Unidirectional pipe support is free to move in one direction like +Y, +X, +Z, etc here the supports are free to move in +y, +x, and +z respectively. There are many piping codes and standards that could be used during a pipe stress analysis depending on the application (power, process chemical, gas distribution) and location (country or local jurisdiction). for steam generators or fire tube sections; Piping ≥ 6″ dia. Our customer's PID declares a number of pipe weldments to be stress relieved, but that's the only information they give. eval(ez_write_tag([[300,250],'whatispiping_com-mobile-leaderboard-1','ezslot_21',195,'0','0']));As per ASME code B 31.3 (Clause 302.3.5) the allowable displacement stress range (SA) can be given by the equation (Fig.2): Here, f= Stress range reduction factor and Sc=basic allowable stress at minimum metal temp, eval(ez_write_tag([[300,250],'whatispiping_com-narrow-sky-1','ezslot_23',615,'0','0']));Piping stresses can be reduced by various methods like, eval(ez_write_tag([[300,250],'whatispiping_com-mobile-leaderboard-2','ezslot_22',616,'0','0']));There are two types of loads which act on a piping system: Static loads and Dynamic Loads, Static loads are those loads that act very slowly and the system gets enough time to react against it. This stress tends to open-up the pipe wall and is caused by internal pressure. The coefficient of thermal expansion of a substance is 1.8 mm/m/Deg.F. Commentdocument.getElementById("comment").setAttribute( "id", "a7b31805373aa1c429b3ebba19373c5e" );document.getElementById("h6fa31e2a5").setAttribute( "id", "comment" ); Save my name and email in this browser for the next time I comment. "Residual Stress Relief in Post-Weld Heat Treatment." Piping stress analysis, in one way is the selection of proper supports and placing them in correct location to avoid detrimental stresses in the piping systems. This article will explain the basic points for Piping Stress Analysis. Limiting sagging & displacement within allowable values. )eval(ez_write_tag([[250,250],'whatispiping_com-banner-1','ezslot_3',662,'0','0'])); Following are the codes and standards used for Piping stress analysis of process piping:eval(ez_write_tag([[250,250],'whatispiping_com-box-4','ezslot_1',635,'0','0'])); Sustained Stresses are the stresses generated by sustained loads. The extent of relaxation of the residual stresses depends on the material type and composition, the temperature of PWHT and the soaking time at that temperature. To learn the above-mentioned points in details refer to the following video: Few more piping resources for you.. The code does not explicitly explain the stresses generated due to vibration. Dear Anup, I have one question ? R&R STRESS RELIEVING SERVICE LTD Heat Treating Specialists. This website is my first venture into the world of blogging with the aim of connecting with other piping engineers around the world. Consultant at DOW chemicals int.pvt.Ltd. Wind and earthquake effects shall be checked in formal computer analysis, if experienced stress engineers decide it necessary. Pressure relief devices (relief valves, rupture discs) shall be accessible and installed for easy removal from deck or permanent platform. Package Design Engineer at Fichtner Consulting Engineers India P Ltd.  Highly Critical Lines (Steam turbine, Compressor connected pipelines): By Computer Analysis,  Moderately Critical Lines (AFC connected lines): By Computer Analysis,  Low critical Lines: Visual/Simple Manual Calculation/Computer analysis and, Input Collection for Piping Stress Analysis, Interpreting the results and suggesting changes if required, Providing Recommendation based on Analysis, Line Designation Table (LDT) or Line List And P&ID from Process, Equipment GA and Other detailed drawings from Mechanical, Process flow diagram/datasheet if required from the process, PSV/ Control Valve GA and Datasheet from Instrumentation, Soil Characteristics from civil for underground analysis. Stress relief at temperatures below 750°F (400°C) is an acceptable industry practice, but results in only a modest level of stress reduction. Proceedings of the ASME 2008 Pressure Vessels and Piping Conference . 2, September 1997. 3. The piping system must have enough flexibility to handle the expansion. Examples of dynamic loads are shown in Fig.2. Failure against various loading in the life cycle. 2, where only the right half of the pipe is shown, the left half being exactly symmetric. Piping Stress Analysis is also termed as Piping Flexibility Analysis.eval(ez_write_tag([[580,400],'whatispiping_com-medrectangle-3','ezslot_2',626,'0','0'])); eval(ez_write_tag([[300,250],'whatispiping_com-medrectangle-4','ezslot_4',658,'0','0']));Stress Analysis of Critical piping systems are performed to ensure the following objectives. Stress relieving is accomplished by heating the material uniformly to a predetermined temperature below the lower critical temperature, holding at that temperature, and cooling slowly to ambient temperatures. Limiting nozzle loads of the connected equipment within allowable values. No site is beyond our reach. Basic Piping Stress Analysis Articles Piping Stress Analysis using Caesar II Piping Stress Analysis using Start-Prof Piping Design and Layout Basics Piping Materials Basics Tutorials on Piping Design Softwares. Displacement Stress Range due to thermal expansion is calculated based on equation SE per equation 17 from ASME B31.3( clause 319.4.4). Stress relieving offers several benefits. Removing or reducing the residual stresses generated by welding is required for improving the dimensional stability of weldments. 1/3rd of UTS of material at room temperature.  Stress Package final documentation for records, Rohr-2 by SIGMA Ingenieurgesellschaft mbH (Germany). The necessity for PWHT depends on the material and the service requirements. Mechanical stress relieving 177 r P 1-~ 1I I i _"~j I 1 Solution domain radius of pipe outer surface; ri is the radius of pipe inner surface; and ze the half pipe length. Wind loading shall be considered for sizes 24NB and over, for heights more than 10 m above grade where not shielded. Only surface roughness of the contact point does. This article will explain the basic points for Piping Stress Analysis. After a hold time, the part is control-cooled to between 600 and 800 degrees. Piping System - It covers the overall systems of pipes and piping components, e.g. Can you please add step by step manual pipe stress calculation for any piping system on your blog. These metallurgical changes can reduce the hardness of the as-welded structure, improving ductility and reducing the risks of brittle fracture. Thermal expansion and contraction happens when a pipe heats up and cools down. It will be a great help for a beginner to understand all the steps carried out during pipe stress analysis. Calculation of the total strength of the static pressure vessels and tanks made of metal and nonmetal (including composite) materials. fittings, valves, nozzles and supports, that are employed to transfer liquid, gas, steam, etc. Circumferential principal stress, some times called Hoop or tangential stress, acts along the circumference of the pipe. Just want to say your article is as astounding. SIF( Stress Intensification Factor): This is the ratio of the maximum stress intensity to the nominal Stress. Exceeding sustain allowable stress value causes catastrophic failure of the system.eval(ez_write_tag([[300,250],'whatispiping_com-leader-2','ezslot_16',601,'0','0'])); As per ASME B 31.3, (clause 302.3.5) “ The sum of the longitudinal stresses, SL, in any component in a piping system, due to sustained loads such as pressure and weight, shall not exceed “Sh“. On-Site Stress Relieving Services, LP. As metal heat treating specialists, we know that you need quick turnarounds and quality work, which is why our professional technicians typically provide a 24 hour turnaround and, depending on scope of work and cycle times, even same day service. Drawing, forming and machining induce stresses in materials. Which code do we refer to for Refinery Piping? Thanks a million and please carry on the rewarding work. Piping Stress Analysis is the most important activity in Piping Design. We are available 24 hours a day, 7 days a week. Thanks and best regards. Stress relieving and annealing also improve the part’s machinability and promote tighter flatness standards. 2. Few nice points has been discussed on this post in linkedin page. How does this facilitae accuracy with the effect of friction factor when we are working with srface contact for supports resting flat.. By Anup Kumar Dey: Evaluation of durability and service life of pressure vessels and tanks under cyclic variation of the parameters of internal and / or external environment. caused by the conduct referred to as stress relief annealing. It’s important to understand the various types of pipe stresses, the process, and other items related to pipe stress analysis for best practices in performing a pipe stress analysis. Detrimental effects include distortion, temper embrittlement, over-softening and reheat cracking, which means that control of heating and cooling rates, holding temperature tolerances and the times at temperature are extremely important, and must be carefully controlled in order to realise the full benefit of the process. After the soaking time the components should be cooled down slowly in the furnace or in air. Checking the completeness of the piping system received as a stress package. Dear Anup, Hello, Pipe stress analysis is recommended by industry standards for the following applications: Piping ≥ 3″ dia. (Design Temp= 350 degree C and Corrosion allowance= 1.6 mm). Calculation of the overall stress-strain state of piping systems made from both metal and non-metal (including composites) materials, for given values of temperature, pressure, weight of the internal environment, self-weight of the structure, taking into account the kinematic conditions, as well as the friction in the bearings. When two or more principal stresses act at a point on a pipe, a shear stress will be generated. Below procedure defines the basis to establish piping critical line list from line list, P & I Diagrams and Piping Specification. See further information about Materials and Corrosion Management and how we can help with PWHT in the power generation sector. Do you have any general guidelines for not critical line supporting. I am very much passionate about blogging and always tried to do unique things. The temperature at which stress relieving takes place is determined by the transformation temperature, which can be a different figure for various steel alloys. The pressure thickness (t) of a straight pipe can be obtained as per ASME B31.3 from the equation (Clause 304.1.2) mentioned in Fig.1: Click here to learn pipe thickness calculation in details. Do you have any mathcad calculation for Piping stress analysis calculation? That is, yielding or deformation of the part reduces the stress. Stress relief annealing of seamless steel pipe: annealed to remove stress and residual stress in the casting of memory due to plastic deformation processing, welding, etc. The stress is caused by the pipe pushing against some fixed restraint. Codes and Standards specify minimum requirements for safe design and construction (i. e. provides material, design, fabrication, installation, and inspection requirements. From the outline drawing, we need to take the dimensions to some fixed point. Avoiding excessive flexibility and also high loads on supporting structures. The Piping Specifications provide materials, fittings, and fasteners, which meet the pressure design requirements of B31.3.  Datasheets for Special Supports like Sway brace, Struts, Snubbers, etc. As in where to provide guide and anchors for lines which is not critical for stress analysis. and ≥ 350 °F Streamline Stress Relief "Over the years welders have perfected techniques to relieve stress and minimize distortion: preheating in an oven or with a torch, using heat blankets, and when necessary sending parts to an oven for postweld heat treatment. Expansion Loops, Offsets, Inclusion of elbows to change direction. Thermal stresses are “secondary stresses” because they are self-limiting. 1/3rd of Ultimate Tensile Strength (UTS) of Material at operating temperature. Once, pipes are routed following design guidelines, those needs to be verified by piping stress analysis to ensure those will work smoothly throughout its design life. Sachin Laxman Ratnaparkhi Mobile no 9082016401,9867242493. For structural grade materials basic allowable stress=0.92 times the lowest value obtained from 1 through 5 above. It does not reduce when used as point contact. Soaking time is about one to two hours. By Mr Rao:  Unmatched Quality & Workmanship. During modeling of the above ele… Occasional Loads due to the wind, seismic disturbances, PSV discharge, etc. is a specialty industrial heat treating company offering portable on-site services to oil & gas processing facilities, refinery and petrochemical plants, power generation plants, fabricating companies, manufacturing companies, and off shore equipment companies. In stress relieving we heat a material to a specific temperature; hold it at this temperature for a specified amount of time in order to reduce or eliminate residual stresses; and then cool it at a slow enough rate to prevent these stresses from redeveloping. Pressure Stresses are taken care of by calculating and selecting proper pipe thickness. Other factors that influence the need for PWHT are the welding parameters and the likely mechanism of failure. It will be easy for a beginner to understand how the pipe stress analysis is carried out for any piping system and what all steps and checks need to be carried out in the safe design of a piping system. My self sr.piping designer, and I am retired from MNC company in 2015. Calculation of the strength of the joints, bends, tees, valves elements of pipeline systems involving 3D-geometric and finite element modeling. Dear Mr.Anup, These are self-limiting or self-relenting. 3. Your email address will not be published. 3.5. Pl.send me PDF of these books if you have this books. eval(ez_write_tag([[250,250],'whatispiping_com-large-leaderboard-2','ezslot_7',612,'0','0']));Resistive force arising out of sustained stresses balance the external forces keeping the system in equilibrium. Where Sh=Basic allowable stress at the metal temperature for the operating condition being considered. What are the various types of loads which cause stresses in the piping system? Well with your permission let me to grab your feed to keep updated with forthcoming post. Volume 6: Materials and Fabrication, Parts A and B . Sachin Laxman Ratnaparkhi. link to Slug Catcher: Definition, Types, Selection & Design Steps, Governing Codes and Standards for Pipe Stress Analysis, Basic Allowable Stress/ Pipe Material Stress, Work Flow Diagram for Pipe Stress Analysis, Basics of Piping Stress Analysis Tutorial Video. In some standards, PWHT is mandatory for certain grades or thicknesses, but where there is an option, cost and potential adverse effects need to be balanced against possible benefits. What is its value in mm/mm/Deg.C.? The extent of relaxation of the residual stresses depends on the material type and composition, the temperature of PWHT and the soaking time at that temperature. Piping Stress Analysis is the most important activity in Piping Design. Determination hydrodynamic loads “facilities” of fluid flow. Pipe stress analysis is normally performed in four steps as listed below: Whether to accept the system or to suggest necessary changes in layout and supporting to make the system acceptable as per standard requirements. For modeling the pump we require vendor general arrangement drawing or outline drawing. Stress relieving at 800°F to 1700°F (425°C to 925°C) significantly re-duces residual stresses that otherwise might lead to However, bi-directional piping support arrests movement in both direction like Y, X, or Z supports. Once, pipes are routed following design guidelines, those needs to be verified by piping stress analysis to ensure those will work smoothly throughout its design life. In ceaser analysis all supports are considered as point contact which is not true practically. In addition to reduction and redistribution of residual stresses during the welding process, PWHT at higher temperatures permits some tempering, precipitation or ageing effects to occur. Copyright © 2021 TWI Ltd. All rights reserved. 301.2.2 - Required Pressure Containment or Relief Piping systems are designed to either safely contain or relieve the maximum pressure As for example if the contact is between CS to CS the friction factor is normally 0.3 or 0.4. Let us take the example of the outline drawing shown in figure 2. Post Weld Heat Treatment (PWHT), or stress relief as it is sometimes known, is a method for reducing and redistributing the residual stresses in the material that have been introduced by welding. connected to rotating equipment; Piping ≥ 3″ dia. Stress relieving is applied to both ferrous and non-ferrous alloys. One cannot see the formulas and methodology used by any software to analyse the piping system. These loads are present continuously throughout plant life. MYD series of induction heating system are used for weld, bending, piping, coating, fitting, stress relief, pre-weld heat and post-weld heat treatment Model and Technical Parameters Model At node 5020 we will provide fixed anchor. and at temperatures ≤ -20°F; Piping ≥ 4″ dia. My proposals for the calculations on the strength of pipelines, tanks and pressure vessels. Providing Supports at suitable span to reduce Weight (Sustained) stresses. National Structural Integrity Research Centre, Post Weld Heat Treatment (PWHT), or stress relief as it is sometimes known, is a method for reducing and redistributing the residual stresses in the material that have been introduced by, Granta Park, Great Abington, Cambridge, CB21 6AL, UK, About postweld heat treatment/stress relief heat treatment. Parts may be stress relieved during manufacturing to promote dimensional stability or … Determination of displacements and stresses in the individual fragments of the pipeline circuit different geometry in the presence of poles at a given temperature, pressure, weight of the internal environment on the basis of three-dimensional modeling of cladding and finite elements. Temp, Fluid density, Material, Line Size and. Thanks and best regards; As per ASME B31.3, clause 302.3.6 “The sum of the longitudinal stresses, SL, due to sustained loads, such as pressure and weight, and of the stresses produced by occasional loads, such as wind or earthquake should be ≤ 1.33 times the basic allowable stress, Sh”. If necessary, stress relieving can be performed in a furnace with protective gas, to protect surfaces from oxidation. Sir, horizontal force applied will be friction factor * normal reaction force.this horizontal force will be applied against movement of pipe axis.hence place of this force will be different. What is the value of f stress range reduction factor? The... Slug Catcher: Definition, Types, Selection & Design Steps. Stress Relieving - Uniform heating … Kindly answer. Currently, I work in a reputed MNC as a Senior Piping Stress Engineer. Follow this link to access those: https://www.linkedin.com/groups/http-wwwwhatispipingcom-basicsofpipestressanalysis-59422.S.5970562625166127107?view=&item=5970562625166127107&type=member&gid=59422&trk=eml-group_discussion_new_comment-discussion-title-link&midToken=AQH3kT0n6EEJKA&fromEmail=fromEmail&ut=0OXgM9Rbpz56E1. Piping design, layout and stress analysis L-002 Rev. Limiting stresses below code allowable. In some steels, however, ageing/precipitation processes can cause deterioration in the mechanical properties of the steel, in which case, specialist advice should be taken on the appropriate times and temperatures to use. between the equipment such as tanks, pumps, vessels and so forth. Estimation of seismic stability of pipeline systems as a whole, as well as separate areas and support units. Stress-relieving is the process generally specified after welding of most materials. How can we calculate the value of f? In extre… Could someone with some experience in stress relieving carbon steel process piping give me some insight on the B31.3 code requirements for this process? It contains sufficient buffer volume to handle the largest expected slug from the... Hi There! Mobile Units are 6 to 24 control zones and completely self-contained with power generators, cables, resistance elements, thermocouples and instrumentation. Stress Relieving – Soak Temperature 1100-1200˚ Stress Relieving is a heat treating process that consists of heating the steel to a temperature below the critical range to relieve the residual stresses resulting from hot rolling, welding , shearing, or gas cutting. Now SA=f( 1.25SC+ 0.25 Sh) By Mr. SATISH KUMAR But if we can make the surface polished then the same will reduce. Calculate the minimum pipe thickness of a seamless 10” NB A106- Gr B material with a design pressure of 20 bars. Occasional Stresses are generated by occasional loads such as Wind, seismic, PSV discharge, etc. Carbon steels may be stress relieved by holding a temperature at 1100 to 1250°F (600 to 675°C) for 1 hour per inch (25 mm) of thickness. eval(ez_write_tag([[250,250],'whatispiping_com-large-mobile-banner-1','ezslot_9',614,'0','0']));This SE value shall not exceed SA value where SA= Allowable Displacement Stress Range. Topic Welding Industry / Inspection & Qualification / Stress Relieving ??? Your email address will not be published. Seismic resistance of tanks and pressure vessels, including partially filled with liquid – allowance for the interaction design with a liquid using “technology” – coupled Eulerian-Lagrangian (CEL) analyses. However for the convenience of my readers i am reproducing those here. Sir, In my opinion The point contact and surface contact does not affect the friction factor. We prioritize your schedule and your budget. Is there any criteria or any table to select it ? Modeling the piping system in Caesar using parameters from stress Iso. Plot Plan for finding HPP elevation and equipment orientation. Note one common thread among all … Providing Flexibility to reduce piping expansion stresses generated by thermal loading Eg. Filling the design parameters (Design temp, pressure, Ope. Improving the machinability and dimensional stability after machining. Stress relieving is a heat treatment process in which a metal is subjected to a constant temperature that is below the metal's critical temperature, followed by controlled cooling. The designer must address all design conditions. Through this platform, I will share my experiences and knowledge with you in an innovative way. The typical stress-relieving procedure requires a step to 600 to 800 degrees F, followed by a ramp or controlled temperature rise to a soak temperature of approximately 1,250 degrees. 3:eval(ez_write_tag([[300,250],'whatispiping_com-netboard-2','ezslot_27',197,'0','0'])); Caesar II by Hexagon is the most popular and widely used international pipe stress analysis software. I am a Mechanical Engineer turned into a Piping Engineer. In certain applications, internal residual stresses can sum up with those generated by externally applied loads. Subscribe to our newsletter to receive the latest news and events from TWI: Post Weld Heat Treatment (PWHT), or stress relief as it is sometimes known, is a method for reducing and redistributing the residual stresses in the material that have been introduced by welding. Stress Relieving/ Post Weld Heat Treatment help’s restore the original materials mechanical properties to what it was before welding took place. Table C-1M provides thermal co-efficient values in the metric system. Temp, Min. A slow cooling speed is important to avoid tensions caused by temperature differences in the material, this is especially important when stress relieving larger components. Because basic Carbon steel is a much more forgiving material and much more ductile than chrome steels, less likely to harden after welding unless fairly thick sections are used (12mm+), PWHT is not required. Design adequacy for the pressure of the carrying fluid. Analyzing the system and obtaining results. Stresses above the yield point can be acceptable, however, o… So be with me for the next couple of years! From the above drawing, we can get the dimensions for elements 10-5000 as 8.5 inches and element 5000-5020 as 6.19 inches. SIF factors for different components can be obtained from Appendix D of ASME B31.3. Quenched and tempered (Q&T) steels have the PWHT temperature limited to below the original tempering temperature of the steel, as higher temperatures can change the microstructure of the base material from what was expected or required. The interaction of the Piping Stress team with other disciplines in any organization is shown in Fig. These loads act in a piping system for a very small period of time, usually less than 10% of the total working period. Higher stresses are allowed than in the primary case because of this self limiting behavior. The thermal Co-efficient “B” of table C-1 denotes total linear thermal expansion between 70 degrees F to Indicated temp (unit=in/100ft). How to select the value of stress reduction factor f? Pressure, Weight). S tress relieving is a form of post weld heat treatment. Required fields are marked *. As discussed above in the section on design pressure, the piping system must either be designed to safely contain the maximum, expected, possible pressure, considering such factors as failure of control devices and dynamic events such as surge, or be provided with over pressure protection, such as a safety relief valve.This basic requirement is provided in para. Examples of static loads are shown in Fig.1, eval(ez_write_tag([[300,250],'whatispiping_com-narrow-sky-2','ezslot_24',617,'0','0']));On the other hand, dynamic loads act so quickly that the system does not get enough time to react against it. All rotary equipments are modeled as a weightless rigid body in Caesar II. 2/3rd of Yield Tensile Strength (YTS) of material at operating temperature. Various types of supports are used in the piping and pipeline industry like, In piping stress analysis supports can be classified in two groups. The stress relieving temperature is normally between 550 and 650°C for steel parts. Expansion stresses are generated when the free thermal growth due to temperature change is restricted. Welcome to my space, I am Anup Kumar Dey, an experienced piping engineer from the last 15 years. (e.g. The energy costs are generally significant due to the high temperatures and long times involved, but costs associated with time delays may be more important. Change in length of a pipe of length L due to temp change (ΔT) is given by ΔL=L α ΔT  Here, α =Co efficient of thermal expansion = change in length of unit length element due to unit change in temp. The calculation of the strength of the underground part of the pipeline at a given temperature and pressure of the internal environment, taking into account not elastic properties of the soil (model Mohr-Coulomb, Drucker-Prager, Cam-Clay, Cap-model), the depth of the pipe, soil temperature, pipe friction on the ground. Stress relieving steel is a heat treatment process that involves subjecting a steel workpiece or part to a specific temperature for a particular amount of time. Boundary conditions for thermal and residual stress analysis is also shown in Fig. Continental Stress can be anywhere, anytime, economically. A commonly used guideline for PWHT is that the joint should be soaked at peak temperature for 1 hour for each 25mm (1 inch) of thickness, although for certain cases a minimum soak time will be specified. Longitudinal Principal stress, LPS = PD/4T A project kickoff meeting is the first meeting between a project team and the client or stakeholder/sponsor of a project to discuss the project's basic elements and overall planning activities. Piping Stress Analysis - Wind and Earthquake Effects 3.5.1. Two “α” values (denoted by A and B) in Code (Table C-1 and C-1M in ASME B31.3 Appendix C): The thermal Co-efficient “A” of Table C-1 denotes the mean coefficient of linear thermal expansion between 70 degrees F to indicated temp (μin/in/. The vibration problems are solved by engineering judgment and experience. Aim towards an optimal design for both piping and structure. SA=f(1.225Sc +0.25Sh) Dear sir First of all thank you for creating the website I am a Mechanical Engineer studying Piping Stress Analysis. Relief valves shall be installed with the stem in the vertical position. There are a few other pipe stress analysis software are available in the market which are used as alternatives to Caesar II softwares like, Pipe Stress Analysis will be incomplete without a few words about piping supports. Dear sir Good day.First of all thank you for the website.Now the point. I would like to know extra knowledge of stress analysis books are available in the market, Relieving the residual stresses to safe levels reducing the chances of premature failure by brittle fracture, fatigue or stress corrosion. Specifications in Appendix A. 100% of average stress for a creep rate of 0.01% per 1000 hr. The clearness in your post is just cool and i could assume you’re an expert on this subject. Determination of pipes, joints, fittings elements with hydraulic shock. If possible kindly send your mobile nos.I wish to talk to you if you permit . Which standard governs the design of Pumps? What is a Slug Catcher?A slug catcher is a piece of static equipment in the form of a vessel or piping network.

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