Ag Hdpe Stress Analysis

Evaluation of Design Methods for Above Ground High Density Polyethylene Pipe

2010 TECHNICAL REPORT

Evaluation of Design Methods for Above Ground High Density Polyethylene Pipe 1021094

Final Report, December 2010

EPRI Project Manager J. Hamel

This document does NOT meet the requirements of 10CFR50 Appendix B, 10CFR Part 21, ANSI N45.2-1977 and/or the intent of ISO-9001 (1994)

ELECTRIC POWER RESEARCH INSTITUTE 3420 Hillview Avenue, Palo Alto, California 94304-1338 ▪ PO Box 10412, Palo Alto, California 94303-0813 ▪ USA 800.313.3774 ▪ 650.855.2121 ▪ [email protected] ▪ www.epri.com

DISCLAIMER OF WARRANTIES AND LIMITATION OF LIABILITIES THIS DOCUMENT WAS PREPARED BY THE ORGANIZATION(S) NAMED BELOW AS AN ACCOUNT OF WORK SPONSORED OR COSPONSORED BY THE ELECTRIC POWER RESEARCH INSTITUTE, INC. (EPRI). NEITHER EPRI, ANY MEMBER OF EPRI, ANY COSPONSOR, THE ORGANIZATION(S) BELOW, NOR ANY PERSON ACTING ON BEHALF OF ANY OF THEM: (A) MAKES ANY WARRANTY OR REPRESENTATION WHATSOEVER, EXPRESS OR IMPLIED, (I) WITH RESPECT TO THE USE OF ANY INFORMATION, APPARATUS, METHOD, PROCESS, OR SIMILAR ITEM DISCLOSED IN THIS DOCUMENT, INCLUDING MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, OR (II) THAT SUCH USE DOES NOT INFRINGE ON OR INTERFERE WITH PRIVATELY OWNED RIGHTS, INCLUDING ANY PARTY'S INTELLECTUAL PROPERTY, OR (III) THAT THIS DOCUMENT IS SUITABLE TO ANY PARTICULAR USER'S CIRCUMSTANCE; OR (B) ASSUMES RESPONSIBILITY FOR ANY DAMAGES OR OTHER LIABILITY WHATSOEVER (INCLUDING ANY CONSEQUENTIAL DAMAGES, EVEN IF EPRI OR ANY EPRI REPRESENTATIVE HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES) RESULTING FROM YOUR SELECTION OR USE OF THIS DOCUMENT OR ANY INFORMATION, APPARATUS, METHOD, PROCESS, OR SIMILAR ITEM DISCLOSED IN THIS DOCUMENT. THE FOLLOWING ORGANIZATION(S), UNDER CONTRACT TO EPRI, PREPARED THIS REPORT: Becht Nuclear Services

THE TECHNICAL CONTENTS OF THIS DOCUMENT WERE NOT PREPARED IN ACCORDANCE WITH THE EPRI NUCLEAR QUALITY ASSURANCE PROGRAM MANUAL THAT FULFILLS THE REQUIREMENTS OF 10 CFR 50, APPENDIX B AND 10 CFR PART 21, ANSI N45.2-1977 AND/OR THE INTENT OF ISO-9001 (1994). USE OF THE CONTENTS OF THIS DOCUMENT IN NUCLEAR SAFETY OR NUCLEAR QUALITY APPLICATIONS REQUIRES ADDITIONAL ACTIONS BY USER PURSUANT TO THEIR INTERNAL PROCEDURES.

NOTE For further information about EPRI, call the EPRI Customer Assistance Center at 800.313.3774 or e-mail [email protected]. Electric Power Research Institute, EPRI, and TOGETHER…SHAPING THE FUTURE OF ELECTRICITY are registered service marks of the Electric Power Research Institute, Inc. Copyright © 2010 Electric Power Research Institute, Inc. All rights reserved.

ACKNOWLEDGMENTS The following organization, under contract to the Electric Power Research Institute (EPRI), prepared this report: Becht Nuclear Services 5225 Woodside Executive Court Aiken, SC 29803 Principal Investigators G.A. Antaki C. Becht V

This report describes research sponsored by EPRI. This publication is a corporate document that should be cited in the literature in the following manner: Evaluation of Design Methods for Above Ground High Density Polyethylene Pipe. EPRI, Palo Alto, CA: 2010. 1021094.

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REPORT SUMMARY The results in this report are intended to support the development of an American Society of Mechanical Engineers (ASME) Section III Code Case for use of high-density polyethylene (HDPE) in above ground safety related piping applications. It examines the some of the differences in material and system behavior from metal pipe, at least at low temperatures. These differences include low temperature creep, potentially large displacements associated with the high coefficient of thermal expansion and low modulus of elasticity, strain rate sensitivity, and existence of slow crack growth (SCG) as a credible failure mechanism. It includes development of proposed ASME Code design rules. The report is intended to be complementary to other ongoing EPRI activities that have the overall objectives to determine the material and engineering properties needed for the design of safety related buried and above ground piping systems. That work includes determining fullrange stress-strain data, fatigue data, stress intensification factors and flexibility factors for selected piping components, determination of SCG behavior, damping values for the seismic event, determination of modulus of elasticity at seismic strain rates, develop and demonstrate methods to protect HDPE piping from postulated fire events, and perform seismic qualification of candidate vent and drain valve configurations. Background Degradation of raw water piping systems is a major issue facing nuclear power plant owners, and many plants will require repair or replacement of existing carbon steel piping components. New plants wish to build on the lessons learned from operating plants and use piping materials that are expected to last the design lifetime. HDPE has been used in non-safety service water systems for over nine years, in both below ground and above ground applications, and found to perform well. Since the cost of installing HDPE piping is much lower than the cost for steel pipe, the use of HDPE pipe in safety related applications is desirable. ASME Code Case 755 was initiated to establish requirements for the use of HDPE piping in buried safety related systems, and it is desired to extend this work to above ground applications.. Objective To evaluate the issues associated with the use of HDPE for above ground safety related piping systems and support the development of appropriate ASME Code rules to achieve a safe and reliable design.

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Approach Material properties and failure modes applicable to the design of HDPE piping systems for above ground use were identified and evaluated. Existing Section III Code rules for safety class 2 and 3 metal piping systems, and rules for the design of below ground safety related HDPE piping systems as contained in Code Case N-755, and current code committee activities were evaluated. A set of proposed above ground rules were developed and applied to an example piping system with pressure, thermal, weight, and seismic loads. The piping system was evaluated using a standard piping analysis code (Caesar II) as well as the Abaqus code with both a beam and a 3-D formulations including large displacement effects. Results in terms of pipe stresses and deflections, as well as support loads were compared. Results and Findings Evaluation of a sample problem using proposed code rules found that they could be successfully implemented using standard piping software. The example problem evaluated in this report found that for well restrained piping systems, designed to withstand seismic events, minimize sag between supports, and prevent displacement interferences with other plant equipment, results from a standard piping stress code based on small displacement theory compared well with a finite element code based on large displacement theory. This conclusion may or may not be applicable to systems which are not well restrained. EPRI Perspective Successful application of HDPE for below ground ASME Class 3 piping systems has resulted in increased industry interest in the use of HDPE for above ground piping systems, particularly for new plant builds. New ASME Code rules will be needed to support such use, either as a revision to Code Case N-755, or as a new parallel code case. This report is intended to provide a starting point for the development of such rules. Additional evaluations of candidate piping systems will likely be required after current EPRI and industry efforts to further quantify engineering and material properties of HDPE, and further industry development of ASME code rules. Additional information about the overall HDPE project is available in reports 1011836, 1013549, 1013572, 1013479, 1014902, 1018351, 1019180 and 1020439. Keywords High-density polyethylene HDPE ASME piping design Above ground piping

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ABSTRACT The purpose of this report is to present and illustrate the method for the design analysis and qualification of safety class 2 and 3 above ground high density polyethylene (HDPE) piping systems. There are potential economic and safety benefits for pursuing the use of HDPE pipe aboveground due to its resistance to microbial attack and corrosion. Buried HDPE pipe has been used successfully used in many industries, including the nuclear power industry. HDPE has also been used extensively above-ground, typically near the ground on closely spaced, ground-mounted supports. In this report we examine its use in suspended systems, a viable option, as evidenced by applications in non-nuclear industries, and in a non-safety application in the turbine building at the Catawba Nuclear Station. ASME Code Case N-755 has established a method for the design analysis and qualification of buried class 2 and 3 HDPE piping systems. Enclosed in this report are proposed design rules for above ground piping which relies primarily on the technical basis of Code Case N-755, but also addresses issues specific to above-ground piping. Design issues addressed by the proposed above-ground code case include sustained loads, seismic loads, thermal expansion loads, joint flexibility, piping supports and the concept of long-term and short-term HDPE properties. Included is an example problem for which all of the criteria in the proposed code rules are analyzed. This example problem incorporates both hand solutions to some of the code-case equations and numerical solution utilizing Caesar II v5.20 software. Attached in Appendix B is an independent check of the CAESAR II software with the Finite Element Analysis (FEA) software package, Abaqus 6.10-1.

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CONTENTS

1 INTRODUCTION ....................................................................................................................1-1 1.1 Scope ..............................................................................................................................1-1 1.2 Background .....................................................................................................................1-1 2 DESIGN AND ENGINEERING OF HDPE PIPING SYSTEMS ...............................................2-1 2.1 Material Properties ..........................................................................................................2-1 2.2 Failure Mechanisms ........................................................................................................2-1 2.2.1 Creep Rupture .........................................................................................................2-1 2.2.2 Slow Crack Growth..................................................................................................2-4 2.2.3 Fatigue.....................................................................................................................2-5 2.2.4 Creep-Fatigue Interaction........................................................................................2-6 2.2.5 Burst or Balloon Failure ...........................................................................................2-8 2.3 Design .............................................................................................................................2-8 2.3.1 Pressure Design ......................................................................................................2-8 2.3.2 Pipe Support............................................................................................................2-9 2.3.3 Thermal Flexibility..................................................................................................2-11 2.3.4 Seismic Design......................................................................................................2-12 2.3.5 Consideration of Large Displacement Theory .......................................................2-12 3 PROPOSED CODE CASE – DESIGN REQUIREMENTS .....................................................3-1 -1000 GENERAL REQUIREMENTS .....................................................................................3-1 -1100 SCOPE .......................................................................................................................3-1 -1200 QUALIFICATION OF SUPPLIERS .............................................................................3-1 -1300 OPEN ITEMS ..............................................................................................................3-1 -2000 MATERIALS................................................................................................................3-2 -3000 DESIGN ......................................................................................................................3-3 -3100 SCOPE .......................................................................................................................3-3 -3110 NOMENCLATURE ......................................................................................................3-3

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-3120 DESIGN LIFE..............................................................................................................3-3 -3130 DESIGN AND SERVICE LOADING............................................................................3-3 -3131 Pressure Design of Pipe .............................................................................................3-4 -3131.1 Minimum Required Wall Thickness..........................................................................3-4 -3131.2 Allowable Service Level Spikes Due to Transients Pressure...................................3-4 -3132 Pressure Design of Joints and Fittings........................................................................3-4 -3223 Longitudinal Stress Design .........................................................................................3-5 -3223.1 Longitudinal Applied Mechanical Loads...................................................................3-5 -3223.2 Short Duration Longitudinal Applied Mechanical Loads...........................................3-5 -3300 TEMPERATURE DESIGN ..........................................................................................3-5 -3310 MINIMUM TEMPERATURE........................................................................................3-5 -3311 Design for Expansion and Contraction........................................................................3-5 -3400 SEISMIC DESIGN.......................................................................................................3-6 -3410 SEISMIC INDUCED STRESSES................................................................................3-6 -3420 NONREPEATED ANCHOR MOTIONS ......................................................................3-6 4 EXAMPLE HDPE PIPING SYSTEM ANALYSIS ...................................................................4-1 4.1 System Description .........................................................................................................4-1 4.2 Design Analysis Work Flow.............................................................................................4-2 4.3 Loading Conditions..........................................................................................................4-3 4.3.1 Design Life...............................................................................................................4-3 4.3.2 Design Pressure and Temperature .........................................................................4-3 4.3.3 Service Level Pressure and Temperature ...............................................................4-3 4.3.4 Weights and Mechanical Loads...............................................................................4-4 4.3.5 Seismic Input ...........................................................................................................4-4 4.4 Piping System Model.......................................................................................................4-4 4.4.1 Caesar Model ..........................................................................................................4-5 4.4.2 Abaqus Models........................................................................................................4-5 4.4.3 Load Cases .............................................................................................................4-6 4.5 Mechanical Properties.....................................................................................................4-6 4.6 Physical Properties..........................................................................................................4-6 4.6.1 Modulus of Elasticity................................................................................................4-6 4.6.2 Poisson’s Ratio........................................................................................................4-6 4.6.3 Coefficient of Thermal Expansion............................................................................4-6 4.7 Preliminary Support Arrangement ...................................................................................4-7

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4.8 Results ............................................................................................................................4-7 4.9 Abaqus and CAESAR II Comparison ..............................................................................4-7 5 CONCLUSIONS .....................................................................................................................5-1 6 REFERENCES .......................................................................................................................6-1 A PIPE STRESS ANALYSIS (CAESAR II) INPUT .................................................................. A-1 B FINITE ELEMENT ANALYSIS USING ABAQUS................................................................. B-1

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LIST OF FIGURES Figure 2-1 Load-Controlled Loading under Creep Conditions ...................................................2-3 Figure 2-2 Strain Controlled Loading under Creep Conditions ..................................................2-3 Figure 2-3 Stress Relaxation from a 2.7% strain induced in PE4710 Material using the Apparent Modulus from Code Case N-755 ........................................................................2-4 Figure 2-4 Stress-Rupture Characteristics of a Material Which Shows Two Unique Type of Failure Mechanisms [7] ..................................................................................................2-5 Figure 2-5 Damage Interaction Diagram for Type 304SS and 9Cr-1Mo-V ................................2-7 Figure 2-6 Recommended Pipe Support Arrangement-1 [1] ...................................................2-10 Figure 2-7 Recommended Pipe Support Arrangement-2 [3] ...................................................2-11 Figure 2-8 Recommended Pipe Support Arrangement-3 [3] ...................................................2-11 Figure 4-1 Caesar II Model Layout ............................................................................................4-1 Figure 4-2 Nodal Layout of Caesar II Model ..............................................................................4-2 Figure 4-3 Workflow for Analysis and Qualification ...................................................................4-3 Figure 4-4 Seismic Response Spectrum ...................................................................................4-4 Figure 4-5 Convergence of Seismic Stresses due to Increased Nodal Density ........................4-5 Figure B-1 Layout of Simplified Pipe Section............................................................................ B-2 Figure B-2 Restraint Layout ...................................................................................................... B-4 Figure B-3 Abaqus Model ......................................................................................................... B-5 Figure B-4 Long Term Deflection (in) Calculated by Abaqus.................................................. B-10

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LIST OF TABLES Table 2-1 ASME Code References for Calculating Expansion Stresses ...................................2-6 Table 3-1 Table -3131-1(a) Long Term Allowable Stress S for Polyethylene (psi) ....................3-7 Table 3-2 Table 3223-1 Stress Indices B1 and B2 ....................................................................3-7 Table 3-3 Table 3223-2 Design and Service Level Longitudinal Stress Factors, k....................3-8 Table 3-4 Table 3223-3 Short Duration (≤5 minutes) Allowable Longitudinal Tensile Stress Factors, k ................................................................................................................3-8 Table 3-5 Table 3311.2-1 Stress Intensification Factor i ...........................................................3-8 Table 4-1 Valve Weights and Dimensions ................................................................................4-2 Table 4-2 CAESAR II Results for Design Conditions.................................................................4-7 Table 4-3 CAESAR II Results for Service Level D.....................................................................4-7 Table 4-4 Comparison of Displacements due to Thermal Expansion ........................................4-8 Table B-1 Force versus Displacement...................................................................................... B-2 Table B-2 Reaction Forces due to Δ30ºF Temperature Increase ............................................. B-3 Table B-3 Results for Gravity.................................................................................................... B-6 Table B-4 Results for Thermal Expansion ................................................................................ B-7 Table B-5 Results for Seismic Analysis .................................................................................... B-8 Table B-6 Natural Frequencies ................................................................................................. B-9

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1 INTRODUCTION

1.1 Scope The purpose of this project is to present a set of proposed American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (BPVC) rules for design of Class 2 and 3 above ground piping constructed of high density polyethylene (HDPE). The rules are similar in many ways to those contained in Code Case N-755 for buried HDPE, but addressing the unique features of above-ground, suspended HDPE pipe. Additionally this report discusses the method for the design analysis and qualification of above ground HDPE piping systems. There is an example problem which demonstrates how to apply the proposed code rules. The example problem uses the closed form equations from the proposed code rules, a numerical solution using the piping code Caesar II v5.20, and the Abaqus 6.10-1 finite element analysis code to solve the load cases.

1.2 Background The interest in the use of HDPE piping at nuclear facilities is to provide a cost-effective solution to prevent corrosion and microbial attack often found in raw water systems. HDPE piping is impervious to these deterioration mechanisms and is a reliable and economical alternative to metallic pipe. Many non-nuclear industries apply HDPE above-ground. The Catawba Nuclear Station has had successful operating experience with both above-ground and below ground HDPE piping in both non-safety related and safety-related piping systems. Code Case N-755 for buried HDPE pipe, and HDPE pipe manufacturer guidelines serve as the starting point for the rules for above-ground HDPE. .

1-1

2 DESIGN AND ENGINEERING OF HDPE PIPING SYSTEMS

2.1 Material Properties Understanding the similarities and differences between metal and HDPE is essential for establishing a safe and appropriate set of design analysis and qualification rules for aboveground HDPE. HDPE material response is driven by a semi-crystalline polymeric structure which behaves differently than the crystalline and grain structure of steel [1]. However, like steel, HDPE experiences an elastic response to a load up to yield at which point both materials develop plastic strains with increasing load. However, the HDPE yield point is not as clearly defined and its elastic behavior is different than metal. Both materials have a visco-elastic response to a load after a critical temperature. For metal this temperature is above 700ºF; for HDPE this visco-elastic response occurs at ambient temperature [1]. One method for calculating long-term creep due to primary loads and the stress relaxation of secondary loads for a material experiencing creep is an isochronous stress-strain curve. Isochronous means to occur at the same time, and with respect to creep this means the stressstrain curve at a given point in time. The HDPE industry uses a term called apparent modulus, which is defined as the “initial applied stress divided by the creep-strain at a given time and pressure, this ratio clearly decreases as the duration of loading increases” [1]. This definition appears to exclude elastic strain; however the elastic strain would be small compared to the creep strain. If a point is chosen on the isochronous stress-strain curve for a given time at load and a line is drawn back to the origin from this point, then the slope of the line would be the apparent modulus, excluding the elastic-strain component. It does not represent the actual modulus of elasticity of the material, which the HDPE industry defines as the flexural or tensile modulus [1].

2.2 Failure Mechanisms Establishing criteria for design of above-ground HDPE pipe requires understanding the failure mechanisms. This report will discuss five failure mechanisms, Creep Rupture, Slow Crack Growth (SCG), Fatigue, Burst (balloon), and Creep-Fatigue Interaction. 2.2.1 Creep Rupture Time to creep-rupture is the method the HDPE industry uses to qualify pipe for long-term service. ASTM D 2837-08 [12] contains the methodology for performing the creep rupture tests 2-1

Design and Engineering of HDPE Piping Systems

and how the data is extrapolated to long-term service. This specification states that in order to acquire a hydrostatic design basis (HDB) rating of 1,600 psi, the pipe must undergo a 10,000 hr creep rupture test which qualifies it for a minimum of 100,000 hours at a stress of 1,530 psi [7]. A design factor of 0.50 is then applied which qualifies the pipe for 50 year service at 800 psi stress. The ASME Code Section II, Part D has a different margin for stress for creep rupture in metals and has one additional requirement. For metals operating at less than 1,500ºF the allowable stress per ASME Section VIII Part D is the minimum of (100% the avg. stress to produce a creep rate of 0.01%/1,000 hour, 67% of the avg. stress to cause rupture at 100,000 hours, 80% of the min. stress to cause rupture at the 100,000 hours) [9]. Creep damage can be tracked for different operating conditions. For example, excursions to higher temperatures and pressures would accumulate creep damage at a rate faster than the design temperature and pressure condition and therefore would reduce the overall life of the pipe. ⎛ Δt ⎞ ⎟⎟ ≤ 1 ⎝ d ⎠k

∑ ⎜⎜ T Where  

(Δt)k = actual time at stress level, k (Td)k = allowable time at stress level, k

A paper by Ifwarson discusses testing done to validate long term cyclic service for medium density polyethylene (MDPE), PE, and cross linked polyethylene (PEX) pipe. Unfortunately, it does not address HDPE pipe. The testing only focused on different creep conditions via temperature cycles and did not study cyclic stress. Table 1 from the paper shows that the above equation was non conservative for MDPE, PEX, and in some cases PB material [10]. This implies that HDPE might need to be tested for the effect of different creep conditions. However, this should not be a priority as it has been demonstrated that creep rupture is not a realistic long term failure mode, and the margin the plastic industry uses (50%) is much more conservative than the margin that the metal industry uses (80%). It is important to distinguish between load-controlled, or primary, and displacement controlled, or secondary, loads. Some typical primary loads are internal pressure, mechanical loading, weight, inertial seismic forces, and elastic follow up. Typical secondary loads include thermal expansion, anchor motion, and through-wall thermal gradients. Figure 2-1 and Figure 2-2 show how primary and secondary loads, respectively, behave differently in the creep regime. In a loadcontrolled loading the stress remains constant and creep strain continues to accumulate until a creep-rupture failure occurs. In a strain-controlled loading the strain remains constant and the stress decreases as the elastic strain is replaced by creep strain.

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Design and Engineering of HDPE Piping Systems

Figure 2-1 Load-Controlled Loading under Creep Conditions

Figure 2-2 Strain Controlled Loading under Creep Conditions

The HDB is a design allowable based on a primary load failure mechanism, creep rupture. A strain controlled loading would behave differently because the stress would relax over time and there would be no additional elongation. Figure 2-3 plots a 2.7% strain induced in PE4710 using the apparent modulus at ambient temperature from Code Case N-755. The stress was calculated by multiplying the strain by the apparently modulus at each point in time.

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Design and Engineering of HDPE Piping Systems

Figure 2-3 Stress Relaxation from a 2.7% strain induced in PE4710 Material using the Apparent Modulus from Code Case N-755

On the reverse cycle the total strain would go to zero, and the elastic strain would be the negative of the creep strain thereby introducing a negative stress in the piping system. Therefore, even with creep relaxation, the total range of stress due to cyclic strain ranges would be the same. Eventually, the system would reach a quasi equilibrium when the creep strain is equal to half of the total strain range, and the elastic range would go from negative the half of the total strain range to the positive of half the total strain range. 2.2.2 Slow Crack Growth Another long term failure mechanism for HDPE pipe is the initiation and growth of a crack under a constant load condition. A similar type of crack growth can occur in metals when a crack reaches a critical crack size. However, in metal the failure is much more rapid once a critical crack size is achieved. The initiation and growth of a crack can result in a shift in the slope of the stress-rupture lifetime plot of a material. Once the slow crack mechanism starts to dominate over the creep-rupture mechanism the slope decreases significantly and it is impossible to achieve a long term life. Appendix X1 in ASTM D 2837-08 discusses this behavior which is illustrated in Figure 2-4.

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Design and Engineering of HDPE Piping Systems

Figure 2-4 Stress-Rupture Characteristics of a Material Which Shows Two Unique Type of Failure Mechanisms [7]

Quantifying an allowable crack size will depend on understanding the visco-elastic fracture mechanics of HDPE material. Work is currently progressing on developing the fracture mechanics methodology for HDPE Pipe. At the Vancouver ASME BPVC meeting in November 2010, work done by the “Task Group on Flaw Evaluation for HDPE Pipe” was presented on developing KI, the Stress Intensity Factor. The next step in developing the fracture mechanics methodology will be determining the crack growth rates for a given stress intensity or range of stress intensity. 2.2.3 Fatigue Fatigue failure is a strain controlled mechanism that traditionally results from alternating displacement controlled loads. For above ground pipe the most common source of the alternating displacement controlled loads is thermal expansion and contraction with startup and shutdown. For above-ground metallic pipe, Markl’s work in the 1940’s and 1950’s is at the origin of the current design analysis rules in ASME Section III and in ASME B31. The allowable stress range is artificial in that the Markl tests were strain controlled and were then multiplied by a reference modulus of elasticity. This is why B31.3 states “the range of bending and torsional stresses shall be computed using the reference modulus of elasticity at 21ºC (70ºF), except as provided in Para. 319.2.2(b)(4)” [4]. Therefore, when metallic pipe is designed at creep temperatures, such as 1,200ºF, the modulus at 70ºF is used to calculate the stress range, even though an apparent modulus could be calculated. This is because the most accurate comparison to an S-N curve 2-5

Design and Engineering of HDPE Piping Systems

generated by using a reference modulus is to perform a piping evaluation at with the same reference modulus. Table 2-1 references the ASME precedence for calculating the expansion stress range. Table 2-1 ASME Code References for Calculating Expansion Stresses ASME Code

Para.

Method

Section III - Div 1 - NB

NB - 3672.5

calculate expansion stress with Eh and then multiply by Ec/Eh

Section III - Div 1 - NC

NC - 3672.6

Use Ec to calculate expansion stress

Section III - Div 1 - ND

ND - 3672.6

Use Ec to calculate expansion stress

Section VIII - Div 2

3.F.1.2

Calculate expansion stress with Et and then multiply by Efc/Eh

B31.3

319.4.4(a)

Use Ea to calculate expansion stress

Where: EFC = modulus of elasticity used to establish the design fatigue curve Et = modulus of elasticity of the material under evaluation at the average temperature of the cycle EC = modulus at room temperature Eh = hot modulus Ea = reference modulus of elasticity at 21ºC (70ºF) EPRI is sponsoring a study that is investigating the fatigue life of 4710 material which includes a butt fusion joint. This study follows the methods used by Markl and has completed its work on PE4710, cell classification 445474C material. These findings show that the 1,100 psi limit found in CC N-755 has approximately a factor of 2 on stress to failure for temperatures ranging from 70ºF to 140ºF [5, 6, 11], See Figure 3-1 of [11]. This factor is the same as for metallic pipe and therefore provides support to the 1,100 psi limit. When a piping stress analysis is performed for an above ground piping system the reference tensile modulus at 70ºF should be used for comparison to the fatigue limit. Upcoming EPRI fatigue studies will be performed on a cell classification 445574C that is compliant to the material requirements of the November 2010 draft revision 1 to Code Case N-755. 2.2.4 Creep-Fatigue Interaction In metallic piping it is sometimes possible to focus only on fatigue as a failure mechanism. This is not possible for HDPE above ground piping because creep occurs in conjunction with fatigue. The mechanisms for creep failure and fatigue failure are different and therefore when both mechanisms occur their interaction must be taken into consideration. For metals this interaction is modeled by using Miners rule which is shown in the below equation [8]. This is explained in Para 12.3.7.1 in the Companion Guide to ASME for Subsection NH.

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Design and Engineering of HDPE Piping Systems

⎛ Δt ⎞ ⎛ n ⎞ ⎟⎟ + ∑ ⎜⎜ ⎟⎟ ≤ D ⎝ D ⎠j ⎝ Td ⎠ k

∑ ⎜⎜ N Where:

D = allowable creep-fatigue damage factor (Nd)j = number of design allowable cycles of type, j. (n)j = actual number of cycles of type, j The factor D depends on how much fatigue damage and creep damage has been accumulated. For instance for Type 304SS the damage interaction curve, taken from the Companion Guide is plotted in Figure 2-5 [8]. This material, which demonstrates strong resistance to creep-fatigue failure, has its focal point of the curve at Df = Dc = 0.3. This means that if 30% of the allowable fatigue damage is accumulated with 30% of the allowable creep damage then the material has reached its design life. If 0% of the allowable fatigue damage is accumulated then 100% of the allowable creep damage may be accumulated. A metal like 9Cr-1Mo-V exhibits extremely poor creep-fatigue interaction and has a focal point at 10% fatigue, 1% creep damage [8].

Figure 2-5 Damage Interaction Diagram for Type 304SS and 9Cr-1Mo-V

While HDPE creep and fatigue mechanisms are different than metal, it is likely that a creepfatigue interaction diagram, with an appropriate focal point, could be constructed from fatigue 2-7

Design and Engineering of HDPE Piping Systems

tests performed over long time periods. Understanding how well or poor HDPE responds to creep-fatigue interaction is required for establishing an allowable, D. 2.2.5 Burst or Balloon Failure This failure mode is demonstrated in quick pressure burst tests. If a critical pressure is achieved in the pipe, then the pipe continues to expand until it experiences a ductile burst. The margin on this failure mode could be used as a basis for establishing a short term transient allowable. However if the transient occurs over a long enough duration then it’s effect on the creep life should be considered as described in the Creep-Rupture section.

2.3 Design 2.3.1 Pressure Design HDPE Pipe can be specified as Iron Pipe Size (IPS) or Ductile Iron Pipe Size (DIPS) and as OD or ID controlled. The industry classifies different thicknesses of a nominal pipe size by the dimensional ratio. For OD-controlled pipe this term is DR, for ID-controlled pipe the term is IDR. Pressure rating of pipe is typically quantified in the HDPE industry with the hydrostatic design basis (HDB). The following equation can be used to calculate a required thickness of pipe using the typical industry practice [1]. However, this equation should not be used in lieu of Code requirements; it is merely representative of how vendors specify their pipe. t min =

Do ⎡ 2 * HBD * DF * FT ⎤ + 1⎥ ⎢ PD ⎣ ⎦

Where: Do = OD-controlled pipe outside diameter, in HDB = Hydrostatic Design Basis, psi DF = design factor FT = service temperature design factor, if elevated temperature HDB is not used PDesign = design pressure tmin = minimum thickness for pressure design, in Once a minimum required thickness is calculated then an appropriate DR can be chosen. For fittings, CC N-755 states that mitered elbows shall be one DR less than that of the connecting pipe [2]. Therefore, the elbows will be thicker than the pipe.

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Design and Engineering of HDPE Piping Systems

2.3.2 Pipe Support A preliminary support arrangement, before performing the stress analysis, may be established by limiting the long-term deflection between supports to 1 inch, as recommend by Performance Pipe Technical Note PP 815-TN. The corresponding support spacing is shown below [3].

LS = 4

384E/S y

5(w p + w f )

Where: E = apparent modulus for the design life, psi Ls = spacing between supports, in Sy = yield stress, psi Wp = Weight of Pipe per unit Length, lb/in WF = Weight of Fluid per unit Length, lb/in Pipe supports must be carefully designed in HDPE applications because of multiple issues unique to HDPE piping. The first issue is that HDPE material is very soft and therefore it is easy to damage the piping with rough surfaces or lack of a large enough support area to distribute the load. Additionally, HDPE piping requires significantly more pipe supports than steel piping and therefore the piping system could become over constrained for thermal expansion if not carefully designed. Chapter 8 in the PE handbook has figures for typical support designs for HDPE piping systems, as shown below.

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Design and Engineering of HDPE Piping Systems

Figure 2-6 Recommended Pipe Support Arrangement-1 [1]

Pipe Performance Technical Note PP 815-TN also provides some guidance for pipe support as shown in the following figures.

2-10

Design and Engineering of HDPE Piping Systems

Figure 2-7 Recommended Pipe Support Arrangement-2 [3]

Figure 2-8 Recommended Pipe Support Arrangement-3 [3]

The qualification of pipe supports should be performed in the same manner as if the pipe was metallic, following the project-specific methods and criteria. The loads on the supports shall consider a full load based on tensile modulus and also a reverse load that results from the residual stress due to creep relaxation. 2.3.3 Thermal Flexibility A reference for flexibility analysis of above-ground piping systems may be gleaned from ASME B31.3 which contains a chapter on non-metallic piping. However, ASME B31.3-2008 broadly states that if a system replicates a previous design or can be readily judged, then it is acceptable [4]. If the HDPE piping system does not meet these criteria then B31.3 states “the designer shall demonstrate adequate flexibility”[Para A319.4.2. 7]. Unfortunately, B31.3 provides no guidance on what the appropriate allowable stress basis for the stress amplitude is, nor does it gives insight into the appropriate stress intensification factors (SIFs). Code Case N-755, which was developed for buried HDPE systems, provides more thorough guidance for “alternative thermal expansion or contraction evaluation” [2]. This assumes a limited number of cycles. 2-11

Design and Engineering of HDPE Piping Systems

EPRI has sponsored significant work in the area of fatigue testing of HDPE and this section will reference some of the key points for justifying the application of the Code Case N-755 stress limit to above ground piping. Fatigue testing detailed in the Section 2.6 in the 2007 Technical Update of project 1014902 suggested the 1,100 psi limit has a margin of 2 on fatigue capacity [5]. It demonstrates this capacity for both the tests at 70ºF and 140ºF. The final report supports this claim as shown in Figure 3-1 of [11]. A lot of work went into the EPRI sponsored tests and this report will attempt to summarize the key points. The fatigue tests were performed following the practice from Markl’s work on metal. A pipe under slight pressure was fixed at one end near a butt fusion joint and then the opposite end of the pipe was displaced a fixed distance in both directions, with a mean displacement of zero. The testing differs from Markl’s work in the conversion of the displacement range to stress. Markl only used one modulus to convert all the displacement tests to a unified S-N curve. The EPRI report used the stiffness from the first half cycle of each specimen to develop that specimen’s stress [see 2.4.2 of 11]. This naturally results in the 160ºF and 140ºF tests having a lower allowable stress range because the stiffness is lower, with the 50ºF and 70ºF tests having a higher allowable stress range because the stiffness is higher. This report recommends analysis of the strain-N data to see if it collapses when the modulus is simply ignored. Given the scatter in fatigue tests, it is likely that it wouldn’t collapse completely. The goal of having a collapsed strain-N curve would be to produce a more uniform process of pipe analysis that would allow for a pipe designer to only consider one modulus, which is the current practice of the ASME code. In the case that the data doesn’t collapse, then temperature effects would have to be included as described in Section 3.7 of EPRI’s fatigue report [11]. 2.3.4 Seismic Design For above ground piping, stress due to seismic events is primarily calculated using a response spectrum analysis. This involves first calculating the natural frequencies of the piping system. The natural frequencies depend on the elastic modulus and, because of the short duration of the seismic event, the tensile modulus should be used. Once the accelerations are calculated using the natural frequencies and response spectrum, then the problem becomes load-controlled and therefore the modulus is no longer relevant for calculating stresses. Testing is being done by EPRI to determine if the tensile modulus is different for the strain rates experienced during seismic events. Work is also being done by EPRI to calculate the damping values of HDPE. EPRI plans on using the log decrement method to determine damping from cantilevered pipe vibration tests. 2.3.5 Consideration of Large Displacement Theory In Appendix B, this report compares an analysis by the pipe stress software package Caesar II to an analysis by the FEA software package Abaqus. This comparison was done to address the possibility that codes which do not consider large displacement theory may not accurately capture HDPE behavior. The comparison is made by studying the restraint forces because comparing stresses would result in an erroneous comparison because Caesar II modifies the 2-12

Design and Engineering of HDPE Piping Systems

stress output to meet Code rules. The Appendix shows almost uniform agreement for the thermal expansion case; however the results differ for the seismic case, ~50% in some cases. It is possible that not enough nodes were placed between the supports in the Caesar II model, as Figure 4-5 shows that convergence for seismic stresses depends on a sufficient number of nodes between supports in Caesar II. Additionally, it should be noted that under design conditions HDPE pipe may deflect less than metallic pipe under design conditions. Metallic pipe systems can experience more thermal expansion that HDPE pipe. This is because the allowable temperature range for metal far exceeds that of HDPE, which makes up for the difference in the coefficient of thermal expansion. Additionally, metal pipe can creep further than HDPE because the HDPE design basis creep strain at 50 years is 3.1%. However metal pipe has no limitation under Section VIII Division 1 & 2 and can creep up to 1% per 100,000 hours which can exceed the 3% creep strain. Piping analysis has always been a more crude analysis compared to vessel design. However the safety margins are sufficient enough that decades of experience with pipe that sometimes has greater growth than HDPE under design conditions show advanced analysis is not required.

2-13

3 PROPOSED CODE CASE – DESIGN REQUIREMENTS

-1000 GENERAL REQUIREMENTS -1100 SCOPE (a) This Case contains rules for the construction of Class 2 and Class 3 polyethylene pressure piping components at Design Temperatures not exceeding 140ºF (60ºC), and for maximum Service Levels B, C or D temperatures not exceeding those for which allowable stresses are provided in this Case. Use of these materials is permitted only for above ground plant service and cooling water systems that are classified as Class 2 and 3. (b) Terms relating to polyethylene as used in this Case are defined in -9000 -1200 QUALIFICATION OF SUPPLIERS Not covered in this proposed Code Case. -1300 OPEN ITEMS This proposed code case only addresses the design requirements and will rely on the extensive work done on Code Case N-755 for addressing the many requirements of manufacturing, fabricating, qualifying and installing HDPE pipe systems. To address the proposed failure mechanics in Chapter 2, this code case relies on a combination of rules from Code Case N-755, new criteria, and also leaves some failure mechanisms as open items. This code case refers to Code Case N-755 to protect against slow crack growth, creep rupture, and burst (short-term) failure. The slow crack growth and creep rupture are addressed by the long term allowable stress in Table 3131-1(a) and the limitation on allowable scratch depth of article 2310 of [2]. This long term allowable stress is based on the Hydrostatic Design Basis (HDB) which protects against both creep rupture and slow crack growth. The quick burst failure is protected against by the short term allowable in 3131.2 and 3223.2, which come from Code Case N-755. This code case proposes a slightly different method than Code Case N-755 for addressing fatigue. It is proposed that a reference modulus of elasticity be used for calculating stress ranges resulting from secondary load cycles. For now, the allowable range is set to 1,100 psi with the 3-1

Proposed Code Case – Design Requirements

stipulation that the number of design cycles shall not exceed 10,000. Ultimately it is proposed that the qualification of fatigue cycles in the code case rely on an S-N curve generated from a displacement controlled test ε-N curve multiplied by the reference modulus proposed in Para. 3311. This proposed code case does not address creep-fatigue interaction; however it is possible to demonstrate why it may not be a large concern for HDPE. Table 1 in PP 820-TN [13] shows that the projected stress life intercept for 1,000 psi is 1010 years. This means that almost none of the creep life for a pipe operating at 800 psi for 60 years will be consumed. Discussions with industry experts seems to confirm that creep rupture is not a realistic failure mode and rather slow crack growth is a more realistic long-term failure mechanism for pipe operating at the allowable stress. So in Figure 2-5 if a HDPE condition was plotted after 60 years of service Dc would be practically zero. However, this does not guarantee that there is no creep-fatigue interaction. The only way to confirm this is to perform a step-wise fatigue tests (rather than saw tooth) with long holds (10 minutes to an hour). A final consideration for HDPE is whether or not the piping systems will deflect so greatly as compared to steel design in the past that new analysis techniques are required. However, under design conditions HDPE deflection is not very different from high temperature steel piping. For one, the amount of creep strain accumulated from load controlled stresses within the allowable after 50 years is only 3.1% (670/21,200 @ 100ºF). Additionally, while the thermal expansion may be upwards of 10 times higher than steel, the maximum allowable temperature is far below that of steel. The maximum realistic range allowed in this code case would be around 50ºF to 176ºF (for loads to 1 year) which is a range of 126°F. Meanwhile metal piping in other industries can be designed for thermal ranges of 50ºF to 1200ºF and greater, which is a range of 1,150ºF or ~10 times larger than a realistic range for HDPE pipe. So the thermal growths are quite comparable. These high temperature metal piping systems have been designed quite successfully for decades using the same rules proposed in this code case. Additionally, enclosed in Appendix B is a check of Caesar II using Abaqus with large displacement theory. Although the sample problem is fairly well restrained, the calculated restraint forces due to thermal expansion were almost identical, while the seismic stresses were under predicted in the Caesar model. This implies that more nodes should have been introduced in the Caesar model to capture all the modes. However, it shows that fundamentally Caesar can capture all the important affects that a large-scale FEA model would capture

-2000 MATERIALS Materials will be referenced to the ASME Section II Code.

3-2

Proposed Code Case – Design Requirements

-3000 DESIGN -3100 SCOPE The design rules of this Section are limited to above ground polyethylene piping systems constructed of straight pipe, three and five segment mitered elbows, fusion joints, and flanged connections.

-3110 NOMENCLATURE A = cross-sectional area of pipe, in2 B1 = stress index, Table-3223-1 [2] B2 = stress index, Table-3223-1 [2] c = corrosion allowance, in D = outside diameter of pipe, in Fa = axial force due to the specified Design applied mechanical loads, lb FaC = axial force range due to thermal expansion or contraction FaD = axial force due to the non repeated anchor motion, lb FaE = axial force range due to the effects of seismic inertia, lb i = stress intensification factor k = factor from Table-3223-2 [2] M = resultant bending moment due to the specified Design applied mechanical loads, in-lb MC = resultant moment range due to thermal expansion or contraction, in-lb MD = resultant moment due to the non repeated anchor motion, in-lb ME = resultant moment due to the effects of seismic inertia, in-lb PD = design pressure, psi tdesign = design thickness, in tmin = minimum thickness for pressure design, in t = thickness of pipe, in S = allowable stress, psi Z = section modulus of pipe cross section B

B

-3120 DESIGN LIFE (a) The Design Specification shall specify the design life of the system, not to exceed 60 years. (b) The duration of load shall be specified for each load case, and the PE pipe physical and mechanical properties shall be based on the duration of load.

-3130 DESIGN AND SERVICE LOADING Design loads shall be as defined in NC/ND-3112.1 through NC/ND-3112.3. Loads applied to PE pipe shall be defined in the Design Specification, and shall include, as a minimum the following:

3-3

Proposed Code Case – Design Requirements

(a) Maximum and minimum internal design gage pressure PD, for pressure design in accordance with -3131 and -3132. (b) Maximum and minimum temperature T, for the selection of allowable stress and design for temperature effects in accordance with -3300. The maximum Service Level A temperature shall be the Design Temperature, TD. (c) The stress limits for the loads resulting from the maximum flow velocity, v, shall be as provided in -3131.2. (d) Non-repeated anchor movements in accordance with –3420 (e) Seismic inertia for Seismic design in accordance with –3410

-3131 Pressure Design of Pipe -3131.1 Minimum Required Wall Thickness The minimum required wall thickness of straight sections of pipe for pressure design shall be determined by the following: t design = t min + c

t min =

PD D (2S + PD )

-3131.2 Allowable Service Level Spikes Due to Transients Pressure The sum of the maximum anticipated operating pressure plus the maximum anticipated Level B pressure spikes due to transients shall be no greater than 1.5 times the piping system Design Pressure, PD, (see -3131.1). The sum of the maximum anticipated operating pressure plus the maximum anticipated Level C and D pressure spikes due to transients shall be no greater than 2 times the piping system Design Pressure (see -3131.1).

-3132 Pressure Design of Joints and Fittings (a) Polyethylene pipe shall be joined using the butt fusion process. All connections to metallic piping shall be flanged joints. (b) Sustained pressure and pressure rating of polyethylene pipe fittings shall comply with the specifications listed in Code Case N-755 Mandatory Appendix III [2]. The Design Pressure, PD, for the fittings shall be greater than or equal to the Design Pressure of the attached pipe. 3-4

Proposed Code Case – Design Requirements

(c) Flanged connections shall include a metallic backup ring and shall provide a leak tight joint up to and including the piping hydrostatic test pressure. In addition, the maximum surge pressure per -3131.2 shall not cause permanent deformation of the pipe. (d) Mitered elbows shall comply with the requirements of ND-3644, excluding ND-3644(b). In place of ND-3644(e) butt fusion joints shall be used in accordance with this standard. In addition, the mitered elbows shall be one dimension ratio (DR) lower than the DR of the attached straight pipe.

-3223 Longitudinal Stress Design -3223.1 Longitudinal Applied Mechanical Loads Longitudinal stresses due to axial forces and bending moments resulting from applied mechanical loads shall not exceed k x S. Where

B1 x

F PD xD M + 2xB1 x a + B 2 x ≤ kxS 2xt A Z

-3223.2 Short Duration Longitudinal Applied Mechanical Loads For the assessment of short duration loads (less than five minutes) the allowable stress, S, may be replaced by one of the two following two alternatives (a) 40% of the material tensile strength at yield (b) The values in Table 3223-3

-3300 TEMPERATURE DESIGN -3310 MINIMUM TEMPERATURE The polyethylene material shall not be used at a temperature below the manufacturer limit, but in no case shall the temperature be less than minus 50ºF.

-3311 Design for Expansion and Contraction The stresses shall satisfy the following equation:

3-5

Proposed Code Case – Design Requirements

iM c FaC + ≤ 1100psi Z A For displacement controlled conditions, the effective loads shall be calculated using the reference tensile modulus of elasticity from the fatigue tests that ultimately establish the allowable stress range. However, for the time being it is recommended that the tensile modulus of elasticity at 70ºF be used, 110,000 psi.

-3400 SEISMIC DESIGN -3410 SEISMIC INDUCED STRESSES The stresses in the above ground PE piping system due to inertial seismic loading, or repeated anchor motion, shall satisfy the following equation:

iM E FaE + ≤ 1100psi Z A Seismic inertial loadings shall be combined by square root sum of the squares. The calculation of natural frequency depends on the modulus of elasticity; however the stresses resulting from the inertial loading, which is based on the natural frequency, are independent of modulus. The designer shall consider the strain rate effect on the modulus of elasticity. (Note to reviewers: this is the subject of a current EPRI test program.)

-3420 NONREPEATED ANCHOR MOTIONS The effects of any single non-repeated anchor movement shall meet the requirements of the following equation:

iM D FaD + < 2S Z A

3-6

Proposed Code Case – Design Requirements Table 3-1 Table -3131-1(a) Long Term Allowable Stress S for Polyethylene (psi) Temperature (ºF)

≤ 50 years

Temperature (ºF)

≤ 50 years

Temperature (ºF)

≤ 50 years

≤ 73

800

96

689

119

587

74

795

97

684

120

582

75

790

98

680

121

578

76

785

99

675

122

574

77

780

100

670

123

570

78

775

101

666

124

565

79

770

102

661

125

561

80

765

103

657

126

557

81

760

104

652

127

553

82

755

105

648

128

549

83

751

106

643

129

545

84

746

107

639

130

540

85

741

108

634

131

536

86

736

109

630

132

532

87

731

110

626

133

528

88

726

111

621

134

524

89

722

112

617

135

520

90

717

113

612

136

516

91

712

114

608

137

512

92

708

115

604

138

508

93

703

116

599

139

504

94

698

117

595

140

500

95

694

118

591

Table 3-2 Table 3223-1 Stress Indices B1 and B2 DR 7

DR 9

DR 11

DR 13.5

B1 Straight and Butt Fused Joint

0.5

0.5

0.5

0.5

B2 Straight and Butt Fused Joint

1.0

1.0

1.0

1.0

B1 Miter [Note (1)]

0.69

0.69

0.69

0.69

B2 Miter [Note (1)]

1.38

1.64

1.91

2.21

B

B

B

B

NOTE: (1) Mitered elbows shall not exceed 22.5º (±3º) angle of change in direction at mitered joint

3-7

Proposed Code Case – Design Requirements Table 3-3 Table 3223-2 Design and Service Level Longitudinal Stress Factors, k Service Level

Design

A

B

C

D

k

1.0

1.0

1.1

1.33

1.33

Table 3-4 Table 3223-3 Short Duration (•5 minutes) Allowable Longitudinal Tensile Stress Factors, k Temp, ºF

≤70

100

120

140

176

S, psi

1200

940

770

630

400

Table 3-5 Table 3311.2-1 Stress Intensification Factor i Fitting or Joint

i

Straight Pipe

1.0

Butt Fusion

1.0

Mitered Elbows

2.2

3-8

4 EXAMPLE HDPE PIPING SYSTEM ANALYSIS

4.1 System Description The piping system is illustrated in Figure 4-1 and 4-2. It is HDPE 4710 pipe, and is 4 inch nominal size. The system has a bypass line and a pressure relief valve. Butterfly valves are used to isolate the bypass line and the main control valve which is a globe valve. The valves are carbon steel, class 150, with weights and lengths shown in Table 4-1.

Figure 4-1 Caesar II Model Layout

4-1

Example HDPE Piping System Analysis

Figure 4-2 Nodal Layout of Caesar II Model

Table 4-1 Valve Weights and Dimensions Valve

Nominal Size

Weight, lb

Length, in

Butterfly

4

20

2.12

Globe

4

110

9

4.2 Design Analysis Work Flow Figure 4-3 details the analysis and qualification workflow that was followed for this example problem.

4-2

Example HDPE Piping System Analysis

Define Loading Conditions

Select Pipe Size by Pressure Design

Develop Piping System Stress Model

System Layout Mechanical Properties Physical Properties

Select a Preliminary Support Arrangement

Run Stress Analysis

Qualify Stresses and Loads

Design Support Attachments and Qualify Supports

Figure 4-3 Workflow for Analysis and Qualification

4.3 Loading Conditions 4.3.1 Design Life The design life of the system is 60 years. 4.3.2 Design Pressure and Temperature PD = 150 psi TD = 100 ºF 4.3.3 Service Level Pressure and Temperature PA_service = PB_service = PC_service = 150 psi PD_service = 200 psi for 30 days maximum TA_service = TB_service = TC_service = 100 ºF TD_service = 140 ºF for 30 days maximum

4-3

Example HDPE Piping System Analysis

4.3.4 Weights and Mechanical Loads Pipe size = 4” nominal (4.5” OD) Pipe Weight = 2.51 lb/ft Fluid Weight = 4.25 lb/ft Valve Weights are listed in Table 4-1. There are no additional mechanical loads in this example problem. 4.3.5 Seismic Input The seismic input response spectra are plotted in Figure 4-4. The seismic damping is 3% (Note to reviewers: This is the subject of a current EPRI sponsored test program). The seismic input is 3 dimensional (North-South, East-West, vertical) with component vectors combined by SRSS. In this example there was no seismic anchor motion, the end vessels are assumed to be rigid and rigidly anchored.

Figure 4-4 Seismic Response Spectrum

4.4 Piping System Model The system layout and the model geometry are based on the isometric, and are illustrated in Figure 4-1.

4-4

Example HDPE Piping System Analysis

4.4.1 Caesar Model Caesar II v5.20 was used in this example to calculate the stresses due to sustained (deadweight) loads, seismic loads and thermal expansion loads. The model is shown in Figure 4-1, with guide restraints approximately every 4 feet or less. Appendix A contains the input echo of the Caesar II v5.20 model. Consideration was given to the mesh density of the model (number of nodes between each restraint) for lumped mass programs. Figure 4-5 shows the convergence of stress due to inertial loading for a simply supported beam. Based on this convergence study, three nodes were placed in between every support.

Figure 4-5 Convergence of Seismic Stresses due to Increased Nodal Density

This example primarily follows Code Case N-755 which uses Section III code stress calculations, therefore Class III Subsection ND was chosen as the code in Caesar II [14]. This code allows the use of user-defined stress indexes, B1 & B2, and SIF’s. 4.4.2 Abaqus Models The FEA software package Abaqus version 6.10-1 was used to check the CAESAR II results. Initially, two models were made for the elbow shown in Figure B-1. The first model was a full 3D model and the second model used Abaqus beam elements which use beam theory based on the pipe’s section properties. This elbow model tested the performance of the Abaqus beam model which would be required for modeling the full system because a 3D analysis would have been too computationally demanding. A full model of the piping system was made with Abaqus beam elements after the elbow test demonstrated that the beam model would be conservative.

4-5

Example HDPE Piping System Analysis

4.4.3 Load Cases Four cases were run, for Service Levels A-C. One case was run for Service level D to check the deflection due to sustained weight and another to calculate the stress results for the sustained, thermal and seismic load cases. The apparent modulus from Table -3210-1(a) [2] was used for the deflection check and the tensile modulus was used for the code stress calculations.

4.5 Mechanical Properties The long term allowable stresses for PE4710 are 800 psi and 670 psi, for ambient and design temperatures, respectively. These stresses are from Code Case N-755 Table -3210-3(a) and are used for evaluating the long term applied loads to the piping system. The HDB, which comes from the Plastic Pipe Institute listed material, is 1277 psi [2]. The HDB is used for initially sizing the pipe, although the thickness it calculates was checked against -3131 in the proposed code case. The short term allowable stresses for PE4710 are 1200 psi and 940 psi, for ambient and design temperatures, respectively. The stresses are from Code Case N-755, Table 3223-3 and are used for evaluating any short duration (≤ 5 minutes) loads. These allowable stresses would be used for evaluating transients; however this example does not contain any.

4.6 Physical Properties 4.6.1 Modulus of Elasticity The modulus of elasticity for HDPE Pipe for PE4710 comes from Code Case N-755 Table 32101(a) [2]. The long-term apparent modulus is 29 ksi and 21.2 ksi for ambient and design temperatures, respectively. The tensile modulus, are 110 ksi and 100 ksi for ambient and design temperatures, respectively. The short term modulus is used for calculating the code stresses for the different load cases and the long-term apparent modulus is used for calculating the deflection of the piping system. 4.6.2 Poisson’s Ratio Poisson’s ratio varies depending on whether the load is a short duration of long duration load. Code Case N-755 states the value for Poisson’s ratio is either 0.35 (≤5 minutes duration) or 0.45 [3]. The same issues regarding the apparent modulus might apply here, however this was not been investigated in this report. 4.6.3 Coefficient of Thermal Expansion The coefficient of thermal expansion used in this study was α = 1.0E-4 in/in-ºF [6]. 4-6

Example HDPE Piping System Analysis

4.7 Preliminary Support Arrangement In this example the Performance Pipe recommended spacing equation results in a support spacing of 5.5 ft. However, the supports were placed on 4’ horizontal spacing due to the layout of the system. A hanger support was also added to the long vertical section. Guides were placed at either end of the metal valves.

4.8 Results The results for the sustained, thermal, seismic and deflection analyses for the design conditions are shown in Table 4-2. This table shows that all the requirements are met for the design conditions. Table 4-2 CAESAR II Results for Design Conditions

   Sustained Thermal Seismic Long-term Deflection

Node 1018 230 510 1000

Check Stress (psi) Stress (psi) Stress (psi) Y-Displacement (in)

Value 366.3 900.9 567.6 0.0175

Allow 670 1100 1100 1

The results for the Service Level D analysis are shown in Table 4-3. In this case the design fails to meet the thermal expansion criteria, but it meets all the other criteria. Table 4-3 CAESAR II Results for Service Level D

Sustained Thermal Seismic Long-term Deflection

Node 1018 230 510 1000

Check Stress (psi) Stress (psi) Stress (psi) Y-Displacement (in)

Value 477 2109.4 575.3 0.0175

Allow 500 1100 1100 1

4.9 Abaqus and CAESAR II Comparison Appendix B details the Abaqus analysis that was used to check the CAESAR II results. As a first step, a simple elbow was used to compare a full 3D analysis in Abaqus, a beam model in Abaqus, and a CAESAR II analysis. This study showed that the CAESAR II model calculates the highest elbow stiffness. This is because CAESAR II incorporates the Code flexibility factors which are more conservative than the true elbow flexibility. The full model analysis showed that for the thermal expansion case, the Abaqus beam model calculates the same restraint reactions as the CAESAR II model, as shown in Table B-5. However, Table 4-4 shows that the calculated displacements don’t exactly line up. This could be 4-7

Example HDPE Piping System Analysis

related to the elbow model in CAESAR II being stiffer so the pipe is more restrained. However, the restraint reactions end up being the same because more force is exerted for a given displacement. Table 4-4 Comparison of Displacements due to Thermal Expansion Displacement (in) Node 620 330 230 120

4-8

Program

Δx

Δy

Δz

Abaqus

0.00

0.09

0.16

CAESAR

0.00

0.10

0.16

Abaqus

0.10

0.06

0.01

CAESAR

0.08

0.07

0.05

Abaqus

0.27

0.00

-0.30

CAESAR

0.14

0.00

-0.25

Abaqus

-0.41

0.00

0.00

CAESAR

-0.34

0.00

0.00

5 CONCLUSIONS

This report has presented a number of potential failure modes that may require attention for above ground piping applications. Existing work addresses most of these failure modes, but more work might need to be done to ensure that HDPE can be designed to protect against all failure modes for above ground applications. This report also notes that in some cases there is not a significant difference between HDPE and steel behavior, and that the method of analyses for above ground applications can be similar. Therefore, the design analysis that includes all the failure modes doesn’t necessarily require starting from scratch, but rather it can borrow from previous experience with metallic pipe in the creep regime. The example problem contained in this report demonstrates that a lump mass analysis tool can match the results from a more detailed FEA analysis. While the seismic load case did not match exactly, a solution is presented that would work and the lack of a match is a demonstration of why proper nodal density must be included in the lumped mass analysis package. The example problem is a relatively small scale piping system so it might fully capture behavior that would happen in something like a 40’ length of pipe.

5-1

6 REFERENCES 1. PPI Handbook of Polyethylene Pipe. Plastics Pipe Institute, www.plasticpipe.org. 2. ASME Code Case N-755 “Use of Polyethylene (PE) Plastic Pipe Section III, Division 1, and Section XI.” proposed revision 1 dated 9-02-2010. 3. Performance Pipe Technical Note PP-815-TN, “Above Grade Pipe Supports”, Chevron Phillips Chemical Company LP, 2007. 4. ASME Code for Pressure Piping, B31, B31.3 “Process Piping”, 2008. 5. Fatigue and Capacity Testing of High Density Polyethylene Pipe and Pipe Components Fabricated from PE4710. EPRI, Palo Alto, CA: 2007. 1015062. 6. Fatigue Testing of High-Density Polyethylene Pipe and Pipe Components Fabricated from PE 4710 – 2008 Update. EPRI, Palo Alto, CA: 2008. 1016719. 7. Annual Book of ASTM Standards-2004, Section 8 “Plastics” Volume 08.04 Plastic Pipe and Building Products. ©2004 ASTM International, West Conshohocken, PA. 8. Companion Guide to the ASME Boiler & Pressure Vessel Code - Criteria and commentary on Select Aspects of the Boiler & Pressure Vessel and Piping Codes Second Edition. Volume 1. ©2006 by ASME, New York, NY. 9. 2010 ASME Boiler and Pressure Vessel Code Section II Part D Properties (Customary). ©2010 by ASME, New York, NY. 10. Ifwarson M, Leijström H. Results and Experiences Obtained by Studsvik from Long-Term Pressure Tests on Plastic Pipes for Validation of Miner’s Rule. Studsvik Polymer AB, www.studsvik.se/polymer. 11. Stress Intensification and Flexibility Factors of High Density Polyethylene Pipe Fittings: Volume 1: Testing Results. EPRI, Palo Alto, CA: 2010. 1020439, V1. 12. ASTM D2837 - 08 Standard Test Method for Obtaining Hydrostatic Design Basis for Thermoplastic Pipe Materials or Pressure Design Basis for Thermoplastic Pipe Products, West Conshohocken, PA. 13. Performance Pipe Technical Note PP-820-TN, “Design Factor for HDPE Pipe”, Chevron Phillips Chemical Company LP, 2007. 14. “Boiler & Pressure Vessel Code, Section III, Division 1, Nuclear Components,” American Society of Mechanical Engineers, New York, NY.

6-1

A PIPE STRESS ANALYSIS (CAESAR II) INPUT

LISTING OF STATIC LOAD CASES FOR THIS ANALYSIS 1 (OPE) W+T1+P1 2 (SUS) W+P1 3 (EXP) L3=L1-L2

Job Description:

PROJECT:

CLIENT :

ANALYST:

NOTES :

PIPE DATA --------------------------------------------------------------------------------------------------------------------------------------------------------A-1

Pipe Stress Analysis (Caesar II) Input

From 10 To 20 DY= 1.000 ft. PIPE Dia= 4.500 in. Wall= .484 in. Insul= .000 in. Mill%(-)= .00 GENERAL T1= 100 F P1= 150.0000 lb./sq.in. Mat= (454)PE 4710 ST E= 110,000 lb./sq.in. EH1= 100,000 lb./sq.in. EH2= 110,000 lb./sq.in. EH3= 110,000 lb./sq.in. EH4= 110,000 lb./sq.in. EH5= 110,000 lb./sq.in. EH6= 110,000 lb./sq.in. EH7= 110,000 lb./sq.in. EH8= 110,000 lb./sq.in. EH9= 110,000 lb./sq.in. v = .350 Density= .0343 lb./cu.in. Fluid= .0361100 lb./cu.in. RESTRAINTS Node 10 ANC ALLOWABLE STRESSES ASME ND (2007)

Sc= 800 lb./sq.in. Sh1= 627 lb./sq.in.

Sh2= 800 lb./sq.in. Sh3= 800 lb./sq.in. Sh4= 800 lb./sq.in. Sh5= 800 lb./sq.in. Sh6= 800 lb./sq.in. Sh7= 800 lb./sq.in. Sh8= 800 lb./sq.in. Sh9= 800 lb./sq.in. ----------------------------------------------------------------------------From 20 To 30 DY= 1.000 ft. ALLOWABLE STRESSES ASME ND (2007)

Sc= 800 lb./sq.in. Sh1= 627 lb./sq.in.

Sh2= 800 lb./sq.in. Sh3= 800 lb./sq.in. Sh4= 800 lb./sq.in. Sh5= 800 lb./sq.in. Sh6= 800 lb./sq.in. Sh7= 800 lb./sq.in. A-2

Pipe Stress Analysis (Caesar II) Input

Sh8= 800 lb./sq.in. Sh9= 800 lb./sq.in. ----------------------------------------------------------------------------From 30 To 40 DY= 1.000 ft. ALLOWABLE STRESSES ASME ND (2007)

Sc= 800 lb./sq.in. Sh1= 627 lb./sq.in.

Sh2= 800 lb./sq.in. Sh3= 800 lb./sq.in. Sh4= 800 lb./sq.in. Sh5= 800 lb./sq.in. Sh6= 800 lb./sq.in. Sh7= 800 lb./sq.in. Sh8= 800 lb./sq.in. Sh9= 800 lb./sq.in. ----------------------------------------------------------------------------From 40 To 50 DY= 1.000 ft. PIPE Dia= 4.500 in. Wall= .484 in. Insul= .000 in. GENERAL Mat= (454)PE 4710 ST E= 110,000 lb./sq.in. EH1= 100,000 lb./sq.in. EH2= 110,000 lb./sq.in. EH3= 110,000 lb./sq.in. EH4= 110,000 lb./sq.in. EH5= 110,000 lb./sq.in. EH6= 110,000 lb./sq.in. EH7= 110,000 lb./sq.in. EH8= 110,000 lb./sq.in. EH9= 110,000 lb./sq.in. v = .350 Density= .0343 lb./cu.in. BEND at "TO" end Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 49 Angle/Node @2= .00 48 Miters= 4 Ftg Thk= .616 in. SIF's & TEE's Node 50 Sif(in)= 2.200 B1= .690 B2= 1.640 A-3

Pipe Stress Analysis (Caesar II) Input

Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF ALLOWABLE STRESSES ASME ND (2007)

Sc= 800 lb./sq.in. Sh1= 627 lb./sq.in.

Sh2= 800 lb./sq.in. Sh3= 800 lb./sq.in. Sh4= 800 lb./sq.in. Sh5= 800 lb./sq.in. Sh6= 800 lb./sq.in. Sh7= 800 lb./sq.in. Sh8= 800 lb./sq.in. Sh9= 800 lb./sq.in. ----------------------------------------------------------------------------From 50 To 60 DX= -.562 ft. PIPE Dia= 4.500 in. Wall= .484 in. Insul= .000 in. ----------------------------------------------------------------------------From 60 To 70 DX= -1.146 ft. RESTRAINTS Node 60 Y Node 60 Z ----------------------------------------------------------------------------From 70 To 80 DX= -1.146 ft. ----------------------------------------------------------------------------From 80 To 90 DX= -1.146 ft. RESTRAINTS Node 90 Z Node 90 Y ----------------------------------------------------------------------------A-4

Pipe Stress Analysis (Caesar II) Input

From 90 To 100 DX= -1.146 ft. ----------------------------------------------------------------------------From 100 To 110 DX= -1.146 ft. ----------------------------------------------------------------------------From 110 To 120 DX= -1.146 ft. RESTRAINTS Node 120 Y Node 120 Z ----------------------------------------------------------------------------From 120 To 130 DX= -.562 ft. PIPE Dia= 4.500 in. Wall= .484 in. Insul= .000 in. BEND at "TO" end Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 129 Angle/Node @2= .00 128 Miters= 4 Ftg Thk= .616 in. SIF's & TEE's Node 130 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF ----------------------------------------------------------------------------From 130 To 140 DY= -1.000 ft. PIPE Dia= 4.500 in. Wall= .484 in. Insul= .000 in. ----------------------------------------------------------------------------A-5

Pipe Stress Analysis (Caesar II) Input

From 140 To 150 DY= -1.000 ft. ----------------------------------------------------------------------------From 150 To 160 DY= -1.000 ft. ----------------------------------------------------------------------------From 160 To 170 DY= -1.000 ft. ----------------------------------------------------------------------------From 170 To 180 DY= -1.000 ft. RESTRAINTS Node 180 X Node 180 Y Node 180 Z ----------------------------------------------------------------------------From 180 To 190 DY= -1.000 ft. ----------------------------------------------------------------------------From 190 To 200 DY= -1.000 ft. ----------------------------------------------------------------------------From 200 To 210 DY= -1.000 ft. ----------------------------------------------------------------------------From 210 To 220 DY= -1.000 ft. ----------------------------------------------------------------------------From 220 To 230 DY= -1.000 ft. PIPE Dia= 4.500 in. Wall= .484 in. Insul= .000 in. A-6

Pipe Stress Analysis (Caesar II) Input

BEND at "TO" end Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 229 Angle/Node @2= .00 228 Miters= 4 Ftg Thk= .616 in. RESTRAINTS Node 230 Y SIF's & TEE's Node 230 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF ----------------------------------------------------------------------------From 230 To 240 DZ= 1.000 ft. PIPE Dia= 4.500 in. Wall= .484 in. Insul= .000 in. ----------------------------------------------------------------------------From 240 To 250 DZ= .500 ft. ----------------------------------------------------------------------------From 250 To 260 DZ= .500 ft. ----------------------------------------------------------------------------From 260 To 270 DZ= .500 ft. RESTRAINTS Node 270 X Node 270 Y ----------------------------------------------------------------------------From 270 To 280 DZ= 1.000 ft. A-7

Pipe Stress Analysis (Caesar II) Input

SIF's & TEE's Node 280 Reinforced Tee Sif(in)= 1.000 B1= .500 B2= 1.000 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF ----------------------------------------------------------------------------From 280 To 290 DZ= 1.000 ft. RESTRAINTS Node 290 X Node 290 Y ----------------------------------------------------------------------------From 290 To 300 DZ= .500 ft. ----------------------------------------------------------------------------From 300 To 310 DZ= .500 ft. ----------------------------------------------------------------------------From 310 To 320 DZ= .500 ft. ----------------------------------------------------------------------------From 320 To 330 DZ= 1.000 ft. PIPE Dia= 4.500 in. Wall= .484 in. Insul= .000 in. BEND at "TO" end Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 329 Angle/Node @2= .00 328 Miters= 4 Ftg Thk= .616 in. RESTRAINTS Node 328 Y A-8

Pipe Stress Analysis (Caesar II) Input

SIF's & TEE's Node 330 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF ----------------------------------------------------------------------------From 330 To 340 DY= -1.000 ft. PIPE Dia= 4.500 in. Wall= .484 in. Insul= .000 in. ----------------------------------------------------------------------------From 340 To 350 DY= -1.000 ft. ----------------------------------------------------------------------------From 350 To 360 DY= -1.000 ft. RESTRAINTS Node 360 X Node 360 Y Node 360 Z ----------------------------------------------------------------------------From 360 To 370 DY= -1.000 ft. SIF's & TEE's Node 370 Reinforced Tee Sif(in)= 1.000 B1= .500 B2= 1.000 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF ----------------------------------------------------------------------------From 370 To 380 DY= -1.000 ft. ----------------------------------------------------------------------------A-9

Pipe Stress Analysis (Caesar II) Input

From 380 To 390 DY= -.823 ft. ----------------------------------------------------------------------------From 390 To 400 DY= -.177 ft. RIGID Weight= 22.00 lb. ----------------------------------------------------------------------------From 400 To 410 DY= -2.000 ft. PIPE Dia= 4.500 in. Wall= .484 in. Insul= .000 in. BEND at "TO" end Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 409 Angle/Node @2= .00 408 Miters= 4 Ftg Thk= .616 in. RESTRAINTS Node 420 Z Node 420 Y SIF's & TEE's Node 410 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF ----------------------------------------------------------------------------From 410 To 420 DX= 1.000 ft. PIPE Dia= 4.500 in. Wall= .484 in. Insul= .000 in. ----------------------------------------------------------------------------From 420 To 430 DX= 1.000 ft. A-10

Pipe Stress Analysis (Caesar II) Input

----------------------------------------------------------------------------From 430 To 440 DX= 1.000 ft. ----------------------------------------------------------------------------From 440 To 450 DX= 1.000 ft. RESTRAINTS Node 450 Z Node 450 Y ----------------------------------------------------------------------------From 450 To 460 DX= .625 ft. ----------------------------------------------------------------------------From 460 To 470 DX= .750 ft. RIGID Weight= 112.00 lb. ----------------------------------------------------------------------------From 470 To 480 DX= .625 ft. RESTRAINTS Node 480 Z Node 480 Y ----------------------------------------------------------------------------From 480 To 490 DX= 1.000 ft. ----------------------------------------------------------------------------From 490 To 500 DX= 2.000 ft. ----------------------------------------------------------------------------From 500 To 510 DX= 1.000 ft. A-11

Pipe Stress Analysis (Caesar II) Input

PIPE Dia= 4.500 in. Wall= .484 in. Insul= .000 in. BEND at "TO" end Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 509 Angle/Node @2= .00 508 Miters= 4 Ftg Thk= .616 in. RESTRAINTS Node 500 Z Node 500 Y SIF's & TEE's Node 510 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF ----------------------------------------------------------------------------From 510 To 520 DY= 2.000 ft. PIPE Dia= 4.500 in. Wall= .484 in. Insul= .000 in. ----------------------------------------------------------------------------From 520 To 530 DY= .177 ft. RIGID Weight= 22.00 lb. ----------------------------------------------------------------------------From 530 To 540 DY= .823 ft. ----------------------------------------------------------------------------From 540 To 550 DY= 1.000 ft. SIF's & TEE's A-12

Pipe Stress Analysis (Caesar II) Input

Node 550 Reinforced Tee Sif(in)= 1.000 B1= .500 B2= 1.000 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF ----------------------------------------------------------------------------From 550 To 560 DY= 1.000 ft. RESTRAINTS Node 560 Y Node 560 X Node 560 Z ----------------------------------------------------------------------------From 560 To 570 DY= 1.000 ft. ----------------------------------------------------------------------------From 570 To 580 DY= 1.000 ft. ----------------------------------------------------------------------------From 580 To 590 DY= 1.000 ft. ----------------------------------------------------------------------------From 590 To 600 DY= 1.000 ft. ----------------------------------------------------------------------------From 600 To 610 DY= 1.000 ft. ----------------------------------------------------------------------------From 610 To 620 DY= 1.000 ft. BEND at "TO" end Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 619 Angle/Node @2= .00 618 Miters= 4 Ftg Thk= .616 in. A-13

Pipe Stress Analysis (Caesar II) Input

SIF's & TEE's Node 620 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF ----------------------------------------------------------------------------From 620 To 630 DZ= -1.000 ft. RESTRAINTS Node 630 X Node 630 Y ----------------------------------------------------------------------------From 630 To 640 DZ= -1.000 ft. ----------------------------------------------------------------------------From 640 To 650 DZ= -1.000 ft. ----------------------------------------------------------------------------From 650 To 660 DZ= -.500 ft. SIF's & TEE's Node 660 Reinforced Tee

Meets 3673.2b-2, Notes 10,11 = ON

Ferric Mat, Note 3673.2b-1.3 = OFF ----------------------------------------------------------------------------From 660 To 670 DZ= -.500 ft. RESTRAINTS Node 670 Y Node 670 X ----------------------------------------------------------------------------A-14

Pipe Stress Analysis (Caesar II) Input

From 670 To 680 DZ= -1.000 ft. RESTRAINTS Node 680 ANC ----------------------------------------------------------------------------From 370 To 1000 DZ= 1.823 ft. ----------------------------------------------------------------------------From 1000 To 1010 DZ= .177 ft. RIGID Weight= 22.00 lb. ----------------------------------------------------------------------------From 1010 To 1020 DZ= 1.000 ft. BEND at "TO" end Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 1019 Angle/Node @2= .00 1018 Miters= 4 Ftg Thk= .616 in. SIF's & TEE's Node 1020 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF ----------------------------------------------------------------------------From 1020 To 1030 DX= 1.000 ft. RESTRAINTS Node 1020 Y ----------------------------------------------------------------------------From 1030 To 1040 DX= 1.000 ft. ----------------------------------------------------------------------------A-15

Pipe Stress Analysis (Caesar II) Input

From 1040 To 1050 DX= 1.000 ft. ----------------------------------------------------------------------------From 1050 To 1060 DX= 1.000 ft. RESTRAINTS Node 1060 Z Node 1060 Y ----------------------------------------------------------------------------From 1060 To 1070 DX= 1.000 ft. ----------------------------------------------------------------------------From 1070 To 1080 DX= 1.000 ft. RESTRAINTS Node 1080 Z Node 1080 Y ----------------------------------------------------------------------------From 1080 To 1090 DX= 1.000 ft. ----------------------------------------------------------------------------From 1090 To 1100 DX= 1.000 ft. ----------------------------------------------------------------------------From 1100 To 1110 DX= 1.000 ft. ----------------------------------------------------------------------------From 1110 To 1120 DX= 1.000 ft. BEND at "TO" end Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 1119 A-16

Pipe Stress Analysis (Caesar II) Input

Angle/Node @2= .00 1118 Miters= 4 Ftg Thk= .616 in. RESTRAINTS Node 1118 Y SIF's & TEE's Node 1120 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF ----------------------------------------------------------------------------From 1120 To 1130 DZ= -1.000 ft. ----------------------------------------------------------------------------From 1130 To 1140 DZ= -.177 ft. RIGID Weight= 22.00 lb. ----------------------------------------------------------------------------From 1140 To 550 DZ= -1.823 ft. ----------------------------------------------------------------------------From 280 To 2010 DY= 1.000 ft. ----------------------------------------------------------------------------From 2010 To 2020 DY= .177 ft. RIGID Weight= 22.00 lb. ----------------------------------------------------------------------------From 2020 To 2030 DY= .823 ft. ----------------------------------------------------------------------------From 2030 To 2040 DY= 1.000 ft. BEND at "TO" end A-17

Pipe Stress Analysis (Caesar II) Input

Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 2039 Angle/Node @2= .00 2038 Miters= 4 Ftg Thk= .616 in. SIF's & TEE's Node 2040 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF ----------------------------------------------------------------------------From 2040 To 2050 DX= 1.000 ft. RESTRAINTS Node 2050 Y ----------------------------------------------------------------------------From 2050 To 2060 DX= 1.000 ft. ----------------------------------------------------------------------------From 2060 To 2070 DX= 1.000 ft. ----------------------------------------------------------------------------From 2070 To 2080 DX= 1.000 ft. RESTRAINTS Node 2080 Z Node 2080 Y ----------------------------------------------------------------------------From 2080 To 2090 DX= 1.000 ft. ----------------------------------------------------------------------------From 2090 To 2100 DX= 1.000 ft. RESTRAINTS A-18

Pipe Stress Analysis (Caesar II) Input

Node 2100 Z Node 2100 Y ----------------------------------------------------------------------------From 2100 To 2110 DX= 1.000 ft. ----------------------------------------------------------------------------From 2110 To 2120 DX= 1.000 ft. ----------------------------------------------------------------------------From 2120 To 2130 DX= 1.000 ft. ----------------------------------------------------------------------------From 2130 To 660 DX= 1.000 ft.

MATERIAL Changes: 10

20

Mat= (454)PE 4710 ST E= 110,000 lb./sq.in. v = .350 Density= .0343 lb./cu.in.

40

50

Mat= (454)PE 4710 ST E= 110,000 lb./sq.in. v = .350 Density= .0343 lb./cu.in.

JOBNAME: L:\PROJECTS\18000'S\18208\CALC\18208-HDPE-SYSTEM V2

ALLOWABLE STRESS Changes 10

20

ASME ND (2007)

Sc= 800 lb./sq.in.

Sh1= 627 lb./sq.in. Sh2= 800 lb./sq.in. A-19

Pipe Stress Analysis (Caesar II) Input

Sh3= 800 lb./sq.in. Sh4= 800 lb./sq.in. Sh5= 800 lb./sq.in. Sh6= 800 lb./sq.in. Sh7= 800 lb./sq.in. Sh8= 800 lb./sq.in. Sh9= 800 lb./sq.in. 20

30

ASME ND (2007)

Sc= 800 lb./sq.in.

Sh1= 627 lb./sq.in. Sh2= 800 lb./sq.in. Sh3= 800 lb./sq.in. Sh4= 800 lb./sq.in. Sh5= 800 lb./sq.in. Sh6= 800 lb./sq.in. Sh7= 800 lb./sq.in. Sh8= 800 lb./sq.in. Sh9= 800 lb./sq.in. 30

40

ASME ND (2007)

Sc= 800 lb./sq.in.

Sh1= 627 lb./sq.in. Sh2= 800 lb./sq.in. Sh3= 800 lb./sq.in. Sh4= 800 lb./sq.in. Sh5= 800 lb./sq.in. Sh6= 800 lb./sq.in. Sh7= 800 lb./sq.in. Sh8= 800 lb./sq.in. Sh9= 800 lb./sq.in. 40

50

ASME ND (2007)

Sc= 800 lb./sq.in.

Sh1= 627 lb./sq.in. Sh2= 800 lb./sq.in. Sh3= 800 lb./sq.in. Sh4= 800 lb./sq.in. Sh5= 800 lb./sq.in. Sh6= 800 lb./sq.in. Sh7= 800 lb./sq.in. Sh8= 800 lb./sq.in. Sh9= 800 lb./sq.in.

A-20

Pipe Stress Analysis (Caesar II) Input

BEND ELEMENTS 40

50

Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 49 Angle/Node @2= .00 48 Miters= 4 Ftg Thk= .616 in.

120

130

Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 129 Angle/Node @2= .00 128 Miters= 4 Ftg Thk= .616 in.

220

230

Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 229 Angle/Node @2= .00 228 Miters= 4 Ftg Thk= .616 in.

320

330

Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 329 Angle/Node @2= .00 328 Miters= 4 Ftg Thk= .616 in.

400

410

Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 409 Angle/Node @2= .00 408 Miters= 4 Ftg Thk= .616 in. A-21

Pipe Stress Analysis (Caesar II) Input

500

510

Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 509 Angle/Node @2= .00 508 Miters= 4 Ftg Thk= .616 in.

610

620

Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 619 Angle/Node @2= .00 618 Miters= 4 Ftg Thk= .616 in.

1010

1020

Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 1019 Angle/Node @2= .00 1018 Miters= 4 Ftg Thk= .616 in.

1110

1120

Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 1119 Angle/Node @2= .00 1118 Miters= 4 Ftg Thk= .616 in.

2030

2040

Radius= 6.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 2039 Angle/Node @2= .00 2038 Miters= 4 Ftg Thk= .616 in.

A-22

Pipe Stress Analysis (Caesar II) Input

RIGIDS 390

400

RIGID Weight= 22.00 lb.

460

470

RIGID Weight= 112.00 lb.

520

530

RIGID Weight= 22.00 lb.

1000

1010

RIGID Weight= 22.00 lb.

1130

1140

RIGID Weight= 22.00 lb.

2010

2020

RIGID Weight= 22.00 lb.

SIF's & TEE's 40

50

Node 50 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF

120

130

Node 130 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF

220

230

Node 230 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF A-23

Pipe Stress Analysis (Caesar II) Input

270

280

Node 280 Reinforced Tee Sif(in)= 1.000 B1= .500 B2= 1.000 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF

320

330

Node 330 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF

360

370

Node 370 Reinforced Tee Sif(in)= 1.000 B1= .500 B2= 1.000 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF

400

410

Node 410 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF

500

510

Node 510 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF

540

550

Node 550 Reinforced Tee Sif(in)= 1.000 B1= .500 B2= 1.000 Meets 3673.2b-2, Notes 10,11 = ON

A-24

Pipe Stress Analysis (Caesar II) Input

Ferric Mat, Note 3673.2b-1.3 = OFF 610

620

Node 620 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF

650

660

Node 660 Reinforced Tee Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF

1010

1020

Node 1020 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF

1110

1120

Node 1120 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF

2030

2040

Node 2040 Sif(in)= 2.200 B1= .690 B2= 1.640 Meets 3673.2b-2, Notes 10,11 = ON Ferric Mat, Note 3673.2b-1.3 = OFF

RESTRAINTS

Len GAP

YIELD

MU Dir A-25

Pipe Stress Analysis (Caesar II) Input

NODE TYPE

CNODE

STIF1

STIF2

FORCE

Vectors

-------+-------+------+----------+----------+----------+--------------------10 ANC

.000 .000 .000

60 Y

.000 1.000 .000

60 Z

.000 .000 1.000

90 Z

.000 .000 1.000

90 Y

.000 1.000 .000

120 Y

.000 1.000 .000

120 Z

.000 .000 1.000

180 X

1.000 .000 .000

180 Y

.000 1.000 .000

180 Z

.000 .000 1.000

230 Y

.000 1.000 .000

270 X

1.000 .000 .000

270 Y

.000 1.000 .000

290 X

1.000 .000 .000

290 Y

.000 1.000 .000

328 Y

.000 1.000 .000

360 X

1.000 .000 .000

360 Y

.000 1.000 .000

360 Z

.000 .000 1.000

420 Z

.000 .000 1.000

420 Y

.000 1.000 .000

A-26

Pipe Stress Analysis (Caesar II) Input

450 Z

.000 .000 1.000

450 Y

.000 1.000 .000

480 Z

.000 .000 1.000

480 Y

.000 1.000 .000

500 Z

.000 .000 1.000

500 Y

.000 1.000 .000

560 Y

.000 1.000 .000

560 X

1.000 .000 .000

560 Z

.000 .000 1.000

630 X

1.000 .000 .000

630 Y

.000 1.000 .000

670 Y

.000 1.000 .000

670 X

1.000 .000 .000

680 ANC

.000 .000 .000

1020 Y

.000 1.000 .000

1060 Z

.000 .000 1.000

1060 Y

.000 1.000 .000

1080 Z

.000 .000 1.000

1080 Y

.000 1.000 .000

1118 Y

.000 1.000 .000

2050 Y

.000 1.000 .000

2080 Z

.000 .000 1.000

2080 Y

.000 1.000 .000 A-27

Pipe Stress Analysis (Caesar II) Input

2100 Z

.000 .000 1.000

2100 Y

.000 1.000 .000

INPUT UNITS USED...

UNITS= ENGLISH NOM/SCH INPUT= ON LENGTH FORCE

inches

x

1.000 = in.

pounds

x

1.000 = lb.

MASS(dynamics)

pounds

MOMENTS(INPUT)

psig

x

1.000 = F

1.000 = lb./sq.in.

ELASTIC MODULUS lbs./sq.in. x PIPE DENSITY

lbs./cu.in. x

TRANSL. STIF

lbs./cu.in. x lbs./in.

x

G LOAD WIND LOAD A-28

g's

lb./in. x

1.000 = lb./cu.in. 1.000 = lb./cu.in.

1.000 = lb./in.

ROTATIONAL STIF in.lb./deg. x UNIFORM LOAD

1.000 = lb./sq.in.

1.000 = lb./cu.in.

INSULATION DENS. lbs./cu.in. x FLUID DENSITY

0.083 = ft.lb.

1.000 = lb./sq.in.

degrees F. x

PRESSURE

1.000 = in.lb.

inch-pounds x

lbs./sq.in. x

TEMP. SCALE

1.000 = lbm

inch-pounds x

MOMENTS(OUTPUT) STRESS

x

x

1.000 = in.lb./deg 1.000 = lb./in.

1.000 = g's

lbs./sq.in. x 144.000 = lb./sq.ft.

Pipe Stress Analysis (Caesar II) Input

ELEVATION

inches

x

0.083 = ft.

COMPOUND LENGTH inches DIAMETER

inches

WALL THICKNESS

x

x

0.083 = ft.

1.000 = in.

inches

x

1.000 = in.

SETUP FILE PARAMETERS -----------------------------------------------------------------------------CONNECT GEOMETRY THRU CNODES = MIN ALLOWED BEND ANGLE =

YES

5.00000

MAX ALLOWED BEND ANGLE =

95.0000

BEND LENGTH ATTACHMENT PERCENT = MIN ANGLE TO ADJACENT BEND PT = LOOP CLOSURE TOLERANCE =

5.00000

1.00000

THERMAL BOWING HORZ TOLERANCE = AUTO NODE NUMBER INCREMENT= Z AXIS UP=

in.

0.100000E-03 10.0000

NO

USE PRESSURE STIFFENING =

YES

ALPHA TOLERANCE =

0.500000E-01

RESLD-FORCE =

NO

HGR DEF RESWGT STIF =

0.100000E+13 lb./in.

DECOMP SNG TOL =

0.100000E+11

BEND AXIAL SHAPE =

YES

FRICT STIF =

1.00000

0.100000E+07 lb./in. A-29

Pipe Stress Analysis (Caesar II) Input

FRICT NORM FORCE VAR =

0.150000

FRICT ANGLE VAR =

15.0000

FRICT SLIDE MULT =

1.00000

ROD TOLERANCE =

1.00000

ROD INC =

2.00000

INCORE NUMERICAL CHECK =

NO

OUTCORE NUMERICAL CHECK =

NO

DEFAULT TRANS RESTRAINT STIFF=

0.100000E+13

DEFAULT ROT RESTRAINT STIFF=

lb./in.

0.100000E+13 in.lb./deg

IGNORE SPRING HANGER STIFFNESS = NO MISSING MASS ZPA =

EXTRACTED

MIN WALL MILL TOLERANCE = WRC-107 VERSION =

12.5000

MAR 79 1B1/2B1

WRC-107 INTERPOLATION =

LAST VALUE

DEFAULT AMBIENT TEMPERATURE= BOURDON PRESSURE=

70.0000

NONE

COEFFICIENT OF FRICTION (MU) = INCLUDE SPRG STIF IN HGR OPE =

0.000000 NO

INCLUDE INSULATION IN HYDROTEST = NO REDUCED INTERSECTION = USE WRC329

B31.1(POST1980)

NO

NO REDUCED SIF FOR RFT AND WLT B31.1 REDUCED Z FIX = A-30

YES

NO

F

Pipe Stress Analysis (Caesar II) Input

CLASS 1 BRANCH FLEX

NO

ALL STRESS CASES CORRODED =

NO

ADD TORSION IN SL STRESS = ADD F/A IN STRESS =

DEFAULT

DEFAULT

OCCASIONAL LOAD FACTOR = DEFAULT CODE =

0.000000

B31.3

B31.3 SUS CASE SIF FACTOR = ALLOW USERS BEND SIF =

1.00000 YES

USE SCHNEIDER

NO

YIELD CRITERION STRESS = USE PD/4T

MAX 3D SHEAR

NO

BASE HOOP STRESS ON ? =

ID

EN13480 USE IN OUTPLANE SIFS=

NO

LIBERAL EXPANSION ALLOWABLE= B31.3 SEC 319.2.3C SAXIAL=

YES

NO

B31.3 WELDING/CONTOUR TEE ISB16.9 NO PRESSURE VARIATION IN EXP CASE= DEFAULT IMPLEMENT B313 APP-P

NO

IMPLEMENT B313 CODE CASE 178 IGNORE B31.3 Wc FACTOR= USE FRP SIF =

NO NO

YES

USE FRP FLEX = BS 7159 Pressure Stiffening=

YES Design Strain A-31

Pipe Stress Analysis (Caesar II) Input

FRP Property Data File=

CAESAR.FRP

FRP Emod (axial) =

0.320000E+07 lb./sq.in.

FRP Ratio Gmod/Emod (axial) =

0.250000

FRP Ea/Eh*Vh/a =

0.152730

FRP Laminate Type =

THREE

FRP Alpha =

12.0000

F

FRP Density =

0.600000E-01 lb./cu.in.

EXCLUDE f2 FROM UKOOA BENDING = NO

EXECUTION CONTROL PARAMETERS

Rigid/ExpJt Print Flag .....

1.000

Bourdon Option .............

.000

Loop Closure Flag ..........

.000

Thermal Bowing Delta Temp ..

.000 F

Liberal Allowable Flag .....

1.000

Uniform Load Option ........

.000

Ambient Temperature ........ 70.000 F Plastic (FRP) Alpha ........ 12.000 Plastic (FRP) GMOD/EMODa ... Plastic (FRP) Laminate Type. A-32

.250

3.000

Pipe Stress Analysis (Caesar II) Input

Eqn Optimizer ..............

.000

Node Selection .............

.000

Eqn Ordering ...............

.000

Collins ....................

.000

Degree Determination ....... User Eqn Control ...........

.000 .000

COORDINATE REPORT /--------------------(in.)----------------------/ NODE

X

Y

Z

10

.0000

.0000

.0000

20

.0000

12.0000

.0000

30

.0000

24.0000

.0000

40

.0000

36.0000

.0000

50

.0000

48.0000

.0000

60

-6.7500

48.0000

.0000

70

-20.5000

48.0000

.0000

80

-34.2500

48.0000

.0000

90

-48.0000

48.0000

.0000

100

-61.7500

48.0000

.0000

110

-75.5000

48.0000

.0000

120

-89.2500

48.0000

.0000

130

-96.0000

48.0000

.0000 A-33

Pipe Stress Analysis (Caesar II) Input

140

-96.0000

36.0000

.0000

150

-96.0000

24.0000

.0000

160

-96.0000

12.0000

.0000

170

-96.0000

.0000

180

-96.0000

-12.0000

.0000

190

-96.0000

-24.0000

.0000

200

-96.0000

-36.0000

.0000

210

-96.0000

-48.0000

.0000

220

-96.0000

-60.0000

.0000

230

-96.0000

-72.0000

.0000

240

-96.0000

-72.0000

12.0000

250

-96.0000

-72.0000

18.0000

260

-96.0000

-72.0000

24.0000

270

-96.0000

-72.0000

30.0000

280

-96.0000

-72.0000

42.0000

290

-96.0000

-72.0000

54.0000

300

-96.0000

-72.0000

60.0000

310

-96.0000

-72.0000

66.0000

320

-96.0000

-72.0000

72.0000

330

-96.0000

-72.0000

84.0000

340

-96.0000

-84.0000

84.0000

350

-96.0000

-96.0000

84.0000

360

-96.0000

-108.0000

84.0000

A-34

.0000

Pipe Stress Analysis (Caesar II) Input

370

-96.0000

-120.0000

84.0000

380

-96.0000

-132.0000

84.0000

390

-96.0000

-141.8800

84.0000

400

-96.0000

-144.0000

84.0000

410

-96.0000

-168.0000

84.0000

420

-84.0000

-168.0000

84.0000

430

-72.0000

-168.0000

84.0000

440

-60.0000

-168.0000

84.0000

450

-48.0000

-168.0000

84.0000

460

-40.5000

-168.0000

84.0000

470

-31.5000

-168.0000

84.0000

480

-24.0000

-168.0000

84.0000

490

-12.0000

-168.0000

84.0000

500

12.0000

-168.0000

84.0000

510

24.0000

-168.0000

84.0000

520

24.0000

-144.0000

84.0000

530

24.0000

-141.8800

84.0000

540

24.0000

-132.0000

84.0000

550

24.0000

-120.0000

84.0000

560

24.0000

-108.0000

84.0000

570

24.0000

-96.0000

84.0000

580

24.0000

-84.0000

84.0000

590

24.0000

-72.0000

84.0000 A-35

Pipe Stress Analysis (Caesar II) Input

600

24.0000

-60.0000

84.0000

610

24.0000

-48.0000

84.0000

620

24.0000

-36.0000

84.0000

630

24.0000

-36.0000

72.0000

640

24.0000

-36.0000

60.0000

650

24.0000

-36.0000

48.0000

660

24.0000

-36.0000

42.0000

670

24.0000

-36.0000

36.0000

680

24.0000

-36.0000

24.0000

370

-96.0000

-120.0000

84.0000

1000

-96.0000

-120.0000

105.8800

1010

-96.0000

-120.0000

108.0000

1020

-96.0000

-120.0000

120.0000

1030

-84.0000

-120.0000

120.0000

1040

-72.0000

-120.0000

120.0000

1050

-60.0000

-120.0000

120.0000

1060

-48.0000

-120.0000

120.0000

1070

-36.0000

-120.0000

120.0000

1080

-24.0000

-120.0000

120.0000

1090

-12.0000

-120.0000

120.0000

1100

.0000

1110

12.0000

-120.0000

120.0000

1120

24.0000

-120.0000

120.0000

A-36

-120.0000

120.0000

Pipe Stress Analysis (Caesar II) Input

1130

24.0000

-120.0000

108.0000

1140

24.0000

-120.0000

105.8800

1140

24.0000

-120.0000

105.8800

550

24.0000

-120.0000

84.0000

280

-96.0000

-72.0000

42.0000

2010

-96.0000

-60.0000

42.0000

2020

-96.0000

-57.8800

42.0000

2030

-96.0000

-48.0000

42.0000

2040

-96.0000

-36.0000

42.0000

2050

-84.0000

-36.0000

42.0000

2060

-72.0000

-36.0000

42.0000

2070

-60.0000

-36.0000

42.0000

2080

-48.0000

-36.0000

42.0000

2090

-36.0000

-36.0000

42.0000

2100

-24.0000

-36.0000

42.0000

2110

-12.0000

-36.0000

42.0000

2120

.0000

2130

12.0000

-36.0000

42.0000

2130

12.0000

-36.0000

42.0000

-36.0000

42.0000

A-37

B FINITE ELEMENT ANALYSIS USING ABAQUS

The purpose of this appendix is to compare results obtained using a standard pipe stress code (CAESAR II 5.20) to those obtained using a finite element code (Abaqus) for system response to sustained loads, thermal loads, and seismic loads, and considering large displacement effects. One concern was that a lumped mass system can’t accurately track the deflections and loads in a HDPE system. A second concern was that the small displacement theory assumed in standard piping codes may not accurately determine system response for a material with a low modulus of elasticity and high coefficient of thermal expansion, potentially leading to large displacements. Abaqus v6.10-1 was the Finite Element Analysis (FEA) program used to check CAESAR II. The material properties were the same as presented in Chapter 4. Before the entire piping arrangement in Chapter 4 was analyzed, a simplified example was first used to check the general differences of CAESAR II, an Abaqus 3-D model, and an Abaqus beam model. This simplified model uses the same pipe specification as Chapter 4 and is an L-shaped pipe arrangement that is 48” x 48” long, with a 6” radius elbow. The elbow is 0.616” thick, while the pipe itself is 0.484” thick, per the requirements in the proposed code case in Chapter 3.

B-1

Finite Element Analysis Using Abaqus

Figure B-1 Layout of Simplified Pipe Section

The results for +/- 4" vertical displacement at the top right node are listed in Table B-1. These results show that the Abaqus Beam and CAESAR analyses are more conservative than the full Abaqus 3D analysis. Table B-1 Force versus Displacement Force (lb) Disp (in)

Abaqus 3D

Abaqus Beam

CAESAR

-4

-31.9

-34.6

-35

0

0

0

0

4

33.7

36.5

35

A 30ºF temperature change was then applied to the model with both ends fixed. Table B-2 shows that once again the Abaqus 3D model predicts the lowest restraint reactions. CAESAR II predicted a reaction force between the Abaqus 3-D analysis and the Abaqus beam analysis.

B-2

Finite Element Analysis Using Abaqus

Table B-2 Reaction Forces due to Δ30ºF Temperature Increase Y - Force (lb)

X - Force (lb)

19

19

Abaqus Beam

20.2262

20.2262

Abaqus 3D

18.3592

18.3592

CAESAR

The preliminary tests presented have shown that CAESAR II is consistent with a FEA analysis using beam theory and more conservative than a full 3-D model with respect to elbow flexibility. The next step was to analyze the full piping system presented in Chapter 4 using the Abaqus beam element. Pressure design was not studied with Abaqus because it would have required a full 3-D analysis. The analysis covered gravity, thermal, and seismic loadings. The thermal analysis was performed using the tensile modulus at 70ºF, the seismic load was calculated using the tensile modulus at design temperature, and the long term deflection was calculated using the long term apparent modulus at design temperature. Reaction forces at the restraints was chosen as a comparison method because CAESAR II manipulates the stresses per ASME Code rules. Therefore the stress output from Abaqus would not have matched the CAESAR II stress output. The position and label of all the restraints is shown in Figure B-2. The Abaqus beam model is shown in Figure B-3.

B-3

Finite Element Analysis Using Abaqus

Figure B-2 Restraint Layout

B-4

Finite Element Analysis Using Abaqus

Figure B-3 Abaqus Model

The results for the gravity case are shown in Table B-3. There is a difference shown for Guides G-8 through G-11. This difference is due to the fact that the valve is modeled as a rigid element in CAESAR II, but not in the Abaqus beam model. Therefore, Abaqus is predicting a bending force in that section of the pipe which increases the load on G-9 and G-10 and decreases the load on G-8 and G-11.

B-5

Finite Element Analysis Using Abaqus Table B-3 Results for Gravity Gravity Y-Force (lb) X-Axis Guides

Abaqus Node

Caesar Node

G-1

34

G-2

Abaqus

CAESAR

60

23

22

33

90

24

24

G-3

32

120

24

24

G-6

43

1060

17

17

G-7

42

1080

17

17

G-8

16

420

12

17

G-9

15

450

76

74

G-10

13

480

76

74

G-11

12

500

12

17

G-14

48

2080

11

11

G-15

38

2100

25

25

G-4

26

270

33

31

G-5

24

290

32

32

G-12

4

630

24

24

G-13

2

670

31

31

A-1

37

10

17

17

A-2

3

680

-4

-4

Z-Axis Guides

Anchors

Vertical Section Supports VS-1

29

180

52

53

VS-2

21

360

96

93

VS-3

7

560

111

108

Y-1

27

230

14

10

Y-2

23

328

6

6

Y-3

44

1020

36

36

Y-4

41

1118

36

36

Y-5

49

2050

29

29

Y-Support

The results for the thermal expansion case are shown in Table B-4. The agreement between Abaqus and CAESAR is excellent for this particular case. While both programs might handle the relatively large scale deflection due to thermal expansion differently, it appears the results end up being the same. B-6

Finite Element Analysis Using Abaqus Table B-4 Results for Thermal Expansion Thermal Y-Force (lb) Abaqus

CAESAR

G-1

-500

-510

G-2

122

121

G-3

-615

-618

G-6

5

4

G-7

4

4

G-8

255

260

X-Axis Guides

G-9

-43

-47

G-10

-43

-47

G-11

254

260

G-14

28

31

G-15

-8

-8

G-4

-45

-67

G-5

267

249

G-12

-284

-286

G-13

111

112

A-1

442

452

A-2

-53

-54

VS-1

-111

-133

VS-2

327

312

VS-3

10

5

Y-1

747

793

Y-2

-655

-636

Y-3

2

2

Y-4

6

4

Y-5

-209

-200

Z-Axis Guides

Anchors

Vertical Section Supports

Y-Support

The results for the seismic case are shown in Table B-5. CAESAR II underpredicted the forces resulting from the seismic case detailed in Chapter 4. Based on Figure 4-5 it seems that more nodes should have been placed in the CAESAR analysis. This is something that designers should be aware of when using any lumped mass analysis program. The natural frequencies calculated by Abaqus and CAESAR II are shown in Table B-6. B-7

Finite Element Analysis Using Abaqus Table B-5 Results for Seismic Analysis Seismic X-Force (lb) Caesar

Z-Force (lb)

Abaqus

Caesar

Abaqus

Caesar

G-1

218

165

4

3

G-2

2

5

10

6

G-3

87

65

23

11

G-6

43

41

92

59

G-7

41

41

88

58

G-8

207

204

47

24

X-Axis Guides

Abaqus

Y-Force (lb)

G-9

13

14

35

25

G-10

13

14

39

24

G-11

206

204

39

18

G-14

5

4

82

52

G-15

8

6

54

34

Z-Axis Guides G-4

164

65

30

13

G-5

159

86

39

10

G-12

44

33

27

10

G-13

66

29

6

6

A-1

74

10

222

167

4

2

22

10

3

1

23

11

47

30

147

99

34

26

VS-2

177

139

439

281

125

74

VS-3

137

111

203

203

78

35

Y-1

79

60

Y-2

304

198

Y-3

46

24

Y-4

32

20

Y-5

19

8

Anchors A-2 Vertical Section Supports VS-1

Y-Support

B-8

Finite Element Analysis Using Abaqus

Table B-6 Natural Frequencies Abaqus

CAESAR

Mode

frequency

Mode

frequency

1

1.43499

1

1.906

2

3.12814

2

3.549

3

3.42907

3

4.304

4

3.47339

4

4.423

5

5.44691

5

8.422

6

8.41883

6

9.836

7

8.84009

7

10.351

8

9.33047

8

10.83

9

9.58568

9

11.329

10

10.0486

10

11.737

11

11.9803

11

15.279

12

14.4327

12

15.85

13

15.2776

13

16.531

14

15.5904

14

17.036

15

15.7669

15

20.055

16

19.2821

16

22.038

17

20.0373

17

22.923

18

20.1901

18

23.722

19

20.5438

19

24.084

20

21.2177

20

24.272

21

21.514

21

25.137

22

22.2086

22

25.282

23

22.6629

23

26.459

24

22.9386

24

27.146

25

23.6985

25

28.179

26

24.2744

26

28.405

27

24.7447

27

28.985

28

25.8307

28

31.151

29

26.273

29

31.54

30

27.7447

30

32.574

31

28.2473

31

32.836

32

29.7155

32

34.148

33

31.5729

34

32.4389

35

32.6791

B-9

Finite Element Analysis Using Abaqus

A plot of the long term deflection due to gravity calculated by the Abaqus beam model is shown in Figure B-4. This shows a maximum deflection of 0.1”, which is greater than the 0.0175” calculated by CAESAR. It is possible that enough nodes were not placed inbetween the valves and the supports. Additionally, the valves were modeled as point masses in Abaqus on flexible pipe, whereas in CAESAR they were modeled as rigid elements. Therefore the Abaqus model overpredicts the weight because it includes a section of pipe where the valve rests, and it also overpedicts the valve’s flexibility. An more precise comparison can be performed with a single beam model.

Figure B-4 Long Term Deflection (in) Calculated by Abaqus

B-10

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