MINISTY OF HIGHER EDUCATION AINSHAMS UNIVERSITY FACULTY OF ENGINEERING RD 3 YEAR MECHATRONICS DEPARTMENT
Mechatronics (1) Pipelines stress analysis Supervised By : Dr Wagdy El-Desouki Abdel-Ghany
Group: 5 Sec. 1 Sec. 1 Sec. 1 Sec. 2 Sec. 2 Sec. 2
احمد عبد الشكور عبد الفتاح الحسينى عالم احمد عبد العزيز الركايبى شريف مصطفى محمد جمال الدين السيد الطوخى محمود سليمان محمود عجالن محمود يحيى محمد امين جاد يحيى زكريا محمد عبد هللا سعيد Submitting date 06/2011
Contents 1
Introduction ............................................................................................................ 4
2
Objective and scope .............................................................................................. 6
3
Methodology ........................................................................................................... 7
4
5
3.1
Classification of loads and failure modes ........................................................................................................7
3.2
Primary Loads ..................................................................................................................................................7
3.3
Secondary Loads ..............................................................................................................................................8
3.4
Static vs. Dynamic loads ................................................................................................................................10
3.5
Sustained vs. Occasional loads ......................................................................................................................12
3.6
The Stresses ...................................................................................................................................................12
Normal and Shear Stresses from Applied Load ................................................ 14 4.1
Axial Load ......................................................................................................................................................15
4.2
Internal / External Pressure ...........................................................................................................................16
4.3
Bending Load .................................................................................................................................................18
4.4
Shear Load .....................................................................................................................................................22
4.5
Torsional Load ...............................................................................................................................................22
Allowable stresses & theories of Failure ........................................................... 23 5.1
Maximum Stress Theory ................................................................................................................................25
5.2
Maximum Shear Theory ................................................................................................................................27
5.3
Octahedral Shear Theory ...............................................................................................................................28
6
Design under Secondary Load ........................................................................... 28
7
Piping Codes: ....................................................................................................... 29 7.1
Limits of stresses set by code ANSI / ASME B 31.3 ........................................................................................30
2
7.2
ASME B31.1 power piping .............................................................................................................................31
7.3
ASME B31.3 Process Piping ...........................................................................................................................46
7.4
ASME B31.9 Building Services Piping.............................................................................................................59
Flexibility analysis ............................................................................................... 60
8
8.1
Methods of Flexibility Analysis ......................................................................................................................61
Pipe supports ....................................................................................................... 63
9
9.1
Introduction ...................................................................................................................................................63
9.2
Pipe supports standards ................................................................................................................................64
9.3
Types of supports ..........................................................................................................................................64
9.4
Pipe system support designing ......................................................................................................................75
Buried Pipe Design .............................................................................................. 83
10
Introduction and Overview .......................................................................................................................83
10.2
Soil Mechanics ..........................................................................................................................................85
10.3
Strength of Materials ................................................................................................................................86
10.4
Water Systems ..........................................................................................................................................89
10.5
Design for Value .......................................................................................................................................90
11
10.1
Conclusion.......................................................................................................... 105
3
1 Introduction Pipes are the most delicate components in any process plant. They are also the busiest entities. They are subjected to almost all kinds of loads, intentional or unintentional. It is very important to take note of all potential loads that a piping system would encounter during operation as well as during other stages in the life cycle of a process plant. Ignoring any such load while designing, erecting, hydro-testing, start-up shut-down, normal operation, maintenance etc. can lead to inadequate design and engineering of a piping system. The system may fail on the first occurrence of this overlooked load. Failure of a piping system may trigger a Domino effect and cause a major disaster. Stress analysis and safe design normally require appreciation of several related concepts. An approximate list of the steps that would be involved is as follows. 1. Identify potential loads that would come on to the pipe or piping system during its entire life. 2. Relate each one of these loads to the stresses and strains that would be developed in the crystals/grains of the Material of Construction (MoC) of the piping system. 3. Decide the worst three dimensional stress state that the MoC can withstand without failure 4. Get the cumulative effect of all the potential, loads on the 3-D stress scenario in the piping system under consideration. 5. Alter piping system design to ensure that the stress pattern is within failure limits. The goal of quantification and analysis of pipe stresses is to provide safe design through the above steps. There could be several designs that could be safe. A piping engineer would have a lot of scope to choose from such alternatives, the one which is most economical, or most suitable etc. Good piping system design is always a mixture of sound knowledge base in the basics and a lot of ingenuity.
4
Pipes are required for carrying fluids. These fluids can be of various states of matter. Gaseous fluids (like LP), Liquid Fluids (like Water) and Solid or Semi-solid (like plastic pellets). The pipes in Process Industry like in Reliance are used for transferring fluids at higher temperature and pressure. The various processes in a Process plant cause the liquids to be pressurized and to be heated up. Thus the liquids passing through the pipes attain a high pressure and/or a high temperature. When a metal is heated it expands. If this metal of pipe is allowed to expand freely, there is no overstress in the same. But suppose the free movement is restricted by any means, stress is introduced in the system. The case becomes more complicated by considering weight of the pipe, the insulation, weights of the valves, flanges and other fittings and the pressure of the fluids that is flowing through the piping. So the task of the Stress Engineer is 1) To select a piping layout with an adequate flexibility between points of anchorage to absorb its thermal expansion without exceeding allowable material stress levels, also reacting thrusts & moments at the points of anchorage must be kept below certain limits. 2) To limit the additional stresses due to the dead weight of the piping by providing suitable supporting system effective for cold as well as hot conditions. Piping systems are not self supporting and hence they require pipe supports to prevent from collapsing. Pipe supports are of different types like Rest, Guides, Line stops, Hangers, Snubbers, and Struts. Each type of pipe support plays a vital role in supporting the pipe system. Pipe supports are desirable to reduce the weight, wind and where possible, expansion and transient effects, so that piping system stress range is not excessive for the anticipating cycles of operation, us avoiding fatigue failure. Limiting the line movement at specific locations may be desirable to protect sensitive equipment, to control vibration or to resist external influences such as wind, earthquake, or shock loadings.
All these objectives are achieved by:5
1) Limiting the sagging of the piping system within allowable limits ( i.e. In Sustain case the max vertical movement should be less than 10mm ). 2) Directing the line movements so as protect sensitive equipments against overloading (i.e. nozzle loads are always kept under the allowable nozzle loading provided by the vendor). 3) Resisting pipe system to collapse in case of earthquake, wind or shock loadings.
2 Objective and scope With piping, as with other structures, the analysis of stresses may be carried to varying degrees of refinement. Manual systems allow for the analysis of simple systems, whereas there are methods like chart solutions (for three-dimensional routings) and rules of thumb (for number and placement of supports) etc. involving long and tedious computations and high expense. But these methods have a scope and value that cannot be defined as their accuracy and reliability depends upon the experience and skill of the user. All such methods may be classified as follows: 1. Approximate methods dealing only with special piping configurations of two-, three or four-member systems having two terminals with complete fixity and the piping layout usually restricted to square corners. Solutions are usually obtained from charts or tables. The approximate methods falling into this category are limited in scope of direct application, but they are sometimes usable as a rough guide on more complex problems by assuming subdivisions of the model into anchored sections fitting the contours of the previously solved cases. 2. Methods restricted to square-corner, single-plane systems with two fixed ends, but without limit as to the number of members. 3. Methods adaptable to space configurations with square corners and two fixed ends. 4. Extensions of the previous methods to provide for the special properties of curved pipe by indirect means, usually a virtual length correction factor.
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3 Methodology 3.1 Classification of loads and failure modes Pressure design of piping or equipment uses one criterion for design. Under a steady application of load (e.g. pressure), it ensures against failure of the system as perceived by one of the failure theories. If a pipe designed for a certain pressure experiences a much higher pressure, the pipe would rupture even if such load (pressure) is applied only once. The failure or rupture is sudden and complete. Such a failure is called catastrophic failure. It takes place only when the load exceeds far beyond the load for which design was carried out. Over the years, it has been realized that systems, especially piping, systems can fail even when the loads are always under the limits considered safe, but the load application is cyclic (e.g. high pressure, low pressure, high pressure, ..). Such a failure is not guarded against by conventional pressure design formula or compliance with failure theories. For piping system design, it is well established that these two types of loads must be treated separately and together guard against catastrophic and fatigue failure. The loads the piping system (or for that matter any structural part) faces are broadly classified as primary loads and secondary loads. The failure of the piping system may be sudden failure due to onetime loading or fatigue failure due to cyclic loading. The sudden failure is attributed to primary loadings and the fatigue failure to secondary loading.
3.2 Primary Loads These are typically steady or sustained types of loads such as internal fluid pressure, external pressure, gravitational forces acting on the pipe such as weight of pipe and
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fluid, forces due to relief or blow down pressure waves generated due to water hammer effects. The last two loads are not necessarily sustained loads. All these loads occur because of forces created and acting on the pipe. In fact, primary loads have their origin in some force acting on the pipe causing tension, compression, torsion etc leading to normal and shear stresses. A large load of this type often leads to plastic deformation. The deformation is limited only if the material shows strain hardening characteristics. If it has no strain hardening property or if the load is so excessive that the plastic instability sets in, the system would continue to deform till rupture. Primary loads are not self-limiting. It means that the stresses continue to exist as long as the load persists and deformation does not stop because the system has deformed into a no-stress condition but because strain hardening has come into play. In short •
Primary loads are usually force driven (gravity pressure, spring forces, relief valve, fluid hammer etc.)
•
Primary loads are not self-limiting. Once plastic deformation begins it continues till the failure of the cross section results.
•
Allowable limits of primary stresses are related to ultimate tensile strength.
•
Primary loads are not cyclic in nature.
•
Design requirements due to primary loads are encompassed in minimum wall thickness requirements.
3.3 Secondary Loads Just as the primary loads have their origin in some force; secondary loads are caused by displacement of some kind. For example, the pipe connected to a storage tank may be under load if the tank nozzle to which it is connected moves down due to tank settlement. Similarly, pipe connected to a vessel is pulled upwards because the vessel nozzle moves up due to vessel expansion. Also, a pipe may vibrate due to vibrations in the
8
rotating equipment it is attached to. A pipe may experience expansion or contraction once it is subjected to temperatures higher or lower respectively as compared to temperature at which it was assembled. The secondary loads are often cyclic but not always. For example load due to tank settlement is not cyclic. The load due to vessel nozzle movement during operation is cyclic because the displacement is withdrawn during shut-down and resurfaces again after fresh start-up. A pipe subjected to a cycle of hot and cold fluid similarly undergoes cyclic loads and deformation. Failure under such loads is often due to fatigue and not catastrophic in nature. Broadly speaking, catastrophic failure is because individual crystals or grains were subjected to stresses which the chemistry and the physics of the solid could not withstand. Fatigue failure is often because the grains collectively failed because their collective characteristics (for example entanglement with each other etc.) changed due to cyclic load. Incremental damage done by each cycle to their collective texture accumulated to such levels that the system failed. In other words, catastrophic failure is more at microscopic level, whereas fatigue failure is at mesoscopic level if not at macroscopic level. In short •
Secondary loads are usually displacement driven (Thermal expansion, Settlement, Vibration etc.)
•
Secondary loads are self-limiting i.e. the loads tends to dissipate as the system deforms through yielding.
•
Allowable loads for secondary stresses are based upon fatigue failure modes.
•
Secondary loads are cyclic in nature (expect settlement).
•
Secondary application of load never produces sudden failure and sudden failure occurs after a number of applications of load.
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3.4 Static vs. Dynamic loads Static loads are those loads applied on to the piping system so slowly that the system has time to respond, react and also to disturb the load. Hence, the system remains in equilibrium. The examples of such loadings are the thermal expansion, weight etc. The dynamic load changes so quickly with time that the system will have no time to distribute the load. Hence the system develops unbalanced forces. The examples of Dynamic loadings are wind load, earthquake, fluid hammer etc. these can be categorized in to mainly three types:Random: In this type of loading the load changes unpredictably with time. The major loads covered under this type are :• Wind load: In most of the cases analysis is done using static equivalent of dynamic model. This is achieved by increasing the static loading by a factor to account for the dynamic effects. • Earthquake: Here again the analysis is done using static equivalent of a dynamic loading model. This is again is approximate. Harmonic: In harmonic type of profile, the load changes in magnitude and direction in a sine profile. The major loads covered under this are:• Equipment Vibration: This is mainly caused by the eccentricity of the equipment drive shaft of the rotating type of equipment connected to the piping.
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• Acoustic Vibration: This is mainly caused by change of fluid flow condition within pipe i.e.from laminar to turbulent e.g. Flow through orifice. Mostly these vibrations follow harmonic patterns with predictable frequencies based on flow conditions. Pulsation: This type of loading occurs due to flow from reciprocating pumps, compressors etc. if this type of profile the loading starts from zero to some value, remains there for certain period of time and then comes back to zero. The major types of loads covered under this are:• Relief valve outlet: When the relief valve opens the flow raises from zero to full value over the opening time of the valve. This causes a jet forces and this remains until the full venting is achieved to overcome the over pressure situation and then valve closes bringing down the force over the closing time to valve. • Fluid hammer: If the flow of fluid is suddenly stopped due to pump trip or sudden closing of valve, there will compression of fluid at one side and relaxation at the other side. This wave propagates causing pulsation flow. Slug flow: This happens mainly due to multi phase flow. In general when fluid changes direction in a piping system, it is balanced by net force in the elbow. This force is equal to change in momentum with respect to time. Normally this force is constant and can be absorbed through tension in pipe wall, to be passed on to adjacent elbow which may have equal and opposite load and gets nullified. Hence, these are normally ignored. However, if density of fluid velocity changes with time similar to slug of liquid in a gas system, this momentum load will change with time as well leading to dynamic load.
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3.5 Sustained vs. Occasional loads The loads on the piping system which are steady and developed due to internal pressure, external pressure, weight etc. affecting the structure design of the piping component are called the sustained loading. These loadings develop longitudinal, shear or hoop stresses in the pipe wall. These could be either tensile or compressive in nature.
3.6 The Stresses The MoC of any piping system is the most tortured non-living being right from its birth. Leaving the furnace in the molten state, the metal solidifies within seconds. It is a very hurried crystallization process. The crystals could be of various lattice structural patterns such as BCC, FCC, HCP etc. depending on the material and the process. The grains, crystals of the material have no time or chance to orient themselves in any particular fashion. They are thus frozen in all random orientations in the cold harmless pipe or structural member that we see. When we calculate stresses, we choose a set of orthogonal directions and define the stresses in this co-ordinate system. For example, in a pipe subjected to internal pressure or any other load, the most used choice of co-ordinate system is the one comprising of axial or longitudinal direction (L), circumferential (or Hoope's) direction (H) and radial direction (R) as shown in figure. Stresses in the pipe wall are expressed as axial (SL), Hoope's (SH) and radial (SR). These stresses which stretch or compress a grain/crystal are called normal stresses because they are normal to the surface of the crystal. But, all grains are not oriented as the grain in Figure 1. In fact the grains would have been oriented in the pipe wall in all possible orientations. The above stresses would also have stress components in direction normal to the faces of such randomly oriented
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crystal. Each crystal thus does face normal stresses. One of these orientations must be such that it maximizes one of the normal stresses.
Figure 1: Hoope's, radial and axial stresses
The mechanics of solids state that it would also be orientation which minimizes some other normal stress. Normal stresses for such orientation (maximum normal stress orientation) are called principal stresses, and are designated S1 (maximum), S2 and S3 (minimum). Solid mechanics also states that the sum of the three normal stresses for all orientation is always the same for any given external load. That is
In addition to the normal stresses, a grain can be subjected to shear stresses as well. These acts parallel to the crystal surfaces as against perpendicular direction applicable for normal stresses. Shear stresses occur if the pipe is subjected to torsion, bending etc. Just as there is an orientation for which normal stresses are maximum, there is an orientation which maximizes shear stress. The maximum shear stress in a 3-D state of stress can be shown to be
i.e. half of the difference between the maximum and minimum principal stresses. The maximum shear stress is important to calculate because failure may occur or may be deemed to occur due to shear stress also. A failure perception may stipulate that maximum shear stress should not cross certain threshold value. It is therefore
13
necessary to take the worst-case scenario for shear stresses also as above and ensure against failure. It is easy to define stresses in the co-ordinate system such as axial-Hoope s-radial (L-HR) that are defined for a pipe. The load bearing cross-section is then well defined and stress components are calculated as ratio of load to load bearing cross-section. Similarly, it is possible to calculate shear stress in a particular plane given the torsional or bending load. What are required for testing failure - safe nature of design are, however, principal stresses and maximum shear stress. These can be calculated from the normal stresses and shear stresses available in any convenient orthogonal coordinate system. In most pipe design cases of interest, the radial component of normal stresses (SR) is negligible as compared to the other two components (SH and SL). The 3-D state of stress thus can be simplified to 2-D state of stress. Use of Mohr's circle then allows calculating the two principle stresses and maximum shear stress as follows:
The third principle stress (minimum i.e. S3) is zero. All failure theories state that these principle or maximum shear stresses or some combination of them should be within allowable limits for the MoC under consideration. To check for compliance of the design would then involve relating the applied load to get the net SH, SL, and then calculate S1, S2 and τmax and some combination of them.
4 Normal and Shear Stresses from Applied Load As said earlier, a pipe is subjected to all kinds of loads. These need to be identified. Each such load would induce in the pipe wall, normal and shear stresses. These need to be calculated from standard relations. The net normal and shear stresses resulting in actual and potential loads are then arrived at and principle and maximum shear
14
stresses calculated. Some potential loads faced by a pipe and their relationships to stresses are summarized here in brief
4.1 Axial Load A pipe may face an axial force (FL) as shown in Figure 2. It could be tensile or compressive.
Figure 2: Pipe under axial load
What is shown is a tensile load. It would lead to normal stress in the axial direction (SL). The load bearing cross-section is the cross-sectional area of the pipe wall normal to the load direction, Am. The stress can then be calculated as
The load bearing cross-section may be calculated rigorously or approximately as follows:
The axial load may be caused due to several reasons. The simplest case is a tall column.
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The metal cross-section at the base of the column is under the weight of the column section above it including the weight of other column accessories such as insulation, trays, ladders etc. Another example is that of cold spring. Many times a pipeline is intentionally cut a little short than the end-to-end length required. It is then connected to the end nozzles by forcibly stretching it. The pipe, as assembled, is under axial tension. When the hot fluid starts moving through the pipe, the pipe expands and compressive stresses are generated. The cold tensile stresses are thus nullified. The thermal expansion stresses are thus taken care of through appropriate assembly-time measures.
4.2 Internal / External Pressure A pipe used for transporting fluid would be under internal pressure load. A pipe such as a jacketed pipe core or tubes in a Shell & Tube exchanger etc. may be under net external pressure. Internal or external pressure induces stresses in the axial as well as circumferential (Hoope s) directions. The pressure also induces stresses in the radial direction, but as argued earlier, these are often neglected. The internal pressure exerts an axial force equal to pressure times the internal crosssection of pipe.
This then induces axial stress calculated as earlier. If outer pipe diameter is used for calculating approximate metal cross section as well as pipe cross- section, the axial stress can often be approximated as follows:
The internal pressure also induces stresses in the circumferential direction as shown in Figure 3.
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Figure 3: Hoope's stresses
The stresses are maximum for grains situated at the inner radius and minimum for those situated at the outer radius. The Hoope's stress at any in between radial position (r) is given as follows (Lame's equation)
For thin walled pipes, the radial stress variation can be neglected. From membrane theory, SH may then be approximated as follows.
Radial stresses are also induced due to internal pressure as can be seen in Figure 4.
17
Figure 4: Radial stresses due to internal pressure
At the outer skin, the radial stress is compressive and equal to atmospheric pressure (Patm ) or external pressure (Pext) on the pipe. At inner radius, it is also compressive but equal to absolute fluid pressure (Pabs). In between, it varies. As mentioned earlier, the radial component is often neglected.
4.3 Bending Load A pipe can face sustained loads causing bending. The bending moment can be related to normal and shear stresses. Pipe bending is caused mainly due to two reasons: Uniform weight load and concentrated weight load. A pipe span supported at two ends would sag between these supports due to its own weight and the weight of insulation (if any) when not in operation. It may sag due to its weight and weight of hydrostatic test fluid it contains during hydrostatic test. It may sag due to its own weight, insulation weight and the weight of fluid it is carrying during operation. All these weights are distributed uniformly across the unsupported span, and lead to maximum bending moment either at the centre of the span or at the end points of the span (support location) depending upon the type of the support used. Let the total weight of the pipe, insulation and fluid be W and the length of the unsupported span be L (see Figure 5).
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Figure 5: Pipe under bending load
The weight per unit length, w, is then calculated (w = W/L). The maximum bending moment, Mmax, which occurs at the centre for the pinned support is then given by the beam theory as follows:
For Fixed Supports, the maximum bending moment occurs at the ends and is given by beam theory as follows:
The pipe configuration and support types used in process industry do not confirm to any of these ideal support types and can be best considered as somewhere in between. As a result, a common practice is to use the following average formula to calculate bending moment for practical pipe configurations, as follows: .
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Also, the maximum bending moment in the case of actual supports would occur somewhere between the ends and the middle of the span. Another load that the pipe span would face is the concentrated load. A good example is a valve on a pipe run (see Figure 6):
Figure 6 : Point load
The load is then approximated as acting at the centre of gravity of the valve and the maximum bending moment occurs at the point of loading for pinned supports and is given as:
For rigid supports, the maximum bending moment occurs at the end nearer to the pointed load and is given as
a is to be taken as the longer of the two arms (a and b) in using the above formula. As can be seen, the bending moment can be reduced to zero by making either a or b zero,
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I.e. by locating one of the supports right at the point where the load is acting. In actual practice, it would mean supporting the valve itself. As that is difficult, it is a common practice to locate one support as close to the valve (or any other pointed and significant load) as possible. With that done, the bending moment due to pointed load is minimal and can be neglected.
Whenever the pipe bends, the skin of the pipe wall experiences both tensile and compressive stresses in the axial direction as shown in Figure 7:
Figure 7: Stresses on pipe cross section due to bending
The axial stress changes from maximum tensile on one side of the pipe to maximum compressive on the other side. Obviously, there is a neutral axis along which the bending moment does not induce any axial stresses. This is also the axis of the pipe. The axial tensile stress for a bending moment of M, at any location c as measured from the neutral axis is given as follows.
I is the moment of inertia of the pipe cross-section. For a circular cross-section pipe, I is given as
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The maximum tensile stress occurs where c is equal to the outer radius of the pipe and is given as follows.
Where Z (= I/ro) is the section modulus of the pipe.
4.4 Shear Load Shear load causes shear stresses. Shear load may be of different types. One common load is the shear force (V) acting on the cross-section of the pipe as shown in Figure 8:
Figure 8: Shear force acting on a pipe
It causes shear stresses which are maximum along the pipe axis and minimum along the outer skin of the pipe. This being exactly opposite of the axial stress pattern caused by bending moment and also because these stresses are small in magnitude, these are often not taken in account in pipe stress analysis. If necessary, these are calculated as
Where Q is the shear form factor and Am is the metal cross-section.
4.5 Torsional Load This load (see Figure 9) also causes shear stresses.
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Figure 9: Torsional load on a pipe
The shear stress caused due to torsion is maximum at outer pipe radius. And it is given in terms of the torsional moment and pipe dimensions as follows.
RT is the torsional resistance (= twice the moment of inertia). All known loads on the pipe should be used to calculate contributions to S L, SH and t. These then are used to calculate the principal stresses and maximum shear stress. These derived quantities are then used to check whether the pipe system design is adequate based on one or more theories of failure.
5 Allowable stresses & theories of Failure Allowable stresses as specified in the various codes are based on the material properties. These can be classified in two categories as below.
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Time Independent stresses Time independent allowable is based on either yield stress or the ultimate tensile strength measured in a simple tensile test. The yield stress is the elastic limit and that is the value below which the stresses are proportional to strain and when the load is removed, there is no permanent distortion. The tensile strength is the highest load, which the specimen can be subject to without failure. The code ANSI / ASME B 31.1 permits smaller of ¼ of the tensile strength or 5/8 of the yield strength. ANSI / ASME B 31.3 uses lower of 1/3 of the tensile strength or 2/3 of the yield strength. Time dependent stresses The time dependent allowable is related to ―Creep rupture strength‖ at high temperature. This is best explained for a piping system as follows. Pipe running between two equipments expands as it gets heated up. The increased length can be accommodated only by straining the pipe as its ends are not free to move. This straining induces stress in the pipe. However when the line is cooled during shutdown to ambient temperature the expansion returns to zero, the straining no longer exists and hence stress also disappears. Every time the plant starts from a stress free condition i.e. cold condition and soon gets to stressed with maximum at operating conditions from cold get stressed with stress reaching maximum at operating condition and then reducing to zero when operating stops and system cools down. The actual performances of the piping system do not exactly follow the above path. The piping system can absorb large displacement without returning to exactly to previous configuration. Relaxation to the sustaining level of material will tend to establish a condition of stability in few cycles, each cycle lowering the upper limit of hot stress until a state of equilibrium is reached in which the system is completely relaxed and capable of maintaining constant level of stress. The stress at which the material is relieved due to relaxation appears as stress in opposite sign. Thus the system which originally was
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stress less could within a few cycles accommodate stress in the cold condition and spring itself without the application of external load. This phenomenon is called ―Self springing‖. This is also called the Elastic shake down. Here the maximum stress range is set to 2 Sy or more accurately the sum of hot and the cold yield stresses in order to ensure eventual elastic cycling. The degree of self springing will depend upon the magnitude of the initial hot stresses and temperature, so that while hot stresses will gradually decrease with time, the sum of the hot and cold stress will stay the same. This sum is called the Expansion Stress range. This concepts lead to the selection of an allowable stress range. For materials below the creep range the allowable stresses are 62.5% of the yield stress, so that bending stress at which plastic flow starts at elevated temperature is 1.6 Sh and by same reasoning 1.6 Sc will be stress at which flow would take place at minimum temperature. Hence, the sum of this could make the maximum stress the system could be subjected to without flow occurring in either the hot or cold condition. Therefore, Smax = 1.6(Sc+Sh). A piping system in particular or a structural part in general is deemed to fail when a stipulated function of various stresses and strains in the system or structural part crosses a certain threshold value. It is a normal practice to define failure as occurring when this function in the actual system crosses the value of a similar function in a solid rod specimen at the point of yield. There are various theories of failure that have been put forth. These theories differ only in the way the above mentioned function is defined. Important theories in common use are considered here.
5.1 Maximum Stress Theory This is also called Rankine Theory. According to this theory, failure occurs when the maximum principle stress in a system (S1) is greater than the maximum tensile principle stress at yield in a specimen subjected to uni-axial tension test.
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Uni-axial tension test is the most common test carried out for any MoC. The tensile stress in a constant cross-section specimen at yield is what is reported as yield stress (Sy) for any material and is normally available. In uni-axial test, the applied load gives rise only to axial stress (SL) and SH and SR as well as shear stresses are absent. SL is thus also the principle normal stress (i.e. S1). That is, in a specimen under uni-axial tension test, at yield, the following holds. SL = SY, SH = 0, SR = 0 S1 = SY, S2 = 0 and S3 = 0. The maximum tensile principle stress at yield is thus equal to the conventionally reported yield stress (load at yield/ cross-sectional area of specimen). The Rankine theory thus just says that failure occurs when the maximum principle stress in a system (S1) is more than the yield stress of the material (Sy). The maximum principle stress in the system should be calculated as earlier. It is interesting to check the implication of this theory on the case when a cylinder (or pipe) is subjected to internal pressure. As per the membrane theory for pressure design of cylinder, as long as the Hoope's stress is less than the yield stress of the MoC, the design is safe. It is also known that Hoope's stress (SH) induced by external pressure is twice the axial stress (SL). The stresses in the cylinder as per the earlier given formula would be:
The maximum principle stress in this case is S2 (=SH). The Rankine theory and the design criterion used in the membrane theory are thus compatible.
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This theory is widely used for pressure thickness calculation for pressure vessels and piping design uses Rankine theory as a criterion for failure.
5.2 Maximum Shear Theory This is also called Tresca theory. According to this theory, failure occurs when the maximum shear stress in a system τmax is greater than the maximum shear stress at yield in a specimen subjected to uni-axial tension test. Note that it is similar in wording, to the statement of the earlier theory except that maximum shear stress is used as criterion for comparison as against maximum principle stress used in the Rankine theory. In uniaxial test, the maximum shear stress at yield condition of maximum shear test given earlier is
The Tresca theory thus just says that failure occurs when the maximum shear stress in a system is more than half the yield stress of the material (Sy). The maximum shear stress in the system should be calculated as earlier. It should also be interesting to check the implication of this theory on the case when a cylinder (or pipe) is subjected to internal pressure. As the Hoope's stress induced by internal pressure (SH) is twice the axial stress (SL) and the shear stress is not induced directly (τ = 0) the maximum shear stress in the cylinder as per the earlier given formula would be
27
This should be less than 0.5Sy, as per Tresca theory for safe design. This leads to a different criterion that Hoope's stress in a cylinder should be less than twice the yield stress. The Tresca theory and the design criterion used in the membrane theory for cylinder are thus incompatible.
5.3 Octahedral Shear Theory This is also called Von Mises theory. According to this theory, failure occurs when the octahedral shear stress in a system is greater than the octahedral shear stress at yield in a specimen subjected to uniaxial tension test. It is similar in wording to the statement of the earlier two theories except that octahedral shear stress is used as criterion for comparison as against maximum principle stress used in the Rankine theory or maximum shear stress used in Tresca theory. The octahedral shear stress is defined in terms of the three principle stresses as follows.
In view of the principle stresses defined for a specimen under uni-axial load earlier, the octahedral shear stress at yield in the specimen can be shown to be as follows.
The Von Mises theory thus states that failure occurs in a system when octahedral shear stress in the system exceeds √ 2 Sy / 3. For stress analysis related calculations, most of the present day piping codes uses a modified version of Tresca theory.
6 Design under Secondary Load 28
As pointed earlier, a pipe designed to withstand primary loads and to avoid catastrophic failure may fall after a sufficient amount of time due to secondary cyclic load causing, fatigue failure. The secondary loads are often cyclic in nature. The number of cycles to failure is a property of the material of construction just as yield stress is. While yield stress is cardinal to the design under primary sustained loads, this number of cycles to failure is the corresponding material property important in design under cyclic loads aim at ensuring that the failure does not take place within a certain period for which the system is to be designed. While yield stress is measured by subjecting a specimen to uni-axial tensile load, fatigue test is carried out on a similar specimen subjected to cycles of uni-axial tensile and compressive loads of certain amplitude, i.e. magnitude of the tensile and compressive loads. Normally the tests are carried out with zero mean loads. This means, that the specimen is subjected to a gradually increasing load leading to a maximum tensile load of W, then the load is removed gradually till it passes through zero and becomes gradually a compressive load of W (i.e. a load of W), then a tensile load of W and so on. Time averaged load is thus zero. The cycles to failure are then measured; the experiments are repeated with different amplitudes of load.
7 Piping Codes: There are many different piping codes for process and high-pressure lines in use throughout the world. Some countries, like Canada, take advantage of the considerable body of knowledge contained in the U.S. codes. In the U.S. we follow the ASME Code for Pressure Piping, B31. The code was first published in 1935 by the ASA (American Standards Association, now known as ANSI, the American National Standards Institute). The responsibility for developing the code was assigned to the ASME (American Society of Mechanical Engineers). The ASME Code is so extensive that it was more convenient to break it up into several separate documents, which represent various industries. The code now consists of:
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B31.1 Power Piping
B31.3 Process Piping
B31.4 Pipeline Transportation Systems for Liquid Hydrocarbons and Other Liquids
B31.5 Refrigeration Piping
B31.8 Gas Transportation and Distribution Piping
B31.9 Building Services Piping
B31.11 Slurry Transportation Piping Systems.
Usually, by the time you get involved in a project, most of the piping specifications are written, and the codes to be used have been laid out in the specifications. But how did the engineer who wrote the specs know which codes to apply? Much of the time the answer lies in the codes themselves. The codes will explain what their intended scope is. But the codes are often applied to piping systems that are outside their scope. This sound like it might be a big problem, but the intelligent application of a piping code outside of its scope is not necessarily bad. Of the seven B31 codes, most design engineers find that they spend most of their time dealing with B31.1, B31.3, and B31.9. The remainder is confined to an overview of these codes.
7.1 Limits of stresses set by code ANSI / ASME B 31.3 Limits of Calculated stresses due to Occasional loads ANSI / ASME B 31.3 in clause 302.3.6 specifies that the sum of longitudinal stresses due to pressure, weight and other sustained loadings and of the stresses due to produced by occasional loads such as wind or earthquake, may be as much as 1.33 times the basic allowable stress. Wind and earthquake forces need not be considered
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as acting concurrently. When the piping system is tested, it is not necessary to consider other occasional loads such as wind and earthquake as occurring concurrently with test loads. Limits of calculated stresses due to Sustained loads ANSI / ASME B 31.3 in clause 302.3.5 specifies that the sum of longitudinal stresses, SL in any component in a piping system due to pressure, weight and other sustained loadings shall not exceed the allowable stress at the design temperature. The thickness of pipe used in calculating the SL shall be the nominal thickness less the allowable due to corrosion and erosion. Limits of Displacement stress range ANSI / ASME B 31.3 limits the allowable stress range to 78% of the maximum stress the system could be subjected to without flow occurring either in hot or cold condition.
7.2 ASME B31.1 power piping ―Power piping‖ in this case means the piping that is used around boilers. It is called power piping because often a boiler is used to make steam for power generation. This is done by converting pressure and temperature energy into kinetic energy in a turbine, which then produces electrical energy. Mechanical engineering is the technical field associated with transforming energy into work. A steam generator is a perfect example of that. This code relates particularly to piping that would be found in electrical power plants, commercial and institutional plants, geothermal plants, and central heating and cooling plants. This code is primarily concerned with the effects of temperature and pressure on the piping components. Scope
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Around a boiler, the scope of B31.1 begins where the boiler proper ends, at either: 1. The first circumferential weld joint 2. The face of the first flange 3. The first threaded joint This piping is collectively referred to as ―boiler external piping,‖ since it is not considered part of the boiler. Power piping may include steam, water, oil, gas, and air services. But it is not limited to these, and as mentioned before, there is nothing that says you cannot apply B31.1 to other piping systems unrelated to boilers or power generation, as long as they would not be better classified as within other piping codes, which may be more stringent. Not in Scope B31.1 does NOT apply to: 1. Components covered by the ASME Boiler and Pressure Vessel Code. 2. Building heating and distribution steam and condensate piping if it designed for 15 psig or less. 3. Building heating and distribution hot water piping if it is designed for 30 psi or less. 4. Piping for hydraulic or pneumatic tools (and all of their components downstream of the first block valve off of the system header). 5. Piping for marine or other installations under federal control 6. Structural components 7. Tanks 8. Mechanical equipment 9. Instrumentation
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Pressure Design of Straight Pipe This section contains several extremely useful formulas for determining either the design pressure of a particular pipe or the required wall thickness of a pipe operating at a certain pressure. These formulas are:
Where tm = Minimum required wall thickness[in. or mm] P = Internal design gage pressure [psi or kPa] The pressure is either given or solved for in the equations. Do = Outside diameter of the pipe [in or mm] The outside diameter will be the OD of a commercially available pipe. d = Inside diameter of the pipe [in or mm] The inside diameter will be the ID of a commercially available pipe. S = Maximum allowable stress values in tension for the material at the design temperature [psi or kPa] E = Weld joint efficiency, shown in ASME B31.1, Appendix A. These values depend on the material used and the method of manufacture. Naturally, if the
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material is a cast product, there is no weld. In that case the casting factor F is used. F = Casting factor shown in ASME B31.1, Appendix A. Where a cast material is used . A = Additional thickness [in or mm].
Piping is generally purchased based on commercially available schedules or wall thicknesses (unless specially ordered, which is usually prohibitively expensive). These thicknesses must take into account the mill tolerance, which may be as much as 12.5 percent less than the nominal thickness. These values are tabulated in ASME B31.1, Appendix A. Note that they are dependent on the temperature to which the material will be exposed. This temperature is the metal temperature. This would normally be the temperature of the fluid in the pipe, but if a pipe was to be exposed to a high temperature externally, it would be the fluid temperature outside the pipe. Note that the values tabulated in Appendix A include the Weld Joint Efficiencies and the Casting Factors. Therefore, the tabulated values are the values of S, SE, or SF. See General Note (f) at the end of each table.
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The power piping Code ANSI B 31.1 specifies that the developed stresses due to the sustained, occasional and expansion stresses be calculated in the following manner. Limits for Sustained and Displacement Stresses This section addresses cyclic stresses among other things. Note that the Stress Range Reduction Factors apply only to thermal cycling and NOT to pressure cycles.
where, 35
Ss = Sustained stress. i = Stress Intensification factor. MA = Resultant moment due to primary loads = ( Mx² + My² + Mz² ) 0.5 Sh = Basic allowable stress at the operating temperature Z = Section modulus. Limits for occasional stresses
where, So = Occasional stress. MB = Resultant range of moments due to occasional loads = ( Mx² + My² + Mz² ) 0.5 K = Occasional load factor = 1.2 for loads occurring less than 1% of the time = 1.15 for loads occurring less than 10% of the time. Limits for expansion
Where, Mc = Resultant range of moments due to Expansion (secondary) loads = ( Mx² + My² + Mz² ) 0.5 SA = Allowable expansion stress range 36
104.3 Branch Connections Branch connections are often made using fittings designed for the application. Such fittings are manufactured according to the standards listed in ASME B31.1, Table 126.1. But branch connections are often made in other ways. Especially where large bore piping is concerned, some branch connections are made without the use of a manufactured fitting. It might be helpful now to make a distinction between ―manufactured‖ and ―fabricated.‖ A manufactured fitting is one that could be purchased from a supplier. The supplier would sell it to you just as he received it from a factory. It would be (or should be) made to a specification; perhaps one of the specifications listed in ASME B31.1‘s Table 126.1. A fabricated fitting would be made in a shop, or in the field, with pieces of pipe and/or plate. There are a few reasons why it may be advantageous to use a fabricated fitting instead of a manufactured fitting: •Lack of availability of the specific fitting. For instance, a 20 in 304SS lateral may not be available. • The cost of the manufactured fitting is very high compared to the ability to fabricate it. • The cost of making the welds on a manufactured fitting is higher than on a fabricated fitting Consider an 18‖ diameter run of piping, and a 14 in diameter branch connection. There are several ways that this could be accomplished. One method might be to insert a full-size butt-welding tee, with an 18 in x 14 in reducer exiting the branch, as shown in Figure 10. Another method might be to use a reducing tee as shown in Figure 4.2. Figure 11shows still a third method, in which the 14 in branch pipe is stubbed directly into the 18 in run pipe. The type of cuts required to join pipes like this is called a ―fishmouth‖ by pipefitters.
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Figure 10: Branch connection using full size tee and reducing tee
Figure 11: A branch connection using a nozzle weld without a fitting.
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Obviously, the types of fabrications one could concoct are limited only by one‘s imagination. In order to achieve safe designs that can withstand the same pressures as other pipe configurations, these fabrications are subject to the requirements of this code section. Whenever a run pipe as shown in Figure 11is cut to accommodate a branch connection, the strength of the run pipe is compromised due to the material that is removed. The larger the branch the more material removed, and the worse the situation. If a manufactured fitting is chosen (for example in Figure 10) to provide the branch connection, and if the manufacturer‘s specification is listed in Table 126.1 in the ASME B31.1, then no further analysis is required. A situation similar to Figure 11 above might require additional engineering analysis, and Section 104.3 provides the guidance to perform that analysis. The first thing to note is that fittings manufactured in accordance with the ASTM standards listed in ASME‘s Table 126.1 are satisfactory in meeting the code (Refer to Section 104.3.1 [B.1]). For example, if your specification designated that ―all tees had to meet ASTM A234 Piping Fittings of Wrought Carbon Steel and Alloy Steel for Moderate and Elevated Temperatures,‖ then you would be covered. No further qualifications would be necessary for those tees (other than to establish that they were installed in the piping system correctly5). If, on the other hand, you decided that you really didn‘t want to spend the money on an 18 in diameter tee manufactured fitting, but would rather fabricate the fitting, then in order to satisfy the code, you would have to follow the requirement set forth in Section 104.3.1(D). These requirements specify the extent to which branch connections must be reinforced. In practice, it is unusual to use a fabricated fitting when the branch diameter is the same size as the run diameter. The reason for this is the cut and weld for the branch would have to extend to the centerline of the pipe (halfway around the circumference). This would require extensive cutting, welding, and reinforcement, and would not be an
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economical choice. Most pipe specs indicate that full-size branch connections be made with a manufactured fitting (a tee). For a single size reduction of the branch pipe, a reducing tee is often used. Below one size reduction, the branches are most often fabricated until the branch size is small enough that a manufactured welding fitting such as a Weld-o-let® may be used. These fittings are described in 104.3.1 (B.2). We will discuss these connections later in the chapter covering fittings. Extruded outlets are described in Sections 104.3.1 (B.3) and 104.3.1 (G). They are manufactured by pulling a die through the wall of a pipe. Due to the custom nature of these fittings, they are unusual in general industrial applications, but can be found in the power industry. This section pertains to branch connections where the axes of the main run and the branch intersect, and the angle formed by the main run of the pipe and the branch is between 45° and 90°. If both of these conditions do not exist, additional tests or analysis must be performed to ensure that adequate strength is provided. Section 104.3.1 (D) relates to branch connections subject to internal pressure. The code designates a region surrounding the intersection known as the ―reinforcement zone.‖ The reinforcement zone bounds the region of concern at the branch with a parallelogram. All of the analysis is confined to this zone, and any required reinforcement must fall within this zone. Imagine a plane passing through the intersecting axes of the branch connection. See Figure 12. The discussion of ―areas‖ in this code section refers to the cross-sectional areas that appear in this imaginary section.
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Figure 12: ASME B31.1-2001 figure 104.3.1 (D) Example B, showing the various reinforcement areas for a branch connection.
The area of the material that is removed when the hole is cut in the run pipe must be offset by material that is present in other components within the reinforcement zone.
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Credit is given for what is referred to as ―excess pipe wall.‖ Consider that piping systems are rarely operated at the maximum design pressure calculated by Formula (4) in Section 104.1.2. For one thing, the piping used is the commercially available pipe wall. This means that there is usually some inherent excess of pipe wall available in either the run pipe or the branch pipe or both. The code allows you to take this excess pipe wall into account when determining the need for additional reinforcement. This excess pipe wall would be the difference between the nominal pipe wall minus the mill tolerance, minus any additional thickness allowance, minus the wall thickness required by Formula (3) or (3A) in paragraph 104.1.2(A). In other words, Excess pipe wall = (nominal wall thickness x 0.875) - (corrosion, erosion, threading, or grooving allowance) - (tm, as calculated by Formula (3) or (3A)) The 0.875 term accounts for the Mill tolerance (12.5 percent). Therefore, one place that can make up the amount of material removed by the hole in the run pipe is any excess pipe wall present in the reinforcement zone. This is designated A1 for the run pipe (also known as the ―header‖) and A2 for the branch pipe. Another source of excess material is the area of the fillet weld, designated A3. Sometimes a reinforcing pad (or ―re-pad‖) is placed around the branch connection to add strength to the joint. The ratio of the width of the re-pad to its height should be as close as possible to 4:1 (within the limits of the reinforcing zone). It should never be less than 1:1. This material‘s area is designated A4. Still another method of reinforcing a branch connection is to weld on a saddle. These are limited to use on 90° branches. Their use in general industry is not as common as other methods of preparing branch connections, but they remain a viable alternative. The metal contained in the saddle along the run pipe in the reinforcement zone constitutes the additional metal that may be used to offset the material lost in cutting the hole in the run pipe. The area of the metal in the saddle along the run pipe is designated A5.
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So there are a total of five areas that can be added together to offset the loss of material created by the hole in the run pipe, which is designated as A7. Since the pipe is expected to retain its integrity throughout its design life, the wall thickness expected at the end of the pipe‘s design life is the thickness that must be used in the calculations. The newer versions of the code call this pressure design area at the end of the service life A6.
Where tmh= The required minimum wall thickness in the header pipe A = the additional thickness added to account for corrosion, erosion, grooving or threading
Where α = angle between the axes of the run and branch pipes Another way of stating this is that the required reinforcement area must be less than any combination of: 1- A1 = Area of any excess pipe wall contained in the run =
—
2- A2 = Area of an excess pipe wall contained in the branch. = 3- A3 = Area of any welds beyond the outside diameters of either pipes or of weld attachments of pads, rings, or saddles. 4- A4 = Area provided by any rings, pads, or integral reinforcement.
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5- A5 = Area provided by a saddle on a right angle connection. = In practice, if you were using a saddle, you would not also have a re-pad, and viceversa. Therefore, A4 and A5 can be considered mutually exclusive. The code lists specific requirements for closely spaced branch connections, branch connections subject to external forces and moments. The Pipe Fabrication Institute publishes worksheets (designated ES36) that aid in these calculations. Miters Miters are perfectly acceptable fabricated fittings for pressure piping, if constructed in accordance with the requirements of Paragraph 104.3.3. Note however that they are usually only used in large bore piping where manufactured elbows are either unavailable or very expensive. Miters require much fit-up and welding. It is easier to simply purchase an elbow that conforms to one of the standards listed in Table 126.1 if these are available. 137 Pressure Tests After a pipe system is installed in the field, it is usually pressure tested to ensure that there are no leaks. Once a system is in operation, it is difficult, if not impossible, to repair leaks. ASME B31.1 has established procedures for applying pressure tests to piping systems. There are generally two types of pressure tests applied to a piping system. One is a hydrotest and the other is a pneumatic test. The hydrotest is greatly preferred for the following reasons:
Leaks are easier to locate.
A hydrotest will lose pressure more quickly than a pneumatic test if leaks are present.
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Pneumatic tests are more dangerous, due to the stored pressure energy and possibility of rapid expansion should a failure occur.
On the other hand, if a piping system cannot tolerate trace levels of the testing medium (for instance, a medical oxygen system) then a pneumatic test is preferred. 137.4 Hydrostatic Testing It is important to provide high point vents and low point drains in all piping systems to be hydrotested. The high point vents are to permit the venting of air, which if trapped during the hydrotest may result in fluctuating pressure levels during the test period. The drains are to allow the piping to be emptied of the test medium prior to filling with the operating fluid. (Low point drains are always a good idea though since they facilitate cleaning and maintenance.) A hydrotest is to be held at a test pressure not less than 1.5 times the design pressure. The system should be able to hold the test pressure for at least 10 minutes, after which the pressure may be reduced to the design pressure while the system is examined for leaks. A test gauge should be sensitive enough to measure any loss of pressure due to leaks, especially if portions of the system are not visible for inspection. The test medium for a hydrotest is usually clean water, unless another fluid is specified by the Owner. Care must be taken to select a medium that minimizes corrosion. 137.5 Pneumatic Testing The test medium must be nonflammable and nontoxic. It is most often compressed air, but may also be nitrogen, especially for fuel gases or oxygen service. Note that compressed air often contains both oil and water, so care must be exercised in specifying an appropriate test medium. A preliminary pneumatic test is often applied, holding the test pressure at 25 psig to locate leaks prior to testing at the test pressure. The test pressure for pneumatic tests is to be at least 1.2 but not more than 1.5 times the design pressure. The pneumatic test must be held at least 10 minutes, after which time it must be reduced to the lower of the design pressure or 100 psig (700 kPa gage) until an inspection for leaks is conducted. 45
If a high degree of sensitivity is required, other tests are available such as massspectrometer or halide tests.
7.3 ASME B31.3 Process Piping The term ―process piping‖ may be thought of as any piping that does not fall under the other B31 codes. It is generally considered to be the piping that one may find in chemical plants, refineries, paper mills, and other manufacturing plants. This code is structured similar to B31.1 in that it is organized into chapters, parts, and paragraphs. Note that while the paragraphs of B31.1 are numbered in the 100s, those in B31.3 are numbered in the 300s. This convention follows throughout the B31 codes. There are several very important concepts in this code that should be identified before we delve too far into the particulars. Because we have entered into the realm of process piping, it is necessary to recognize some of the inherent hazards associated with handling dangerous chemicals. Scope The scope of this code includes all fluids. This scope specifically excludes the following: 1. Piping with an internal design pressure between 0 and 15 psi (105 kPa) 2. Power boilers and BEP which is required to be in accordance with B31.1 3. Tubes inside fired heaters 4. Pressure vessels, heat exchangers, pumps, or compressors. Definitions There are several very important definitions included in this paragraph under the term ―fluid service‖: a) Category D fluids are those in which all of the following apply: 1. The fluid is nonflammable, nontoxic, and not damaging to human tissue.
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2. The design pressure does not exceed 150 psig (1035 kPa). 3. The design temperature is between -20°F and 366°F (-29°C and 186°C). b) Category M fluids are those in which a single exposure to a very small quantity could lead to serious irreversible harm, even if prompt restorative measures are taken. c) High pressure fluids are those in which the Owner has specified that the pressures will be in excess of that allowed by the ASME B16.5 PN420 (Class 2500) rating for the specified design temperature and material group. d) Normal fluids are everything else that does not fit into the above categories. These are the fluids most often used with this code. Design Conditions This section requires the designer to consider the various temperatures, pressures, and loads that the piping system may be subject to. While it is a good checklist, most of the items contained are common sense. Uninsulated Components This paragraph describes how to determine the design temperature of uninsulated piping and components. Of particular interest is the description of how to determine component temperatures using the fluid temperature? The instructions indicate that for fluid temperatures above 150°F (65°C) the temperature for uninsulated components shall be no less than a certain percentage of the fluid temperature. For example, the temperature used for lap joint flanges shall be 85 percent of the fluid temperature. Note that unless you use the absolute temperature in degrees Rankine or Kelvin, such a calculation has no meaning, since a percentage cannot be applied to the Fahrenheit or Celsius scales. Design Criteria Note that B31.3 also has a Table 326.1 that corresponds to B31.1‘s Table 126.1. A comparison between the two tables shows that Table 126.1 is focused more on steel
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pipe and fittings, while Table 326.1 pertains more to nonmetallic pipe and fittings. The obvious reason is that process piping deals with more fluids that are corrosive to steel. In many cases, thermoplastics, thermosetting plastics, and resins will be more appropriate materials for the fluids handled in the purview of the process piping code. This set of paragraphs states that if the components listed in Table 326.1 are rated for a specific temperature/pressure condition, then they are suitable for the design pressures and temperatures allowed by this code. If they have no specific temperature/pressure rating, but are instead based on the ratings of straight seamless pipe, then the component must be de-rated by 12.5 percent, less any mechanical and corrosion allowances. In other words, you have to determine the minimum wall thickness of the straight pipe based on the design temperature and pressure, as well as the mechanical and corrosion allowances. Once you apply the mill tolerance of 12.5 percent, you will be safe in selecting a fitting that satisfies the same requirements as the straight pipe to which it is connected. Allowances for Pressure and Temperature Variations There are paragraphs in both B31.1 and B31.3 that describe allowable deviations from operating conditions. These are called ―allowances for pressure and temperature variations.‖ The rules for such operating excursions are not complicated, but inpractice industrial users do not chart how often the operating pressures exceed the allowable pressures. Most often, any pressure excursions are prevented through the use of pressure relief devices, such as pressure relief valves, pressure safety valves, or rupture disks. Also, it is important to note that the allowable stresses are temperature dependent. So if there are temperature excursions (as allowed for in both B31.1 and B31.3) the allowable stress may vary. Unless someone has taken the trouble to build a database of the relationships between operating temperature and pressure, and allowable temperature and pressure, then the designer will be well-advised to base the design pressure on the
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MAXIMUM temperature that the system will ever see, and not to rely on the allowance for temperature variations. Therefore, from a practical standpoint, it is best to not rely upon any allowances for temperature or pressure excursions above the design conditions. Choose your design conditions so that the temperature and pressure will not be exceeded. Pressure Design of Straight Pipe As we noted above, we are required to calculate the required wall thickness to satisfy the design temperature and pressure conditions. We did the same thing for B31.1. But B31.3 handles things a little differently.
where tm = Minimum required wall thickness [in or mm]. This minimum wall thickness includes any mechanical, corrosion, or erosion allowances. If the piping system contains bends (not elbows), then you also must compensate for thinning of the bends, as in ASME B31.1. Because this is not common, the interested reader is referred to ASME B31.3 Paragraph 304.2.1 for the formulas required to determine after-bend thicknesses t = Pressure design thickness, as determined by any of the Formulas (3a) through (3b) [in or mm].
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c = Mechanical, corrosion, or erosion allowances [in or mm]. Note that for unspecified tolerances on thread or groove depth, the code specifies that an additional 0.02 in (0.5 mm) shall be added to the depth of the cut to take the unspecified tolerance into account. T = Pipe wall thickness, either measured or minimum per purchase specification [in or mm]. Unless specially ordered (which is usually prohibitively expensive) piping is generally purchased based on commercially available schedules (or wall thicknesses). These thicknesses must take into account the mill tolerance which may be as much as 12.5 percent less than the nominal thickness. Therefore, under ordinary circumstances, the pipe wall thickness (T) will be 87.5 percent of the thickness of the listed schedule. d = Inside diameter of pipe [in or mm]. P = Internal design gage pressure [psig or kPa (gage)] The pressure is either given, or solved for in the equations. D = Outside diameter of pipe [in or mm] The outside diameter will be the OD of a commercially available pipe. Carbon steel pipe dimensions are shown in Appendix 1 of this text. E = Quality Factor from ASME Table A-1A or A-1B. Table A-1A relates exclusively to castings. Table A-1B relates to longitudinal weld joints. The quality factor is a means of de-rating the pressure based on the material and method of manufacture. Thus, for A106 seamless pipe, the quality factor E = 1.00. Casting quality factors may be increased if the procedures and inspections listed in ASME B31.3 Table 302.3.3C are utilized. The quality factors are in place to account for imperfections in castings, such as inclusions and voids. Machining all of the surfaces of a casting to a finish of 250
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micro inches (6.3 μm) improves the effectiveness of surface examinations such as magnetic particle, liquid penetrant, or ultrasonic examinations. The Quality Factor E is analogous to the Weld Joint Efficiency E or Casting Factor F in B31.1. But note that the Quality Factor E in B31.3 is NOT included in the stress values provided in B31.3 Tables A-1 and A-2. See Paragraph 302.3.1(a). S = Stress in material at the design temperature [psi or kPa]. These values are tabulated in ASME B31.3, Appendix A. Note that they are dependent on the temperature to which the material will be exposed. This temperature is the metal temperature. This would normally be the temperature of the fluid in the pipe, but if a pipe was to be exposed to a high temperature externally, it would be the fluid temperature outside the pipe. See also Paragrah 301. Once again, note that the values tabulated in ASME B31.3 Appendix A DO NOT include the Quality Factors. Therefore, the tabulated values are only the values of S. W = Weld Joint Strength Factor. This factor accounts for the long term strength of weld joints at elevated temperatures. In the absence of specific data such as creep testing, W is taken as 1.0 at temperatures of 950°F (510°C) and below. W falls linearly to 0.5 at 1500°F (815°C). Y = A coefficient used to account for material creep, as in B31.1. The table of Y coefficients in B31.3 is virtually identical to the table given in B31.1. As pre- viously noted, the variation of Y with temperature allows the wall thick- ness equation to behave in accordance to the ―Modified Lamé Equation‖ at low temperatures (with Y = 0.4), and in accordance with a creep-rupture equation at high temperatures (with Y = 0.7). The values are taken from Table 304.1.1 for t < D/6. For ductile metals (including steel), the value is 0.4 across the range of temperatures. For t >= D/6,
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Note that the difference between Formulas (3a) and (3b) is that (3a) begins with the OD of the pipe, and (3b) begins with the ID of the pipe. B31.3 Chapter VII deals with nonmetallic piping and piping lined with nonmetals. Paragraph A304 explains how to calculate minimum wall thicknesses in such cases. The method and equations closely parallel Paragraph 304.1.1. The Allowable Stresses are replaced with Hydrostatic Design Stresses for nonmetals in Table B-1. Pressure design of high-pressure piping (pressures in excess of the Class 2500 rating for the design temperature and material group), is covered in Paragraph K304. The equations given use Table K-1 for the basic allowable stresses. These stresses are higher than those listed in Table A-1 for the same materials. Limits for sustained stresses
where, FAX = Axial force due to sustained ( primary ) loading Mi = In-plane loading moment due to sustained ( primary ) Mo = Out-plane loading moment due to sustained ( primary ) loading. ii , io = in-plane and out –plane stress intensification factors. Sh = Basic allowable stress at operating temperature. Limits for occasional stresses The code states that in order to calculate the stresses due to sustained and occasional loads independently as per the above equation and then add them absolutely. The sum should not exceed 1.33 Sh.
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Limits for Expansion
where, SE = Expansion stress range Mi = Range of in plane bending moment due to expansion (secondary) load Mo= range of out plane bending moment due to expansion (secondary) load MT = Range or torsional bending moment due to expansion load SA = Allowable stress range. 304.3 Branch Connections Similar to B31.1, B31.3 permits fabrication of branch connections. We are faced with the following prerequisites: 1. The run pipe diameter-to-thickness ratio (Dh/Th) < 100 and the branch-to-run diameter ratio (Db/Dh) is not greater than 1.0. If we examine the tables of commerciallyavailable pipe data, we see that the first condition in which we might see a diameter-tothickness ratio in excess of 100 would be 24 in diameter Schedule 5S, which has a wall thickness of 0.218 in. For thicknesses above the standard wall thickness, there is little chance that the ratio will exceed 100. So it is clear that while this is an important consideration for large bore, thin wall pipes, it is a situation that most of us are not likely to encounter. Looking next at the requirement that the branch-to-run ratio is not greater than 1.0, we see that this means only that it is impossible to stub a larger branch onto a smaller run. And if we tried to do that, we might be inclined to reverse the names of the branch and run. In other words, the branch pipe is always the smaller diameter, unless they are both the same diameter. Whichever pipe is designated as the run pipe, must still satisfy (Dh/Th) < 100.
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2. If Dh/Th >= 100, the branch diameter Db has to be less than one-half the run diameter Dh. 3. The angle between the branch and run is at least 45°. See Figure 4.8. This is analogous to B31.1‘s angle ∝ . We will examine the similarities and differences between B31.1 and B31.3 regarding the branch connection calculations. 4. The axes of the branch and run pipe must intersect each other. This was also a requirement of B31.1. Once the prerequisites are established, we can examine any requirements for reinforcing the branch connection. Here is an example of how the codes complicate matters. The names assigned to the various reinforcing areas in B31.3 are different than those we examined in B31.1. See Table 4.1 for a comparison of the terminology as they pertain to branch connections. For B31.3:
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The subscripts b and h refer to the branch and run pipe (or header pipe) respectively. In order to satisfy the reinforcement requirements of B31.3, A2 + A3 + A4 >= A1
Formula (6a)
As in B31.1, we have a reinforcement zone bounded by the parallelogram shown in Figure 4.9. Also, as in B31.1, there are also specific requirements for closely spaced nozzles (overlapping reinforcement zones) and branch connections subject to external pressure, forces, or moments.
305.2 Specific Requirements This section describes what piping may be used for certain services. A review of the four fluid services reveals that the most benign service is Category D, followed by normal fluids, and then perhaps high pressure fluids with Category M fluids constituting
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the most hazardous service. If you were dealing with water in a plant it would most likely be a Category D fluid service, regardless of whether it is potable or cooling water or general service water. Most water service in a manufacturing facility does not exceed 150 psig or 366°F. Paragraph 305.2.1 specifies that there are three pipe specifications that are suitable only for these benign Category D services. They are:
API 5L, Furnace Butt-Welded
ASTM A53, Type F (also Furnace Butt-Welded)
ASTM A 134 if made from other than ASTM A285 plate
These pipes are not suitable for the more hazardous services of B31.3. The furnace butt-weld pipes have a Weld Joint Quality Factor Ej of only 0.6. These pipes are made with a continuous longitudinal butt weld. The furnace butt weld process is a continuous forge weld that is made through the application of mechanical pressure. It is not as strong as electric resistance welded pipe, electric fusion welded pipe, or seamless pipe. Paragraph 305.2.2 discusses pipe that requires safeguarding. The two pipe specifications that require safeguarding for services other than Category D are: • ASTM A 134 if made from ASTM A285 plate • ASTMA139. Because safeguarding is an added expense in terms of both design and installation, the designer would be better off using a more suitable pipe material. But this avoids the concept of safeguarding altogether, which may be required in other circumstances. For example, suppose you are faced with designing a piping system that handles dilute hydrochloric acid. You realize that it is corrosive to carbon steel, and stainless steel is not suitable due to the possibility of stress corrosion cracking. You select a PVC piping system that is impervious to the HCl, but might not hold up so well against fork truck traffic. The pipe system must be ―safeguarded.‖
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ASME B31.3 Appendix G addresses the concept of safeguarding. Safeguarding is the provision of protective measures to minimize the risk of accidental damage to a piping system, or to mitigate the consequences of a possible pipe failure. Such provisions include, but are not limited to: • Physical barriers •Guards around pipe flanges to prevent spraying of fluids if a gasket fails •Isolation of hazardous areas •
Installation of fire protection systems
•Process controls to shut down systems in the event of a failure •Grounding of static charges to prevent ignition of flammable vapors •Implementation of special operating or maintenance procedures. These are considerations that are often addressed in a HAZOP analysis. Paragraph 305.2.3 lists piping that may be used under severe cyclic conditions. Severe cyclic conditions are defined in Paragraph 300.2 as those in which the number of cycles exceeds 7000, and the Displacement Stress Range (SE) exceeds the 80 percent of the Allowable Displacement Stress Range (SA). As in ASME B31.1, the cycles referred to in this section of B31.3 are temperature cycles and not pressure cycles. The allowable displacement stress (SA) is dependent only on the material, the temperature fluctuations during the operating cycles, and the number of cycles. The Displacement Stress Range (SE) is dependent only on the loading conditions and the pipe geometry. The calculation of the resultant stresses is best left to a computer program, as it becomes cumbersome. For the moment, it is enough to realize that severe cyclic conditions are not common, since thermal cycles above 7000 over the expected life of the system are not common.
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345 Testing B31.3 requires that all piping designed in accordance with B31.3 be leak tested. For the benign Category D fluids, a service test may be conducted using the service fluid as the test medium, and setting the test pressure at the operating pressure. This is in lieu of conducting a hydrostatic test. Of course, a hydrostatic test may be applied at the Owner‘s discretion. It is not required however. The B31.3 hydrostatic test is similar to that described in B31.1. It is most often conducted with clean water, unless that would pose a problem such as contamination or corrosion, and it is held for 10 minutes at 1.5 times the design pressure. Due to the possibility of brittle fracture of nonmetallic piping which may be found in systems under the scope of B31.3, a pneumatic leak test requires a pressure relief device having a set pressure of the test pressure plus the smaller of 50 psi or 10 percent of the test pressure. Because chemical piping can involve core complicated equipment and piping designs, there may be additional factors to be considered in a pressure test. Internal piping of a jacketed line should be tested at the more critical of either the internal or jacket design pressure (Paragraph 345.2.5). Because there may be elevated temperatures, Paragraph 345.4.2 includes a provision for establishing a more appropriate test pressure:
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7.4 ASME B31.9 Building Services Piping The scope of this code envelopes industrial, institutional, commercial, public buildings and multi-unit residences. Because the most demanding service that one might
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encounter in such a facility would be steam and condensate, one might expect this code to rely on ASME B31.1. In fact, there are many similarities between B31.9 and B31.1. Both codes cover boiler external piping. However, B31.9 includes steam boilers up to 15 psig maximum, while B31.1 uses 15 psig as a lower limit of its scope. Similarly, B31.9 includes water heating units up to 160 psig maximum, while B31.1 uses 160 psig as its lower limit for hot water. Pressure Design of Components B31.9 permits pressure and wall thickness calculations to be performed in accordance with B31.1. Alternately, it permits these to be calculated using the following formulas:
Where the variables are defined as in ASME B31.1. As with B31.1, the Maximum Allowable Stress Values tabulated in Table A-1 already include the weld joint efficiency factor E. That is, the values tabulated are equal to SE.
8 Flexibility analysis Flexibility analysis is done on the piping system to study its behavior when its temperature changes from ambient to operating, so as to arrive at the most economical layout with adequate safety. The following are the considerations that decide the minimum acceptable flexibility on a piping configuration. 1. The maximum allowable stress range in the system. 2. The limiting values of forces and moments that the piping system is permitted to impose on the equipment to which it is connected.
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3. The displacements within the piping system. 4. The maximum allowable load on the supporting structure.
8.1 Methods of Flexibility Analysis There are two methods of flexibility analysis which involve manual calculations. 1. Check as per clause 119.7.1/319.4.1 of the piping code This clause specifies that no formal analysis is required in systems which are of uniform size, have no more than two points of fixation, no intermediate restraints and fall within the empirical equation.
D = the outside diameter of the pipe Y = resultant of total displacement strains to be absorbed by the piping system. L = developed length between anchors. U = anchor distance, straight line between anchors. K = 0.03 for FPS units. = 208.3 for SI units. 2. Guided Cantilever Method Guide cantilever is based on the simple concept of "minimum length".
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Figure 13: Guided cantilever method
When two vessels are connected by a straight pipe, the pipe may buckle or dent the sides of the vessel when operating at high temperature due to expansion. To overcome this difficulty a bend is provided as shown in figure above. So that the movement δ due to expansion will be absorbed and stresses are restricted to a given value. The minimum length for this configuration to absorb movement can be calculated as
Where, L = minimum leg length. f = maximum bending stress. δ = movement. E = Young's modulus. D = outer diameter of the pipe.
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9 Pipe supports 9.1 Introduction The term ―supports‖ or ―supporting elements‖ encompasses the entire range of various methods of carrying the weight of pipeline and the contents. It therefore includes ―hangers‖ which generally carry the weight from above, with the supporting members being mainly in tension. Likewise, it includes ―supports‖ which on occasion are delineated as those which carry weight from below, with supporting member being in compression. If it transmits the load from pipe to structures or pressure equipment e.g.: Spring Hangers, Guides. These are called Fixtures. Attachment like clips, clamps, strips are called Structural Attachments. Pipe supports bear the dead loading, live loading, wind, snow, and seismic loadings, as well as the loads imposed or caused by variations in temperatures, both ambient and the contained fluid. Pipe supports must prevent exceeding the stress limit of the piping material, and prevent excessive forces and moments on the equipment to which the piping is attached. Also more problems to be considered:
Piping stress in excess of those permitted in the standard code.
Leakage at joints due to misaligned flanges.
Excessive thrust and moments on connected equipment (such as pumps and turbines).
Excessive stresses in the supporting (or restraining) elements.
Resonance with imposed fluid induced vibrations
Excessive interference with thermal expansion and contraction in a piping system, which is otherwise adequately flexible.
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Unintentional disengagement of piping from its supports.
Excessive piping sags in systems requiring drainage slope.
9.2 Pipe supports standards Design of pipe supports are addressed in Standards such as:
ANSI31.1 &31.3 i.e. Power Piping & Process Piping.
MSS–SP 58 Pipe Hangers and Support: Materials, Design & Manufacturers.
MSS–SP 69 Pipe Hangers and Supports: Selection & Application.
MSS–SP 77 Guidelines for Pipe Supports Contractual Relationships.
MSS–SP 89 Pipe Hangers and Supports: Fabrication & Installation practices.
MSS–SP 90 Guide lines on Terminology of Pipe Hangers & Su p p o r t s.
Design of Non-standard pipe supporting elements (beams, columns, welds, etc.) should be in accordance with the requirements as prescribed by the American Institute of Steel Construction standards, or unless another standard is specified.
9.3 Types of supports There are six main types of supports: 1. Rigid or weight supports & hangers. 2. Variable effort supports & hangers. 3. Constant effort supports. 4. Spring loaded sway braces. 5. Dynamic restraints. 6. Snubbers & shock absorbers.
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7. Ancillary items 1. Rigid or weight supports & hangers Rigid Hangers are normally used at suspension points where no vertical movement (i.e. along the ―Y‖ Axis) occurs and the only considerations are the Load at the point of support, line temperature, Pipe Material of construction, and insulation thickness.
Figure 14: Rigid hangers
Rigid supports support the Pipe line from the bottom and usually rest on the floor, pipe rack or structure. Pipe line subjected to horizontal expansions only in the ―X‖ or ―Z‖ direction may be supported by Pipe roller guides and when both ―X‖ & ―Z‖ direction movement takes place pipe lines are supported by pipe shoes with low friction slide bearings beneath them. It is understood that there is no movement of pipe line in the ―Y‖ i.e. vertical direction. A pipe shoe or pipe base is also a rigid support as it supports the pipe line from beneath & normally rests or welded to structure.
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2. Variable effort supports & hangers
Figure 15: Variable effort hanger
Variable effort supports also known as variable hangers or variables are used to support pipe lines subjected to moderate (approximately up to 50mm) vertical thermal movements. Variable effort supports are used to support the weight of pipe work or equipments along with weight of fluids (gases are considered weightless) while allowing certain quantum of movement with respect to the structure supporting it. Spring supports may also be used to support lines subject to relative movements occurring typically due to subsidence or earthquakes. 3. Constant effort supports and hangers When confronted with large vertical movements typically 150 mm or 250 mm, there is no choice but to select a constant effort support (CES). When the Load variation percentage exceeds 25% or the specified max LV% in a variable hanger, the choice is to go for a CES‘s. For pipes which are critical to the performance of the system or so called critical piping where no residual stresses are to be transferred to the pipe it is a common practice to use CES‗s.
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So why is it called a Constant? Because in a constant effort support the load remains constant when the pipe moves from its cold position to the hot position. Thus irrespective of travel the load remains constant over the complete range of movement. Therefore it‘s called a constant load hanger. Compared to a variable load hanger where with movement the load varies & the hot load & cold load are two different values governed by the travel & spring constant. Simply put the operation of a constant effort support can be equated to a pipe supported via a wire rope , with the pipe at one end , a dead weight equal to the pipe at the other & the wire passing over a weightless frictionless pulley. The figure below illustrates then same.
Figure 16: Equivalent operation of constant effort support
When the pipe moves up due to thermal expansion the dead weight moves down & vice versa. In the olden days pipes were supported like this, but the system was discontinued due to the compact nature of modern pipe work installations & the cost of materials and the fact that the pulley wire rope business was prone to a lot of maintenance activities. Thanks to helical coil springs, bell crank levers & the marvels of modern engineering the constant effort support was developed to support pipe lines by occupying a very small envelope & costing a fraction of their large rope pulley cousins.
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Figure 17: Constant effort supports
4. Spring loaded sway braces
Figure 18: Sway Braces
A standard variable spring hanger unit is used to support tensile loads (Hanging types) or compressive loads, but never a combination of both. Sway braces are essentially double acting variable spring units which mean they can handle both tensile & compressive loads. As the name suggests ―sway‖ braces are spring loaded units mounted on pipe work to limit the swaying or vibration induced by external forces by applying an opposing force
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on the pipe. A sway brace will try & prevent the pipe vibrating at its resonant frequency (if the pipe vibrates at its resonant frequency, the amplitude will double & can lead to failures in supporting structure & attached equipments.), but it will not stop the vibration as long as the force inducing the vibration is present. 5. Neutral Adjustment: After installing sway braces & the plant start operating, the pipe may have thermal movements. This may cause the spring in the sway brace to compress by an amount equal to the thermal movement. At this point the sway brace will be exerting a force on the pipe line equal to the pre-load + (movement * spring constant). The load has to be released by doing ―Neutral adjustment‖. This is achieved by rotating the Rod coupling in a direction such that the piston plate gets released & rests against the end plate. In this condition the sway brace will not exert any force on the pipe. During shut down, as the pipe cools & gets in to the cold position, the sway brace will exert a force on the pipe as the spring will get compressed. Sway braces are normally designed to allow a movement of ±70mm. 6. Dynamic restraints
Figure 19: Dynamic restraints “Shock absorbers”
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The restraint system performs an entirely different function to that of the supports. The latter is intended to carry the weight of the pipe work and allow it to move freely under normal operating conditions. The restraint system is intended to protect the pipe work, the plant and the structure from abnormal conditions; it should not impede the function of the supports. Conditions that necessitate the use of restraints are as follows:
Earthquake.
Fluid disturbance.
Certain system functions.
Environmental influences.
In areas that are situated on or near to geological fault lines it is common practice to protect the plant from potential earthquake activity. In such plant there will be a very large requirement for dynamic restraints. Fluid disturbance can be caused by the effect of pumps and compressors or occasionally fluid in a liquid state entering a pipe intended for the transportation of gas or steam. Some system functions such as rapid valve closure, pulsation due to pumping and the operation of safety relief valves will cause irregular and sudden loading patterns within the piping system. The environment can cause disturbance due to high wind loadings or in the case of offshore oil and gas rigs, impact by ocean waves. The restraint system will be designed to cater for all of these influences. So what is a restraint? A restraint is a device that prevents either the pipe work or the plant to which the pipe work is connected being damaged due to the occurrence of any one or more of the above phenomenon.
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It is designed to absorb and transfer sudden increases in load from the pipe into the building structure and to deaden any opposing oscillation between the pipe and the structure. Therefore dynamic restraints are required to be very stiff, to have high load capacity and to minimize free movement between pipe and structure. Snubbers and shock absorbers are usually used as a part of the dynamic restraints. More details about them are in the next section. 7. Snubbers and shock absorbers Hydraulic snubbers: Similar to an automobile shock arrestor the hydraulic snubber is built around a cylinder containing hydraulic fluid with a piston that displaces the fluid from one end of the cylinder to the other. Displacement of fluid results from the movement of the pipe causing the piston to displace within the cylinder resulting in high pressure in one end of the cylinder and a relatively low pressure in the other.
Figure 20: Hydraulic Snubbers
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The fluid passes through a spring-loaded valve, the spring being used to hold the valve open. If the differential pressure across the valve exceeds the effective pressure exerted by the spring, the valve will close. This causes the snubber to become rigid and further displacement is substantially prevented. The hydraulic snubber is normally used when the axis of restraint is in the direction of expansion and contraction of the pipe. The snubber is therefore required to extend or retract with the normal operation of the pipe work. The snubber has low resistance to movement at very low velocities. Mechanical snubbers: Whilst having the same application as the hydraulic snubber, retardation of the pipe is due to centrifugal braking within the snubber. A split flywheel is made to rotate at high velocity causing steel balls to be forced radially outwards. The flywheel is forced apart by the steel balls causing braking plates to come together thus retarding the axial displacement of the snubber.
Figure 21: Mechanical snubbers
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Rotation of the flywheel is generated by the linear displacement of the main rod acting on a ball-screw or similar device. It‘s a very complicated system and also very expensive. 8. Ancillary items Ancillaries are the hardware that complement spring supports and allow the connection of the pipe to the building structure, sometimes as simple as a pipe shoe or comprised of many items from a beam clamp through hanger rods, spreader beams and pipe clamps.
Figure 22: Different ancillary items used in pipe supports
Selecting ancillary items The three main factors that will decide on which ancillary items you require are:
The weight of the pipe being supported.
The general arrangement of the support being designed.
The temperature of both the pipe and the surrounding environment.
When thinking about the weight of the pipe or the load that the ancillaries will be expected to carry it is important to consider all possible loadings.
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Normal operating load, including the weight of heavy pipe clips, riser clamps or spreader beams should be taken into account.
Beam attachments may carry substantially higher loads than the actual design load of the pipe. Eccentric loading on beam attachments such as our figure 172 need very special design consideration and should be shown to a competent engineer before final detailing.
Hydraulic test loading must be considered in conjunction with the additional weight of the hanger assembly; our components are designed with a safety factor that allows up to 100% additional loading. If the combined loading is greater than twice the specified safe working load you must refer the problem to a competent engineer.
It is important to consider any other factors that may cause increased loading during the whole operating life of the plant; snow loading, wind loading, surge loading, temporary loads due to access and many other possibilities.
Normally it is reasonable to expect the Customer to advise all design and plant life loadings.
How the support is fixed; is it hanging from or standing on steelwork or concrete?
Is there a clear path to the pipe from the point of attachment to the structure?
Is the pipe moving horizontally and vertically?
In which direction are the forces being applied?
Finally, temperature has a significant influence on the ability of steel to withstand stress. High temperatures (above 350°C) cause steel to lose strength and we must begin to consider the phenomenon of creep. Low temperature, below 0°C causes steel to become brittle and reduce its ability to withstand sudden increases in load.
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Quite obviously the temperature of the fluid within the pipe will affect the pipe clip or attachment to the pipe. The material of the pipe will be specified to suit its operating temperature and this may also dictate the material of the pipe clamp regardless of the actual design temperature. Often and not so obvious, the temperature of the surroundings may affect the choice of ancillary and the type of material we can use. A plant in Siberia will experience ambient temperatures as low as -45° C and so all components of the pipe support will need to be manufactured from low temperature carbon steel or even austenitic stainless steel. Similarly, a pipe suspended within the boiler casing of a power plant may operate at a temperature of 570°C dictating that we use a CrMo alloy pipe clamp. However the load bolt of the clamp, the hanger rod and weld less eye nut will be exposed to the same temperature because they too are within the boiler casing.
9.4 Pipe system support designing 1. Supports specifications These specifications must be taken into consideration by the designer. The exact hot or operating load required to be supported during the working condition.
Hydrostatic test load.
The total travel.
The direction of travel either upwards or downwards from the erected position.
The set pin locking position.
The basic model.
Requirements of bottom accessory components such as rods, clamps etc.
Any hazardous environmental conditions.
Any special finish on the body such as galvanizing.
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2. Location of supports Supports should be located at near as possible to concentrated loads as valves, flanges etc. to keep the bending stresses to the minimum. When changes of direction in a horizontal plane occur, it is suggested that the spacing be limited to 75% of the tabulated values to promote stability and reduce eccentric loadings. The standard span does not apply to vertical run pipes (risers) since no moment and no stress will develop due to gravity load in the riser. The support should be located on the upper half of a riser to prevent instability in overturning of pipe under its own weight. Table 1: Suggested maximum span for a given pipe nominal bore Pipe (N.B.)
Suggested maximum span Water. Mtrs. (ft.)
Air/Steam .Mtrs. (ft.)
1
2.1 (7)
2.7 (9)
2
3.0 (10)
4.0 (13)
3
3.7 (12)
4.6 (15)
4
4.3 (14)
5.2 (17)
6
5.2 (17)
6.4 (21)
8
5.8 (19)
7.3 (24)
12
7.0 (23)
9.1 (30)
16
8.2 (27)
10.7 (35)
20
9.1 (30)
11.9 (39)
24
9.8 (32)
12.8 (42)
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Figure 23: The support should be located on the upper half of a riser
3. Thermal movement in pipe supports Modern process & Power plants are very compact & have complex piping routings, layouts. Now days with modern software & powerful computers pipe lines are modeled in 3D. Pipe lines which carry fluids have a tendency to expand with increase in temperature.
Figure 24: Effect of thermal expansion on pipes
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Metal will expand with rise in temperature, expansion being equal to coefficient of thermal expansion applicable to that metal & will take place in all 3 axes i.e. X, Y & Z. In the figure above a piece of steel round rod is clamped & heated ,due to thermal expansion it will bend as it is prevented from expanding linearly by the clamping device. Similarly a pipe line will expand in the linear direction (when hot fluids are transported through it). When the pipe line is complex consisting of horizontal runs, vertical risers, U bends, elbows, loops etc. with fittings like valves, flanges, insulation etc the expansion profile becomes very complex. Typically pipe line isometric drawing is prepared showing pipe line dimensions, sizes, length, temperature, fittings etc. This drawing will also show possible positions of pipe hangers based on spacing of pipe supports i.e. span between adjacent supports, availability of structural members, columns, beams, floors etc from where pipe supports can be suspended or placed. This data is fed into pipe stress analysis software package. The output of the stress analysis provides data on the forces, moments & movements at various points in the 3 axes namely X Y & Z. X & Z movements & forces are in the horizontal / lateral plane and the Y axis movements are in the vertical plane. So if we take the figure below as an example; a resting type pressure vessel fixed to the ground is generating steam. The steam is evacuated from the vessel by means of a pipe line connected to the flange at the nozzle at the top of the vessel. The pipe line has a long vertical run, takes a 90° bend then again a 90° bend & rises up. The entire weight of the pipe line is supported by the resting type Pipe shoe assembly fixed at point ―B‖ to a structural member as shown.
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Figure 25: The effect of hot loading
Hence no weight is transferred to the nozzle in this condition. Pressure vessel nozzles (Point ―A‖) are highly stressed components as they are operating under high pressure & elevated temperatures hence it is not desirable to transfer piping loads on to them. As the steam starts flowing in the pipe, due to heating of the line, thermal expansion takes place & Point ―B‖ will lift off the resting pedestal. In this condition the entire weight of the pipe line is now transferred to the nozzle. This situation is not desirable as the nozzle is stressed beyond its designed loadings. To avoid this situation a flexible support is introduced at Point ―C‖ which will allow the Pipe to move vertically and at the same time support the load of the pipe to prevent its weight being transferred to the nozzle. This is achieved by using a spring hanger, the spring supporting the load & being flexible allows movement.
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Figure 26: Using spring supports to allow movement
Thus when there is no movement in the ―Y‖ axis pipe lines are supported by means of rigid hangers & when there is movement in the Y axis the pipes are supported by means of spring hangers which support the pipe load & at the same time allow pipe to move when subjected to thermal expansion. 4. Maximum Load Variation This is the variation in load or stress imposed on the pipe work system when moving from the cold condition to the hot condition. This is usually expressed as a percentage of the hot load. Hot Load This is the working load of the support in the ―Hot‖ condition i.e. when the pipe has traveled from the cold condition to the hot or working condition. The pipe is presumed to be in the cold condition when the plant or the line is not working. As the steam or other hot fluids start flowing in the line, it gets heated, starts expanding causing thermal movement. This condition after the expected thermal movement takes place is known as the hot condition. It is assumed that in the hot condition the downward force exerted 80
by the pipe along with the weight of fluids, self weight of pipe & fittings is equal & opposite to the upward reaction of the spring as it is in a compressed state. Thus the line is theoretically supposed to be ―floating‖ or perfectly counter balanced. As the pipe is suspended or supported directly on the spring any thermal movement of pipe line will force the support to expand or compress causing either a decrease or increase in load. This differential change in load is known as Load Variation expressed as a percentage. Normally MSS-SP58 specifies max Load Variation (popularly called LV) as 25%. However designers sometimes impose a cap on the load variation for certain supports on critical pipe work to reduce the differential stresses experienced by it, this only means using pipe supports with a softer spring constant to achieve it. Load Variation:
5. Example The following worked examples will explain the concepts discussed above. For the selection of variable effort hanger or support: All spring hanger manufacturers publish catalogues of products manufactured by them. The catalogue will have a support selection shart, giving sizes, loads, spring constants & working movements. A part of a typical table is reproduced below. Steps for selection of hangers to suit specified loads & travels: 1. Determine the required supporting effort (operating load or preset load as the case maybe) & pipe movement (up or down) installed to operating.
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2. Locate the spring size which accommodates the required Load; ensure that required travel can be achieved with in the ―working range‖ as shown in catalogues. 3. Compute the preset load based on operating load, travel & spring constant for the chosen size. Here it is advised to choose the spring constant for V1 series first & if found unsuitable due to reasons such as LV% exceeding max LV specified , choose V2 series & so on where V2 springs are softer. 4. Formulae for calculating Cold Load: the travel should be with the correct direction i.e. + for up travel & - for down travel. 5. Ensure that both the cold load & hot load can be accommodated in the same size i.e. the same vertical column under the spring size. 6. If the Loads & travel cannot be accommodated, try the next size or the next travel range. Continue this iteration process till the following criteria are met:
Operating & Preset Load in the same size.
Load variation less than specified LV%.
Smallest possible size selected.
Case I: Operating Load as the Basis Operating Load = 1000 Kg; travel = + 20 mm Selected Size from Selection table = Size 19 Spring Rate for V1 = 16.27 kg/mm Cold Load = 1000 + (16.27 x 20) = 1325.4 Kg (Out of Load Range) Load Variation = (1325.4 ~1000) x 100/1000=32.5 % Not Acceptable as it is more than 25%
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Spring rate for V2 = 8.13 Kg/mm Cold load =1000 + (8.13 x 20) = 1162.6 Kg. Load variation = (1162.6~1000) x 100/1000 = 16.3% Hence Selected Size = V2-19 Case II: Preset Load as the Basis Preset Load = 1000 Kg; travel = + 20mm Selected Size from Table = Size 12 Hot Load = 1000 – (8.13 x 20) = 837.4 Kg Load variation = (837.4~1000) x 100/1000 = 16.3% Selected Size = V2-19
10 Buried Pipe Design 10.1 Introduction and Overview Underground conduits have served to improve people‘s standard of living since the dawn of civilization. Remnants of such structures from ancient civilizations have been found in Europe, Asia, and even the western hemisphere, where some of the ancient inhabitants of Southland Central America had water and sewer systems. These early engineering structures are often referred to as examples of the art of engineering. Nevertheless, whether art or science, engineers and scientists still stand amazed at these early water and sewer projects. Today, underground conduits serve in diverse applications such as sewer lines, drain lines, water mains, gas lines, telephone and electrical conduits, culverts, oil lines, coal slurry lines, subway tunnels, and heat distribution lines. It is now possible to use engineering science to design these underground conduits with a degree of precision comparable with that obtained in designing buildings and bridges. In the early 1900s,
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Anson Marston developed a method of calculating the earth load to which a buried conduit is subjected in service. Engineers and planners realize that the subsurface infrastructure is an absolute necessity to the modern community. It is true we must ―build down‖ before we can ―build up.‖ The underground water systems serve as arteries to the cities, and the sewer systems serve as veins to carry off the waste. The water system is the lifeblood of the city, providing culinary, irrigation, and fire protection needs. Sewage is collected at its source and carried via buried conduits to a treatment facility. Treatment standards and controls are becoming continually more stringent, and treatment costs are high. Because of these higher standards, the infiltration of groundwater or surface water into sewer systems has become a major issue. In the past, sewer pipe joining systems were not tight and permitted infiltration. Today, however, tight rubber ring joints or cemented joints have become mandatory. Even though septic tanks and cesspools are still widely used today, they are no longer accepted in urban or suburban regions. Only in the truly rural (farm) areas are they sanctioned by health departments. Today, more sewer systems are being installed. This produces a demand for quality piping systems. Thus, the need for water systems that deliver quality water and for tight sanitary sewers has produced a demand for highquality piping materials and precisely designed systems that are properly installed. Old and deteriorating conduits frequently fail. These failures can cause substantial property damage those results in tremendous cost, inconvenience, and loss of public goodwill. Utilities have programs to replace or rejuvenate deteriorating pipes to minimize failures and associated costs. In urban areas, trenching to remove the old and install the new can be very difficult and extremely expensive. Relining and micro tunneling are viable options in certain situations where it is difficult and extremely disruptive to construct using an open trench.
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10.2 Soil Mechanics Various parameters must be considered in the design of a buried piping system. However, no design should overlook pipe material properties or the characteristics of the soil envelope surrounding the pipe. The word soil means different things to different people. To engineers, soil is any earthen material excluding bedrock. The solid particles of which soil is composed are products of both physical and chemical action, sometimes called weathering of rock. Soil has been used as a construction material throughout history. It is used for roads, embankments, dams, and so forth. In the case of sewers, culverts, tunnels, and other underground conduits, soil is important, not only as a material upon which the structure rests, but also as a support and load-transfer material. The enveloping soil transfers surface and gravity loads to, from, and around the structure. Much has been written about soil mechanics and soil structure interaction. Such variables as soil type, soil density, moisture content, and depth of the installation are commonly considered. If finite element analysis is used, many soil characteristics are required as input to the mathematical soil model. These soil properties are usually determined from triaxial shear tests. Standards organizations such as the American Association of State Highway and Transportation Officials (AASHTO) and the American Society for Testing and Materials (ASTM) issue standard test methods for classifying soil and for the determination of various soil properties. Of the various methods of soil classification, the Unified Soil Classification System (USCS) is most commonly used in the construction industry. Complete details on this system can be found in any textbook or manual on soils engineering. The project engineer often requires a soil survey along the route of a proposed pipeline. Information from the survey helps to determine the necessary trench configuration and to decide whether an imported soil will be required to be placed around the pipe. Soil parameters such as soil type, soil density, and moisture content are usually considered in a design. Soil stiffness (modulus) is an extremely important soil property and is the
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main contributor to the pipe-soil system performance. Experience has shown that a high soil density will ensure high. soil stiffness. Therefore, soil density is usually given special importance in piping system design. Economy in any design is always a prime consideration. The engineer must consider the cost of compaction compared to the cost of bringing in a select material such as pea gravel which will flow into place in a fairly dense state. For piping systems, a compacted, well-graded, angular, granular material provides the best structural support. However, such is not always required. In selecting a backfill material, the designer will consider such things as depth of cover, depth of water table, pipe materials, compaction methods available, and so forth.
10.3 Strength of Materials There are many types of piping materials on the market today ranging from rigid concrete to flexible thermal plastic. Proponents of each lay claim to certain advantages for their material. Such things as inherent strength, stiffness, corrosion resistance, lightness, flexibility, and ease of joining are some characteristics that are often given as reasons for using a particular material. A pipe must have enough strength and/or stiffness to perform its intended function. It must also be durable enough to last for its design life. The term strength as used here is the ability to resist stress. Stresses in a conduit may be caused by such loadings as internal pressure, soil loads, live loads, differential settlement, and longitudinal bending, to name a few. The term stiffness refers to the material‘s ability to resist deflection. Stiffness is directly related to the modulus of elasticity of the pipe material and the second moment of the cross section of the pipe wall. Durability is a measure of the pipe‘s ability to withstand environmental effects with time. Such terms as corrosion resistance and abrasion resistance are durability factors. Piping materials are generally placed in one of two classifications: rigid or flexible. A flexible pipe has been defined as one that will deflect at least 2 percent without structural distress. Materials that do not meet this criterion are usually considered to be rigid. Claims that a particular pipe is neither flexible nor rigid, but somewhere in between
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have little importance since current design standards are based either on the concept of a flexible conduit or on the concept of a rigid conduit. See Figure 27. Concrete and clay pipes are examples of materials which are usually considered to be rigid. Steel and plastic pipes are usually considered to be flexible. Each type of pipe may have one or more performance limits which must be considered by the design engineer. For rigid pipes, strength to resist wall stresses due to the combined effects of internal pressure and external load is usually critical. For flexible pipes, stiffness may be important in resisting ring deflection and possible buckling. Each manufacturer or industry goes to great lengths to establish characteristics of its particular product. These parameters are readily available to the design engineer. The desire to have products with high strength has given rise to reinforced products such as steel-reinforced concrete and glass-reinforced thermal setting plastic. For such products, other performance limits often arise such as strain limit to prevent cracking. For a thermal plastic pipe, such as PVC pipe, strength is measured in terms of a long-term hydrostatic design hoop stress. Thus, it can be seen that not all installations of all products will be designed in exactly the same manner. The engineer must be familiar with design criteria for the various pipe products and know where proper design parameters can be obtained.
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Figure 27: The effect of soil settlement on (a) rigid and (b) flexible pipes. S represents settlement of backfill for a rigid pipe. D represents vertical deflection of a flexible pipe as it deflects under earth pressure
Pipe Hydraulics The field of study of fluid flow in pipes is often referred to as hydraulics. Designers of water or sewer systems need some knowledge of pipe hydraulics. Flow in pipes is usually classified as pressure flow for systems where pipes are flowing full or open-channel flow when pipes are not flowing full. Water systems are pressure systems and are considered to be flowing full. On the other hand, sewer systems, for the most part, are open-channel systems. The exception to this is forced sewer mains where lift pumps are used to pump sewage under pressure. The relatively small concentrations of solids found in sanitary or storm sewage is not sufficient to make it behave significantly different from water hydraulically. Thus, sewage is accepted to have the same hydraulic flow characteristics as water. Of course, the design engineer must be aware of the possibility of the deposition of solids and hydrogen sulfide gas generation in sanitary sewers. These considerations are not within the scope of this text. In case, pressure flow or open channel flow, the fluid encounters frictional resistance. This resistance produces head loss, which is a function of the inside surface finish or pipe roughness. The smoother the inside surface, the better the flow. Many
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theories and empirical equations have been developed to describe flow in pipes. The solution of most flow problems requires experimentally derived coefficients which are used in conjunction with empirical equations. For pressure flow, the Hazen-Williams equation is widely accepted. Another equation that has a more theoretical basis is attributed to Darcy and Weisback. For open-channel flow, the Manning equation is normally used. These equations, or others, are used to calculate head loss as a function of flow or vice versa.
10.4 Water Systems Water systems are lifelines of communities. They consist of such items as valves, fittings, thrust restraints, pumps, reservoirs, and, of course, pipes and other miscellaneous appurtenances. The water system is sometimes divided into two parts: the transmission lines and the distribution system. The transmission system is that part of the system which brings water from the source to the distribution system. Transmission lines have few, if any, interconnections. Because of this, flow in such a line is usually considered to be quasi-steady with only relatively small transients. Such lines are normally placed in fairly shallow soil cover. The prime design consideration is internal pressure. Other design considerations include longitudinal stresses, ring deflection, buckling, and thrust restraints. The distribution piping system distributes water to the various users. It includes many connections, loops, and so forth. The design is somewhat similar to that of transmission lines except that a substantial surge allowance for possible water hammer is included in the pressure design. Also, greater care is usually taken in designing the backfill for around the pipe, fittings, and connections. This is done to prevent longitudinal bending and differential settlement. Distribution systems are made up of an interconnected pipe network. The hydraulic analysis of such a system is almost impossible by ―hand‖ methods, but is readily accomplished using programming methods via digital computers.
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10.5 Design for Value The piping system must be strong enough to withstand induced stresses, have relatively smooth walls, have a tight joining system, and be somewhat chemically inert with respect to soil and water. The piping systems must be designed to perform for an extended period. The normal design life for such systems should be 50 years minimum. However, 50 years is not long enough. Government and private agencies cannot afford to replace all the buried pipe infrastructures on a 50-year basis. A 100-year design life should be considered minimum. Pipe manufacturers warrant their products to be free from manufacturing defects, but cannot guarantee the pipe will perform for a given length of time. This is because the life of the pipe, after it is installed, is not just a function of the pipe material, but is largely a function of the loading conditions and the environment to which it is subjected. It is the design engineer‘s responsibility to assess all factors and formulate a design with a predicted design life. The cost of the system should be based on life considerations, not just initial cost. Most piping system contracts are awarded to the lowest bidder. Contractors will usually bid materials and construction methods which allow for the lower initial cost with little thought to future maintenance or life of the system. Even for the owner, the lowest initial cost is often the overriding factor. However, the owner and the engineer should insist on a design based on value. For engineers, economics is always an important consideration; any economic evaluation must include more than just initial cost. Annual maintenance and life of the system must also be considered. Initial cost may include such things as piping materials, trenching, select backfill, compaction, site improvements and restoration, and engineering and inspection. Pipe cost is related to pipe material and to pipe diameter. Diameter is controlled by the design flow rate and pipe roughness. That is, a smaller diameter may be possible if a pipe with a smooth interior wall is selected. Annual maintenance cost includes cleaning, repair, and replacement due to erosion, corrosion, and so forth. Life is directly related to durability and is affected by such things as severe loading conditions, corrosion, erosion, and other types of environmental degradation. It is important to design the installation to minimize detrimental effects.
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The question is not whether the pipe will last, but how long it will perform its designed function. Generally, metals corrode in wet clayey soils and corrode at an accelerated rate in the presence of hydrogen sulfide sewer gas. Concrete-type structures are also attacked by hydrogen sulfide and the resulting sulfuric acid. Care should be taken when selecting a pipe product for any service application and installation conditions to ensure that environmental effects upon the life of the system have been taken into consideration. The system should be designed for value. 1. External loads i.
Soil Pressure
The subject of soil structure interaction has been of engineering interest since the early 1900s. The horseless carriage had its volume-production start with the Oldsmobile in 1902, and the need for improved roads was immediately apparent. Many projects for road drainage were begun using clay tile and concrete drain tile. One major problem existed, however. There was no rational method of determining the earth load these buried drains would be subjected to. As a result, there were many failures of pipelines. The loads imposed on conduits buried in the soil depend upon the stiffness properties of both the pipe structure and the surrounding soil. This results in a statically indeterminate problem in which the pressure of the soil on the structure produces deflections that, in turn, determine the soil pressure. a) Rigid pipe Marston load theory. Anson Marston, who was dean of engineering at Iowa State University, investigated the problem of determining loads on buried conduits. In 1913, Marston published his original paper, ―The Theory of Loads on Pipes in Ditches and Tests of Cement and Clay Drain Tile and Sewer Pipe.‖ This work was the beginning of methods for calculating earth loads on buried pipes. The formula is now recognized the world over as the Marston load equation. More recently, demands to protect and improve our environment and rising construction costs have produced research that has substantially increased our knowledge of soil structure interaction phenomenon.
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However, much of this knowledge has yet to be applied to design practice. Many questions are as yet unresolved. Trench condition. The Marston load theory is based on the concept of a prism of soil in the trench that imposes a load on the pipe, as shown in Figure 28. A trench (ditch) conduit as defined by Marston was a relatively narrow ditch dug in undisturbed soil. Marston reasoned that settlement of the backfill and pipe generates shearing or friction forces at the sides of the trench. He also assumed that cohesion would be negligible since (1) considerable time would have to elapse before cohesion could develop and (2) the assumption of no cohesion would yield the maximum load on the pipe. The vertical pressure V at the top of any differential volume element Bd(1) dh is balanced by an upward vertical force at the bottom of the element V + dV (see Fig. 2.1). The volume element is Bd wide, dh tall, and of unit length along the axis of the pipe and trench. The weight of the elemental section is its volume times its unit weight, expressed as
Where (Bd)(dh)(1) is volume of the element and γ is the specific weight density. The lateral pressure P L at the sides of the element at depth h is
OR
The shearing forces per unit length Fs on the sides of the differential element, induced by these lateral pressures, are Fs = K (V/Bd) (µ‘) dh where µ‘ coefficient of friction. The vertical forces on the element are summed and set equal to zero.
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Or, the upward vertical forces are equal to the downward vertical forces. Thus, for equilibrium, vertical force at bottom + shear force at sides = vertical force at top + weight of the element, (dimensionally, force per length), or
Figure 28: Basis for Marston’s theory of load on buried pipes
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Figure 29: Computational diagram for earth loads on trench conduits completely buried in trenches.
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The solution to the differential Equation (2.1) is
Embankment conditions. Not all pipes are installed in ditches (trenches); therefore, it is necessary to treat the problem of pipes buried in embankments. An embankment is where the top of the pipe is above the natural ground. Marston defined this type of installation as a positive projecting conduit. Typical examples are railway and highway culverts. Figure 2.4 shows two cases of positive projecting conduits as proposed by Marston. In case I, the ground at the sides of the pipe settles more than the top of the pipe. In case II, the top of the pipe settles more than the soil at the sides of the pipe. Case I was called the projection condition by Marston and is characterized by a positive settlement ratio rsd, defined as (see Figure 30)
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Figure 30: Comparison of positive projecting conduits: (a) Projection conditions; (b) ditch condition.
All the above discussed parameters affect the load on the pipe and are incorporated in Marston‘s load equation for positive projecting (embankment) conduits
Where
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Figure 31: Diagram for coefficient Cc for positive projecting conduits.
Tunnel construction. Marston‘s theory may be used to determine soil loads on pipes that are in tunnels or that are jacked into place through undisturbed soil. The Marston tunnel load equation is
Where Wt is the load on the pipe in pounds per linear foot and is specific weight. The load coefficient Ct is obtained in the same way that Cd was determined
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And Bt is the maximum tunnel width; or if the pipe is jacked, Bt is the OD of the pipe. The coefficient C is called the cohesion coefficient and is, dimensionally, force per unit area (lb/ft^2). It is readily apparent that the theory for loads on pipes in tunnels or being jacked through undisturbed soil is almost identical to the theory for loads on pipes in trenches. The tunnel load will be somewhat less because of the soil cohesion. It is also apparent that C is very important in determining the load. Unfortunately, values of the coefficient C have a wide range of variation even for similar soils. The value of C may be determined by laboratory tests on undisturbed samples. Conservative values of C should be used in design to account for possible saturation of the soil. It has been suggested that about one-third of the laboratory determined value should be used for design. b) Flexible pipe A flexible pipe derives its soil-load-carrying capacity from its flexibility. Under soil load, the pipe tends to deflect, thereby developing passive Soil support at the sides of the pipe. At the same time, the ring deflection relieves the pipe of the major portion of the vertical soil load which is picked up by the surrounding soil in an arching action over the pipe. The effective strength of the flexible pipe-soil system is remarkably high. For example, tests at Utah State University indicate that a rigid pipe with a three-edge bearing strength of 3300 lb/ft buried in class C bedding will fail by wall fracture with a soil load of about 5000 lb/ft. However, under identical soil conditions and loading, a PVC sewer pipe deflects only 5 percent. This is far below the deflection that would cause damage to the PVC pipe wall. Thus the rigid pipe has failed, but the flexible pipe performed successfully and still has a factor of safety with respect to failure of 4 or greater. Of course in flat-plate or three-edge loading, the rigid pipe will support much more than the flexible pipe. This anomaly tends to mislead some engineers because they relate low flat-plate supporting strength with in-soil load capacity—something one can do for rigid pipes but cannot do for flexible pipes.
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Table 2: Recommended safe values of cohesion C
Marston load theory. For the special case when the side fill and pipe have the same stiffness, the amount of load V that is proportioned to the pipe can be found merely on a width basis. This means that if the pipe and the soil at the sides of the pipe have the same stiffness, the load V will be uniformly distributed as shown in Figure 32. By simple proportion the load becomes
Pipe stiffness versus soil compressibility. Measurements made by Marston and Spangler revealed that the load on a flexible pipe is substantially less than that on a rigid pipe. The magnitude of this difference in loads may be a little shocking. The following analogy will help us to understand what happens in the ground as a flexible pipe deflects. Suppose a weight is placed on a spring. We realize the spring will deform, resisting deflection because of its spring stiffness. When load versus deflection is plotted, we find that this relationship is linear up to the elastic limit of the spring (Figure 33). When a load is placed on a flexible pipe, the pipe also deflects and resists deflection because of its stiffness. It is even possible to think of soil as being a nonlinear spring that resists movement or deflection because of its stiffness (Figure 34).
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Figure 32: Load proportioning according to Marston’s theory for a flexible pipe.
Figure 33: Graphic of linear spring.
Figure 34: Graphic of spring, pipe, and soil.
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When we draw an analogy between a rigid pipe represented by a stiff spring in comparison to soil at its sides, represented by more flexible springs, and then place a load or weight on this spring system representing a rigid pipe in soil, we can easily visualize the soil deforming and the pipe carrying the majority of the load (see a in Figure 35). If the situation is reversed and we place a flexible spring between two springs which are much stiffer, representing the soil, we can again picture the pipe deflecting as a load is applied and the soil in this case being forced to carry the load to a greater extent (see b in Figure 35). When a flexible pipe is buried in the soil, the pipe and soil then work as a system in resisting the load (Figure 36). The system is statically indeterminate. That is, the deflection of the pipe is a function of the load on the pipe, but the load on the pipe is a function of the deflection. The reduction in load imposed on a pipe because of its flexibility is sometimes referred to as arching. However, the overall performance of a flexible pipe is not just due to this so-called arching, but is also due to the soil at the sides of the pipe resisting deflection (see Figure 37).
Figure 35: Flexible and stiff springs working together
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Figure 36: Graphic of pipe and soil working together as a system
Figure 37: Graphic showing the contribution of sidefill soil in the performance of a flexible pipe
Equation (2.10) has become known as the Marston-Spangler load equation for flexible pipes. It should be remembered, however, that the assumption of soil friction resisting the downward movement of the central soil prism has been used in its development, and that it should not be used merely because a pipe is flexible. The maximum loads on rigid and flexible pipes as predicted by the Marston equations, Eqs. (2.4) and (2.10), do not take place instantaneously and may not occur for some time. In certain cases the initial load may be 20 to 25 percent less than the maximum load predicted by Marston, and the long-term load may be greater than that predicted.
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Prism load. Again, Eq. (2.4) represents a maximum-type loading condition, and Eq. (2.10) represents a minimum. For a flexible pipe, the maximum load is always much too large since this is the load acting on a rigid pipe. The minimum is just that, a minimum. The actual load will lie somewhere between these limits. A more realistic design load for a flexible pipe would be the prism load, which is the weight of a vertical prism of soil over the pipe. Also, a true trench condition may or may not result in significant load reductions on the flexible conduit since a reduction depends upon the direction of the frictional forces in the soil. Research data indicate that the effective load on a flexible conduit lies somewhere between the minimum predicted by Marston and the prism load. On a long-term basis, the load may approach the prism load. Thus, if one desires to calculate the effective load on a flexible conduit, the prism load is suggested as a basis for design. The prism or embankment load is given by the following equation (see Figure 38):
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Figure 38: Graphic depiction of the prism load on a pipe
To obtain load in pounds per foot, multiply the above by the pipe OD in feet:
The Marston load for this example is 56 percent of the prism load and is nonconservative for design. Again, for flexible conduits, the prism load theory represents a realistic estimate of the maximum load and is slightly conservative. Trench condition. The Marston-Spangler equation for the load on a flexible pipe in a trench is given by Eq. (2.10). The load coefficient Cd is obtained from. One may ask, under what conditions, if any, will the prism load and the ditch (trench) load be equal?
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Multiply the prism load by Bc (to express in pounds per foot, as in the Marston load) and set it equal to the Marston load.
Tunnel loadings. There are few documented data dealing with loads on flexible pipes placed in unsupported tunnels. However, since a flexible pipe develops a large percentage of its load-carrying capacity from passive side support, this support must be provided, or the pipe will tend to deflect until the sides of the pipe are being supported by the sides of the tunnel. When a flexible pipe is jacked into undisturbed soil, the load may be calculated by the prism load, Eq. (2.11), or Eq. (2.9).
The prism load in this case will be very conservative because it neglects not only friction but also the cohesion of the soil. If Ct is taken as H/Bt and the cohesion coefficient is zero, then the two methods of calculating loads give the same results.
11 Conclusion Stresses in pipe or piping systems are generated due to loads experienced by the system. These loads can have origin in process requirement, the way pipes are supported, piping system s static properties such as own weight or simple transmitted loads due to
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problems in connecting equipments such as settlement or vibrations. Whatever may be the origin of load, these stresses the fabric of the MoC and failure may occur. Fatigue failure is an important aspect in flexibility analysis of piping systems. Often cyclic stresses in piping systems subjected to thermal cycles get transferred to flexibility providing components such as elbows. These become the components susceptible to fatigue failure. Thermal stress analysis or flexibility analysis attempts to guard against such failure through very involved calculations.
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