# PRESSURE VESSEL DESIGN HANDBOOK PDF

Pressure Vessel Design Handbook 2nd Ed - Henry H. Bednar (Krieger Pub) - Free ebook download as PDF File .pdf) or view presentation slides online. Library of Congress Cataloging-in-PublicationData Moss, Dennis R. Pressure vessel design manual: illustrated procedures for solving major pressure vessel. Thank you very much for reading pressure vessel design handbook. As you may know, PDF Download Pressure Vessel Design Manual Free. BEDNAR.

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Pressure vessel design manual: illustrated procedures for solving major pressure Pressure vessels-Design and construction Handbooks, manuals, etc. I. Title. chapter oneOverview of pressure vessels Contents Introduction Pressure Vessels: Design and Practice (Mechanical Engineering). Home · Pressure Vessels: .. DOWNLOAD PDF Mechanical Engineer's Handbook ( Engineering). PRESSURE VESSELS ONLINE COURSE, Part I – Instructor Javier Tirenti - Pressure Vessel Design Handbook – HENRY BEDNAR. -Modern Flange.

Nasman, G. Pai, D. Windenberg, D. Within the context of pressure vessel design, this primarily involves strength considerations. It might include aspects of fuel system design, reactor design, or thermal hydraulic design. Although the aspect of thermal hydraulic design is intricately related to the structural design, especially for thermal transient loadings, we will not be discussing them in any detail.

It will be assumed that the temperature distribution associated with a particular thermal transient has already been evaluated in a typical design application. However, in these cases the designer still has to consider how the desired configurations of the vessel are to be designed from a structural standpoint and how these designs will perform their intended service.

The role of engineering mechanics in the pressure vessel design process is to provide descriptions of the pressure vessel parts and materials in terms Copyright by CRC Press, Inc. Even the so-called simple models that can be solved in closed form might involve fairly complex mathematics.

In a few isolated instances, intelligent applications of well-known principles have led to simplifying concepts. However, in a majority of cases, especially when advanced materials and alloys are at a premium, there is a need to make the optimum use of the materials necessitating application of advanced structural analysis. As the complexity of the analysis increases, the aspect of interpretation of the results of the analysis becomes increasingly extensive.

Furthermore, a large number of these models approximate the material behavior along with the extent of yielding.

As we understand material behavior more and more, the uncertainties and omitted factors in design become more apparent. The improvement will continue as knowledge and cognizance of influencing design and material parameters increase and are put to engineering and economic use. The safety demands within the nuclear industry have accelerated studies on pressure vessel material behavior and advanced the state of the art of stress analysis. For instance, the nuclear reactor, with its extremely large heavy section cover flanges and nozzle reinforcement operating under severe thermal transients in a neutron irradiation environment, has focused considerable attention on research in this area which has been directly responsible for improved materials, knowledge of their behavior in specific environments, and new stress analysis methods.

High-strength materials created by alloying elements, manufacturing processes, or heat treatments, are developed to satisfy economic or engineering demands such as reduced vessel thickness.

They are continually being tested to establish design limits consistent with their higher strength and adapted to vessel design as experimental and fabrication knowledge justifies their use. There is no one perfect material for pressure vessels suitable for all environments, but material selection must match application and environment.

This has become especially important in chemical reactors because of the embrittlement effects of gaseous absorption, and in nuclear reactors because of the irradiation damage from neutron bombardment.

Major improvements, extensions and developments in analytical and experimental stress analysis are permitting fuller utilization of material properties with confidence and justification.

Many previously insoluble equations of elasticity are now being solved numerically. These together with experimental techniques are being used to study the structural discontinuities at nozzle openings, attachments, and so on. It is therefore apparent that the stress concentrations at vessel nozzle openings, attachments, and weldments are of prime importance, and Copyright by CRC Press, Inc.

Control of proper construction details results in a vessel of balanced design and maximum integrity. In the area of pressure vessel design there are important roles played by the disciplines of structural mechanics as well as material science. As mentioned earlier, we try to provide a description of pressure vessel components in terms of mathematical models that are amenable to closedform solutions, as well as numerical solutions.

The development of computer methods sometimes referred to as computer-aided design, or CAD has had a profound impact on the stress and deflection analysis of pressure vessel components. Their use has been extended to include the evaluation criteria as well, by a suitable combination of postprocessing of the solutions and visual representation of numerical results.

In a number of cases advanced software systems are dedicated to present animation that aids the visualization and subsequent appreciation of the analysis. A number of design and analysis codes have been developed that proceed from the conceptual design through the analysis, sometimes modeling the nonlinear geometric and material behavior.

Results such as temperatures, deflections and stresses are routinely obtained, but the analysis often extends to further evaluations covering creep, fatigue, and fracture mechanics. With the advent of three-dimensional CAD software and their parametric, feature-driven automated design technology, it is now possible to ensure the integrity of designs by capturing changes anywhere in the product development process, and updating the model and all engineering deliverables automatically.

Pressure vessel designs that once averaged 24 hours to finish are completed in about 2 hours. Such productivity gains translate into substantial savings in engineering labor associated with each new pressure vessel design.

The typical design of a pressure vessel component would entail looking at the geometry and manufacturing construction details, and subsequently at the loads experienced by the component.

The load experienced by the vessel is related to factors such as design pressure, design temperature, and mechanical loads due to dead weight and piping thermal expansion along with the postulated transients typically those due to temperature and pressure that are anticipated during the life of the plant.

These transients generally reflect the fluid temperature and pressure excursions of the mode of operation of the equipment.

The type of fluid that will be contained in the pressure vessel of course is an important design parameter, especially if it is radioactive or toxic. Also included is the information on site location that would provide loads due to earthquake seismic , and other postulated accident loads.

In assessing the structural integrity of the pressure vessel and associated equipment, an elastic analysis, an inelastic analysis elastic—plastic or plastic or a limit analysis may be invoked. The design philosophy then is to determine the stresses for the purpose of identifying the stress concentration, the proximity to the yield strength, or to determine the Copyright by CRC Press, Inc. The stress concentration effects are then employed for detailed fatigue evaluation to assess structural integrity under cyclic loading.

In some situations a crack growth analysis may be warranted, while in other situations, stability or buckling issues may be critical. For demonstrating adequacy for cyclic operation, the specific cycles and the associated loadings must be known a priori. In this context, it is important for a pressure vessel designer to understand the nature of loading and the structural response to the loading.

This generally decides what type of analysis needs to be performed, as well as what would be the magnitude of the allowable stresses or strains.

Generally the loads acting on a structure can be classified as sustained, deformation controlled, or thermal. These three load types may be applied in a steady or a cyclic manner. When the load is applied cyclically a failure due to fatigue is likely; this is termed failure due to high cycle fatigue. Cyclic loads or cyclic temperature distributions can produce plastic deformations that alternate in tension and compression and cause fatigue failure, termed low cycle fatigue.

Such distribution of loads could be of such a magnitude that it produces plastic deformations in some regions when initially applied, but upon removal these deformations become elastic, and subsequent loading results in predominantly elastic action.

This is termed shakedown. Under cyclic loading fatigue failure is likely and because of elastic action, this would be termed as low cycle fatigue.

This produces cycling straining of the material which in turn produces incremental growth cyclic leading to what is called an incremental collapse. This can also lead to low cycle fatigue. Such environmental conditions include corrosion, neutron irradiation, hydrogen embrittlement, and so on. General Design Procedure General Vessel Formulas [1,2] Procedure External Pressure Design Procedure Properties of Stiffening Rings Procedure Code Case [1,8,21] Procedure Design of Cones Procedure Design of Toriconical Transitions [1,3] Procedure Design of Intermediate Heads [1,3] Procedure Design of Flat Heads [1,2,4,5,6] Procedure Optimum Vessel Proportions [][] Procedure Design of Jacketed Vessels Procedure Flange Design Introduction Procedure Design of Flanges [1—4] Procedure Design of Spherically Dished Covers Procedure Design of Blind Flanges with Openings [1,4] Procedure Design of Studding Outlets Procedure Reinforcement for Studding Outlets Procedure Studding Flanges Procedure Design of Elliptical, Internal Manways Procedure Through Nozzles References 4.

Design of Vessel Supports Introduction: Support Structures Procedure Seismic Design — General Procedure Seismic Design for Vessels [2] Procedure Seismic Design — Vessel on Rings [4,5,8] Procedure Seismic Design — Vessel on Lugs [5,8—13] Procedure Seismic Design — Vessel on Skirt [1,2,3] Procedure Design of Horizontal Vessel on Saddles [1,3,14,15] Procedure Design of Base Plates for Legs [20,21] Procedure Design of Lug Supports Procedure Properties of Concrete References 5.

Vessel Internals Procedure Design of Internal Support Beds Procedure Design of Lattice Beams Procedure Design of Support Blocks Procedure Hub Rings used for Bed Supports Procedure Design of Internal Pipe Distributors Procedure Design of Trays Procedure Flow Over Weirs Procedure Design of Demisters Procedure Let us consider a long thin cylindrical shell of radius R and thickness t, subject to an internal pressure p. If the ends of the cylindrical shell are closed, there will be stresses in the hoop as well as the axial longitudinal directions.

A section of such a shell is shown in Figure 5. Consider a thick cylindrical shell of inside radius Ri and outside radius Ro subjected to an internal pressure p as shown in Figure 5. Figure 5. The allowable stress, Sm, is replaced by the term SE to be explained later. In both of the above equations, S is the allowable stress and E is the joint efficiency. This joint efficiency is employed because cylindrical shells are often fabricated by welding. The values of E depend on the type of radiographic examination performed at various welded seams of the shell.

The cylinder is in a stable configuration as long as it remains circular in shape.

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If there is an initial ellipticity, the cylinder will be in an unstable condition and will eventually buckle. Do The basic Eq. For the first case above, a factor of safety of 3.

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For the second case, a variable factor of safety is used starting with a factor of safety of 3. As the cylinder becomes progressively thicker, the buckling ceases to be a plausible mode of failure. The ASME procedure is an involved one in which two sets of curves have to be used to investigate buckling. For simplicity let us assume the spherical head and the cylindrical shell are of the same thickness.

If the mean radius and the thickness of the shell are denoted by Rm and t respectively, then the hoop and the longitudinal stresses in the cylindrical shell are given by: These discontinuity forces produce local bending stresses in the adjacent portions of the vessel. The deflection and the slope induced at the edges of the cylindrical and spherical portions by the force V are equal. In Eq. Flugge, W. Timoshenko, S. Hetenyi, M. Find the thickness of a cylindrical shell 2 m in diameter if it is required to contain an internal pressure of 7 MPa.

The allowable stress in the material is MPa. A thick cylindrical shell of 1. Determine the following: Magnitude and location of the maximum hoop stress b. Magnitude of the maximum radial stress and its location c.

Average hoop stress 3. A thick cylinder has an inside diameter of mm and an outside diameter of mm. If the allowable stress is MPa, what is the maximum internal pressure that can be applied?

A cylinder has an inside radius of 1. What is the required thickness if the allowable stress is MPa? For problem 4, what is the required thickness if thick cylinder equations were used? The allowable stress Sm of the material is 14 MPa.

The inside diameter of a boiler made of alloy steel is 2 m. The internal pressure is 0. The allowable stress is MPa and the joint efficiency is 70 percent. What thickness is to be used? A thick vessel is to be designed to withstand an internal pressure of 50 MPa. An internal diameter of mm is specified and steel with a yield stress of MPa is to be used. Calculate the wall thickness using the Tresca and von Mises criteria using a factor of safety of 1. Hemispherical heads under internal pressure ASME equation for hemispherical heads Example problem The ends of the vessels are closed by means of heads before putting them into operation.

The heads are normally made from the same material as the shell and may be welded to the shell itself. They also may be integral with the shell in forged or cast construction. The head geometrical design is dependent on the geometry of the shell as well as other design parameters such as operating temperature and pressure. The heads may be of various types such as: The geometry of the head is selected based on the function as well as on economic considerations, and methods of forming and space requirements.

The elliptical and torispherical heads are most commonly used. The carbon steel hemispherical heads are not so economical because of the high manufacturing costs associated with them. They are thinner than the cylindrical shell to which they are attached, and require a smooth transition between the two to avoid stress concentration effects. The thickness values of the elliptical and torispherical heads are typically the same as the cylindrical shell sections to which they are attached.

Conical and toriconical heads are used in hoppers and towers. Because of the geometrical symmetry, the membrane stresses in the circumferential and the meridional directions are the same, and are denoted by S.

This allowable stress is MPa. K is given by the following expression: Based on plastic analysis,1 the following expression is used for t: The allowable stress is MPa and the internal pressure is KPa. We also have r 0: Hence a minimum thickness The design is therefore dictated by stability of the knuckle region of the head. Accordingly, the thickness, tc in the cone region is calculated using conical head equations and that in the head transition section is calculated using torispherical head equations.

Referring to Figure 6. L r from Eq. Most common is of course the torispherical head, which is characterized by inside diameter, crown radius, and knuckle radius. The designer selects a head configuration that minimizes the total cost of the plate material and its formation.

Figure 6. They are either integrally formed with the shell, or may be attached by bolts. The value of C could range anywhere from 0. We wish to determine the thickness of the head if the allowable stress in the material is limited to MPa.

We have from Eq. Roark, R. Stress concentration about a circular hole Cylindrical shell with a circular hole under internal pressure Spherical shell with a circular hole under internal pressure Reinforcement of openings In some cases we have nozzles and piping that are attached to the openings, while in other cases there could be a manway cover plate or a handhole cover plate that is welded or attached by bolts to the pad area of the opening.

The design of openings and nozzles is based on two considerations: Primary membrane stress in the vessel must be within the limits set by allowable tensile stress. Peak stresses should be kept within acceptable limits to ensure satisfactory fatigue life.

Because of removal of material at the location of the holes, there is a general weakening of the shell. The amount of weakening is of course dependent on the diameter of the hole, the number of holes, and how far the holes are spaced from one another.

One of the ways the weakening is accommodated for is by introducing material either by weld deposits or by forging. The aspects of stress intensification as well as reinforcement will be addressed in this chapter.

The biaxial tension would correspond to a cylindrical shell or a spherical shell subject to internal pressure. For the case of a cylindrical shell, the biaxiality is 2: The radial and tangential components of the stresses at a distance r from the center of the hole of radius a see Figure 7. Figure 7. This gives the following stress distribution: This gives the following stress distributions see Figure 7. The additional material is deemed effective in carrying the higher loads.

On most vessels, is provided on the outside of the vessel. In some vessels, the reinforcement appears inside, while in others both inside and outside regions are reinforced. On many vessels, however, the arrangement is such that no reinforcement can be placed on the inside because of interfering components. The placement of this additional material is important. So this distance is generally taken at the boundary limit for the effective reinforcement to the vessel surface.

This is indicated in Figure 7. We have seen that the stress intensity factor for an opening in either a cylindrical shell or a spherical shell is greater at the edge of the opening and diminishes away from the opening.

Therefore providing additional material near the edge would bring down the average stresses. Generally the limits of reinforcement extend in a direction parallel and perpendicular to the surface of the shell, and are based on the assumption that the added reinforcement adequately compensates for the loss of structural integrity as a result of material removal at the opening. The limit parallel to the surface of the shell is typically set as the larger of two quantities: If we consider d as the controlling dimension then the stress intensity factor at a distance d from the center of the hole in a cylindrical shell is 1.

It is judged that with the added reinforcement the nominal stress could be reduced close to that of a solid shell.

The limit normal to the surface of the shell measured inward or outward is typically set as the smaller of a 2. The shell and the nozzle allowable stress is MPa. The shell and nozzle thickness are 25 mm and 32 mm, respectively. Parallel to the shell the limit is therefore mm.

The limit normal to the surface of the shell is the smaller of a 2. Therefore the limit is 2. The reinforcement scheme is shown in Figure 7. An alternative form of reinforcement is shown in Figure 7. The additional area is 2dtp, where we have provided an extra thickness tp on the shell for reinforcement purposes. One of the main disadvantages of this reinforcement method is that it gives no information on stresses and these can vary significantly from one design to another resulting in differing performances, especially for cyclic loadings.

Leckie and Penny3 treat the case of nozzles in spherical vessels in their analysis of an intersecting cylinder and sphere. The maximum stress occurring in the sphere was presented in a graphical form. Both flush and protruding nozzles were considered in the analysis.

The stress concentration factors have been calculated in terms of the maximum stress in the sphere by neglecting the bending stresses.

## Pressure vessel design handbook

These are the nozzle and sphere diameters d and D, and the corresponding thicknesses t and T. This is evident from Figure 7. However because of the thin-shell assumptions concerning the joining of the nozzle and the sphere, the solutions can only be expected to describe the gross structural behavior. To obtain a suitable stress concentration factor for a nozzle in a cylindrical vessel, an approximate axisymmetric model is sometimes used.

A popular approximation used is where the equivalent sphere has twice the diameter of the shell.

## Pressure Vessels: Design and Practice (Mechanical Engineering)

The general trend of the experimental results is shown in Figure 7. Leckie, F. Stated simply, fatigue failure is caused by the cyclic action of loads and thermal conditions. In many design situations, the expected number of cycles is in millions and for all practical purposes can be considered as infinite. Accordingly, the concept of endurance limit has been employed in a number of design rules. Endurance limit is the stress that can be applied for an infinite number of cycles without producing failure.

However, the typical number of stress cycles rarely exceeds , and frequently only a few thousand. Therefore, fatigue analysis requires somewhat more involved concepts than just the endurance limit.

Fatigue refers to the behavior of material under repeated loads, which is distinct from the behavior under monotonically applied loading. The fatigue process itself occurs over a period of time. However, failure may occur suddenly and without prior warning, in which case the damage mechanisms may have been operating since loading was first introduced. This period of time is often referred to as the usage period. The fatigue process appears to initiate from local areas that have high stresses.

These highly stressed regions are due to abrupt changes in geometry leading to high stress concentrations, due to temperature differentials, imperfections, or the presence of residual stress. The failure takes place when the crack after repeated cycling grows to a point at which the material can no longer withstand the loads and a complete separation occurs.

Metallurgical defects such as a void or an inclusion often act as sites for fatigue crack initiation. The fatigue process consists of crack initiation, crack propagation, and eventual fracture.

Another way to look at the process is to postulate it in terms of initiation of microcracks, coalescence of these microcracks into macrocracks, followed by growth to unstable fracture.

Fatigue has been classified as one of high cycle and low cycle. High cycle fatigue involves very little plastic action. The low cycle fatigue failure involves a few thousand cycles and involves strains in excess of yield strain. Fatigue damage in the low cycle has been found to be related to plastic strain and fatigue curves for use in this region should be based on strain ranges.

For the high cycle fatigue cases, the stress ranges can be used. The procedure of using strain amplitude as a function of number of cycles forms the cornerstone of fatigue analysis. The design curve is based on strain-controlled data. The best-fit curves were reduced by a factor of 2 on stress and 20 on cycles to account for environment, size effect, and scatter of data. Fatigue failure typically occurs at structural discontinuities which give rise to stress concentration.

The stress concentration factors are generally based on theoretical analysis involving statically applied loads. These are directly applicable to fatigue analysis only when the nominal stress multiplied by the stress concentration factor is below the material yield strength. When it exceeds the yield strength, there is a redistribution of stress and strain.

For sharp geometries, using values of stress concentrations obtained elastically leads to underprediction of fatigue lives when compared with the actual test data. In fact under no circumstances does a value of more than 5 need be applied, and it is observed that the value of these factors do not vary with the magnitude of cyclic strain and associated fatigue life. In the design of pressure vessels, the stress concentration — which is really the strain concentration — is limited to 5 and for most discontinuities such as grooves and fillets no more than a value of 4 is used.

The motivation for this effort stems from the fact that most pressure vessels are subjected to limited number of pressure and temperature cycles during their lifetime, and therefore considerable design effort could be saved by defining conditions that do not require a fatigue evaluation to be performed, an approach first proposed by Langer. The six rules are as follows: The specified number of pressure cycling does not exceed the number of cycles on the design fatigue curve, corresponding to the stress amplitude of 3Sm typically twice the yield strength.

The specified full range of mechanical loads does not result in load stresses whose range exceeds Sa, a value obtained from the design fatigue curve for total specified number of significant load fluctuations. A load fluctuation is considered significant if the total excursion of load stress exceeds the value of Sa for cycles. The fatigue exemption rules outlined above are based on a set of assumptions, some of which are conservative and some of which are not so conservative.

It is believed, however, that conservative ones outweigh the nonconservative ones. A stress concentration factor of 2 is assumed at a point where the nominal stress is 3Sm.

This leads to a peak stress of 6Sm due to pressure and is thus quite conservative. This value bounds all the applicable cases of linear thermal gradient, thermal shock, and gross thermal mismatch, and the assumption is indeed a very conservative one.

Here S refers to the applied stress, usually taken as the alternating stress, Sa and N is the number of cycles to failure complete fracture or separation. Constant amplitude S—N curves are usually plotted on a semi-log or log—log coordinates and often contains data points with scatter as shown in Figure 8.

Some of the fatigue curves show a curve that slopes continuously downward with the number of cycles. Other fatigue curves contain a discontinuity or a knee in the S—N curve as shown in Figure 8.

The number of cycles causing fatigue failure depends on the strain level incurred during each cycle. The fatigue curves obtained from experimental data provide the variation of cyclic strain amplitude elastic plus plastic strain with the number of cycles to failure. The critical strain amplitude, at which a material may be cycled indefinitely without Figure 8. Figure 8. Fatigue data in the form of S—N curve are generally obtained at room temperature. The strain range obtained from the test is converted to nominal stress range by multiplying by the modulus of elasticity.

Half of the stress range is the alternating stress, Sa which appears along the ordinate of the S—N curve. The endurance limit, as mentioned earlier, is the cyclic stress amplitude which will not cause fatigue failure regardless of the number of cycles of load application.

The exact endurance limit is never really found, since no test specimen is cycled to infinite number of cycles. For pressure vessels the components are normally not cycled beyond cycles and therefore the fatigue limit is defined as the stress amplitude that will cause fatigue failure in cycles. In most situations, fatigue limit and the endurance limit are used interchangeably and obviously signify stress amplitude that produces fatigue failure in cycles. Strain—life fatigue data are obtained from tests using small polished unnotched axial fatigue specimens under constant amplitude reversed cycles of strain.

Steady-state hysteresis loops can predominate through most of the fatigue life, and this can be reduced to elastic and plastic strain ranges. A typical strain—life curve on a log—log scale is shown in Figure 8. At a given value of N the number of cycles to failure the total strain range is the sum of elastic and plastic strain ranges. Both the elastic and plastic strain curves are straight lines in the log—log plot, having a slope of b and c, respectively.

To determine the local strain range, the cyclic stress strain curve is used, since under the influence of cyclic loads, the material will soon approach the stable cyclic condition. The fatigue curve needed by the designer is one which shows stress, Sa, versus cycles to failure, N, and which contains sufficient safety factors to give safe allowable design stress for a given number of operating cycles, or conversely, allowable operating cycles for a given value of calculated stress. The ordinate value is Sa, as modified by Eq.

The abscissa for the fatigue curve is the number of cycles, N, allowed by the alternating stress intensity, Sa. The design fatigue curves for carbon steel to account for the adjustment for maximum mean stress is shown in Figure 8. Similar curves for austenitic steels and nickel—chrome steels are shown in Figure 8. When, however, such stress ranges are applied concurrently, the stress ranges get added up. These ratios are called partial usage factors. Adding up all these individual partial usage factors, we obtain the cumulative fatigue usage factor, which if less than unity ensures that the component is safe from fatigue failure due to cyclic loadings.

Usage factor must be below unity to satisfy ASME code compliance. When there are two Figure 8. In determining n1, n2, n3, etc, consideration shall be given to the superposition of cycles of various origins which produce a total stress difference range greater than the stress difference ranges of the individual cycles. However, this is by far the simplest method and has been backed up by tests7 that show that the linear assumption is quite good when the cycles of large and small stress magnitude are fairly evenly distributed throughout the life of the vessel.

It is obvious that when the sequence of the stress cycles is known in considerable detail, better accuracy can be obtained. The history is first rearranged to start with the highest peak. Starting from the highest peak we go down to the next reversal.

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If there is no range going down from the level of the valley that we have stopped, we go upward to the next reversal. Looking at Figure 8. This procedure is called rainflow counting because the lines going horizontally from a reversal to a succeeding range resembles rain flowing down a pagoda roof when the history of peaks and valleys is turned around 90 degrees.

Generally speaking this would be the case when the number of cycles associated with each peak or valley is completely exhausted in the counting process. In actual stress time histories there may be cycles left over which should be used for the next count involving the next lesser stress range and so on. The allowable number of cycles is obtained from the design fatigue curve and incremental fatigue usages are obtained by determining the ratios of calculated number of cycles.

The incremental usages are then added to obtain the cumulative fatigue usage. The fatigue evaluation methodology is based on the minimum shear stress theory of failure. This consists of finding the amplitude one half of the range through which the maximum shear stress fluctuates.

This is obtained in the ASME Code procedure by using stress difference and stress intensities twice the maximum shear stress. The principal stresses are calculated from the six components of the stress tensor.

The stress differences are calculated as a function of time for the complete cycle and the largest absolute magnitude of any stress difference at any time is determined.

The alternating stress intensity Sa is one half of this quantity. The specific process used is outlined as follows. This procedure is employed for all the other loadings.

Half of Sr is the stress amplitude, which is used for component fatigue evaluation. For the general multiaxial loading in which the principal axes are no longer fixed but indeed moving then the fatigue evaluation is modified as follows. Half of Sr is the stress amplitude which is used for entering into the design fatigue curve. It may be necessary to investigate many pairs of instants to find the maximum value of Sr. Is a fatigue failure likely? For the stress range of MPa — that is an alternating stress of MPa — the number of cycles to failure from Figure 8.

For the stress range of MPa alternating stress of MPa the number of cycles to failure is ; that for the stress range of MPa alternating stress of MPa , the number of cycles to failure is 20, Therefore fatigue failure is unlikely to occur. Langer, B. Basic Eng. Fuchs, H. Neuber, H.

Osgood, C. Miner, M. Cumulative damage in fatigue, J. Baldwin, E. A stainless steel pressure vessel is subjected to pressure cycles where the stress alternates between zero and MPa. This is followed by 10, cycles of thermal stresses that alternate between zero and MPa. Determine the cumulative fatigue usage. A carbon steel pressure vessel is subjected to pressure cycles at a temperature where the elastic modulus may be taken as MPa.

The stress varies from zero to MPa. This is followed by thermal cycles where the stress varies from — MPa to MPa. Is the vessel safe from fatigue failure? A pressure vessel made from carbon steel is subjected to a number of transients wherein the stress ranges are listed in decreasing order. The alternating stresses and the corresponding number of operating cycles are indicated in the table below.

Determine the cumulative fatigue usage factor. Transient range 1 2 3 4 5 Alternating stress: MPa Number of cycles 10 50 4.

Consider a stress discontinuity in the vessel of Problem 3 that gives rise to an effective stress concentration factor of 1. Gasket joint behavior Design of bolts Their importance stems from two important functions: A representative bolted flanged joint is shown in Figure 9. This is typically comprised of a flange ring and a tapered hub, which is welded to the pressure vessel.

## Pressure Vessel Design Manual

The flange is a seat for the gasket, and the cover along with the gasket is bolted to the flange by a number of bolts. The preload on the bolts is extremely important for the successful performance of the connection. The preload must be sufficiently large to seat the gasket and at the same time not excessive enough to crush it. The bolts should be designed to contain the pressure and for the preload required to prevent leakage through the gasket. The flange region should be designed to resist bending that occurs in the spacing between the bolt locations.

The gasket, which is really the focal point of the bolted flange connection, is subjected to compressive force by the bolts. Figure 9. The fluid pressure tends to reduce the bolt preload, which reduces gasket compression and tends to separate the flange faces.

The gaskets are therefore required to expand to maintain the leakproof boundary. Gaskets are made of nonmetallic materials with composite construction.

The serrated surfaces of the flange faces help to maintain the leak-proof joint as the material expands to fill up the irregularities on the face of the flanges. The mechanics of the bolted joint with gaskets is extremely complex to track analytically and experimental results are often used as bases for design. Some of the factors are determined experimentally. The design calculations use two gasket factors, the gasket seating stress, y, and the gasket factor at operating conditions, m. A higher gasket seating stress ensures better sealing performance.

When the joint is in service, the fluid pressure load unloads the joint, resulting in a reduced gasket stress a process illustrated in Figure 9. Under operating conditions it is advantageous to have a residual gasket stress greater than the fluid Copyright by CRC Press, Inc. For good sealing performance, the ASME Code recommends the residual stress at operating conditions be at least two to three times the contained pressure.

The relationship between the initial seating stress and the residual seating stress is indicated by the gasket stress vs. SG2 is the initial seating stress and SG1 is the operating gasket stress. During assembly, the gasket follows the nonlinear portion of the curve from zero to SG2.

When the operating pressure unloads the gasket, the gasket follows the unloading curve from points SG2 to SG1. Here Wm1 is the operating bolt load, and p is the design pressure. The first term in Eq. The second term is the joint contact load. There must not be any chemical or galvanic action between the materials to preclude the possibility of thread seizure.

The total minimum required cross-sectional area of the bolts should be the greater of the following areas: Wm2 Sa and Wm1 Sb Here Sa is the allowable bolt stress at room temperature, and Sb is the allowable bolt stress at design temperature.

Should twelve mm diameter bolts be adequate to ensure a leak-proof joint? Therefore, 12 bolts of diameter 50 mm give a bolt area of 23, mm2 and should be adequate. The gasket reaction location and the effective width are calculated as follows: For this application we will use 24 bolts of 39 mm major diameter for which the minor diameter area root area is mm2.

The minimum required thickness of the cover plate is calculated by assuming the plate to be simply supported at the gasket load line at diameter G in Figure 9. The thickness of the cover is calculated for two cases and the larger dimension is used for design: Case a: Case b: With a corrosion allowance of 3 mm, the required thickness is 92 mm. For the bolted flange connections that we have discussed, the gaskets are assumed to be entirely within the bolt circle.

The m and y factors used in the design have been in existence since the s. Over the years these factors are being continuously revised to reflect further understanding of the joint performance.

Recently research investigations on flanged joints have focused on tightness-based design. This concept is based on the understanding that all flange joints leak. The objective therefore is to design a flange joint that would ensure an acceptable leakage rate for the enclosed fluid.

Problems Calculate the required cover thickness for a test pressure vessel with the following design conditions: The support has to be designed to withstand the dead weight and seismic loadings from the pressure vessel and to limit the heat flow from the vessel wall to the base.

The pressure vessel support structure should be able to withstand the dead weight of the vessel and internals and the contained fluid without experiencing permanent deformation. The metal temperature of the pressure vessel is usually different to the ambient conditions during its installation.

The differential displacement between the supports due to the temperature change should be considered in design. In a large number of cases the design of support requires adequacy to operate in a severe thermal environment during normal operation as well as to sustain some thermal transients. The other source of thermal loading arises from the thermal expansion of the piping attached to the vessel.

The design must therefore consider the various combination of piping loads on the vessel to determine the most severe load combinations.

In addition the vessel is also subject to mechanical loads due to the action of seismic accelerations on the attached piping. Finally, loads due to handling during installation should be carefully considered in design. The supports for pressure vessels can be of various types including lug support, support skirts, and saddle supports. Such a support is shown in Figure If the vessel is made of carbon steel, the lugs may be directly welded to the vessel.

The method consists of determining the stresses in the vicinity of a support lug of height 2C1 and width 2C2 as shown in Figure The maximum primary plus secondary stress in the shell wall is given as a combination of direct stress due to the thrust, W, bending stress due to longitudinal moment, ML, bending stress due to circumferential moment, MC, and the torsional shear stress due to the twisting moment, MT, with appropriate coefficients.

The earlier work by Bijlaard1 involves representing ML, MC, and MT, by double Fourier series, which enables one to obtain the stresses and deformations in the form of the series. Figure This representation is used for different forms of vessel loadings, where the direct and moment loadings are expressed as double Fourier series and introduced into the shell equations to obtain the values of stress resultants and displacements.

In order to represent the patch load from the lug it is often necessary to have a large number of terms typically about in both the circumferential and axial directions. This approach has been used to draw up the curves presented in WRC They have utilized a finite-element technique using node doubly curved shell elements.However, in a majority of cases, especially when advanced materials and alloys are at a premium, there is a need to make the optimum use of the materials necessitating application of advanced structural analysis.

Pierre, D. The steam generator produces the steam that passes through the turbine, condenser, condensate pumps, feed pump, feed water heaters and back to the steam generator.

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Roark, R. Also we shall discuss the case of cylindrical shells under external pressure where there is a propensity of buckling or collapse. Harvey, J.