES test is one of the basic tests for the B31 SSI, along with lower bound limit estimates. For piping in B31 the TES test safety factor form the TES load is 0.5. This puts any primary (or secondary) load that reaches the TES load at a point where it will always return (theoretically) to its non-deformed state. Section VIII Div 2, Art 6 – 2006 used a limit of 75% of the TES load, which is closer to the straight pipe limit specified in the Sect. III B₂ indices. All other components appear to use 50% of the TES load. The TES load philosophy for piping can be considered as the service criteria in ASME VIII-2 5.2.4.3 (b). In the nonlinear (plastic) solver the user would ask to find the TES (M2) value for any given load case. For design loads, if the resulting load factor (LF) > 2, and the load deflection and load strain nonlinear curves are uniform without inflection points then it would be usual to consider that Service Limits are satisfied. This is the only theoretical check that B31 components verify for external loading for primary loads, assuming non-redundant systems.

Fig. TES-3

Note: Usually the basic pressure design is performed by the DesignCalcs or Finglow Design By Rule (DBR) modules of the PVPT Design Suite. External loads and the vessel interaction with the environment around it is determined by FEA or similar methods. When the external loads are zero the FEA is performing the local pressure design of the component. This is generally not the intent and users should be very careful that all DBR concerns are considered by a competent pressure vessel design engineer utilizing Finglow or DesignCalcs modules of the PVPT Design Suite when using FEA for local stress analysis.

Old design approaches using area replacement methods are effective, limited and in most cases conservative.

The method used in VIII-2 Part 4 accounted for over-conservatisms and used a calculation of the membrane stress as a guide for the required nozzle thickness and reinforcement.

The VIII-2 Part 4 method also made adjustments for large D/T and d/D branch connections via the vessel parameter l = (D/T)^0.5 (d/D). This adjustment was first observed in a test by Jacobsen, and then duplicated by Paulin in two large (D/T)^0.5 (d/D) geometries of laterals and cylinders designed, fabricated, and tested to support the updated VIII-2 Part 4 effort. An adjustment to the calculated membrane stress is included to recognize the transition of bending to membrane stress during plastic deformation of high l nozzles and the associated increase in pressure capacity and generally small displacements. The overall intention as it relates to code design was to be able to accurately predict pressure capacity as it relates to boundary failure. Pressure failures in large lambda vessels tended to be pin-hole leaks and benign, while failures in small lambda vessels (and pipe) tend to be fish-mouth failures. As thicknesses of vessels approach dimensions where triaxial stress states exist, failures can become fragmented, spreading metal fragments over often large distances when rupture occurs.

Ke – Strain Concentration Factor

The ASME Strain concentration factor is developed for a single load application but used for cyclic operations in high plasticity problems. In this problem, multiple cycles should be considered and cumulative damage considered for each cycle until the strain range becomes uniform for each subsequent cycle. The Ke calculation is a simplification of a very complex problem. The maximum strain switches from place to place as reversed load applies and plastic deformation occurs.

PRG’s experience is that estimates of Ke using the approach described below for multiple cycles will conservatively predict fatigue damage. Very low cycle fatigue damage, especially where bending is across a full cross section can result in considerable plastic deformation, thinning, and geometry change as part of the cycle life. Using elastic predictions for these complex problems is difficult. Users should take additional care when life prediction is less than 250 cycles. The updated Ke is scaled by the displacements since incremental straining can influence the displacements, which should be used to correct the strain prediction.

Fig. Ke Predictions

Section 4 - Allowable Nozzle Loads

The Allowable Nozzle Loads feature now runs automatically when vertical vessels are brought into NozzlePRO Vessel Link from some sources. This feature is now included in Pad, Unreinforced, and Hillside FEPipe models.

Section 5 - Updating Buckling Guidelines for Nozzles, Branches, and Pipe Shoes

To get accurate estimates of local buckling modes, there should be several element edge lengths within 3 (RT)^0.5 in the high cycle zone as a guideline. For the circumferential head buckling shown in the Figure below, the element edge lengths should be about this size in the circumferential direction. Generally, for FEPIPE and NozzlePRO models, there will be a discontinuity in these areas that will generate small elements but to evaluate buckling tendencies in zones where there are no discontinuities modeled the user must place the elements manually.

Either distribute a large number of elements over the entire shape or using mesh control in FEPipe – place a small enough number of elements in the compressive stressed zone. In this case some perturbation in this area or 2% wall thickness change (that can be easily entered in the drawing tools) will help evaluate the tendency to buckle in these areas.

Ability to Compute Hoop Direction Compressive Loads in Head Knuckles

Compressive stresses can be evaluated in any shell geometry. Access to nonlinear analysis may include an elastic-plastic model of the geometry, large rotation, large strain, and arc-length control of load stepping (for snap thru behavior). The user must be aware that in “buckled” areas element lengths should be less than (RT)^0.5.

Fig. Load Failure in a Fatigue Test (R= -1)

In the image above, cracks occurred internally as the test progressed without distortion. At around the 90^th cycle, the small inside cracks increased in size, a large plastic buckled zone occurred and a subsequent thru-wall crack appeared through about 100 deg of circumference in a single cycle. The bottom failure is controlled by Sy, S, and N. The above failure of the vessel head is controlled by S, t/R, and E.

When “things are thin” the mechanism of transferring membrane to bending can result in large change in geometry and load redistribution. When things are “thick” the transfer is slow and load redistributes uniformly. Plasticity starts with bending and is transferred to the membrane. Collapse starts with the membrane and is transferred to bending. This is why the membrane verses bending stresses and their magnitudes are important.

Where buckling modes are used to perturb a geometry that contains discontinuities such as nozzles or clips and lugs, the user should be sure that multiple modes should be used as part of the perturbed shape so that the weakest perturbed geometry is found. The different perturbation patterns will result in different alterations of the maximum collapse capacity, but at some point, service limits may still need to be used. Different loads require different perturbations.

VIII-2 Part 4 Sect. 4.4 – Design of Shells Under External Pressure and Allowable Compressive Stresses

Stability Processor Considerations:

• Torsional loads are not evaluated for thru vessel loads. The processor was set up for bending, shear, axial, and external pressure loads. There is an external load processor in PCLGOLD that includes all directional loads and torsion.

• Units for metric or SI are in a consistent set. Ensure to enter consistent units like mm, MPa, N., and in. psi and lb.

Loading on Pipe Shoes and Saddles

Loading on pipe shoes is an easy problem to address using beam elements. Pipe weight, Fluid, wind, and seismic loads are evenly distributed along the pipe and result in a reasonable estimate of the primary load acting on the support.

Evaluating local loads for a finite element analysis can be more difficult; however, since boundary conditions may introduce loading distributions that do not reflect the actual local forces and moments, for example liquid loads in horizontal vessels or large D/T pipe, it can result in pressure variations along the line of line-of-load, which can bend the pipe over the supports. Wind loads act over the outside of the pipe on one side and can transfer loads to supports on opposite sides in an arch-like manner introducing a combination of bending and compressive stresses. These different local load effects are often simulated using only the resultant load acting on the support from the beam analysis without replicating the local load redistribution.

When the local load distribution is attempted, the force on the support often tends to be different because of load redistribution in some cases because replicating all the distributed beam loads in a finite element model can be cumbersome.

Care must be exercised when uniform loads acting on a beam centerline are simulated in a finite element model.

Fig. Vertical Load Distribution Over Group of Supports

Fig. Horizontal Load Distribution Over Group of Supports

The uniform loads produce varying shear and moment load distributions as shown when the supports are locally evaluated.

Fig. Shear and Moment Load Distribution Over Supports

A common approach when evaluating local loads is the following:

Fig. Uniform Load to Model Simulation Approach

Perturb the Solution

When perturbing the solution, consider the following calculations:

Fig. 39-Backup and Plot Perturbed Element Files

Perturbing the Geometry Using Buckling Mode Shapes

When perturbing the geometry using mode shapes, note the following considerations:

Plotting the Minimum Principle Membrane Stress (113 or 115)

To plot the minimum membrane stress, enter the load case and 113 for the NOT averaged minimum membrane stress and 115 for the averaged minimum membrane stress. Changing the high compressive (negative) membrane stresses into bending stresses can result in local kinking or elastic buckles. The critical compressive stress must exist over an area dimensionally greater than the local elastic buckling mode size.

The rule-of-thumb for the start of an instability stress is 0.2 x E x (t/R). The compressive load is along the meridonal or axial direction, or for heads - any direction.

The user can perturb the geometry with the collapsed plastic mode with the following options:

• Option #10 – elastic buckling shape (<mode start><mode end><max displacement>

• Option #12 – elastic solution (<start load case>,<end case>,<max displacement>)

• Option #13 – plastic solution (<load case>,<plastic type>,<max displacement>)

Buckled Mode Sizes

Sketching tools can be used to identify locations.

Sketching on the model can be used by interacting with the Drawing Tools to layout local thinned areas and to note lengths of interest. The drawings on the vessel stay in place unless the user deletes the 3d model or clears the drawing space.

Fig. Buckling Mode Local Buckled Shape Sizes

Fig. Measurement Points

Boundary Conditions on Tees (Using in Collective Models)

The user cannot free both run ends of tee geometries from NozzlePRO or the welding tee template due to the resulting model instability. The drawing tools user can apply loads and boundary conditions as they wish and so there is a need to have boundaries at each end of the UFT, RFT, Hillside, or welding tee template. The user can do this by entering the FEPIPE editor and making each run end free. In previous versions, this resulted in a logical fatal error and the user could not proceed. In later versions ,the user will only receive a warning message.

For these templates, the user can also place a -1 node number in the branch node number field to have a spoked wheel surface (and pressure) applied to the branch end. This allows the user to add concentrated forces to the branch end via the drawing tools or the loading editor.

Changing Load Magnitudes

If the user has a lug load that he or she wants to increase by 6.885 times, the user can cycle in the nonlinear solver. The user can put a curve on the model where you want to increase the load. Option 33 is used with the curve and the MULT command to increase the weight loads along curve 1.

Fig. Increasing Weight Loads

Algorithmic Bending Stress Classification

When the algorithmic bending stress algorithm is checked, the stress evaluation algorithm will look at the compressive stress distribution in the region of the model described, and if a sufficiently large area has compressive stresses that exceed 0.55S_y or 0.15Et/R where R is the local radius of the element, then the stresses for that load case will be classified as primary instead of secondary, using the smaller primary allowable stress. The evaluation used for each region is reported in the compressive stress report in the FEPipe or NozzlePRO output.

For a vessel subject only to weight and pressure, a compressive load report is shown below. Most of the stresses in the nodes around the nozzle are in compression. The minimum stress is the smallest principal stress. If the user wishes more information on the algorithmic bending stress classification – please contact PRG for a PS engagement.

The minimum principle stress can be plotted from the Drawing Tools and the curve miscellaneous options as seen in the figure below.

Fig. Plotting from the Drawing Tools

Buckling Mode Model Perturbation

To provide perturbation in the shell, the worst but reasonable case is to provide a perturbation on the compressive side of the loaded discontinuity and a thickness loss within the mechanical tolerance of the vessel also along the perturbation. It is believed that this will give an adequate lower bound. The first eigenvector buckling mode is being selected by the industry as a perturbation shape, but the user having a complex geometry, should evaluate the behavior closely. FEPipe and NozzlePRO make it easy to change the sign of the perturbed shapes, scale them to different values, and combine them with local thinning.

Local buckling areas for cylinders in compressive stress states appear in the sketch.

Fig. Sketch of Cylinders in Compressive Stress States

VIII-2 Part 5 is also updating buckling guidelines and the reader is encouraged to review VIII-2 for the latest guidance.

Buckling Examples and Perturbation

Note: Various notes and examples on buckling and perturbation are included in various locations throughout this document.

To save and then recover an original element file through the ELEMENT tab, consider the following process:

The process outlined is taken from “Cylindrical Shell Buckling: A Characterization of Localization and Periodicity”, G.W. Hunt, G.J. Lord, M.A. Pelletier.

Use function 7 option #3 to save the original element location. One reason to store the original model is that variations of displacements can be automatically calculated using function 8 and 9.

Remember to set the length of the edge to be at least equal to the square root of RT or the amount the edge is changing from starting of the perturbed shape to the ending of the perturbed shape. If Root(RT) = 2.5, then the length of the marked element zone should be at least equal to 5. Inches.

The load and unload workflow process is outlined in the following table:

Buckling Analysis for Shell Geometries

Realistic buckling loads in heads, cylinders, and geometries with nozzles and lugs can be analyzed using large rotation, large strain, and elastic-plastic analysis with perturbation.

Fig. Realistic Buckling Guidelines for Different Types of Geometries and Loadings

Several approaches may be used to create a perturbed geometry. Verification of the results should always be provided. Perturbation is discussed throughout this document.

Ensure that where high compressive stresses might exist that sufficient mesh gradients are present in that area to simulate the local buckle. In the short direction of the wrinkle, this is on the order of the ROOT( RT ). It is often not practical to place elements of this size over the entire geometry, so the user can reduce the thickness to the tolerance value and place elements in a uniform area in the smaller size to determine the buckling capacity. An example of this condition occurs in the knuckle area of a dished head where buckling wrinkles can occur in the meridonal direction. The long axis is in themeridonal direction and the short axis of the wrinkle is in the circumferential direction.

Section 6 - PCLGold Sustained Stress Indexes (SSI) Updates

SSIs are displayed along with SIFs in PCLGold output reports. NozzlePRO and FEBend can generate nonlinear SSI values for any D/T pipe and these are considered the most accurate SSIs available. The SSIs may be entered into PCLGold in the SIF data column.

SSIs for beam-related models can be found at the top of the Pipe B31 Code Stress report. An example of this report is shown below:

Fig. Example Pipe B31 Code Stress Report

Cumulative Damage – TES Calculations

For all load cases, when the TES load is exceeded, strains can be increased beyond elastically predicted limits. The TES load can be exceeded for operating and occasional cases when the actual displacements is more than 1.5 times the calculated displacements. Seismic loads are designed to be 2 to 2.5 times the displacements predicted by elastic stresses, and operating loads can be up to 1.5 times the TES load and still satisfy the B31 allowables.

(SSI)(M/Z) = 1.33Sh, the actual displacement/stress is 2 to 2.5 (Cd) times more than the given stress, so that actual maximum allowable will be 2 x 1.33 to 2.5 x 1.33 = 2.66Sh to 3.325 Sh. For operating stresses, the maximum can be the following calculation (SIF)(M/Z) = 2Sy. The ratio between the thermal or operating moment and the TES moment is: Mo = 2SyZ/(SIF), and Mc=(1.33Sy)Z/SSI, so Mo/Mc, the maximum operating moment divided by the TES moment = 2SyZ(SSI)/[(SIF)(1.33Sy)Z] = (2SSI)/(1.33SIF) = 1.5 x SSI / SIF. The cumulative damage processor will read in pipe stress programs data, such as PCLGold and perform cumulative damage and TES evaluations for piping systems where fatigue or large occasional loads can exist.

Section 7 – Improvements to Modeling Welds

Overreach Fillet Elements

Overreaching fillet elements contains a thickness equal to the throat thickness of the weld are described in VIII-2 Part 5 and in BS 7608. The elements for any particular assembled branch and run (two plates welded at an angle) can include fillet models simulated with the overreach element.

Fig. Overreach Fillet Elements

The PRG weld elements are designed to replace the area and summed inertia of the weld intersection. This model has been shown to provide the most consistent penetration line rotational stiffness. When the fillet legs get large, the model type can become more important and may affect the solution by as much as 40% in certain parameter ranges where fillets are large with respect to the area of the connecting plates.

A calculator is available for cylinder on cylinder intersections that gives the calculated area and section modulus for various model so that the areas and inertias can be compared. As d/D > 0.5, the shape of the intersection weld is controlled somewhat by the angle of cut and the fit up. At d/D = 1.0 there is a cat’s eye-opening variation of the fit up and a draw back from the centerline.

These geometry attributes are seldom included in any finite element model. PVPT Fabrication Suite with ProWrite Welding Procedure and FabMan WeldERP “as-welded” data can assist in proper documentation and validation of weldments and integrate directly with the DesignCalcs and Finglow modules of the PVPT Design Suite.

There are many ways to form the branch connection model of shells, including the ways in the figure below.

Fig. Forming Branch Connections

In FEPipe and NozzlePRO, the user can build the overreach element shown above. The tapered element models are generated by default. There are two tapered models including:

• standard – based on area, Ix inertia, and comparison with burst test results

• 2022 tapered - based on area and Ir results

It is assumed that the area and Ir result comparisons will yield the most accurate models. The Ir value (inertia) can be compared for the model used to the Ir from the exact geometry. These ratios are shown below for the overreach element on the left (shown expanded below) and the 2022 element on the right. The 2022 element surface is flat and close to 1.0 as desired through the horizontal parameter range. The overreach element inertia is larger by more than 6 times when the t/T ratio is small and the fillet leg is larger.

Fig. Ratio

Note: For further configuration options, contact PRG.

The Stability processor includes data for the overreach element showing how the thicknesses and inertias can be calculated and how they affect the overall properties. Notice that the calculations in the stability processor are for the case where the nozzle and vessel shell midsurfaces are normal to each other. This is not the case as a point on a nozzle in a cylinder moves from the longitudinal plane where it is normal to the circumferential plane where it is on the side of the cylinder.

An Options field is displayed where the user can enter parameters.

Fig. Options Field

A model can be selected that approaches the characteristics where the overreach model inertia is larger than the actual cross section inertia. In this case, one might expect the overreach model to be stiffer than the actual geometry. This can be true when the overreach stiffness is of the same order as the attached shell local moments of inertia. Note that t/T < 1 and Leg/T > 1.

Fig. Overreach Model

This shell model results can easily be compared to brick model results using the functions in NozzlePRO.

Fig. NozzlePRO Brick Model Results Functionality

The comparison results for the stiffness are shown below in the table below as displayed in NozzlePRO.

Fig. Comparison Results

Section 8 - Reinforcing Pad Features

Pad UI and Template Features

The following new features are now available within the Pad functionality:

• Nonintegral Pad

• ½ pad calculation option

• Overreach preparation option

• Allowable loads a function of loads thru the run

To prepare for overreach, the thickness of the fillet leg entering and leaving the penetration line must be equal to the shell and branch respectively. The overreach element must then be set to be equal to the thickness of the crotch.

Region File Breakdown and Definitions

Users needing to find the exact region node distribution of the regions can consider the following procedure:

Pad Modifications

In the case that users want to take credit for only half of the entered pad, there is an option for this in rft28.t that allows for modifications.

Fig. Input Modifications in the RFT28 Template

Section 9 - The Drawing Tool Feature

The following features are now available within the Drawing Tool:

• Edge-to-edge model connection

• Perturbing models

• Applying local thin areas interactively

• Locally changing model properties

• Performing mesh-insensitive FEA Calculations

Option #50 – Move the Shell Elements Attached to a Circle and Optionally Connect One Circle of Elements to Another

In Option 50, there is a one and two-curve option. The one-curve option identifies the round section of the model to be moved and provides the coordinate to move it to. The two-curve option provides a “from” and “two” curve. The “from” curve is moved in the direction of the “to” curve. The center of the from curve is moved away from the center of the “to” curve by the vector entered in the parameter field.

Execution of Option #50 moves the set of elements connected to Curve #1 to the position relative to Curve #2. The user can identify Curve #1 and curve #2, and then enters the delta vector. Once the elements are moved, a set of elements is produced in between the two curves.

Fig. Curve 1 and Curve 2 Options

Drawing Tools Useful Commands

File Handling

Perturbation

Printing/Lists

Fig. Analyze Geometry Loads

Fig. Displacements and Rotations Print View

Note: Occasionally, the user may need to Include the word “path” after the orientation of the section normal.

Section 10 - Stability Processor Note Updates

WRC 335 is the basis for the SCF calculations for pressure in the Stability Processor.

Option #55 – After an Elastic Calculation Plot the Minimum Principle Membrane Stress (113 or 115)

To plot the minimum membrane stress, enter the load case and 113 for the NOT averaged minimum membrane stress and 115 for the averaged minimum membrane stress. It is the changing of high compressive (negative) membrane stresses into bending stresses that results into local kinking or elastic buckles. The critical compressive stress must exist over an area dimensionally greater than the local elastic buckling mode size.

The rule-of-thumb for the start of an instability stress is 0.2 x E x (t/R). The compressive load is along the meridonal or axial direction, or for heads - any direction.

The stability processor is available from the NozzlePRO screen. It does not influence any NozzlePRO calculations but is included as a “calculator” to help the user verify the reasonableness of the finite element calculations and to provide documentation to demonstrate the verification effort.

Section 11 - Phased Harmonic Loads

The following recommendations involve the easiest method to use when controlling the phased harmonic solution:

• Setup the model using static solution.

• Enter through the Drawing Tools.

When data on the xd2 and xd3 files are non-zero, generally the phased harmonic solver will start. This includes phased loads that are nonzero that even have a zero phase angle.

Definitions of alpha (a) and beta (b) should be applied carefully. Phased harmonic solutions are considered specialty solutions. Please contact PRG for a PS engagement if you think you need phased (vs. in-phase) harmonic dynamic solution.

Option #52 – Add Density to the Model

Option #52 allows users to add density to model when a curve # is not required. The density should be followed by 2 element types. These are generally shell element types 11 and 12. If there is no input, the default values are used for shell elements 11 and 12, where the density is 0.283 lb/cu.in. and 7.83e-5 kg/cu.mm.

Option #53 – Modify the Solution Options File (.SOP)

The solutions options file specifies the type of analysis to be performed. Parameters control how the command is executed.

If the parameter line is empty, then the solution options file is read and the report tells the user how it is setup. An example output is shown below for a typical static analysis:

Enter an “S” on the line to make sure the system is setup for static solution and “D” for a dynamic solution. Note: The S or D do NOT need to be capitalized.

If a dynamic file is requested, then additional control files <name>.xd3 and <name>.xd3 are read. These files control dynamic loads and solution types. The xd2 file is a general control file and the xd3 file contains loads that can be written by the user or other porgrams. The xd2 file contents is /SLASH file controlled and contains the following command:

Option #53 – Integrate the Solution Options File (.SOP)

The solutions options file specifies the type of analysis to be performed. Parameters control how the command is executed.

If the parameter line is empty, then the solution options file is read and the report tells the user how it is setup. An example output is shown below for a typical static analysis:

Enter an “S” on the line to make sure the system is setup for static solution and “D” for a dynamic solution.

If a dynamic file is requested, then additional control files <name>.xd3 and <name>.xd3 are read. These files control dynamic loads and solution types. The xd2 file is a general control file and the xd3 file contains loads that can be written by the user or other porgrams. The xd2 file contents is /SLASH file controlled and contains the following:

The solutions options file specifies the type of analysis to be performed. Parameters control how the command is executed.

If the parameter line is empty, then the solution options file is read and the report tells the user how it is set up. An example output is shown below for a typical static analysis:

Enter an “S” on the line to make sure the system is set up for static solution and “D” for a dynamic solution.

If a dynamic file is requested, then additional control files <name>.xd3 and <name>.xd3 are read and displayed. The user can edit and save these files to control the dynamic output. These files control dynamic loads and solution types. The xd2 file is a general control file and the xd3 file contains loads that can be written by the user or other programs.

Consider the following process to run a dynamic analysis for a static model:

Build the model and enter the drawing tools.

Note: It’s recommended to perform a static analysis so the user can verify that the loads and boundary conditions are entered correctly.

1. Run curves option #53: with a “D” in the parameter slot.

2. When executed, information will be displayed to the user along with xd2 and xd3 files. The user can change these files as needed to implement changes, loads, etc.

3. When finished – the user can execute the model. If a dynamic analysis is requested the user can still click the Submit for Analysis button to perform any of the analyses requested.

The xd2 file contents is /SLASH file controlled and contains the following command:

The following XML MiM commands control harmonic solutions:

Generally, iphase is determined by the problem. If there is a phase angle with any load, then iphase is set to 1. If there is damping restraints, Newmark Beta damping, or dashpots then the iphase is set to 1. “Ibkdn” tells how many intervals through 2pi to scan for maximum output in a phased solution. 10 to 36 is a typical value. If iphase > 0, then ibkdn is used and defaults to 10 if not entered. Ifixphase = 1 then the intervals through 2pi indicated by “ibkdn” are selected at fixed locations through 2pi. If ifixpase = 0 then the maximum displacement angle in the specified interval is determined and used to compute the displacement, reaction and stress for the intervals. There will still be “ibkdn” intervals.

Note: The averaged stresses should involve only the stresses in the edge element and not the thickened elements.

When running the following file structure is setup:

For PCLGOLD – the dom input file is in the data folder.

For IFU file – from the drawing tools the dynamic solution is run from <name>_BIFMODAL

If the user adds HAR to the line in a curve #25, a load cases setup for a dynamic run displays.

SOP File

G<name>sop

opt1|I5} {opt2|I5} {opt3|I5} {opt4|I5} {bourdon_opt-1|I5} +

{piping_code_type|I5} 0 {user_adjust_jacobian-1|N5} {opt9|N5}

1-average 2-notaverage 3-gauss average 4-gauss not average – drop down in T code and dot files.

<stress type>

0-not averaged

1 - averaged

2-gauss not averaged

3-gauss averaged

Below is a typical SOP file setup for dynamics. When this file is run, the dynamic module is entered. When the dynamic module is entered, the user can use the xd2 or xd3 file to control the solution. User control of the solution allows the user to:

• Perform sturm sequence checks

• Perform eigen solutions

• Perform harmonic solutions

FEPipe and NozzlePRO can be setup for static linear and nonlinear calculations, specialized piping applications (hanger design, etc), and for dynamics.

If the SOP file in the main folder has a 7 set for engine, then using the Submit for Analysis button takes the user into the dynamic module as the dyn file is setup. It is the <name>.dyn file that controls how the dynamic analysis will be run.

The following is a typical <name>.dyn file:

The following values are in the dynamic file:

• Line 1: number of eigenpairs to calculate, freq_start (hz)

• Line 2: recommended subspace size, allowed solution time (sec)

• Line 3: diagonal mass matrix logical

• Line 4: cnvfor, cnvlen, cnvmas (For English: 1, 1, 0.00259) For SI/Metric:

• Line 5: Logical Buckle Shift, Buckle Shift Factor

• Line 6: Logical for Harmonic Analysis (See XD3 file description below)

• Line 7: Loads for harmonic analysis (already used to form load vector)

• Line 8: Harmonic excitation frequencies (1->5)

• Line 9: Harmonic excitation frequencies (6->10)

• Line 10: Logical Eigenvalue Spectrum, Logical Time History, Logical Static Spectrum

• Line 11: Frequency Max, Spectrum Max_1

• Line 12: Spectrum Max_2, Spectrum Max_3

• Line 13: Direction_1, Direction_2, Direction_3

• Line 14: Diagonalization Method

Variation of Damping Ratio

Classical Rayleigh damping is viscous damping, which is proportional to a linear combination of mass and stiffness. The damping matrix C is given by C=μM+λK, where M and K are the mass and stiffness matrices respectively and μ and λ are constants of proportionality. Rayleigh damping does afford certain mathematical conveniences and is widely used to model internal structural damping. One of the less attractive features of Rayleigh damping, however, is that the achieved damping ratio ξ varies with response frequency. The stiffness proportional term contributes damping that is linearly proportional to response frequency and the mass proportional term contributes damping that is inversely proportional to response frequency. This graph illustrates the way in which the mass and stiffness damping terms contribute to the overall damping ratio:

Fig. Variation of Damping Ratio with Frequency

AIV Guidance

/PHASE_DIRECTIVE

<iphase> <istep> <ifixphase> <angle>

/NEWMARK_BETA

<alpha> <beta>

/DAMPING_DATA

<ndamp> <ndash>

/DAMPING_VALUES

<ndamp>

<node1> <node2>

<damp(i,j),j=1,6)

<damp(..,j),j=1,6)

..

<damp(6,j),j=1,6)

/PHASED_FORCES

<node> <idir> <force> <phase> <cx> <cy> <cz>

/STURMCHK

<num ints>

<xint1> … <xint_num ints>

/FREQHI

<high frequency>

/ALLLOW

<low frequency>

/ALLHI

<hi frequency>

/HARMONIC

<num>

<freq(i), i=1, <num>

/INIT_FORCE – the presence of this will initialize the incoming vector and will rely on the user to enter

/phase_forces to provide the harmonic excitation.

Acoustic Induced Vibration (AIV) Update

The AIV update primarily investigates frequency ranges and produces stress results for high frequencies. The user should verify that the model is suitable for the frequency range of interest. This is done by adjusting the sturm sequence calculations to determine where frequency ranges fall. There is a data file that can be created by the user like <jobname>.xd3. This file has a sequence of / commands followed by data. To enter 5 sturm sequence frequencies, the user would enter the following command:

Important: The /sturmchk directive will override the natural frequency calculation, and the software will perform only the sturm sequence calculations. This makes running the solution much quicker and lets the user know where the solutions will fall. Only 10 frequency values may be entered for the multiple frequency checks.

Frequencies will be counted from 0 to 1000 Hz., from 0 to 2000 Hz, and so on. Detailed stresses for shell models can be calculated for 50 separate load cases, so the user should identify the frequency range for the printed result.

To control which frequencies are printed, enter the following values:

• /ALLLOW (Use this to print as many low frequency modes as possible. This is the default).

• /ALLHI (Use this to print as many high frequency modes as possible).

To focus only on high frequencies, the user can specify the first high frequency that should be included in the output stress calculations. The sturm sequence calculations should be performed first so that users will know where the frequency calculations should start. With the /FREQHI command all frequencies below the high frequency will be omitted. The Graham-Schmidt orthogonalization will be used with eigenvectors below the “high frequency” so that no component of low frequency modes will be associated with the higher modes.

Section 12 – Elastic-Plastic Solver Feature Features

The following Features are now available within the Elastic-Plastic Solver:

• Elastic Analysis Comparison Calculation (Load Step Option = 3).

• Updated iso-beam boundary conditions.

• In the 2019 version of ASME VIII-2 Part 5, the Super Alloy m₂ coefficient error was corrected.

Beam and Shell Models

Users can import beam and shell models from NozzlePRO directly into MITCH for elastic plastic and large rotation analysis. Beams can be added from NozzlePRO to apply loads to nozzles.

When the beams are imported, use load step Option 3 to show that the linear analysis matches expected values. Then, the user can change the load step Option to 2 for typical thermal load calculations. Usage of the extend to collapse calculation is contraindicated for thermal loads.

Advanced Nonlinear Features

The following content contains updates the to the Advanced MITCH features.

The user can now evaluate reversed plasticity by entering a negative cycle count in the MITCH nonlinear property data screen. The help available for this screen details the change. When a negative number is entered the specified loading will be applied, removed and then reapplied in the negative direction. This cycle will repeat “N” times.

The arc length solution permits an applied load to be reduced in an attempt to find a subsequent converged load.

Consider the information below for ratcheting options as it applies to your load cases.

Ratcheting options here are for the load cases set up in the main nonlinear form shown below. These cases control how the primary and then range load cases are applied. The max strain limit node will control the output strain window and the strain node used for the Ke calculation. The M2 node and direction will also control the node with the load and displacement for the M2 calculation and for the displacement printout for cycling and the Ke.

• If the number of cycles is negative on the main data panel, then the load will be applied and then removed, and then reversed and applied and removed for an R=-1 fatigue simulation. If pressure should be applied first, then the PL switch and ratcheting options can be used to apply a fixed load first, and then the varying load second. Ensure to run the load combination and cycles on a simple system first so that the results can be manually verified.

• The user can increase the load by selecting the “Extend loads collapse” option, and then limit the maximum load multiplier to a constant. All loads except for ASME load cases and SSI loads will be extended to the multiplier given if the geometry will carry the load.

• The advanced panel uniform load step controls can be used for loading and unloading. For thermal loads the uniform load step control should be changed to 2. The uniform load step parameter will be changed automatically from 0/0.1 to 2 if thermal loads are detected in the model.

Additional MITCH Features

The Features are now available as MITCH features:

• Improvement of the stability parameters of arc-length algorithm so that the speed of arc-length algorithm is improved. Users should find more regularly spaced program selected load steps.

• Cyclic loading (reverse loading cycle or loading-unloading cycle) which includes Bauschinger effect added. The user activates this feature by entering the number of cycles in as negative numbers.

• Iso-beam element with large displacement/rotation, which can couple the nodes on which the torque is applied along drilling dof direction to neighboring elements or nodes. This method improves the stability of torsional and force-follower loads.

• Addition of spar elements.

• Addition of beam elements which includes fixed flexibility factor and large rotation. These beam elements can be used to load shell models.

• New transcendental equation solver for material property convergence is introduced and the speed is faster.

• New algorithm was introduced to handle the drilling stiffness addition.

• New approach for Ke calculation to relate the Ke to the magnitude of the load or displacement.

• Improvement on algorithm to include thickness thinning effect.

• Uniform loading stepping scheme with different time step size combined with automatic time stepping scheme.

• J-integral calculation using virtual crack extension algorithm updated for nonlinear solutions.

Note: Crude meshes typically run through the linear solver without difficulty. The results should not be used, but the crude mesh solution lets the user make sure that the load cases and the model are setup in a reasonable way. Collapse or elastic-plastic solutions occasionally won’t work with crude meshes because of the poorly formed elements and numerical imbalance. In these cases, a small refinement of the model is usually sufficient, and the user can use a “reasonably coarse mesh” to check nonlinear calculations also.

Advanced Panel Options

Fig. Plasticity and Large Rotation Options

Options for ratcheting analysis using noncyclic method (Reinhardt). The Reinhardt procedure applies the range load first and determines a reduction in capacity of each element. Then, the primary load is run. If it satisfies the primary load requirement (does not collapse with the appropriate controls), then ratcheting is assumed to be satisfied. The Reinhardt procedure is much faster than the option 3. The user wishing to use the faster options 0 or 1 should verify that these options are valid for the geometries under study by running at least one option 3 calculation for verification.

• 0: Small displacement/rotation in elastic modulus adjustment procedure

• 1: Large displacement/rotation in elastic modulus adjustment procedure

• 3: No Reinhard ratcheting. In this case the loads will be applied as requested in the load case selection and then the cycling of the load range will be conducted the number of times specified in the cycles. Note that occasionally 10 to 15 cycles are required before the load is stabilized.

The pressure combination method variable. This option decides which load cases pressure is associated with for common primary cases.

• 0-Pressure is combined in the first load case for all but the fatigue case with the other load cases in the case and analyzed as if the pressure rises monotonically with all other loads.

• 1-Pressure is in the first load case when in the case. Other loads are included in a second load case. If the loads cycle then the entire process repeats after returning to zero.

• 2-Then pressure is applied first and then the load is added and then only the second load cycles after the pressure has been added. Note that this does not impact the sustained stress index.

Contains many types of analysis.

• 0/1: Analysis with arc-length scheme.

• 2: Analysis with uniform loading steps combined with automatic time-stepping scheme. This is required for thermal loads but is activated automatically when thermal loads are detected. The user can try the uniform load steps at any time if there is a difficulty getting arc length solutions to converge.

• 3: Linear elastic analysis.

1. Maximum allowable number of iterations per load step. Enter 100 to deactivate kinematic hardening and use isotropic hardening instead when loads are reversed. Kinematic hardening is used to simulate Baushinger effects.

2. Factor for dividing load step in the case of automatic time-stepping scheme.

3. Factor to multiply the magnitude of the occasional loads that are identified in the model. Occasional loads can usually be identified in the <name>.m1f file as 14002 and are specified as wind or seismic loads in FEPipe template input. Users should verify that each combination case provides the applied total load desired. The solution data report for static calculations gives the unbalanced load summation.

4. Relative tolerance used to check for convergence based on energy criterion. Values between 0.001 and 0.005 are recommended.

5. Parameters to define the multi-linear stress-strain curve.

• 0/1: Stress-strain curve with shift by Sy/E

• 2: Stress-strain curve from ASME approach without shift

• 3: Stress-strain curve with shift and yield stress equal to 0.7Sy

• 4: Stress-strain curve with shift and yield stress equal to 0.8Sy

• 5: Stress-strain curve with shift and yield stress equal to 0.9Sy

• 6: Stress-strain curve without shift and yield stress equal to 0.7Sy

• 7: Stress-strain curve without shift and yield stress equal to 0.8Sy

• 8: Stress-strain curve without shift and yield stress equal to 0.9Sy
  
  

1. Same strain with 0.8Sy and 0.7Sy
   
   

2. Used for nonlinear step size. Every load step size is compared against the allowable arc length bound set by alpha. 3 is small – and used when small steps are required. 100 to 300 are generally used when starting if the fixed load step is not set. The fixed load step control is controlled by item c. The user should start with larger values (100 to 300) and then if small values seem to be needed – they can be entered. Starting at and alpha = 3 is often too small and results in load steps that are excessively small.

3. Factor used to limit the maximum displacement increment during a solution step. If the displacement increment exceeds 100 times the displacements in the first load step, the current load step will be repeated with a reduced load factor. Smaller values reduce the arc length size and refines the solution but increases the number of program selected load steps.

4. Elastic-plastic + small displacement/rotation (thickness thinning effect not included).

5. not used at this time

6. not used at this time

7. Elastic-plastic + large displacement/rotation (thickness thinning effect included).

8. Elastic + large displacement/rotation (thickness thinning effect not included).

9. Tresca yield criterion (default is von mises yield criterion).

10. Concentrated forces/moments rotate in nonlinear analysis. This can be critical for the case where torsion is provided by force couples and where loads are applied by elements that rotate with the piping system such as relief valves.
    
    

11. Specify the input node on which effective total strain will be reported. The user can find this by going to the “Element” panel in the Drawing Tools and click on elements of interest. The node numbers for any element are shown on the screen.

12. Specify the input node used to calculate the M2 value.

13. Choose the displacement component for the M2 node specified in s to calculate the M2 value. Note how twice elastic slope below can be very close to three or four times the elastic slope. This is a simplification. When the geometry reaches the M2 load, the displacements are twice those predicted by an elastic analysis. One half of this value results in typically purely elastic loads that return to their precise starting point when the load is removed.
    
    
    

Physical Features of Reversed Plasticity

Consider the following features of reversed plasticity:

• Bauschinger Effect – The hardening increase in strength is removed from the opposite direction yield strength.

• For non-symmetric load-controlled cycling “ratcheting” may be developed. Combinations of displacement controlled cycling ratcheting can also be developed.

• Monotonic vs. Cyclic stress-strain differences.

• Crystal slippage occurs and the material behavior translates from a “plateau” two-term model to a power-law model without a noticeable plateau.

Buckling Mode Model Perturbation

To provide perturbation in the shell, a potentially conservative but reasonable case can be developed by providing a perturbation on the compressive side of the loaded discontinuity with a thickness loss equal to the mechanical tolerance of the vessel also along the perturbation. It is believed that this will give an adequate lower bound. Consider the following process when attempting to achieve a lower bound:

1. Enter the drawing tools for the model to be perturbed.

2. Have an idea where the buckling mode will be placed. Ensure that there is a reasonable mesh in the area. This usually means that an element length is (RT)^0.5 and that there is one element as a minimum on either side of the buckling crevasse.

3. Clip away the back side of the geometry and rotate the model so that the perturbation buckle faces the user.

4. Select the elements on either side of the buckle crevasse using the element selection tool. Get elements on either side of the crevasse (perturbation) dimensions shown that are within (RT)^0.5 of the crevasse edges. The dimensions can generally be larger than those shown here although the horizontal dimension can be any distance while the meridonal dimension should not be too much larger than 2(RT)^0.5 .

1. Open the Element dialog box.

2. Select function #14. No parameters are required if 1% of the radius is a reasonable inward buckle size.

3. Click Execute. A second window appears that shows the exaggerated magnitude of the buckled shape.

4. Close the window when the user is satisfied with the shape.

Note: There are a variety of ways to look at exaggerated shapes. There are also options with function #14 to save the original shape so that the user can move back and forth between perturbed and the original shapes.

Nonlinear Analysis Notes

Whenever performing a nonlinear analysis, the user must ensure that the material type and the yield and tensile stress for the material used in the model are entered. The tensile strength entered should be the engineering tensile stress. The true tensile stress is used in the nonlinear solver, but the conversion of the stress-strain curve from engineering to true (stress, strain) is performed automatically.

Fig. Material Type

When performing a thermal nonlinear analysis, the Riks or arc-length method should likely not be used. Constant interval load stepping is preferred in this situation. A “2” should be placed in the Load Step Control text cell in the Advanced Option Panel as shown below. All other case options, etc. may be performed as normal.

Fig. Entering 2 for Load Step Control

When performing a TES analysis and a TES and post-TES behavior analysis, the user can request that the M₂ value is exceeded. The maximum strain can also be limited so that unnecessary run times do not occur. A maximum strain of 10 to 15% is recommended, (or less). The maximum strain just beyond TES limits can be very geometry sensitive.

Reinhardt ratcheting and ASME/Bree ratcheting are two types of ratcheting behavior that is generally considered.

ASME/Bree Ratcheting

Using the elastic plastic material model, the minimum specified yield temperature should be used. Perform a number of repetitions of the load event. Use at least three repetitions of the event. If the cycles do not stabilize (if the strain continues to increase each cycle for example), then more cycles will be needed. If any one of the below conditions is satisfied, then the ratcheting criteria is satisfied.

• There is no plastic actions, (in other words, the plastic strains have shaken down to elastic action).

• There is an elastic core in the primary load bearing boundary of the component such as a large cross section remains elastic and controls any incremental straining. The user should not see increases in strain during repeated cycling. The plastic strain remains the same during loading and unloading cycles.

• There is not a permenant change in the overall dimensions of the component.

• The figure on the left is ratcheting, while the figure on the right is not ratcheting. The strain range does not necessarily have to change during subsequent ratcheting steps, but the maximum strain is definitely changing.

Fig. Racheting Fig. Not Racheting

There are four basic ratcheting loading sequences that the user can select from noted in the following image:

Ratcheting Process

The first applied load is considered the non-varying load that is the directional driven Bree style ratcheting load case. After the first load case is applied, the second load case is applied along with the first load case and cycled. If this cycling of the varying load case causes incremental straining, then “ratcheting” is occurring and fatigue life may be significantly impacted, large strains and cracking may result, and dimensional changes may occur in the shape.

In the image below the Reinhardt Ratcheting Option is specified. Reinhardt ratcheting is discussed in various papers. There are two options for Reinhardt ratcheting: 0-elastic perfectly plastic option without large rotation, 1-strain hardening option with large rotation. The 0-Reinhardt option is more conservative and is recommended. The 1-option has been shown to match limited test data. The Reinhardt approach first applies the range of loads and then reduces the strength of elements or members that have undergone plastic action. Once the element strength has been reduced, the primary (non-varying) loads are applied. If the solution converges then the Reinhardt approach has been satisfied. Displacements and strains from the result should not be used.

Fig. Reinhardt Racheting Option

The ASME options can be selected by placing a “2” in the Reinhardt Ratcheting Option text cell shown in the figure above. The user should specify the loading as necessary and select one of the ratcheting sequences shown above. For ASME (Bree) ratcheting, the first load is applied and held constant. When the first load (usually pressure and weight – the non-varying loads), have been applied the second load (usually additional load) is applied and removed the number of times specified. A minimum of 3 cycles is recommended. DO NOT CHECK THE Unload checkbox for the ASME/Bree ratcheting.

In some cases for straight pipe, pressure can cause radial ratcheting in the presence of thermal bending loads. It would typically be thought that the incremental strains would occur in the axial direction, whereas instead they occur in the radial direction. This radial ratcheting generally requires a user-written subroutine to be included as part of a finite element evaluation. For this load condition, the Reinhardt method with option 0 is thought to detect this ratcheting condition.

Important: If the number of cycles is negative, then the load will cycle from positive then back to zero then to negative then to zero then to positive.

Energy criteria contains a convergence tolerance of 1/1000, which is typical. 1/100 can be used if the solution is not affected and the running time is improved. The user is recommended to not adjust this parameter.

There are a variety of stress strain curve types, but only 0/1 and 2 are recommended. 0/1 are the same. The curve is linear up until a strain of Sy/E and then is flat until the stress, strain point intersects the curve developed from VIII-2 Part 3. The stress strain curve used can be found in the general output. Option 1 uses the exact stress strain curve from VIII-2 Part 3. The VIII-2 Part 3 curve begins plastic straining relatively early in the load sequence. After the material has undergone any appreciable loading this early (but very small), straining may disappear. Generally, either option can be used without difficulty. The options 0/1 tend to produce more easily detectable slope changes and should be used with the elastic-perfectly plastic material option. Options 3,4 and 5 deviate from the Sy/E linearity at respectively 70%, 80% and 90% of the Sy stress. Options 6,7 and 8 shift the ASME curve to the left to intersection the stress strain point: (Sy, Sy/E).

The Pressure Loading Option

This option in Fig. Reinhardt Racheting Option is used with any general load case that includes pressure. By default, there is a single load case that includes pressure such as W+P, or W+P+T, or OCC+P. Usually, the pressure is included with any other loads and the entire load set is monotonically increased and decreased if there is unloading. There are two other options for pressure combinations:

• 0-(the default): pressure is combined with other specified loads for all but the twice elastic slope fatigue cases. This is the default and assumes that pressure rises monotonically with all other loads in the specified case.

• 1-Pressure is only applied with the first load case with any combination that includes pressure, i.e. option (27) occasional loads + pressure. All other loads are included in the second load case and may be cycled, extended and unloaded, i.e. for case (27), pressure is applied first (load factor = 1 is full pressure) and kept constant while the occasional load is added and or cycled. If the system load is taken to collapse or failure, then the pressure remains constant while the occasional load is increased. This approach allows the user to evaluate how pressure increases the external load capacity.

There are a variety of loading and analysis options available with plastic loading. Used most often are the SSI calculation options, the Automatic ASME VIII-2 Part 5.2 options. Service limit Options can be used to stop the solution at what might be considered a displacement, strain, stress or rotation service limit. The sign on any load (except pressure) may be switched so that tensile and compressive evaluation of the specified loads can be performed.

Fig. Service Limit Options

The box below gives a variety of options available when the number of cycles are specified and the unload converged solutions options. Often service limits are established by whether or not the component returns to its original position after the loads are removed. The switches below defined the loads case options.

The nonlinear models, loads, and results are separated by load type and placed in different folders under the name <jobname8>_MITCH_OUT. The ratcheting cases are in the folders (31), (32), (33), and (34). Each load type is stored and accessed uniquely. If the user runs SSI cases, ASME cases, and ratcheting cases, the output for them all can be accessed under the <jobname8>_MITCH_OUT folder. The file system can be reviewed using the EDIT tab and the Explore Files button in the drawing tools.

An example plot of an ASME/Bree ratcheting case is shown below. In the first case to the “Load Factor” equal to 1, the weight+pressure case is applied. Starting at Load Factor = 1, the operating load is added to the system and the nonlinear analysis performed. The number of cycles = 3, and so the operating load is applied and removed 3 times. In this case, the maximum strain is stable and the low strain is increasing very slightly. The strain plots for this model should be inspected and then if the strain is distributed over a large area then an increased number of cycles analyzed. For this ASME/Bree ratcheting, uniform load steps are used for the load factors from zero to 1, and the arc-length method is to cycle the load for factors (see range axis in the plot above), greater than 1.

Nonlinearity and AxiPRO Flange Model

When running the AxiPRO modeler, the default has been added to deactivate plasticity for those elements in contact with concentrated forces. This is particularly for nut and gasket surfaces to eliminate local stress singularities. The plastic stress calculations are intended to compute plastic strains in the small end of the hub and in the flange ring. To improve the simulation, the user is recommended to review the plastic output and then possibly to increase the number of elements through the flange thickness.

Fig. Nonlinear Solution Control Input

When any of the load cases are checked (see (23) for the operating case above), the default loads for the operating case will be selected. If nonzero temperature is defined for the model, then the temperature will be included. Often for nonlinear analysis temperature in the model is not required. It’s not wholly clear that 0.88b should multiply the temperature load from an elastic analysis to generate a load case.

Temperature loads in most cases have some secondary quality which is a function of the potential energy of the loaded system and the total possible unrestrained thermal expansion. Kinematic leveraging can increase the displacements but an oversimplification would be that a nozzle displacement is limited by LaDT.

Generally thermal loads would be removed from typical nozzle load situations. This can be done during the (30), (23), (24), (25), (28), (29), (31), (32), (33) and (34) nonlinear load cases by removing the temperature loading. Thermal loads can be removed using option #33 in the Miscellaneous Curve dialog box.

Temperature loads are generally part of a force and moment load, and a restrained free end displacement, a thermal differential load or a thru-wall temperature load. In general the restrained free end displacements are simulated on nozzles by applied forces and moments applied in a primary sense, where a primary sense can be defined as F = Constant. A secondary sense can be defined by F = Constant x f(y), where f(y) is a function of the displacement of the nozzle and is a value between 0 and 1. The function f(y) can have any value as a nonlinear function of the displacement vector {y}.

Perturbing Geometries

Consider the following ways to perturb geometries:

• Scaling of one or more buckled mode shapes.

• Scaling of one or more static or dynamic shapes.

• Scaling of one step in a plastic solution.

• Applying an irregarity or skew to the loading.

• Applying a load to produce a pertrubed geometry and then scaling the displaced shape.

• Applying a pattern of deflection (contact PRG regarding a PS engagement).

• Using a scan of the vessel or pipe component and morph the suface nodes to the scanned location.

Variations of these different approaches are described below.

The most convenient way to perturb a geometry is through the shorthand drawing tool options. The drawing tool menus can be accessed from almost every FEPipe or NozzlePRO template. The drawing tools operate on prepared finite element models, so the user should get the model as close as possible to its final loaded and specified state. The Drawing ToolsSet button runs this.

The drawing toolset opens with a model containing nodes with red dots for handles. A control panel holds all options that can be accessed from the drawing tools. There are a large number of actions that can be performed on models and output data sets. Once any modifications have been made, (including setting up different load cases or redefining loads), the user can submit the model for analysis.

A common approach for perturbing a geometry prior to a collapse or buckling analysis is to run an eigensolution. From the control panel, there is a Shell Bifurcation Buckling button, which opens the Bifurcation Buckling Analysis window.

The user clicks each button in the step sequence listed above to show buckling modes. The buckling modes should be investigated so that modes in the area of interest are selected. Perturbations can be anywhere. The user is advised to locally thin the model in this area also within the expected thickness tolerance. This small local thinning can control the mode shape calculation and put perturbed geometries in the location where they are needed.

From the ELEMENT tab, the user can access the Miscellaneous Option on Selected Elements dialog box, where the user can select option #10 (perturb based on buckling modes) as well as include modes 1 and 2 in such a way that the maximum displacement of the disturbed shape is 0.18.”

Note: The maximum radial perturbation displacement (0.18) can be entered as negative to change the orientation of the perturbation. The perturbed geometry will have peaks directed toward the center of the cylinder and away from the center of the cylinder. The largest, most sensitively located peaks pointing toward the center of the cylinder generally have the most significant impact on the reduction of the load capacity due to the perturbation. The plastic analysis of the buckling shape with the perturbation of 0.18” is shown below.

The unperturbed peak load factor is shown to the 2.52 in the two figures below. The perturbed (but not thinned) load factor is 2.11 and the perturbed and thinned load factor is 2.08, or 82.7% of the unperturbed maximum load capacity, a 17% reduction in estimated maximum load capacity.

The user can expect a collapse at around 2.2 using the minimum allowed material properties and some perturbation. With minimum or non-effective perturbation, the user can expect collapse at around 2.52 as demonstrated in the figure below.

Nozzle type geometries where the buckled mode includes the geometry of the nozzle may not experience significant effects due to perturbation where external loads not putting compressive loads on the geometry are involved. Buckling modes due to the local thinning (above) are shown below.

Eigenmodes with irregular thinning for pipe where mill tolerance may be 12.5%.

The collapse moment of a 36” x 0.5” thick pipe would be expected to be around D2TSy/q, where q is an adjustment factor based on length and D/T. D/T = (36-0.5)/0.5 = 71. The D/T is > 50 and so it would be reasonable that the recommended Rodabaugh B₂ adjustment for D/T between 50 and 100 would be used. This adjustment is 1/( 1.3 – 0.006(D/T)) = 1/(1.3-0.006(75)) = 1.144. For a 35 ksi yield material pipe, D²TS_y/1.144 = (35.5)2(0.5)(35000)/1.144 = 19.278e6 in.lb. Z = (3.14159/32)(364-354)/36 = 488.12 cu.in., the collapse stress is 19.278e6 / 488.12 = 39,494 psi.

The collapse strength from perturbed and thinned pipe is 2.0848 x 1e7 in.lb. The comparison of the hand calculation and the perturbed finite element calculation is favorable: 1.928e7 / 2.084e7 = 0.925.

There are several lengths that control cylindrical behavior. A few are listed below.

• (RT)^0.5: Local meridonal direction undulation.

• 1.7(RT)^0.5: When shells buckle in the axial (meridonal) direction, the size of the buckle is estimated by this expression.

• Ovalization Length D^1.4/T^0.4: These can be related to ovalization shapes in lobed shell mode shapes from a natural frequency calculation.

Perturbation Due to Specified Loading

The image below explains the perturbation process specified by a loading.

The image below shows how to scale the perturbation using buckling modes 2 and 3.

The images below further explain this process.