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Steel Plate Engineering Data-Volume 1

Steel Tanks for Liquid Storage Revised Edition-1992

The material presented in this publication is for general information only and should not be used without first securing competent advice with respect to its suitability for any given application. The publication of the material contained herein is not intended as a representation or warranty on the part of American Iron and Steel Institute-or of any other person named herein-that this information is suitable for any general or particular use or of freedom from infringement of any patents. Anyone making use ot this information assumes all liability arising from such use.

Published by AMERICAN IRON AND STEEL INSTITUTE In cooperation with and editorial collaboration by STEEL PLATE FABRICATORS ASSOCIATION, INC. Revised December 1992

Acknowledgements or the preparation of the original version of this technical publication on carbon steel plate materials and tanks for liquid storage, the American Iron and Steel Institute retained Mr. I.E. Boberg as author. For his skillful handling of the assignment, the Institute gratefully acknowledges its appreciation. The American Iron and Steel Institute established a Task Force to produce and supply a special section on stainless steel tanks to this publication, and wishes to acknowledge its appreciation to this group for a commendable effort.

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The Institute also wishes to acknowledge the important and valuable contribution made by members of the Steel Plate Fabricators Association and representatives from the member steel producing companies of American Iron and Steel Institute in reviewing, and later revising and updating, the material for publication in this current edition. Appreciation is expressed to the American Society for Testing and Materials, the American Petroleum Institute and the American WaterWorks Association for their constructive suggestions and review of this material. Much of the illustrative material in this manual appears through their courtesy. American Iron and Steel Institute

It is suggested that inquiries for further information on designs of steel tanks for liquid storage be directed to: Steel Plate Fabricators Association, Inc., 3158 Des Plaines Avenue, Des Plaines, IL 60018.

AMERICAN IRON AND STEEL INSTITUTE 1101 17th Street N.W., Suite 1300, Washington, D.C. 20036-4700

PRINTED IN USA 1992

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Introduction he purpose of this publication is to provide a design reference for the usual design of tanks for liquid storage. For unusual applications, involving materials or liquids not covered within these pages, nor referenced herein, designers should consult more complete treatments of the subject material. For information related to design of bulk storage vessels, refer to SPFA publication "USEFUL INFORMATION ON THE DESIGN OF STEEL BINS AND SILOS" by John R. Buzek.

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Part I contains general information pertaining to all types of carbon plate steels. This section may seem elementary to the metallurgist or to one who is thoroughly familiar with steel industry terminology, practice and classification. For others, it should be helpful to an understanding of what follows. Part II deals with the particular carbon steels applicable to tanks for liquid storage. Part III covers the design of carbon steel tanks for liquid storage. Part IV covers materials, design, and fabrication of stainless steel tanks for liquid storage. It has been revised for this publication by the Committee of Stainless Steel Producers of American Iron and Steel Institute. Inquiries for further information on design of steel tanks should be directed to Steel Plate Fabricators Association, Inc.

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Contents Part Part Part Part

I II III IV

Materials-General ........................... 1 Materials-Carbon Steel Tanks for Liquid Storage. 7 Carbon Steel Tank Design .................... 9 Stainless Steel Tanks for Liquid Storage ........ 27

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Part I Materials-General Designation OSt of the steel specifications referred to in this manual are contained in the Book of ASTM Standards, Part 4, which can be obtained from the American Society for Testing and Materials (ASTM). Each ASTM specification has a number such as A283, and within each specification there may be one or more grades or qualities. Thus an example of a proper reference would be "ASTM designation A283 grade C." In the interest of simplicity, such a reference will be abbreviated to "A283-C." ASTM standards are issued periodically to report new specifications and changes to existing ones having a suffix indicating the year of issue such as "A283-C-79." Thus a summary such as is provided here may gradually become incomplete, and it is important that the designer of steel plate structures have the latest edition of ASTM standards available for reference.

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Definitions At least a nodding acquaintance with the terminology of the steel industry is essential to an understanding of steel specifications. This is especially true because, in common with many other industries, a number of shop and trade terms have become so thoroughly implanted in the language that they are used instead of more precise and descriptive technical terms. The following discussions may be of assistance.

Steelmaking Processes Practically all steel is made by the open hearth furnace process, the electric furnace process or the basic oxygen process. ASTM specifications for the different steels specify which processes are permissible in each case.

Steelmaking Practice The steels with which we are concerned are either strand cast, or cast into ingots which may be hot rolled to convenient size for further processing or alternatively ingots may be hot rolled directly into plates. In most steelmaking processes, the principal

chemical reaction is the combination of carbon and oxygen to form a gas. If the oxygen available for this reaction is not removed, the gaseous products continue to evolve during solidification in the ingot. Cooling and solidification progress from the outer rim of the ingot to the center, and during the solidification of the rim, the concentration of certain elements increases in the liquid portion of the ingot. The resulting product, known as RIMMED STEEL; has marked differences in characteristics across the section and from top to bottom of the ingot. Control of the amount of gas evolved during solidification is accomplished by the addition of a deoxidizing agent, silicon being the most commonly used. If practically no gas evolved, the result is KILLED STEEL, so called because it lies quietly in the ingot. Killed steel is characterized by more uniform chemical composition and properties than other types. Although killed steel is a quality item, the end result is often not so specified by name, but rather by chemical analYSis. Other deoxidizing elements are used, but in general, a specified minimum silicon content of 0.10% on heat analysis indicates that a steel is "fully killed." The term SEMIKILLED designates an intermediate type of steel in which a smaller amount of deoxidizer is added. Gas evolution is sufficiently reduced to prevent rimming action, but not sufficiently reduced to obtain the same degree of uniformity as attained in fully killed steels. This controlled evolution of gas during solidification tends to offset shrinkage, resulting in a higher yield of usable material from the ingot. As a practical matter, therefore, plates originating from ingots are usually furnished as semikilled steel unless a minimum silicon content of 0.10 0/0 on heat analysis is specified.

Chemical Requirements A discussion of the effects of the many elements added to steels would involve a metallurgical treatise far beyond the scope of this work. However, certain elements are common to all steels, and it may be of help to briefly outline the effects of carbon, manganese, phosphorus, and sulfur on the properties of steel. CARBON is the principal hardening element in steel, and as carbon increases, hardness increases.

High Strength Low Alloy Steels

Tensile strength increases, and ductility, notch . toughness and weldability generally decrease wIth increasing carbon content. MANGANESE contributes to strength and hardness, but to a. lesser degree than carbon. Increasing the mf;mganese content generally decreases ductilirv and weldability, but to a lesser degree than carbon. Because of the more moderate effects of manoanese, carbon steels, which attain part of their strength through the addition of manganese, exhibit greater ductility and improved toughness than steels of similar strength achieved through the use of carbon alone. PHOSPHORUS. Phosphorus can result in noticeably hlgher yield strength and decreases in ductility, toughness, and weldability. In the steels under discussion here, it is generally kept below a limit of 0.04 0/0 on heat analysis. SULFUR decreases ductility, toughness, and weldability, and is generally kept below a limit of 0.05 0/0 on heat analysis. HEAT ANALYSIS is the term applied to the chemical analysis representative of a heat of steel and is the analysis reported to the purchaser. It is usually determined by analyzing, for such elements as have been specified, a test ingot sample obtained from the front or middle part of the heat during the pouring of the steel from the ladle. PRODUCT ANALYSIS is a supplementary chf2tmical analysis of the steel in the semifinished or fi mshed product form. It is not, as the term might imply, a duplicate determination to confirm a previous result.

These steels, generally with specified yield point of 50 ksi or higher and containing small amounts of alloying elements, are often employed where high strength or light weight is desired.

Mechanical Requirements Mechanical testing of steel plates includes tension, hardness, and toughness tests. The test specimens and the tests are described in ASTM specifications A6, A20, A370, and A673. From the tension tests are determined the TENSILE STRENGTH and YIELD POINT or YIELD STRENGTH, both of which are factors in selecting an allowable design stress, and the elongation over either a 2" or 8" gage length. Elongation is a measure of ductility and workability. Toughness is a measure of ability to resist brittle fracture. Toughness tests are generally not required unless specified, and then usually because of a low service temperature and/or a relatively high design stress. Conditions under which impact tests are required or suggested will be discussed in connection with specific structures. A number of tests have been developed to demonstrate toughness, and each has its ardent proponents. The test most generally accepted currently, however, is the test using the Charpy V Notch specimen. Details of this specimen and method of testing can be found in ASTM-A370, "Mechanical Testing of Steel Products," and in A20 and A673. Briefly described, an impact test is a dynamic test in which a machined, notched specimen is struck and broken by a single blow in a specially designed testing machine . .The energy expressed in foot-pounds required to break the specimen is a measure of toughness. Toughness decreases at lower temperatures. Hence, when impact tests are required, they are usually performed near temperatures anticipated in service.

Carbon Steel Steel is usually considered to be carbon steel when: 1. No minimum content is specified or required for chromium, cobalt, columbium, molybdenum, nickel, titanium, tungsten, vanadium, zirconium, or any other element added to obtain desired alloying effect; 2. When the maximum content specified for any of the following elements does not exceed the percentages noted: manganese 1.65, copper 0.60, silicon 0.60; 3. When the specified minimum for copper does not exceed 0.40 0/0. There are some exceptions to these rules in High Strength Low Alloy (HSLA) steels.

Grain Size Grain size is affected by both rolling practice and deoxidizing practice. For example, the use of aluminum as a deoxidizer tends to produce finer grains. Unless included in the ASTM specification, or unless otherwise specified, steels may be furnished to either coarse grain or fine grain practice at the producer's option. Fine grain steel is considered to have greater toughness than coarse grain steels. Heat-treated fine grain steels will have greater toughness than as-rolled fine grain steels. The designer is concerned only with the question of under what conditions is it justifiable to pay the extra cost of specifying fine grain practice with or without heat treatment in order to obtain improved toughness. Guidelines will be discussed in later sections.

Alloy Steel Steel is usually considered to be alloy when either: 1. A definite range or definite minimum quantity is required for any of the elements listed above in (1) under carbon steels, or 2. The maximum of the range for alloying elements exceeds .one or more of the limits listed in (2) under carbon steels. Again, the HSLA steels demonstrate some exceptions to these general rules.

Heat Treatment POST-WELD HEAT TREATMENT consists of heating the steel to a temperature between 1100F and

2

and special requirements for which are outlined under separate specification numbers such as A36, A283, A514, etc. Similarly, ASTM designation A20, General Requirements for Steel Plates for Pressure Vessels, covers a group of common requirements and tolerances which apply to a list of about 35 steels, the chemical composition and special requirements for which are outlined under separate ASTM specification numbers. Both A6 and A20 define tolerances for thickness, width, length, and flatness, but for the designer the important difference is in the quality of the finished product as influenced by the difference in the extent of testing. A general comparison of the two qualities follows: 1. Chemical Analysis - The requirements for phosphorus and sulfur are more stringent for pressure vessel quality than for structural quality. Both A6 and A20 require one analysis per heat plus the option of product analysis. Product analysis tolerances for structural steels are given in A6. 2. Testing for mechanical properties. a) In general, all specifications for structural quality require two tension tests per heat, size bracket and strength gradation. A6 specifies the general location of the specimens. b) In general all specifications for pressure vessel quality require either one or two transverse tension tests, depending on heat treatment, from each plate as rolled, * (and as heat-treated, if any). This affords a check on uniformity within a heat. Specification A20 also specifies the location from which the specimens are to be taken. 3. Repair of surface imperfections and the limitations on repair of surface imperfections are more restrictive in A20 than A6.

1250F, furnace cooling until the temperature has reduced to about 600F and then cooling in air. Residual stresses will be reduced by this procedure. NORMALIZING consists of heating the steel to between 1600F and 1700F, holding for a sufficient time to allow transformation, and cooling in air, primarily to effect grain refinement. QUENCHING consists of rapid cooling in a suitable medium from the normalizing temperature. This treatment hardens and strengthens the steel and is normally followed by tempering. TEMPERING consists of reheating the steel to a relatively low temperature (which varies with the particular steel and the properties desired). This temperature normally lies between 1000F and 1250F. Through the quenching and tempering treatment, many steels can attain excellent toughness, and at the same time high strength and good ductility. To illustrate the effect of heat treatment on toughness and strength, refer to Figure 1-1. The numerical values shown apply only to the specific steel described. For other steels, other values would apply, but the trends would be similar. Referring to Figure 1-1, if the designer has selected a Charpy V Notch value of "x" ft.-Ibs, as desirable under special service conditions, it will be noted that the steel illustrated would not be acceptable at temperatures lower than about + 35F in the as-rolled condition. In the normalized condition, the same steel would be acceptable down to about - 55F, and if quenched and tempered, to about - 80F together with an increase in carbon, manganese, or other hardening elements. Note, however, that heat treatment adds to the cost and is indicated only when service conditions indicate the necessity for increased toughness and/or increased strength.

Classification of Steel Plates

Welding

Plate steels are defined or classified in two ways. The first claSSification, which has already been discussed, is based on differences in chemical . composition between CARBON STEELS, ALLOY STEELS and HIGH STRENGTH LOW ALLOY STEELS. The second classification is based primarily on the differences in extent of testing between STRUCTURAL QUALITY STEELS and PRESSURE VESSEL QUALITY STEELS. * It should not be construed that these terms limit the use of a particular steel. Pressure vessel steels are often used in structures other than pressure vessels. The distinction between structural and pressure vessel qualities is best understood by a comparison of the governing ASTM speCifications. ASTM designation A6, General Requirements for Rolled Steel Plates for Structural Use, covers a group of common requirements and tolerances for the steels listed therein, the chemical composition

Inasmuch as practically all plate structures are fabricated by welding, a brief discussion of welding processes follows. Welding consists of joining two pieces of metal by establishing a metallurgical bond between them. There are many different types of welding, but we are concerned only with arc welding. Arc welding is a fusion process in which the bond between the metals is produced by reducing the surfaces to be joined to a liquid state and then allowing the liquid to solidify. The heat required to reduce the metal to liquid state is produced by an electric arc. The arc is formed between the work to be welded and a metal wire which is called the electrode. The electrode may be consumable and add metal to the molten pool, or it may be nonconsumable and of a relatively inert metal, in which case no metal is added to the workpiece.

* Pressure vessel quality steels were previously known as FLANGE

and FIRE-BOX qualities, historically inherited terms used to define differences in the extent of testing, but which have no presentday significance insofar as the end use of the steel is concerned.

*The term "Plate as rolled" refers to the unit plate rolled from a slab or directly from an ingot in relation to the number and location of specimens, not to its condition.

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Electrogas or Electroslag Welding

In the welding of steel plate structures, we are concerned principally with five variations of arc welding: 1. Shielded metal arc process (SMAW) 2. Gas metal arc process (GMAW) 3. Flux-cored arc process (FCAW) 4. Electrogas or Electroslag welding 5. Submerged arc process (SAW)

This process is a method of gas metal-arc welding or flux-cored-arc welding wherein molding shoes confine the molten weld metal for vertical position welding.

Submerged Arc Welding Submerged arc welding is essentially an automatic process, although .semi-automatic applications have been used. The arc between a bare electrode and the work is covered and shielded by a blanket of granular, fusible material deposited on the work ahead of the electrode as it moves relative to the work. Filler metal is obtained either from the electrode or a supplementary welding rod. The fusible shielding material· is known as melt or flux. In submerged arc welding, there is no visible evidence of the arc. The tip of the electrode and the molten weld pool are completely covered by the flux throughout the actual welding operation. High welding speeds are achieved. It will be obvious that the necessity of depositing a granular flux ahead of the electrode lends itself best to welding on work in the down flat pOSition. Nevertheless, ingenious devices have been developed for keeping flux in place, so that the process has been applied to almost all positions except overhead welding.

Shielded Metal Arc Welding In the early days of arc welding, the consumable electrode consisted of a bare wire. The pool of molten metal was exposed to and adversely affected by the gases in the atmosphere. It beca~~ obvious that to produce welds with adequate ductility, the molten metal must be protected or shielded from the atmosphere. This led to the development of the shielded metal arc process, in which the electrode is coated ~ith materials that produce a gas as the electrode IS consumed which shields the arc from the atmosphere. The coating also performs other functions, including the possible adding of all~ying elements as well as slag-forming materials which float to the top and protect the metal during solidification and cooling. In practice, the process is limited primarily to manual manipulation of the electrode. Not too many years ago, this process was almost universally used for practically all welding. It is still widely ,used for position welding, i.e., welding other than In the down flat pOSition. For the down flat position some of the later processes described below are much faster and hence less costly.

Weldability It will be observed from the above that all arc welding processes result in rapid heating of the parent metal near the joint to a very high temperature followed by chilling as the relatively large mass of parent plate conducts heat away from the heat-affected zone. This rapid cooling of the weld metal and heat-affected zone causes local shrinkage relative to the parent plate and resultant residual stresses. Depending on the chemical composition of the steel, plate thickness and external conditions, special welding precautions may be indicated. In very cold weather, or in the case of a highly hardenable material, pre-heating a band on either side of the joint will slow down the cooling rate. In some cases post-heat or stress relief as described earlier in this section is employed to reduce residual stresses to a level approaching the yield strength of the material at the post heat temperature. With respect to chemical composition, carbon is the single most important element because of its contribution to hardness, with other elements contributing to hardness but to lesser degrees. It is beyond our scope to provide a definitive discussion on when special welding precautions are indicated. In general, the necessity is dictated on the basis of practical experience or test programs.

Gas Metal Arc Welding In the gas-shielded arc welding process, the mOI.ten pool of metal is protected by an externally supplied gas, or gas mixture, fed through the electrode holder rather than by decompOSition of the electrode coating. The electrode is a continuous filler-~etal (consumable) bare wire and the gases used Include helium, argon, and carbon dioxide. In some cases, a tubular electrode is used to facilitate the addition of fluxes or addition of alloys and slag-forming materials. Some methods of this process are called MIG and C02 welding. The gas-shielded process lends itself to high rates of deposition and high weldin.g speeds. It can ~e used manually, semi-automatically, or automatically.

Flux-Cored-Arc Welding This is an arc-welding process wherein coalescence is produced by heating with an arc between a continuous filler-material (consumable) electrode and the work. Shielding is obtained from a flux contained within the electrode. Additional shielding mayor may not be obtained from an externally supplied gas or gas mixture.

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Figure 1-1

Typical Effect of Heat Treatment on Notch Toughness of a Fine-Grained C-Mn-Si Steel (1 Inch Thickness)

z 2

Ouenched and Tempered

I0..

a:

a en

Q)

t.:) a:

w

zw =£

u

I-

x

a z

::> >-

0..

cr: ~

:r

C

u

Mn

SI

AI

0.171.260.270.04

I

Tensile Strength

-100

-76

-60

As Rolled

77 .400 psi

62.300 psi

Normalized

76,600 psi

54.800 psi

Ouenched & Temp·d.

83.100 psi

63,000 psi

o

-26

TEMPERATUR~OEGREESFAHRENHBT

5

I Yield Strength

26

50

75

Part II Materials-Carbon Steel Tanks forLiquidStornge~~~~~~~~~_ of inspection. These procedures are represented by the AWWA Appendix C and API basic standards. It will be obvious that inasmuch as the simplified design provisions of both standards allow identical design stresses for any of the permisSible steels, economic considerations will lead to the selection of the least expensive steel that will be satisfactory for the intended service. Steel selection is not so simple and straightforward in the case of tanks built in accordance with either the API or the AWWA refined design provisions. Unstressed portions of such tanks, including bottoms and roofs, will probably be furnished as A36 unless the purchaser specifies otherwise. The selection of material for shell demands further attention. The refined design provisions of both API and AWWA resulted from a desire to utilize newer and improved steels and modern .welding and inspection techniques to build tanks of higher quality. The use of higher stresses demanded attention to other properties of steel, primarily toughness. An exhaustive discussion of toughness is beyond the scope of this work, but it can be pointed out that as the stress level increases and temperature decreases, toughness becomes more important. At the stress level existing in API and AWWA simplified design criteria tanks, experience has demonstrated that the steels used in combination with the specific welding and inspection rules have been adequate for the service temperatures involved. Upon venturing into the field of higher stress levels, steels having greater toughness have been considered a necessary corollary. Thanks to research in metals, such steels are available. A number of factors enter into making a proper selection. For example, for any given steel, toughness generally decreases as thickness increases. The toughness of carbon steels is improved if part of the hardness and strength is obtained by a higher manganese content and lower carbon at the same strength level. Finegrained steels exhibit greater toughness than coarsegrained steels; this can be accomplished in the deoxidizing process, and in heat treatment. Thus as thickness increases and service temperature decreases, more stringent attention

Introduction he intent of this publication is to provide information that may be useful in the design of flat-bottom, vertical cylindrical tanks for the storage of liquids/ at essentially atmospheric pressure. Considerable attention has been directed to tanks storing oil or water, which constitute most of the tanks built. However, suggestions have been included for storage of liquids meriting special attention, such as acid storage tanks. There are two principal standards in general use: American Petroleum Institute (API) Standard 650 covering "Welded Steel Tanks for Oil Storage," and the American Water Works Association (AWWA) Standard 0100 covering "Steel Tanks for Water Storage." The abbreviations API and AWWA will be used for the sake of convenience. Both API and A WW A permit the use of a relatively large number of different steel plate materials. In addition, the basic API Standard 650 and AWWA Standard 0100 Appendix C provide refined design rules for tanks designed at higher stresses in which the selection of steel is intimately related to stress level, thickness and service temperature, as well as the type and degree of inspection. As a result, knowledge of available materials and their limitations is equally as important as familiarity with design principles. . Useful information concerning plate steel In general has been covered in Part I. It is the purpose of this section to assist in the selection of the proper steel or steels in the construction of tanks for liquid storage.

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Factors Affecting Selection of Steel Plate As you will learn in more detail in Part III of the publication, both the AWWA ~nd the API offer . optional methods of shell deSign. The AWWA baSIC and the API Appendix A procedures are based on simplified rules which use the same conservative allowable stress regardless of the plate grade used. The other design methods are based on refined procedures that take into account plate grade, service temperature, thickness and higher standards

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behind technical progress. The extensive research facilities of individual steel producers and American Iron and Steel Institute are constantly searching for ways to better serve the needs of our modern economy. But before any construction standard such as those of API and AWWA can accept and permit a new material, it must have been established that it is suitable for the structure in which it will be used. Usually, but not always, acceptance by API and AWWA implies prior acceptance by ASTM. Primarily this is because ASTM specifications clearly delineate the materials to be furnished, whereas any departure from ASTM requires that the standards involved spell out the requirements in corresponding detail. New ASTM steels mayor may not eventually find their way into the construction standards, depending on economics and the proven properties of the materials. It should be left to those who have acquired the necessary experience in tank design and construction to pioneer in the use of materials not approved by API or AWWA. The designer, the user, and the fabricator assume added responsibilities in working outside of recognized industry standards. On the other hand, such pioneering by qualified organizations in the past led to the progress represented by the refined procedures of Appendix C of AWWA D100 and API-650. As in the case of steels already approved by API and AWWA, time and experience will eventually lead to recognition of the steel or combination of steels that will yield the highest quality tank at least cost.

must be paid to toughness from the standpoint of materials selection and fabrication. The steels permitted by API and AWWA Appendix C for use at these higher stress levels have statistically demonstrated that they do have adequate toughness for the thickness and temperature ranges shown. The API standard includes an Impact Exemption chart which establishes requirements for impact testing, based on thickness, temperature and type of material. In the final analysis the goal is to design the least expensive but acceptable tank for a given set of conditions. API and AWWA rules permitting higher design stresses afford a fairly wide selection of steels and stress levels to choose from, but they do present a problem of selection. A definitive treatment of economics is beyond the scope of this work. Basically, the factors involved are: 1. Cost of material 2. Weight of material as it affects freight and handling 3. Fabrication, erection and welding costs 4. Inspection costs None of these factors is necessarily conclusive in itself. In any given case, the lightest weight or lowest material cost mayor may not be the least expensive overall depending on the relative importance of the factors listed above. The tank fabricator is usually in the best position to judge which steel or combination of steels will permit construction of the most economical, safe tank. It is generally unwise to specify a more expensive steel than can be justified by the application. There are material costs not associated with quality. The cost of plates will vary according to both width and thickness, and from this consideration tank shell plate approximately 8' wide will generally be used. Particular situations may dictate the use of wider or narrower plates ·for all or part of a tank shell. Although both the API and AWWA Standard permit the ordering of plates for certain parts of the tank on a weight rather than thickness basis, there is no longer any economic advantage in doing so.

The Future To this point, only those steels specifically permitted by API or AWWA have been discussed. Other steels have been used to a minor extent by those thoroughly familiar with the problems involved. Among these are the materials referred to in Part I as high strength low alloy steels, manufactured either as proprietary, trade named steels, or to ASTM specifications. Some of these steels offer the additional attraction of improved atmospheric corrosion resistance, thus eliminating the necessity for painting outside surfaces. As is the case with all high strength materials, the designer and user must assure themselves that factors other than strength (toughness for example) are properly allowed for in design and construction. For obvious reasons, all construction codes Jag

8

Part III Carbon Steel Tank Design Introduction

water or oil the designer should consider which philosophy best fits his circumstances. In either case the design standards provide minimum requirements for safe construction and should not be construed as a design manual covering all possible service conditions.

art III will consider the design of flat bottom, vertical, cylindrical, carbon steel tanks for the storage of liquids at essentially atmospheric pressure and near ambient temperatures. Practically aI/ tanks in the United States within the scope of this part are constructed in accordance with API 650 covering welded steel tanks for oil storage or AWWA D100 covering welded steel tanks for water storage. Tanks of other shapes and subject to gas pressure in addition to liquid head; and tanks subject to extreme low or high temperatures present radically different problems. Consult ASME Section VIII, API 650 APPENDICES F & M, and API 620 for further information. API 650 and AWWA D100 contain detailed minimum requirements covering inspection. Any attempt to summarize the inspection requirements of either standard would be voluminous and dangerously misleading. It will be the purpose of Part III to discuss only those portions necessary to understand the various design bases. Anyone concerned with fabrication, erection, or inspection must obtain copies of the complete standards. There are basic differences between the standards of API and AWWA. API 650 is an industry standard especially designed to fit the needs of the petroleum industry. The oil tank is usually located in isolated areas, or in areas zoned for industry where the probable consequences of mishap are limited to the owner's property. The owner is conscious of safety, environmental concerns and potential losses in his operations, and will adjust the minimum requirements to suit more severe service conditions. AWWA D100 is a public standard to be used for the storage of water. The water storage tank is usually located in the midst of a heavily populated area, often on the highest elevation available. The consequence of mishap could not be tolerated in the public interest. The API 650 and AWWA D100 standards have been in existence for many decades and the experience under them has been excellent. Before applying them to tanks storing liquids other than

P

General Design Formula for Tank Shells Membrane theory, as it applies to cylindrical tanks of large diameter, is elementary and needs no explanation here. Starting with the basic premise that circumferential load in a cylinder equals the pressure times the radius, then expressing Hand D in feet for convenience, the circumferential load at any level in ' a vertical cylinder containing water weighing 62.4#/cu. ft., can be expressed as: T=2.6HD (3-1) where T = the circumferential load per inch of shell height H = depth in feet below maximum liquid level D = tank diameter in feet Then the minimum design thickness can be expressed as: t (inches) = 2.6 HDG + C (3-2)

=

SE

contained liquid specific gravity S = allowable design stress in psi E = joint factor C = corrosion allowance in inches Obviously the ideal situation would be to vary the thickness uniformly from bottom to top, but. since steel plates are rolled to a uniform thickness, any given course of plates is uniform throughout its width . Thus a course designed for the stress at its lower edge will have excess thickness at the top, which will help carry part of the load in the lower portion of the course above. API takes advantage of this and designs each course of plates for the stress existing one foot above the bottom of the course in question. AWWA designs on the basis of stress existing at the lower edge of each course. Application of other methods of shell design is permitted and explained in API 650 and AWWA 0100. where G

9

Loads To Be Considered

Negative Pressure (such as partial vacuum) Most tanks of this nature at some time will be subject to a negative pressure (partial vacuum) by design or otherwise. Approximately one-half oz. per square inch negative pressure is built into the shell stability formulae in AWWA 0100 and API 650 . AWWA 0100 tanks are not usually designed for negative pressure but negative pressure due to the evacuation of water is considered in the venting requirements. Occasionally API 650 tanks a.re specified to resist a certain negative pressure, usually expressed in inches of water column. To meet these requirements the shell and roof must be designed to resist the specified negative pressure. It is left to the discretion of the designer to design for the negative pressure as part of the specified shell and roof loads or in addition to said loads. Part III of volume 2 provides design information for negative pressure on cylinders. Also if the negative pressure occurs while the tank is empty, the weight of the bottom plate should be compared against the specified negative pressure.

As outlined in the preceding section, the thickness of the shell is determined by the weight of the product stored. However, there are other loads or forces which a tank may have to resist and which are common to both oil and water tanks.

Wind - Wind pressure is assumed to be 30 psf on vertical plane surfaces which, when applying shape factors of 0.6 and 0.5 respectively, becomes 18 psf on the projected area of a cylindrical surface, and 15 psf on the projected area of a cone or surface of double curvature as in the case of tank roofs. These loads are considered to be the pressure caused by a wind velocity of 100 MPH. For higher or lower wind velocity, these loads are increased or decreased in proportion to the square of the velocity ratio, (V/100)2, where V is expected wind velocity expressed in miles per hour. Other standards for wind design may be specified such as ASCE 7-88 (formerly ANSI A58.1-1982), UBC, BOCA or SSBC. Snow -

Snow load is assumed to be 25 psf on the horizontal projected area of the roof. Lighter loads are not recommended even in areas where snow does not occur because of the live loads that must be resisted during construction and in service. Fixed roofs on tanks are not · usually designed for nonsymmetrical loads but if such load conditions are anticipated, these should be considered by the designer.

Top and Intermediate Wind Girders Open top tanks require stiffening rings at or near the top of the shell to resist distortion or buckling due to wind. These stiffening rings are referred to as wind girders. In addition some tank shells of open top and fixed roof tanks require intermediate wind girders to prevent buckling due to wind. API 650 and AWWA 0100 provide differing design requirements for intermediate wind girders ano are explained in the examples of Appendix A. The formula for maximum height of unstiffened shell is based on the MODIFIED MODEL BASIN FORMULA for the critical uniform external pressure on thin-wall tubes free from end loadings.

Seismic - Because of their flexibility, flat-bottomed cylindrical steel tanks have had an excellent safety record in earthquakes. Steel has the ability to absorb large ~mounts of energy without fracture. Prior to the Alaskan earthquake of 1964, oil tanks had an almost perfect record of surviving all known western hemisphere earthquakes with essentially no effects other than broken pipe connections. In the Alaskan quake, the horizontal oscillations of the tank contents caused vertical shell stresses of sufficient magnitude to permanently deform the shell in a peripheral accordion-like buckle near the bottom. But again the properties of steel were sufficient to accommodate this deformation without fracture of the shell plates. 4 As a result of this satisfactory experience record, it is generally considered that earthquake is not an important consideration in oil tanks where the height- . to-diameter ratio is generally small. The record of water tanks has been correspondingly good, but in the case of a standpipe where the height-to-diameter ratio is high, the problem is obviously aggravated. AWWA 0100 and API 650 contain recommendations for the seismic design of tanks. Seismic probability maps of the United States can be found in each. If applicable, local conditions should be investigated. UBC and ANSI standards may be specified but are not as design specific as AWWA 0100 and API 650 for flat bottom , vertical, cylindrical tanks.

Anchor Bolts The normal proportions of oil tanks are such (diameter greater than height) that anchor bolts are rarely needed. It is quite common, however, for the height of water tanks to be considerably greater than the diameter. There is a limit beyond which there is danger that any empty tank will overturn when subjected to the maximum wind velocity. As a good rule of thumb, if C in the following formula exceeds 0.66, anchor bolts are required: C = 2M where (3-3) dw M = overturning moment due to wind, ft. lb. d = diameter of shell in feet w = weight of shell and portion of roof supported by shell, lb. Design tens!on load per bolt = 4M - W (3-4)

ND

N

where M and Ware as above and N = number of anchor bolts D = diameter of anchor bolt circle, feet The diameter of the anchor bolts shall be determined by an allowable stress of 15000 psi on 10

obtain a copy of the complete standard.

the net section at the root of the thread with appropriate stress increase for wind or earthquake loading. Because of proportionately large loss of section by corrosion on small areas, it is recommended that no anchor bolt be less than 1.25" in diameter. Maximum desirable spacing of anchors as suggested by API 650 and AWWA D100 is 10'-0. This spacing is a matter of judgment and should remain flexible to facilitate plate seams, nozzles and other interferences. For example, for a shell plate 10 pi feet long, it would be advantageous to use three anchors per plate and space the anchors at approximately 10.5 feet. Obviously the anchor bolt circle must be larger than the tank diameter, but care should be taken so interference will not occur between the anchor bolts and foundation reinforcing. Volume 2 part VII provides design rules for anchor bolt chairs.

Shell Design API requires that all joints between shell plates shall be butt welded. Lap joints are permitted only in the roof and bottom and in attaching the top angle to the shell. API 650 offers optional shell design procedures. The refined design procedures permit higher design stresses in return for a more refined engineering design, more rigorous inspection, and the use of shell plate steels which demonstrate improved toughness. The probability of detrimental notches is higher at discontinuities such as shell penetrations. The basic requirements pertaining to welding, stress relief, and inspection relative to the design procedures are important. Tank shells designed in accordance with refined procedures will be thinner than the simplified procedure, and thus will have reduced resistance to buckling under wind load when empty. The shell may or may not need to be stiffened, but must be checked. This is discussed in the section on wind girders.

Corrosion Allowance As a minimum for all tanks, bottom plates should be 1/4" in thickness and lap welded top side only. If corrosion allowance is required for bottom plates, the as-furnished thickness (including corrosion allowance) should be specified. The thickness of annular ring or sketch plates beneath the tank shell may be required to be thicker than the remainder of the bottom plates and any corrosion allowance should be specified as applicable to the calculated thickness or the minimum thickness. API 650 and AWWA D100 specify minimum shell plate thicknesses based on tank diameter for construction purposes. If corrosion allowance is necessary, it should be added in accordance with the respective standard. A required minimum above those stated in the standards may also be specified, but it should be made clear if this minimum includes the necessary corrosion allowance. As a minimum for all tanks, roof plates should be 3/16" in thickness and lap welded top side only. If corrosion allowance is necessary it should be added in accordance with the respective standard. A required minimum greater than 3/16" in thickness may be specified; but it should be made clear if this minimum includes the necessary corrosion allowance. If corrosion allowance is necessary for roof supporting structural members, it should be added in accordance with the respective standard. If a corrosion allowance requirement different from the standards is necessary, it should be made clear what parts of the structure require the additional thickness (flange or web, one side or both sides) and/or the minimum thickness necessary.

Bottoms Tank bottoms are usually lap welded plates having a minimum nominal thickness of 1/4". After trimming, bottom plates shall extend a minimum of 1 inch beyond the outside edge of the weld attaching the , bottom to the shell plates. The attachment weld shall be a continuous fillet inside and out as shown in the following table of sizes: Maximum t of Shell Plate Inches 3/16 over 3/16 to 3/4 over 3/4 to 1-1/4 over 1-1/4 to 1-3/4

Minimum Size of Fillet Weld* Inches 3116 1/4 5/16 3/8

* Maximum size Fillet 1/2"

Butt-welded bottoms are permissible, but because of cost, are seldom used except in special services. Butt-welded bottoms are usually welded from the top side only using backing strips attached to the underside. Welding from both sides presents Significant construction difficulties in order to perform the work in a safe manner.

Top Angle Except for open-top tanks and the special requirements applying to self-supporting roofs, tank shells shall be provided with top angles of not less than the following sizes:

API Standard 650

Tank Diameter 35 feet and less over 35 to 60 ft. incl. over 60 feet

General The following information is based on API 650, eighth edition. Anyone dealing with tanks should

11

Minimum Size of Top Angle 2 x 2 x 3/16 2 x 2 x 1/4 3 x 3 x 3/8

12 inches, and when the cross-sectional area of the roof-to-shell junction does not exceed A = 0.153W (3-5) 30,800 tan 8 where W = total weight of the shell and roof framing supported by the shell in pounds 8 = angle between the roof and a horizontal plane at the roof-to-shell juncture in degrees . the joint may be considered to be frangi~le a~d, in case of excessive internal pressure, Will fall before failure occurs in the tank shell joints or the shell-to-bottom joint. Failure of the roof-toshell joint is usually initiated by buckling of the top angle and followed by teari~g of the 3/16 inch continuous weld at the penphery of the roof plates. 2. Where the weld size exceeds 3/16 inch, or where the slope of the roof at the top-angle attachment is greater than 2 inches in 12 inches, or when the cross-sectional area of the roof-to-shell junction exceeds the value . calculated per equation 3-5, or where fillet welding from both sides is specified, emergency venting devices in accordance with API Standard 2000 shall be provided by the purchaser. The manufacturer shall provide a suitable tank connection for the device and the drawings should reflect the need for such a device to be supplied by the customer. The top angle may be smaller than previously noted when a frangible joint is specified.

Roofs The selection of roof type depends on many factors. In the oil industry, many roofs are selected to minimize evaporation losses. Inasmuch as the ordinary oil tank is designed to withstand pressures only slightly above atmospheric, it must be vented against pressure and vacuum. The space above the liquid is filled with an .air-va~or r:nix~ure .. W~en a nearly empty tank is filled with liqUid this air-vapor mixture expands in the heat of the day an~ the . resulting increase in pressure causes venting. DUring the cool of the night, the remaining air-vapor mixture contracts, more fresh air is drawn in, more vapor evaporates to saturate the air-vapor mixture, and the next day the cycle is repeated . Either the loss of valuable "light ends" to the atmosphere from filling, or the breathing loss due to the expansioncontraction cycle, is a very substantial loss and has led to the development of many roof types designed to minimize such losses. The floating roof is probably the most popular of all conservation devices and is included as Appendices to API Standard 650. The prin?ipl.e of the floating roof is simple. It floats on the liqUid surface; therefore there is no vapor either to be expelled on filling or to expand or contract from day to night. Inasmuch as all such conservation devices are represented by proprietary and often pat~nted designs, they are beyond the scope of t~IS discussion, which will be limited to the fixed roofs covered by API Standards. API 650 provides rules for the design of several types of fixed roofs. The most common fixed roof is the-column supported cone roof, except for relatively small diameters where the added cost of a self-supporting roof is more than offset by saving the cost of a structural framing. The dividing line cannot be accurately defined because different pr~~tice~ and available equipment may affect the decl~lon I~ any given case. If economy is the only consl~eratlon .the purchaser would be well advised to specify the size of tank and let the manufacturer decide whether or not to use a self-supporting roof. A self-supporting roof is sometimes ~esirable for. special service conditions such as an Intern~1 floating roof, or where cleanliness and ease of cleantng are especially important. AU roofs and supporting structures shall be designed to support dead ··Ioad plus a live load of not less than 25 psf. . Roof plates shall have a minimum nominal thickness of 3/16 inch. Structural members shall have a minimum thickness of 0.17 inch. Roof plates shall be attached to t~e top angle with a continuous fillet weld on the top Side only: 1. If the continuous fillet weld between the roof plates and the top angle does not exceed 3/16 inch and the slope of the roof at the top-angle attachment does not exceed 2 inches in

Supported Cone Roofs - Supported cone roofs are usually lap welded from the top side only with continuous full fillet welds. Plates shall not be attached to supporting members, and shall be attached to the top angle by a continuous 3/16" fillet weld or smaller on the top side if specified by purchaser. The usual slope of supported cone roofs is 3/4" in 12". Increased slopes should be used with caution . The columns transmit their loads directly to the supporting soil through bases resting on but not attached to the bottom plates. Some differential settlement can be expected. A relatively flat roof will follow such variations without difficulty. As pitch increases, a cone acquires stiffness, and instead of smoothly following a revised contour, unSightly local buckles may develop. In general, slopes exceeding 1-1/2" in 12" may be undesirable. Rafters in direct contact with the roof plates may be considered to receive adequate lateral support from friction, but this does not apply to truss chord members, rafters deeper than 15", or roof slopes greater than 2" in 12". Rafters are spaced so that, in the outer ring, their centers are not more than 6.28 feet apart at the shell. Spacing on inner rings does not exceed 5.5 feet. All parts of the supporting structure shall be so proportioned that the sum of the maximum calculated stresses shall not exceed the allowable

12

r'

I

such tanks to be built in accordance with API 650. It must be remembered that the API Appendix A design .stress of 21 ,000 psi at 85 0/0 joint factor is predicated on the tank being full of water during test, and that the actual stress in petroleum service is usually considerably less. Because molasses is heavier than water, the full design stress is present in service. Thus if the designer is depending on the long and successful record _of tanks designed in accordance with API 650 Appendix A design, it would be more consistent with the true situation to use a somewhat lower design stress. On the other hand, on tanks built to the basic design ·of API 650 this difference between usual petroleum service stress and design stress does not exist. However, the addition of a corrosion allowance is required when warranted by service conditions.

stresses as stated in the appropriate section of API 650. Self-Supporting Roofs - Self-supporting cone, dome or umbrella roofs shall conform to the appropriate requirements of API 650 unless otherwise specified by the purchaser.

Accessories API 650 contains specific designs for approved accessories which include all dimensions, thicknesses, and welding details. For all cases, OSHA requirements must be satisfied. No details are shown, but specifications are included for stairways, walkways and platforms. All such structures are designed to support a moving concentrated load of 1000 Ibs. and the handrail shall be capable of withstanding a load of 200 Ibs. applied in any direction at any point on the top rail. Normally all pipe connections enter the tank through the lower part of the shell. Historically tank diameters and design stress levels have been such that the elastic movement of the tank shell under load has not been difficult to accommodate. With the trend to larger tanks and higher stresses, the elastic movement of the shell can become an important factor. Steel being an elastic material, the tank shell increases in diameter when subjected to internal pressure. The flat bottom acts as a diaphragm and restrains outward movement of the shell. As a result, the shell is greater in diameter several feet above the bottom than at the bottom. Openings near the bottom of the tank shell will tend to rotate with vertical bending of the shell under hydrostatic loading. Shell openings in this area, having attached piping or other external loads, should be reinforced not only for the static conditions but also for any loads imposed on the shell connections by the restraint of the attached piping to the shell rotations. Preferably the external loads should be minimized or the shell connections relocated outside the rotation area.

Acid and Caustic ·Tanks - To attempt a comprehensive discussion of the subject of storing acids and caustic solutions is beyond the scope of this work. While stainless steel or other high alloy materials are often required, some acids and caustic solutions can be stored successfully in carbon steel tanks, and the following discussion will be limited to such application. In the absence of personal experience, information concerning the corrosive properties of many common solutions can be found in chemistry and chemical engineers' handbooks or in the publications of the National Association of Corrosion Engineers. However, it should be noted that very small differences in content (such as slight impurities) or conditions can influence the corrosive effect of many chemicals. As an example, concentrated sulfuric acid does not attack carbon steel whereas dilute sulfuric acid is extremely corrosive. Thus concentrated sulfur~c acid can often be safely stored in carbon steel tanks provided proper precautions are taken to cope with dilute acid that may form in the upper portions of the tank when acid fumes and water condensation meet in the vapor space. Thus one fundamental requirement for an acid tank is that the interior of the tank be smooth without crevices or pockets where dilute acid condensation can collect. Self-supporting roofs are good practice. If the design of the roof or size of tank requires structural stiffeners, it is desirable that they be placed on the outside. If the roof is lap welded, it should be welded underneath as well as the top. The connection of the roof to the shell should eliminate any pocket which might exist at the top of a standard API tank. When using Appendix A design basis of API 650, a lower design stress should be considered for the same reasons as given under "Molasses Tanks." The tank user should specify the amount of corrosion allowance, if any required, for his particular purpose. In the case of carbon steel tanks storing caustic solutions, both the concentration and temperature are important. Carbon steel tanks should not be used if the combination of concentration and temperature

Tanks Other Than for Oil or Water There are manyapplicatior1s for steel tanks other than the storage of oil or water. Since most such applications are industrial in nature for which no industry standard has been developed, it is quite common to use API Standard 650 as a basis for design and construction. This is a logical approach provided that problems peculiar to the contents stored are taken into account. Tanks designed to store liquified gases at or near atmospheriC pressure are beyond the scope of this document. However, those interested in such storage are referred to API 620 appendices Rand Q. Molasses Tanks - Molasses presents no unusual problems other than the fact that its specific gravity is about 1.48, and the shell design must, of course, take this into account. It is quite common to require

13

AWWA Standard 0100

exceeds the following values and may in some cases be unsatisfactory below these limits: 50 0/0 and 120F 25 0/0 and 150F 5 0/0 and 200F It is most important to make sure that the specified design conditions are not exceeded in service. Automatic temperature controls are recommended. In addition to ordinary corrosion, the principal problem in caustic tanks is one referred to as "caustic embrittlement" or "stress corrosion cracking." In the presence of high local stresses this type of corrosion can rapidly result in cracks and leaks. Local stress concentrations approaching the yield point can exist at shell penetrations, in the vicinity of welds and at other details. In caustic service these are the points where stress corrosion cracking can occur. Thus, in the case of caustic storage tanks, all fittings penetrating the shell or bottom, or any permanent attachments welded to the,interior surface thereof, should be installed in a plate in the shop and the entire assembly thermally stress relieved. Essentially, this leaves only main seam welding to be performed in the field. Self-supporting roofs without structural members immersed in the tank contents are advisable. It is not necessary, however, to eliminate crevices and pockets as is recommended for acid tanks. For caustic tanks, a standard API roof is acceptable. Certain additional precautions in welding should be taken in both acid and caustic tanks. Lap welds in the bottom and the inside bottom-to-shell fillet should be made in at least two passes. Since the bottom-toshell weld usually consists of a fillet ,inside and out, it is advisable to provide a water stop (complete penetration) at each vertical shell joint so that if a leak does occur in the inside fillet, channeling will be limited to one plate length. All other shell joints should be designed for complete penetration and fusion. The inside passes should be made first. The later welding of outside passes will partially heat treat and reduce residual stresses in the inside weld. If anticipated corrosion indicates a bottom plate thickness greater than 3/8", the bottom should be butt welded and the same sequence followed; i.e. weld the inside passes first. Inasmuch as all welds create locally high residual stresses, all brackets, welding lugs, etc. should be kept to a minimum, be located on the outside, and attached with small-diameter electrodes to limit the heat input and consequently the effect on the inside surface. When the corrosive attack is considered sufficiently severe to admit the possibility of local penetration, but not severe enough to warrant the expense of high alloy or clad steel plates, the tank is sometimes supported on a structural grillage to permit inspection from the under side.

General The following information is based on the AWWA Standard D100 issued in 1984. Anyone dealing with tanks should obtain a copy of the complete standard. With the exception of shells, roofs and accessories, the comments made in connection with API tanks also apply to AWWA tanks and will not be repeated here in d~tail. Bottoms may be either lap or butt welded with a minimum thickness of 1/4 inch. AWWA does not specify top angle sizes, but the rules of API represent good practice.

Shell Design AWWA D100 offers two different design bases, the standard or basic design and the alternate deSign basis as outlined in Appendix C. The alternate design basis permits higher design stresses, in return for a more refined engineering design, more rigorous inspection, and the use of shell plate steels with improved toughness. AWWA D 100 Appendix C includes steels of significantly higher strength levels and correspondingly higher design stress levels. This introduces new design problems. For example, for A517 steels, the permissible design stress of 38333 psi will result in reaching the minimum required nominal thickness several courses below the tank top. It would be uneconomical to continue the relatively expensive steel into courses of plates not determined by stress. The obvious answer is to use less expensive steels in the upper rings. To govern this transition, Appendix C adds the followif}g requirements: "In the interest of economy, upper courses may be of weaker material than used in the lower courses of shell plates, but in no instance shall the calculated stress at the bottom of any course be greater than permitted for the material in that course. A plate course may be thicker than the course below it provided the extra thickness is not used in any stress or wind stability calculation. I I Compliance with this requirement will probably result in the course or courses immediately below the transition point being somewhat heavier than required by stress. Using a steel of intermediate strength level as a transition between A517 steel and carbon steel may help the situation. In any event the use of two or more steels will result in plates of the same thickness made of different steels. Careful attention to plain marking for positive identification becomes very important. Consideration might be given to varying plate widths for different materials of the same thickness to aid in identification in the event markings are lost.

Roofs Whereas oil tanks are strictly utilitarian, a pleasing appearance is generally an important consideration in the case of water tanks. Since the roof line has an 14

I f

f

I I I I I I I I

important effect on appearance, this striving for beauty has led to a wide variety of roof designs. Often a self-supporting roof, such as an ellipsoid, will extend a considerable distance above the cylindrical portion of the shell, and the high water level will extend up into the roof itself. The resultant upward pressure on the roof is resisted by the combination of the roof dead load and the weld jOint between the roof and shell. AWWA requires that for all roof plate surfaces in contact with water, the minimum metal thickness shall be 1/4". Roof plate surfaces not in contact with water may be 3/16". As applied to rolled shapes for roof framing, the foregoing minimum thicknesses shall apply to the mean thickness of the flanges regardless of web thickness. Roof plates not subject to hydrostatic pressure from tank contents may be welded from the top side only with either a continuous full fillet or butt joint weld with 90 0/0 jOint penetration. Where roof plates are subjected to hydrostatic pressure, the roof may be continuous double lap welded or butt welded. Roof supports or stiffeners, if used, shall be in accordance with current specifications of the American Institute of Steel Construction covering structural steel for buildings, with the following exceptions: 1. Roof plates are considered to provide the necessary lateral support by friction between roof plates and rafters to eliminate reduction in the basic allowable compressive stress, except where trusses and open web joists are used for rafters, or rafters having nominal depth greater than 15 in. or rafters having a slope greater than 2 in 12. 2. The roof, rafter and purlin depth may be less than fb 600,000 times the span length in incheSl where fb is the maximum bending stress in psi, providing slope of the roof is 3/4 to 12 or greater. 3. The maximum slenderness ratio (Ur) for roof support columns shall be 175. 4. Roof support columns shall be designed as secondary members. 5. Roof trusses, if any, shall be placed above the maximum water level in climates where ice may form. 6. Roof rafters shall preferably be placed above maximum water level, although their lower ends, where connected to the tank shell, may project below the water level.

Accessories AWWA does not provide detailed designs of tank fittings, but specifies the following: 1. Two manholes shall be provided in the first ring of the tank shell. Manholes shall be either a 24" diameter or at least 18" x 22" when elliptical manholes are used. 2. The purchaser shall specify pipe connections, 15

3.

4.

5.

6.

7.

8. 9.

sizes, and locations. Due to freezing hazard these connections are normally made through the tank bottom and as near to the shell as practical. A concrete valve box may be provided to permit access to piping. This valve box must be designed as a part of the ringwall. If a removable silt stop is required, it shall be at least 4" high. If not required, then the connecting pipe shall extend at least 4" above the tank bottom. The purchaser shall specify the overflow size and type. A stub overflow is recommended in cold climates. If an overflow to ground is . required, it should be brought down the outside of the tank and discharged onto a splash block or other appropriate drainage structure. Inside overflows are not recommended. They are easily damaged by ice, and a failure in the overflow will empty the tank to the level of the break. An outside vertical ladder shall begin 8 feet (or as specified) above the tank bottom and afford access to the roof. Need for access to AWWA tanks is infrequent and a conscious effort is made to render access difficult for unauthorized personnel. The contractor shall provide access to the roof hatches and vents. The access must be reached from the outside tank ladder and fulfill the AWWA D100 requirements consistent with the roof slope or as specified by the purchaser. A roof door or hatch whose least dimensions are 24" x 15", with a curb 4" high, provided with a hinged door and clasp for locking shall be placed near the outside tank ladder. A second opening of at least 20" in diameter C;nd with a 4" neck must be provided near the center of the tank. Additional openings may be required for ventilation during painting. Safety devices shall be provided on ladders as required by federal or local regulations, or as purchaser so specifies. Adequate venting shal/be provided to accommodate the maximum filling and emptying rates. These rates should be specified by the purchaser. Venting for outflow (partial vacuum condition) is based upon the unrestricted vent area and the pressure differential that can safely be allowed between the outside and inside of the tank. This differential is established by quantifying the strength of the roof and shell above and beyond other structural requirements; for example, the margin of extra strength of the shell against buckling with respect to the design wind load. Venting for inflow (pressure condition) is again based upon the restricted vent area and the pressure differential that can safely be allowed before lifting the roof plates. For example, if 3/16" roof plates are used, the pressure differential would be 7.65 PSF, 0.053

Calculate she" thickness using the basic equation: t =2.6 hp 0 G (3-8)

psi, or 1.47 inches water column. If the differential is limited to the weight of the roof, the shell/roof juncture does not become involved. The overstress in the shell would be minimal. The equation for outflow vent capacity is: Q = O.SAx110x Y'f'x

[(~~)"2B6

-1t

sE All nomenclature in the above and following equations is defined in the AWWA 0100 standard. Notice that hp in the above equation is the full liquid height above the design point rather than h - 1 as used in API 650. The calculation for ring five (top ring) is:

(3-6)

where Q = vent capacity in cubic feet per second A = minimum clear vent open area in square feet T = air temperature in degrees Rankine Pa = atmospheric pressure · in psia Pi = pressure in tank during withdrawal in psia The equation for inflow vent capacity is: Q = O.SA {6.2S x 106

[(;!)

0.286 -1]} '/2

t5 = 2.6 x 7.66 x 150 x 1.0 = 0.1547" 19,330 x 1.0 The thicknesses for the remaining rings calculate: hp = 15.63' S = 19,330 psi t4 = 0.3152" hp = 23.58' S = 23,330 psi t3 = 0.3942" hp = 31.54' S = 23,330 psi t2 = 0.5273" hp = 39.50' S = 23,330 psi t1 = 0.6603" using A36 steel for rings 4 and 5 and A573 GR70 for rings 1, 2, and 3. Ring 5 will be increased to 0.3125" because of minimum thickness requirements in AWWA 0100. Shell stability is calculated using the basic equation:

(3-7)

h

=

10.625 X 106 x t Pw (0/t)1.5

(3-9)

The calculation for ring five (top ring) is:

APPENDIX A

hs = 10.625 X 106 x 0.3125 = 17.54'> 7.96' 18 x (150/0.3125)1.5

Design Example For typical examples of tank design consider two tanks 150 feet in diameter by 40 feet nominal height with flat cone supported roofs. Consider one tank per AWWA 0100 and the other tank per API 650. See figure 3A·1 for tank dimensions. These examples are for illustration only and are not to be used for an actual design or construction. Design of similar tanks should be accomplished by competent people experienced in the design of like structures and the use of applicable standards. For the AWWA tank consider Appendix C, shell design by equation 3-10 (AWWA 0100), and zone one fixed percentage seismic loads. For the API 650 tank consider the standard (non Appendix A), shell design by the variable point method, 1/16 inch corrosion allowance on the shell only, and zone one API 650 seismic loads. Consider design metal temperature (OMT) of 20°F, standard 100 mph wind loads, standard 25 PSF roof loads, a maximum liquid content height of 39'-6, and a design specific gravity of 1.0 for both tanks. The economics of plate selection with respect to width and grade and structural selection will differ with location and construction capabilities. Factors to consider are plate width and grade availability in a particular locality and structural rolling schedules. Also the availability of plate and structural stock in a particular locality will sometimes influence the selection of material. Further discussion of material selection wi" be beyond the scope of this paper. The following design example covers the AWWA 0100 tank.

For each ring the h calculated is compared to the actual height of shell above the design point. When h calculates less than the height of sheH above, the shell is unstable. This may be corrected by thickening the shell or adding a stiffening ring. For this example we will consider only thickening the shell. h4 = 17.73'> 15.92' h3 = 21.76' < 23.87' Recalculate the thickness of ring 3 by using a lower strength steel (A36). 13 = 0.4758" Recalculate: h3 = 26.37' > 23.87' The shell is now stable above ring 3; continuing; h2 = 34.10' > 31.83' h1 = 45.67'> 39.79' The entire shell is now stable for a design wind velocity of 100 mph. See table 3A-1 for shell thicknesses before and after minimum thickness and wind stability adjustments. For 100 mph wind load, design loads are 18 PSF on projected areas of cylindrical surfaces (shell) and 15 PSF on projected areas of double curved surfaces (roof). Based upon the tank geometry and the design loading, the wind shear is calculated: Shell = 150 x 40.04 x 18 = Roof = ·150 x 4.69 x 0.5 x 15 = Total = 16

108,113Ibs. 5,273 113,386 Ibs.

diameter schedule 20 pipe based upon a design load of 41,400 Ibs., an unsupported column length of 470.6 inches, and a slenderness ratio of 159; using the same design criteria as the center column. See figure 3A-6 for a typical outer column detail. For zone 1 AWWA seismic loading the entire water and dead load mass will be subject to an acceleration of 0.025. For the seismic shear a simple calculation of 0.025 times the accumulated weight of the water and dead load equals 1,102,800 Ibs. For seismic moment the center of gravity of the dead load is a matter of geometry. The water mass is divided into the impulsive and convective modes with appropriate masses and centers of gravity for each. USing the procedure and nomenclature from AWWA 0100: WT = 43,556,600 Ibs.

The minimum required coefficient of friction against sliding is: Wind Shear Tank Weight

=

113,386 734,250

=

0.154

(3-10)

. This coefficient is well below established values which range as high as 0.4 to 0.5. The wind moment at the base of the shell is calculated:

=

Shell 108,113 x 20.02 = Roof = 5,273 x 41.60 = Total =

2,164,421 ft-Ibs. 219,357 2,383,778 ft-Ibs.

The ratio, C =2M/dw, calculates to be 0.076 < 0.666; therefore, no anchors are required to resist overturning due to wind. Roof framing concepts, layout and detail vary among tank designers and suppliers. Rafter spacing is dependent upon roof loading and plate thickness. For reasons .of plate strength and construction a maximum rafter spacing of approximately 7.00 feet is desirable. For this example consider nine girders and outer columns, 36 inner rafters and 72 outer rafters (see figure 3A-2). The outer columns will be located on a 42'-6" radius. The rafter spacing is 6.54 feet at the shell and 6.92 feet at the girder. Consider 25 PSF snow load and 7.65 PSF (3/16" roof plate) dead load. USing an inner support radius of 2.38 ft, which is dependent upon the method of supporting the inner rafters, the maximum design length of the inner rafters is 39.33 ft, as indicated on figure 3A-2. The maximum design moment calculates to be 27,580 ftIbs. Using an AISC allowable stress of 0.66 x Fy, a section modulus of 13.93 in 3 is required. A W12 x 14 section with a section modulus of 14.9 in 3 is chosen. See figure 3A-3 for a typical rafter loading. The maximum design length for the outer rafters is 35.33 ft, as indicated on figure 3A-2. The maximum design moment calculates to be 27,890 ft-Ibs. A section modulus of 14.09 in3 is required and again we will choose a W12 x 14 section. The rafter reactions are placed on the girder at the locations as determined by the roof framing layout. The outer rafter reactions are 3480 Ibs.; the inner rafter reactions are 2840 Ibs.; and the girder design length is 29.07 ft. The maximum design moment calculates to be 150,440 ft-Ibs. Again using AISC allowable stresses, a section modulus of 75.98 in3 .is required. AW18 x 46 section with a section modulus of 78.80 in3 is chosen. See figure 3A-4 for a typical girder loading. For the center column a design load of 74,900 Ibs. is calculated from the accumulated reactions of the inner rafters. Using ·AISC design procedures an allowable compressive stress is determined based upon the unsupported column length of 486.5 inches and a calculated slenderness ratio of 131. A 10" diameter schedule 20 pipe will meet the design criteria. See figure 3A-5 for typical center column detail. For the outer columns we have chosen an 8"

= 0.3

W1

X

WT = 13,067,000 Jbs.

W2 = 0.65 X WT = 28,311,800 Ibs. X1 = 14.615 ft X2 = 20.935 ft From the above criteria the seismic moment calculates to be 19,946,500 ft-Ibs. The ratio M 0 2 (W + Wd calculates less than 0.785; therefore, t

no anchors are required for seismic overturning. WL in the above ratio is determined by the equatior WL = 7.9 tb (fy HG)1!2 (3-11) WL is the portion of the contents that may be used to resist overturning for an unanchored tank. The value of WL is based upon a bottom plate width L that will carry the resisting contents and is calculated by the equation: (3-12) L = 0.216 tb (fy HG)1!2 L is limited ,to 0.0350 which limits the value of WL' tO 1.28 HOG. The following design example covers the API 650 tank. Calculate the shell thicknesses by the VARIABLE POINT OESIGN method as explained in API 650. A detailed example is in the API 650 Appendix. The thickness calculations for rings 1 and 2 are shown in figure 3A-7. The thickness for ring 5 is governed by minimum thickness requirements. Table 3A-2 summarizes final required thicknesses based upon static head, specified corrosion allowance, minimum thickness, and material economics. Shell stability is calculated using the equation:

H = 600,000 t

(3-13)

(0/t)1.5

For API 650 design t is the thickness of the top ring and not the average shell thickness as in AWWA design. H

= 600,000

x 0.3125 (15010.3125)1.5

=

17.83 ft

< 39.79 ft

It should be noted here that unless otherwise specified the as-built thicknesses are used in the shell stability calculations rather than the corroded thicknesses. 17

For zone one seismic loading the effective mass method of API 650 will be used. The design method considers two response modes of the tank and contents: the impulsive and convective modes. The impulsive response mode is the relatively high frequency amplified response to lateral ground motion of the tank shell and roof together with the portion of the contents that moves in unison with the shell. The convective response mode is the relatively low frequency amplified response of the portion of the contents that moves in the fundamental sloshing mode. The content total, impulsive and convective masses, are identical to the AWWA design. The dead load mass is slightly different due to the different shell and framing design criteria of AWWA and API 650. The equation for overturning due to seismic loading applied to the bottom of the shell is: M = 21 (C 1WsXs + C1WrHt + C1W1X1 + C2W2X2) (3-16) For zone one: Z = 0.1875 I = 1.0 C1 = 0.24 C2 = 0.0301 (based upon a natural period of the first sloshing mode of 8.2 sec. and S = 1.5) The moment calculates to be 12,804,400 ft-Ibs. The ratio ___M_ __ calculates less than 0.785; 0 2 (Wt + WJ therefore, no anchors are required for seismic overturning.

Since H calculates less than the shell height, calculate a transposed shell height using the equation:

= W .(tuniform)5/2

(3-14) tactual The transposed shell height is the sum of Wtr for each ring. If H is less than the sum of Wtp the shell is unstable. As in the AWWA design the unstable condition may be corrected by thickening the shell or adding a stiffener ring(s). See figure 3A-8 for Wtr for each ring and the sum of Wtr . H is less than the sum of Wtr ; therefore, the shell is unstable for 100 mph wind loading. For this example consider stabilizing the shell by adding a stiffener ring(s). If one-half the sum of Wtr is greater than H, then two (or more) stiffener rings are required. W tr

I

1/2 x 25.33 = 12.67 ft




VI

Figure 3A-5 -

VIZ

;QO

rr1

Z

;Qrl

Dr

nCl

-l rr1

VI .....

0

0

INNER RAFTERS

Typical Center Column

II ~UMN II II I II II I I BASE PLATE I I ~ BOT~M PLATE II

COLUMN CONE

"t

=

~

GIRDER

\J \J

Z

Cl

VI

VI

\

Z

rl AJ 0

Z

AJrl

Dr

n

rl 1>

~

~

0 VI

0

/

BOTTOM PLATE

BASE PLATE

COLUMN

CAP PLATE

RAFTER

Typical Outer Column

I I, II

I II

I II II II II II

' 'k

~t::'~NNER

Figure 3A-6 -

{:

OUTER RAFTER

VARIABLE POINT DESIGN: API 650 8TH ED. PARA.3.6.4. RING NO.1

DESIGN: D = 150.000 H = 39.500 G = 1.000 S = 28000. CA = 0.0625 Td = 2.6* D*{H -1 )*G/S + CA = 0.5362 + CA = 0.5987 Tld = [1.06-(0.463*D/H)*SQRT(H*G/S)]*2.6*D*H*G/S+CA = Tld = 0.5469 + CA = 0.6094 HYDROTEST: D = 150.000 H = 39.500 G = 1.000 S = 30000. TT = 2.6*D*(H -l)*G/S = 0.5005 T1T = [1.06-(0.463*D/H)*SQRT{H*G/S)]*2.6*D*H*G/S = 0.5115 USE: 0.599 IN. A573 70

LlH = SQRT{6.0*D*T)/H3

= 0.5929 1 Deflection 4>2 Deflection 4>3

0.0138 0.0199 0.0240 0.0264 0.0277 0.0443 0.0616 0.0770 0.0906 0.1017 0.1106 0.1261 0.1671 0.1802

Bib

IValues 2Values 3Values 4Values

·1.5

1.6

1.75

2.0

0.517

0.490 0.569

0.497 0.610

2.12

2.25

2.42

2.67

2.56

2.74

2.97

3.31

of 1.43 [Iog 1 0 Rir + 0.11 (rfR)2 1 of 1.43 [Iog 10 Rir + 0.334 + 0.06 (rfR)2 1 of 6/(3n 4 + 2n2 + 3) of 1.365/(3n4 + 2n2 + 3)

2.5

3.0

5.0

00

0.713

0.741

0.74·8

0.500 0.750

3.03

3.27

3.56

3.70

4.00

3.83

4.18

4.61

4.84

5.30

0.0284 0.1336 0.1400 0.1416 0.1422 0.1843 0.1848 0.1849

SVaJues of 3/(0.42n4 +·nl + 1) 6VaJues of 50/(3n 4 + 2n2 + 12.5) 7Vawes of 13.1/(0.42n4 + n2 + 2.5)

5

4.0

• • • • • •I, V • •I , • • • •I • •I

Part II Large Diameter Plate Tubular Columns~~~~~~~~~~_ e

olume 1, "Steel Tanks for Liquid Storage," covered the design of cylindrical tanks subjected to internal pressure. Cylinders (and cones), however, may also be used as columns, in which case they are subjected to axial compression . This application is discussed in the following. The cylinder-cone junction is discussed in Part V.

0L

Column Formulas for Circular Tubes Small diameter pipe columns have long been designed using conventional column formulas . However, for tubular columns of relatively large diameter and thin plate, when local buckling controls the column strength, the conventional column rules no longer apply. The PIA::;; XY formula, developed in the 1930's for mild carbon steels with minimum yield strengths of 30-33 ksi, has been widely used for design of carbon steel columns. It has been specified for elevated tank column designs by AWWA and ~FPA for the past 50 years. Formulas suitable for use with carbon or alloy steels having higher minimum yield strengths are now available for use. The ASME code, section VIII, Division 1 and the AISC specification for buildings include such formulas, and AWWA is proposing them for the next revision of the water tank standard. The allowable stresses are applicable to axially loaded cones if e s 60 degrees and R1 and t1, at the point being investigated, are substituted for Ro and t respectively, in the formulas. The formulas for tubular columns are useful in determining allowable axial and bending stresses in many structures, such as tanks, buildings, stacks, pipes and skirt-supported vessels. The requirements of the specification, standard or code that is applicable to the specific structure being designed should be used to determine the allowable axial, bending and combined stresses. When forces due to earthquake or wind are included, the allowable stresses may be increased by 113. Only the Proposed AWWA and the AISC formulas are presented here. Persons interested in the current AWWA and the ASME formulas are directed to those documents for information. Values of Fa for KUr = 0 for both the Proposed AWWA and the AISC formulas

Notation

A

= cross sectional

area of column, in. 2

=

n(Do - t)t

Cc

= column

slenderness ratio separating elastic and inelastic buckling for AISC formulas C~ = column slenderness ratio separating elastic and inelastic buckling for Proposed AWWA formulas D; = inside diameter of cylinder, in. Do = outside diameter of cylinder, in. E = modulus of elasticity, ksi Fa = allowable axial compressive stress in the absence of bending moment, ksi Fb = allowable bending stress in the absence of axial force, ksi Fy = yield stress of steel being used, ksi FS = factor of safety I = moment of inertia of column, in.4 =

n(Do4

-

= half apex angle of cone, deg. = critical local buckling stress for Proposed AWWA formulas, ksi

D,A)/64

K = effective length factor K~ = slenderness reduction factor for Proposed AWWA formulas M = moment at design point, in.-kips P = vertical axial load on column, kips Ro = outside radius of cylinder, in. R1 = outside conical radius, in. S = section modulus of column, in.3 = n(D0 4 - D;4)/32 Do =21IDo fa = computed axial stress, ksi = PIA fb = computed bending stress, ksi = MIS L = actual unbraced length of column, in. r = radius of gyration, in. =1/4 v'D02 + D? t = wall thickness of cylinder or column, in. t1 = wall thickness of cone, in. 7

are shown graphically in Fig. 2-1 for Fy in Fig. 2-2 for Fy = 36 ksi.

= 30

For tiRo ~ Fy 11650 Fb = 0.66 Fy (2-13) Fa = the value obtained from formula 2-11 when KUr < Cc or from formula 2-12 when KUr";? Ce· Ce = ""'2 1(2 EIFy (2-14)

ksi and

Proposed AWWA (2-1 ) (2-2)

Fb= oLIFS Fa = oLKetiFS fe/Fa + ft/Fb s: 1

(2-3)

References

~ 34 ksi tiRo Range (} L tiRo $ 0.0031088 3500 tiRo [1.0 + 50000 (tIRo)2) (2-4) 0.0031088 \J.lr-\Hi~ \fH\-Ht-HH-+-H-+-1H-+H-H-tt-H-tH-tt-T-H-t-ttt1---Ht-Ht-HH1t1rt1 \

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::~!=:~~=~:~~~\~v.~X~\~~~~~~~t§ t--:t-+-+-+-+-H-+-H+--+-+--1H--+-+++I\'%~-~1\~~~~~~~~ ~~=t~:~ I 1\1 Il\ l\ I "I "\J I'\. Lf'.

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1t -J...J.I.....".J.'IJ.J.JI ,osa _____~-'-'"""-........I..O-.I.___'"""-........'-'-........I-\.... U....ll..l.l_~II......I......J..ll_.l-.I.I.....I...I.I..I..~J..I. II_"·_.J-...J 111.....J-..I.. 345678V .00001

.0001

3

~56}U

.001

3.56789 .01

3.,56789 .1

FACTOR A

Fig. 5-UGO-28.0 Geometric Chart for Cylindrical Vessels under External or Compressive Loadings (for All Materials) FIGURE 3·1 13

~TE;I s':' iabl~ ~d~d8~11t()( tabUI.J vJu~

-

I

~ ...

-

~

L--' :.-

16.000

...- ...-"- ":"1- JOO1F , fo--

12.000

~~

.,;'"

/,

./

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.........

I"

".

'11/

~

...

.-'"

~

.,.

.....

14.000

I

700 F

-I-

I I

., 900 F

.... r- V

10.000 9,000

800 F fo---

8,000

~--

.J#O .....

.,"

~

Ii",

E • 24.S x 104' E • 22.8 x 10e E - 20.8 )( 10'

.,..,.

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11

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...".

.... i-'~

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....

-,.,-

.......

l,......- ........

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:...--~

~

.E • 29.0 x 10e ......... ...... I E. 27.0 x 10e

.....-

20,000 18.000

I

up to :lOOF ~-

/ ---. l..- I--

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--;;.;,.

./

'1:

3

4 5 6789

.OO(X)1

a: u

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< u..

::3.500 l-

3.000

r;

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2.500

(A~

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7.000 6.000

4.000

{/, '1/ ......

......... I: ~,

'h

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al

5,000

V

, ...

'I

2.000

2

:1

2

3 " 5 6789

4

5 6789

3

045&789

.01

.001

.0001

2

.1

FACTOR A

Fig. 5-UCS-28.1 Chart for Determining Shell Thickness of Cylindrical and Spherical Vessels Under External Pressure When Constructed of Carbon Or Low-Alloy Steels (Specified Minimum Yield Strength 24,000 psi To, But Not Including, '30,000 psi)

NclTE: I se!. iab'~ s-Ld~2'8~ 'f

Of'

25.000

t~ular' Val~.!

./

V ~

V.,.

~

1/",,"

/1

VI

~ .... ~

E - 29.0 27.0

eee-

x 10' x 10' ...... 1-0....

x 10' ~ [j)

E - 20.8 )( 10'

I 1111' 2 .00001

"

.......

---

........

;;;;;;--

:-.-

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-,...

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20,000 18.000

V?OO F-

~~

16,000

----- ,.,.'" -

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800 FII

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~

----

104,000 12.000

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............. ,...

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:1" 5 6789 .0001

rh

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0

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u..

6.000

.... .;'

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~ 'I

2

JO.ooo 9.000 8.000

2.500

3

2

456789

3

4 5 6789

.01

.001

2

3

04 5 6789 .1

FACTOR A

Fig. 5-UCS-28.2 Chart for Determining Shell Thickness of Cylindrical and Spherical Vessels Under External Pressure When Constructed of Carbon Or Low-Alloy Steels (Specified Minimum Yield Strength 30,000 psi and Over Except for Materials Within This Range Where Other Specific Charts Are Referenced) and Type 405 and Type 410 Stainless Steels

FIGURE 3-2 14

aJ

a:

~

U

~

JI/1. "'r--. Illll

24.5 )( 10' 1-0.... 22.8

'I

/

.-~

.- ........ ~

/

'I'

I, II,

.-'"

---

V

.... ., ~i"'"tptJ3lL sao F-

«

Where this situation occurs, design may be in accordance with the following discussion of type C vessels If The Limitations Given Therein Are Followed. Note that the curves in Fig. 3-2 based on material strength (temperature curves) are not straight over their entire length. The procedure outlined for type C vessels is applicable only to the straight portion of the curve, where most type C vessels will fall. If the same rules were applied indiscriminately, inadequate design could result. Where the rules do apply to type B vessels, the safety factor for stiffener spacing should preferably be at least 3, but may be less at the designer's discretion, depending on severity of loading, inherent hazard, etc. Type C. Storage Tanks of Large Diameter Subject

it is recommended that a minimum safety factor of 2 be used. Some vessels may be subjected to external pressures that vary from zero at an upper point on the shell to a maximum at the shell-to-bottom junction. For this type of triangular radial loading, determination of the first lower unsupported span LS1 should be based on the pressure at the bottom. This locates the first intermediate stiffener above the bottom. Then, the next span LS2 should be based on the pressure at the first stiffener. This procedure should be repeated up the shell. For each span, the thickness should be assumed as the thickness of the middle quarter of the span, or the average thickness of the plates in the span. To prevent buckling of the intermediate stiffeners, the moment of inertia should be at least:

to Radial Loads Only, or Small Vacuums Where the Axial Load is Negligible. In determination of stiffener

I~

ring spacing, the safety factor of 3, as specified by the ASME code, seems excessive for storage tanks of this type. Furthermore, the code design of stiffeners assumes that they will buckle into two waves. Stiffeners on short tanks with large diameters may be stayed so that buckling takes place in more than two waves. In that case, design in accordance with the code may be overconservative. The following procedure was developed to provide a more reasonable design basis for such tanks. In using this approach, however, designers should remember that it applies to a special situation, frequently encountered, and is not a general solution for all cylinders subjected to external pressure. (See preceding discussion of type B structures.) The procedure is based on the use of two end stiffeners of sufficient strength to permit installation of small intermediate stiffeners based on the wave pattern postulated for the unstiffened shell between end stiffeners. An .example for a vertical storage tank would be incorporation of one end stiffener at the bottom of the shell and one at the roof or at an upper point of the shell where the radial external pressure becomes zero. Intermediate stiffeners would be located between these end stiffeners.

Do

t' 0:

l

(3-7)

In Eq. 3-7, computation of I~ provided may include a portion of the shell :guivalent to the lesser of 1.1 t Dot = 1.56t Rot or the area As of the stiffener. The moment of inertia for intermediate stiffeners attached to shells under radial pressure only or under both radial and axial pressures should have a minimum safety factor of 2. In Eq. 3-7, N is an integer with approximate value of: N2 = 0.663 s: 100 (3-8)

v

r-IL t' Do

h • Do

To prevent yielding of the stiffener, it should also satisfy the following requirement for minimum crosssectional area: (3-9) As = P.l::.8

Fa

where Fa should be taken as 15,000 psi for mild carbon steel. In determination of As provided, a width equal to 0.78 Rot of the available shell each side of the stiffener should be included in the composite area. To insure a nominal-size stiffener, in no case should the area of the stiffener alone be less than half the required area. Both Eq. 3-7 and 3-9 are based on the assumption that all the circumferential shell force is carried by the stiffeners. This is a very conservative assumption and could be relaxed with a more rigorous analysis.

v

Within the following limitations, the spacing Ls of intermediate stiffeners may be determined from the David Taylor Model Basin formula 1 (Eq. 3-6). The formula, however, does not a2.Q!y if the resulting spacing Ls is less than 0.9 vo;;t.The circumferential stress in the shell alone, not including the stiffeners, should not exceed the allowable working stress for the shell material in compression. The David Taylor Model Basin formula is: f0.45 + 2.42E (tJDQ)2] Fp (1 - ~2)O.7j

FpL s D Q 3

8E (N2 - 1)

Intermediate Stiffener Rings

h = • It

=

End Stiffener Rings For the preceding design procedure for intermediate stiffeners to apply, the ends of the cylindrical shell must be held circular. It is assumed that half the total external radial load on the shell is transferred to the end stiffeners. This load is further distributed to the end stiffeners in inverse proportion to the ratios of their distances from the resultant of the load on the shell to the distance between end

(3-6)

For shells constructed of mild carbon steel under radial pressure only and for temperatures to 3DDoF, 1Col/apse by Instability of Thin Cylindrical Shells Under External Pressure, by Dwight Windenburg and Charles Trilling.

15

assumed as part of the required area. Fa should be taken as 15,000 psi for mild carbon steel.

stiffeners. The required moment of inertia for end stiffeners therefore should be at least I; =

Fph Do 3 16 E(N2_1)

(3-10)

Top Intermediate Stiffener Ring For a cylindrical shell with external pressure on only a portion of its total height, such as a partly buried tank, additional consideration must be given to the distribution of load to the end stiffeners. In any case, always locate the top intermediate stiffener at the surface elevation of the external pressure. N should be taken the same as that recommended for intermediate stiffeners (unless this stiffener is assumed to be the end stiffener). The load on the top intermediate stiffener depends on the distance from this stiffener to the top end of the cylinder. If this distance is greater than twice the greatest intermediate stiffener spacing, assume that no load is transmitted through the shell to the top end of the cylinder. Therefore, the top intermediate stiffener should be designed as a top stiffener. If this distance is less than twice the greatest intermediate stiffener spacing, the regular end stiffener design may be provided at the top of the cylinder, while the load on the top intermediate stiffener is computed as for the other intermediate stiffeners.

For open top tanks, N for the top end stiffener must be taken as 2. When the end stiffener is stayed by a cone roof or radial framing, N equals the number of rafters at the shell. For a flat bottom, a full diaphragm, or a self-supporting roof, N should be calculated in the same way as for intermediate stiffeners. An end stiffener can be a circular girder composed of a portion of a flat bottom fora web, a portion of the shell for one flange, and a circumferential member welded to the bottom for the other flange. The proportions of such a girder should be limited by the AISC rules for compression ·members. The required .cross-sectional area of a composite end stiffener should be at least

As = phDo 4 Fa

(3-11)

If available, a portion of the shell equal to 0.78 y'Rot on each side of the stiffener can be

16

Part IV Membrane

Theory~~~~~~~~~~

ost vessels storing liquid or gas are surfaces of revolution, formed by rotation of one or more continuous pl~me curves about a straight line in their plane. The line is called the axis of revolution. All sections of a shell of revolution perpendicular to the axis of revolution are circles. Usually the axis of revolution of a storage vessel is vertical, in which case all horizontal sections are circles.

Note: Radii R, and R2 lie in the same line, but have different lengths except for a sphere where R1 == R2. T1 and T2 are loads per inch and will give the membrane stress in the plate when divided by the thickness of the plate.

M

General Equation for Membrane Forces Consider an element of a spherical section of unit length in each direction. Figure 4-1 indicates the radii and forces T1 and T2 acting on the element. Figures 4-2 and 4-3 indicate the pressure on the element and the components of the membrane unit forces in the latitudinal and meridional planes. For equilibrium, the summation of forces must be equal to zero.

Notation P

= The

internal pressure on shell. It may be due to gas alone (PG) , liquid alone (Pd, or both together (PG + Pd (psi). T, = The meridional force (sometimes called longitudinal force). This is force in vertical planes, but on horizontal sections (pounds per inch). T, is positive when in tension. T2 = The latitudinal force (sometimes called hoop or ring force). This is Jorce in horizontal planes, but on vertical section (pounds per inch). T2 is positive when in tension. R = Horizontal radius at plane ·under consideration from axis of revolution (in). R1 = Radius of curvature in vertical (meridional) plane at level under consideration (in). Generally R, is negative if it is on the opposite side of the shell from R2. R2 = Length of the normal to the shell at the plane under consideration, measured from the shell to its axis of revolution (in). Generally R2 is positive unless the plane results in more than one circle. W = Total weight of that portion of the vessel and its content, either above or below the plane under consideration, which is treated as a free body in computations for such plane (pounds). W has the same sign as P when acting in the same direction as the pressure on the plane of the free body, and the opposite sign from P when acting in the opposite direction. AT == Cross sectional area of the interior of the vessel at the plane under consideration (square inches). y = Density of product (pounds per cubic inch).

l: Outward Force = P.R2 2.R1 cJ>1 l: Inward Force 2T1 1R22 + 2T2 2R,cJ>,

=

"2

"2

Equating the two: P.R2 2.R11 =

2T1 ,R22 + 2T2 2R1,

"2

2"

:. PR1R2 = T,R2 + T2R, :. p = 11 + 12 (4-1) R1 R2 Equation 4-1 is the general equation for membrane forces. This equation considers membrane forces primarily produced by the product contained within the vessel. The weight of the vessel itself may add to these forces and should be considered in the analysis.

Modified Equations for Membrane Forces In general, the meridional force is the unit force in the wall of the vessel required to support the weight of the product, internal pressure, and plate weights at the plane under consideration. In the free body diagram (figure 4-5), consider the forces acting at plane 1-1. The total forces acting at plane 1-1 from above the plane = p.rr.R2.

17

General Equation for Membrane Forces

PLANE B·B (VERTICAL)

PLANE A·A (NORMAL TO SURFACE)

FIGURE 4·1

Elevation View, Plane B-B

Plan View, Plane A-A

FIGURE 4-3

FIGURE 4-2 18

Modified Equations for Membrane Forces

I

1-'-----'1

FIGURE 4-4

1--~

R = R2 SIN FIGURE 4-5 19

For figures 4-6, 4-7,4-8,4-9, and 4-14, the equations for membrane forces are:

Total forces acting at plane 1-1 from below the plane = W. Total vertical downward force = P.TI.R2 + W Vertical force required along circumference at plane 1-1 to support the downward forces:

T1 =

_ P.TIR2+ W

T

T. =

2TIR

VI -

_ JJLL _

P.TIR2+ W

T1

T, - Sin cI> - 2TIR Sin cI> T,

PR

= 2 Sin cI> = 2

Since

.W + 2TIR Sin cI>

s~n 4> [ p

+

[p -

= R2 and TIR2 = AT

~.

[p

+

~]

T.

= R. [ P

Further Simplifications

(4-2)

-

=~[p+~] 2 AT

The sign of R1, R2, P, W, and AT are shown in table 4-1 and must be included in computing the forces. For any other vessel configuration, a free body diagram can be drawn and the forces T, and T2 calculated in a similar way.

The equations for membrane forces can be further simplified for some of the shapes.

From Equation 4-1

a.Spheres

~~]

For spheres with no product (gas pressure only), the equations reduce to:

These are the equations used in API 620.

=

T,

Simplified Equations for Commonly Used Shapes

II

T2 = R2 .[ P _ R,

Since

T1

PR2] 2R,

= R2 = R

= T2 =

PR

2 where R = radius of sphere.

Level of product in the vessel.

b.

Volume of product to be used in calculating the weight of product above or below the free body diagram.

Cylinders

If the weight of the plate is neglected and there is no internal pressure in the vessel and since

R2 = R:

Area of plate to be used in calculating the weight of plate above or below the free body diagram.

T,

= 2"R [ PL

-

TIR2YH] TI R2

Since rH = PL

For all figures:

T1

P = PG + rH AT

PGR2 2

Figures 4-6 to 4-14 show the common vessel shapes used and the direction and magnitude of the radii, pressure, and weights acting on the free body diagram. Table 4-1 indicates the sign for each variable . The figures use the following notations:

fE[l Wj

~~]

T2 = PR2

n~.]

R

Sin cI>

T, =

R.

For figures 4-10,4-11,4-12, and 4-13 where R1 = co, the equations for membrane forces reduce to:

Membrane force

or

~[P +~] 2 AT

T2

= TIR2

=0 = PL.R

where R = radius of cylinder.

20

I

[ _ ...1-1----

LINE OF SUPPORT

T

R=R2 SIN cp FIGURE 4-6 Spherical Vessel or Segment. Plane below line of support.

R=R2 SIN cp

I l---L---~T-ri~H"'i+.ri.~~T:-ri~r-l · ·

[ ~ :~:.I-I----

LINE OF . SUPPORT

T

FIGURE 4·7 Spherical Vessel or Segment. Plane above line of support. 21

.. .. . ..., .:.

. ... . -: . .:

.. . '

.

. . .. . . .

,' '

.

':

., . .

. '

.

LINEOF

J -T

. SUPPORT

R=R2 SIN cp FIGURE 4·8 Spheroidal Vessel or Segment. Plane below line of support.

R=R2 SIN cp

I

l------L-f't~~~~~r-A~~~~~~~lr-l

-r-·

[LINE OF SUPPORT

-r

FIGURE 4·9 Spheroidal Vessel or Segment. Plane above line of support. 22

LINE OF SUPPORT

I

R-R2 CDS

cp R 1 = .DO

FIGURE 4·10 Conical Vessel or Segment. Plane below line of support.

R=R2 CDS cp

I

1 LINE OF SUPPORT

I

R 1 = DO FIGURE 4·11 Conical Vessel or Segment. Plane above line of support. 23

~~ I

v

I

Rl =

00

FIGURE 4·12 Conical Vessel or Segment. Pressure on convex side. Plane above line of support.

R=R.;:> PGI '~

/

/

/:':'~

,')'

:::;",';

::,~

1

\l

':" /

,r.:: ,'')

",,)

(\'

.":'>,': ',,' y'

:/'::":::/,:':,:,

::':,

...::

I

1-

''':; ::.',

f I

R1 = 00 FIGURE 4·13 Cylindrical Vessel. Plane above line of support. 24

\"

.

I

FIGURE 4-14 Curved Segment. Pressure on convex side. Plane above line of support.

TABLE 4-1 Figure

R1

R2

P

W

AT

4-6

+

+

+

+

+

4-7

+

+

+

-

+

4-8

+

+

+

+

+

4-9

+

+

+

-

+

4-10

co

+

+

+

+

4-11

co

+

+

-

+

4-12

co

+

-

+

+

4-13

co

+

+

-

+

4-14

-

+

+

-

+

25

Part V Self-Supported Stacks ....................._ Scope

a damping device. Such devices might consist of a gunite or similar lining or so-called "wind spoilers" on the exterior of the stack. ' The subject is quite complex. To attempt a brief summarization could be dangerously misleading. Instead, a bibliography of references is appended at the end of this part for the benefit of those who wish to explore the subject more thoroughly.

he scope defined for this Volume stated that stacks would not be discussed in detail because of the complicated problem of resonant vibrations. Apart from this phase, however, there are purely structural facets that may be of interest. For the benefit of those not familiar with the problem, a brief explanation of stack vibration follows:

T

Minimum Thickness and Corrosion In view of the corrosive nature innate to stack operation, it is wise to add a corrosion allowance to the calculated shell thickness. The nature of the flue gasses and moisture content in the area are some important parameters in determining the amount of corrosion for which to allow. Erection requirements usually dictate minimum plate thicknesses and the stress formulae in this part are not considered valid for thicknesses less than Y4". Therefore, the minimum thickness for shell plate is taken to be Y4" nominal.

Wind-Induced Vibrations When a steady wind blows on an unsheltered, unguyed stack, formation and shedding of air vortices on each side of the stack can apply alternating lateral forces that cause movement of the stack perpendicular to the direction of the wind. The frequency of vortex shedding is a function of wind velocity and stack diameter. The term critical velocity denotes the wind velocity at 'A'hich the frequency of vortex shedding equals the natural frequency of the stack. Under such conditions, resonance occurs. Excessive lateral dynamic deflection and vibration of the stack from vortex shedding may occur at wind velocities considerably below the maximum wind velocity expected in the area. One way to avoid resonance and consequent damage to the stack is to proportion the stack so that the critical wind velocity exceeds the highest sustained wind velocity that is likely to occur. In most areas, for example, it is unlikely that a steady wind of more than 75 mph will occur. Hence, a stack having a critical velocity of 75 mph is probably safe in those regions, though gusts of greater velocity might occur. There may be reasons, however, why a stack of such proportions will not serve the purpose. If so, the effects of dynamic vibrations must be thoroughly investigated. If the critical wind velocity is low enough, it may be that the stresses due to dynamic deflections are within design limits. In that case, the stack is structurally adequate if noticeable movement of the stack is not objectionable. If investigation shows that stresses due to vibrations are not within safe limits, the only solutions are to change the stack diameter or to add

Notation A (l

AB As ~

G G'c GL

o Do

E E1

Fa Fb Fe Fer FL Fs

27

= Cross sectional area of base ring, in.2 = Vertical angle of cone to cyl., degrees = Anchor bolt circle, in. = Required area for stack stiffeners, in.2 = Critical damping ratio of .stack = See Fig. 10 Sec. A-A = Euler Factor = Lift coefficient (0.2 for circular cylinder) = Outside diameter of stack, in. = OutSide diameter of cylindrical portion of stack, ft. = Modulus of elasticity, psi at design temperature = Joint efficiency for base plate design = Allowable compressive stress for circumferential stiffeners, 12000 psi (unless otherwise noted) = Allowable bending stress, 0.6 F4, psi for stiffeners = Allowable compressive stress, ksi = Critical buckling stress, ksi = Equivalent static force, Ibltt of height = Allowable compressive stress, psi (in conecylinder junction area)

Fy

= Yield

point of stack material, ksi Factor of safety Overall height of stack, ft. Overall height of stack, in. Required moment of inertia for stack stiffeners, in.4 K4> = Effective length factor K = Slenderness reduction factor Ls = Stiffener spacing, ft. L = length for KUr LS1 = Stiffener spacing, in. M = Moment at any design point, inch-pounds N = Number of anchor bolts Pd = Wind load, psi R 1 = Outside conical radius, in. Ro = Outside radius of cylinder portion of stack, in. S = Strouhal number (0.2 for steel stack) Ss = Required section modulus for stack stiffeners, in.3 T = Load per bolt, lb. V = Total direct load at any design point, lb. Ver1 = Critical wind velocity, mph VCr2 = Critical wind velocity, ftlsec. Vo = Resonance velocity, ft/sec. W = Chord for arc W', in. W' = Arc length of breeching opening, in. Ws = Unit weight of stack shell, Ib.lin. 3 do = Outside diameter of belled stack base, ft. fe = Compression stress, ksi fo = Frequency of the lowest mode of ovaling vibration, cps f t = Natural frequency, cps 9 = Acceleration of gravity, 386 in.lsec. h = Height of stack bell, ft. p = Wind load, psf qer = Dynamic wind pressure, psf r = Radius of gyration, in. = Thickness of stack, in. w = Uniform load over breeching opening, Ib.lin.

FS = H = H1 = Is =

Minimum base diameter do = H/10 (5-1) Minimum bell height h = 0.3H (5-2) Minimum diameter of cylinder, Do = H/13

.r

(5-3)

~

---a..-..-o.-"

/---,-.-

I_

do~

Figure 5-1. Cylindrical Stack with Belled Base. Stacks are likely to be subjected at least to the following loads: 1. Metal Weight. 2. Lining Weight. 3. Wind: Wind load provisions may be found in ASCE 7-88. Local building codes should also be consulted. 4. Icing (if required). 5. Seismic (if required). 6. Thermal cycling (vertical & circumferential). 7. Possible negative pressures. 8. Other requirements of local building codes.

Dynamic Wind Criteria The dynamic influence of wind may be approximated by assuming an equivalent static force, FL, in pounds per foot of height, acting in the direction of oscillations, given by:

FL = CL Do qer/2~ (5-4) NOTE: ~ = Critical damping factor which varies from 1% for an unlined steel stack of small diameter to 5 0/0 for concrete. The dynamic wind pressure, qcr, in psf, is given by: *qer = 0.00119 Vel. The critical wind velocity, Ver2 in fps, for resonant transverse vibration is given by: Veriftlsec)

=~ S

(5-5)

The natural frequency, ft (cps), of vibration of a stack of constant diameter and thickness is given by: ft = 3.52 D [~]\h (5-6) 4nH12 2Ws Critical velocity for a steel stack with an S value of 0.2 is given by:

Static Design Criteria In the suggested static design criteria below, the proportions indicated are those desirable from a structural standpoint. Independent calculations are needed to determine sizes to satisfy draft or capacity requirements. In general, stacks proportioned as suggested will probably have a high critical wind velocity, but a dynamic check should be made to verify this. Short stacks (less than 100 ft. high) may be straight cylinders without a belled base.

Ver1 (mph) = 3.41 Doft (5-7) Values of effective diameters and effective height for stacks of varying diameter and thickness may be determined by methods found in reference number 19. *Reference number 14(b)

28

Critical Wind Velocity for Ovaling Vibrations

P

M~

In addition to transverse swaying oscillations, stacks experience flexural vibration in the cross-sectional plan as a result of vortex shed~ing .. Thi~ freq~ency of the lowest mode of ovaling vibration In a circular shell is:

v

(5-8)

Ro

Resonance occurs when frequency of the lowest mode of ovaling vibration is twice the vortex shedding frequency; thus, the critical wind velocity for ovaling frequency is:

Vo = toDo = (ft/see)

H

v

(5-9)

cos ~

28 Unlined stacks are subject to ovaling vibrations. In order to prevent this phenomenon, the thickness of the stack should not be less than DI250 or intermediate stiffeners are required to raise the resonant velocity above 60 mph. Care should be exercised in coastal areas to give special attention to high winds as outlined in the aforementioned ASCE 7-88.

! Figure

In many applications of tubular columns, it is desirable to use a base cone to provide a broader base for anchorage. At the junction of the cone and cylinder (Fig. 5-2), it is necessary to provide reinforcement to resist the maximum vertical force.

The stresses associated with buckling have four ranges into which they can fall depending on the tlR ratio. They in turn may be affected by the Euler effect or slenderness ratio reduction factor. The stresses calculated in this manner are not to be increased for wind or earthquake stresses.

FY[0.35 + Fy [ 0.8 +

0.017

~:]

< tiRo S

~:]

G

Kc'P

= VRo tan a

(5-14)

Under load, the junction reinforcement, or stiffener, will move elastically inward. This will induce secondary vertical bending stresses on each side of the junction. For that reason, it is desirable to keep allowable stress Fs relatively low. If Fs is inthe,range of 8,000 psi, the secondary stresses can usually be ignored if Do is not greater than about 15 ft. For greater diameters or higher values of Fs it would be advisable to evaluate the secondary stresses. Note that V is the maximum value resulting from both vertical load and bending moment in the cylinder at the junction level. The moment of inertia Is of the stiffener section should not be less than:

0.5 [ C'C]2

=1

(5-13)

Fs

(5-10)

< KUr Kc'P =

If G'e ;::: KUr

= HRo = VRo tan a

The area of reinforcement required is

FS = 2.0

Fe = Kc'PFer/FS

(5-12)

The ring compression to be resisted is

As

=.r/ 2nFer£

(5-11)

nRo2

H = V tan a

Fy/11600

0.01 ~ tiRo S .04

2

+ ~

and the radial thrust

tiRo> .04

If GTe

= -p-

2nR o

Fy/11600 ~ tiRo S 0.01

Fy

G'e

V

tiRo Range

5.8 x 103 tiRo

Loads on Cylinder·Cone Junction

Cylinder-Cone Junction

Stack Stresses

Fer

5~2.

\

KUr

_ 0.5 [ KUr ]2

G'e Tables 5-1, 5-2 and 5-3 have been developed using A8TM A36 steel with a yield of 36 ksi. The value of K is taken as 2 in view of the fact that a stack is normally a cantilever. These allowable stresses will also be used for tapered or belled base stacks using the equivalent cylindrical radius approach as ~hown bel?w. In o~der to arrive at allowable stresses In the cOnical section one would substitute R 1 into the above formulae for

HR o 3 (5-15) £ based on a factor of safety of 3 for critical buckling. The area of reinforcement and computation of Is provided by a stiffener may, include an area of

Ro·

29

and bottom flanges. The shell of the stack will serve as the web. Each ring girder must be capable of carrying a uniform distributed load, in terms of pounds per inch of arch W', of:

cylinder and cone plate equal to

0.78(t vRot +

vR 1t)

t1

where R 1 = Ro

Icos

(5-16)

a

w= ~ + ~

This approach can be used in designing the junction of two cones having different slopes, except that H would be the difference between the horizontal components of the axial loads in the two cones.

reDo

The bending moment in the girder is:

Mq = WW'2

Allowable bending stresses may be chosen using AISC rules.

A stiffener is required at the top of the stack, also intermediate ring stiffeners are required to prevent deformation of the stack shell under wind pressure and to provide structural resistance to negative draft. Spacing of intermediate stiffener Ls is:

v' ~

Base Plates

(5-19)

In addition to bending stresses due to bending loads, the stack base plate must resist ring tension due to the horizontal component of the base cone if one is used. Maximum ring tension should be limited to 10,000 psi to account for secondary bending stresses in the base cone. This value may be varied upward depending upon the extent of secondary stress evaluation. Tension should be checked at the minimum cross-section occurring at the anchor bolt holes or at a weld joint where 85 010 or 100 010 efficiency may be assumed. A base plate area may be calculated by the following equation:

(5-20)

A = VDotana 20,000£,

(5-17)

To insure a nominal size of intermediate stiffener, the spacing is limited within 1.5 times the stack diameter. Intermediate stiffeners should meet the following minimum requirements:

Ss = pL S1 D2

(i n3 )

(5-18)

1100Fb

A s

=

Pd Ls1 D 2Fa

(in2)

(5-23)

12

Circumferential Stiffeners

Ls =60

(5-22)

reDo2

(5-24)

To satisfy the requirements of the above intermediate stiffener d~Sign formulae a port. ion of the stack equal to 1.1 t Dot may be included.

Breeching Opening The breeching opening should be as small as consistent with operating requirements with a maximum width of 20013. The opening must be reinforced vertically to replace the area of material removed increased by the ratio of DelC. Therefore, each vertical stiffener on each side of the opening should have a crosssectional area of:

A = W'tD o s 2C

(5-21).

Each vertical stiffener in conjunction with a portion of the liner shell would be designed as a column. Each stiffener should extend far enough above and below the opening to develop its strength. Horizontal reinforcement should be provided by a ring girder above and below the opening. These girders should be designed as fixed-end beams to carry the load across the opening above and below. The span in bending is the width W between the side column, but the girders should encircle the stack to preserve circularity at the opening. To form each ring girder, stiffener rings should be placed to act as top

A

A

,Fig. 5-4)

(Fig. 5-4)

Figure 5·3. Elevation of Stack.

30

Base plate thickness may be determined by using AISC formulae and allowable bending stresses.

Anchor Bolts Minimum diameter = 1112" Maximum spacing of anchor bolts = 5'-6' Maximum tension at root of threads = 15,000 psi Each bolt should be made to resist a total tension in pounds of:

c

T

= 4M

ND

N

-

V · (#/Bolt)

N

= # of AB

A suggested design procedure for anchor bolt brackets is covered in Part VII.

Figure 5-4. Horizontal Section Through Opening. .(Section A-A, Fig. 5-3)

For tiRo from .0017 through Fyl11600

~ KLir

~

0 17.5 35 52.5 70 87.5 105 122.5 140 157.5 175

.0017

.00192

.00214

.00236

.00258

.0028

.00302

4930 4917 4878 4813 4722 4605 4462 4293 4097 3877 3630

5568 5551 5502 5419 5303 5154 4971 4755 4507 4225 3909

6206 6185 6124 6071 5876 5691 5414 5196 4887 4537 4145

6844 6819 6744 6618 6443 6217 5942 5616 5240 4814 4338

7482 7452 7362 7212 7003 6733 6404 6015 5565 5056 4487

8120 8085 7979 7803 7556 7238 6850 6392 5862 5263 4593

8758 8717 8594 8389 8101 7732 7281 6747 6132 5434 4655

.

Table 5-1 Fe Allowable Compressive Stress (Fy = 36 ksi)

31

(5-25)

For tiRo from Fy/11600 to .01

~ a

.003104

.00425

.0054

.00655

.0077

.00885

.00999

9094 9049 8917 8695 8386 7988 7501 6926 6262

10128 10073 9908 9634 9250 8756 8152 7439 6616

11162 11095 10895 10562 10095 9496 8762 7896 6896

12196 12116 11888 11480 10928 10207 9331 8297

13230 13136 12855 12387 11732 10889 9859 8642

14264 14155 13829 13284 12523 11543 10345 8930

15298 15173 14797 14171 13295 12168 10791 9163

Z~.Q$.

Zg~a

Z~Q~.

~R~$.

~ZR~

5769 4673

Zg$.?

~t?~.~

5769 4673

5769 4673

5769 4673

KUr l

17.5 35 52.5 70 87.5 105 122.5 140 157.5 175

4670

4673

4673

Table 5·2 Fe Allowable Compressive Stress (Fy = 36 ksi)

For tiRo from .01 to ·.04

~ 0

.01

.015

.02

.025

.03

.035

.04

15300 15175 14798 14173 13296 12169 10792

15750 15617 15219 14556 13627 12432 10972

16200 16060 15638 14936 13954 12690 11146

16650 16502 16057 15315 14277 12942 11311

17100 16944 16474 15692 14597 13189 11468

17550 17385 16891 16067 14914 13431 11618

18000 17827 17307 16440 15227 13666 11760

~~.R~

~g~?

~~gQ

~~~$.

~~7.~

~RQ~

7302 5769 4673

7302 5769 4673

~~~~

7302 5769 4673

7302 5769 4673

7302 5769 4673

7302 5769 4673

7302 5769 4673

KUr l

17.5 35 52.5 70 87.5 105 122.5 140 157.5 175

If tiRo> .04

Fe

= .5

X

Fy

X

KcI>

Table 5·3 Fe Allowable Compressive Stress (Fy = 36 ksi) Dotted lines are an indicator at which point G'c> KUr

32

References

13. G.B. Woodruff and J. Kozok, "Wind Forces on Structures: Fundamental Considerations," Proceedings of ASCE, Vol. 84, ST 4, Paper No. 1709,1958, p. 13. 14. -F.B. Farquaharson, "Wind Forces Structures: Structures Subject Oscillations," Proceedings of ASCE, Vol. 84, ST 4, Paper 1712, 1958, p.13. 15. ASCE Transaction Paper #3269 {"Wind Forces on Structure"}. 16. C.F. Cowdrey and J.A. Lewes, "Drag Measurements at High Reynolds Numbers of a Circular Cylinder Fitted with Three Helical Strakes," NPLlAero/384, July 1959. 17. L. Woodgate and J. Maybrey, "Further Experiments on the Use of Helical Strakes for Avoiding Wind-Excited Oscillations of Structures with Circular or Near Circular Cross-Section" NPLlAero/381, July 1959. ' 18. A. Roshko, "On the Wake and Drag Bluff Bodies," presented at Aerodynamics Sessions, Twenty-Second Annual Meeting, lAS, New York, N.Y., January, 1954. 19. J.~. Smith and J.H. McCarthy, "Wind Versus Tall Stacks," Mechanical Engineering, Vol. 87, . January, 1965, pp. 38-41. 20. Gaylord and Gaylord, "Structural Engineering Handbook." 2nd Edition, Chapter 26. 21. R. Stuart III, A.R. Fugini, A. DeVaul, PittsburghDes Moines Corp. Research Report #98528, "Design of Allowable Compressive Stress Cylindrical or Conical Plates, AWWA D100," May, 1981. 22. Roger L. Brockenbrough, Pittsburgh-Des Moines Corp. Research Report 98030, "Determination of The Critical Buckling Stress of Cylindrical Plates Having Low t/R Values." October 5, 1960. 23. Tom Buckwalter, Pittsburgh-Des Moines ··Qorp. Supplement to RP 98030, "Determination of the Critical Buckling Stress in a Cylinder Having a tlR of 0.00426," December 20, 1960. 24. AISC 1989 "Specification for Structural Steel Buildings - Allowable Stress Design and Plastic Design."

1. M.S. Ozker and J.O. Smith, "Factors Influencing the Dynamic Behavior of Tall Stacks Under the Action of Winds," Trans. ASME Vol. 78, 1956, pp. 1381-1391. 2. P. Price, "Suppression of the Fluid-Induced Vibration of Circular Cylinders," Proceedings of ASCE, Vol. 82, EM3, Paper No. 1030, 1956, p. 22. 3. W.L. Dickey and G.B. Woodruff, "The Vibration of Steel Stacks," Proceedings of ASCE, Vol. 80, 1954, p. 20. 4. T. Sarpkaya and C.J. Garison, "Vortex Formation and Resistance in Unsteady Flow," Journal of Applied Mechanics, Vol. 30, Trans. ASME, Vol. 85, Series E, 1963, pp. 16-24. 5. A.W. Marris, "A Review on Vortex Streets, Periodic Wakes, and Induced Vibration Phenomena," Journal of Basic Engineering, Trans. ASME, Series D, Vol. 86, 1964, pp. 185-196. 6. J. Penzien, "Wind Induced Vibration of Cylindrical Structures," Proceedings of ASCE, Vol. 83, EM 1 Paper No. 1141, January, 1957, p. 17. 7. W. Weaver, "Wind-Induced Vibrations in Antenna Members," Transactions of ASCE, Vol. 127, Part 1, 1962, pp. 679-704. 8. C. Scruton and D. Walshe, "A Means of Avoiding Wind-Excited Oscillations of Structures with Circular or Nearly Circular Cross-Section," NPLlAero/335, October 1957. 9. C. Scruton, D. Walshe and L.Woodgate, "The Aerodynamic Investigation for the East Chimney Stack of the Rugeley Generating Station," NPLlAero/352. 10. A. Roshko, "On the Development of Turbulent Wakes from Vortex Streets," NACA Report 1191, 1954. 11. A. Roshko, "On The Drag and Shedding Frequency of Two-Dimensional Bluff Bodies," NACA Technical Note 3169, July 1954. 12. N. Delany and N. Sorensen, "Low-Speed Drag of Cylinders of Various Shapes," NCA Technical Note 3038, November, 1953.

33

Part VI Supports for Horizontal Tanks and Pipe Lines ----------------different distribution of stress in the pipe or vessel wall from that encountered with a full ring support, are discussed in the following paper by L. P. Zick. It includes some revisions of and additions to the original paper published in "The Welding Journal Research Supplement", September, 1951, and reprinted in "Pressure Vessel and Piping Design Collected Papers 1927-1959", published by ASME in 1960.

T

here is considerable information available on design of supports for horizontal cylindrical shells where a complete ring girder is used. There are many installations where a horizontal tank, pressure vessel, or pipe line is supported by a saddle extending less than 180 0 around the lower . part of the cylinder. The effects of vertical deflection of the cylinder and the concentration of stress around ·the horn of the saddle, which result in a

Original paper published in September 1951 liTHE WELDING JOURNAL RESEARCH SUPPLEMENT." This paper contains revisions and additions to the original paper based upon questions raised as to intent and coverage.

Stresses in Large Horizontal Cylindrical Pressure Vessels on Two Saddle Supports Approximate stresses that exist in cylindrical vessels supported on two saddles at various conditions and design of stiffening for vessels which require it

by L.P. Zick

INTRODUCTION

which vessels may be designed for internal pressure alone, and to .design structurally adequate and economical stiffening for the vessels which require it. Formulas are developed to cover various conditions, and a chart is given which covers support designs for pressure vessels made of mild steel for S.torage of liquid weighing 42 lb. per cu. ft.

The design of horizontal cylindrical vessels with dished heads to resist internal pressure is covered by existing codes. However, the method of support is left pretty much up to the designer. In general the cylindrical shell is made a uniform thickness which is determined by the maximum circumferential stress due to the internal pressure. Since the longitudinal stress is only one-half of this circumferential stress, these vessels have available a beam strength which makes the two-saddle support system ideal for a wide range of proportions. However, certain limitations are necessary to make designs consistent with the intent of the code. The purpose of this paper is to indicate the approximate stresses that exist in cylindrical vessels supported on two saddles at various locations. Knowing these stresses, it is possible to determine

HISTORY In a paper1 published in 1933 Herman Schorer pOinted out that a length of cylindrical shell supported by tangential end shears varying proportionately to the sine of the central angle measured from the top of the vessel can support its own metal weight and the full contained liquid weight without circumferential bending moments in the shell. To complete this analysis, rings around the entire circumference are required at the supporting points to transfer these shears to the foundation without distorting the cylindrical shell. Discussions of Schorer's paper by H.C. Boardman and others gave

L.P. Zick is a former Chief Engineer for the Chicago Bridge & Iron Co., Oak Brook, III.

35

Figure 6-1. Strain gage test set up on 30,000 gal. propane tank. approximate solutions for the half full condition. When a ring of uniform cross section is supported on two vertical posts, the full condition governs the design of the ring if the central angle between the post intersections with the ring is less than 126 0, and the half-full condition governs if this angle is more than 126°. However,the full condition governs the design of rings supported directly in or adjacent to saddles. Mr. Boardman's discussion also pointed out that the heads may substitute for the rings provided the supports are near the heads. His unpublished paper has been used successfully since 1941 for vessels supported on saddles near the heads. His method of analysis covering supports near the, heads is included in this paper in a slightly modified form. Discussions of Mr. Scharer's paper also gave Table 6-1 Saddle angle,

e

Maximum lonf}' bending stress,

Mkl. K1 "

= 0.09) = 0.11)

Values of Coefficients in Formulas for Various Support Conditions Tangent. shear,

Circumf. stress top of saddle,

K2

K3t

Additional head stress,

Ring compres. in shell,

K4

Ks

Rinfl. stiffeners Circumf. Direct bending, stress,

K6

K7

Tension across· saddle,

K8

Shell unstiffened

1.171 0.799

0.0528 0.0316

0.880 0.485

0.0132 0.0079

120 0 150 0

0.63 (AIL 0.55 (AIL

120 0 150 0

1.0 (AIL 1.0 (AIL

120 0 150 0

0.23 (AIL = 0.193) 0.23 (AIL = 0.193)

0.319 0.319

120 0 150 0

0.23 (AIL = 0.193) 0.23 (AIL = 0.193)

1.171 0.799

= 0) = 0)

successful and semi-successful examples of unstiffened cylindrical shells supported on saddles, but an analysis is lacking. The semi-successful examples indicated that the shells had actually slumped down over the horns of the saddles while being filled with liquid, but had rounded up again when internal pressure was applied. Testing done by others 2 ,3 gave very useful results in the ranges of their respective tests, but the investigators concluded that analysis was highly indeterminate. In recent years the author has participated in strain gage surveys of several large vessels. 4 A typical test setup is shown in Fig. 6-1. In this paper an attempt has been made to produce an approximate analysis involving certain empirical assumptions which make the theoretical analysis closely approximate the test results.

0.760 0.673

0.204 0.260

Shell stiffened by head, A $ RI2

0.401 0.297

0.760 0.673

0.204 0.260

Shell stiffened by ring in plane of saddle

0.0528 0.0316

0.340 0.303

0.204 0.260

0.0577 0.0353

0.263 0.228

0.204 0.260

Shell stiffened by rings adjacent to saddle

0.0132 0.0079

0.760 0.673

·See Fig. 6·5, which plots K, against AIL, for values of K, corresponding to values of AIL not listed in table. tSe€, Fig. 6·7.

36

~

I"-.

\

""-

\

'"

"-

' " '" " "'" ""

"-

~

.............

~,

............

~

e:

\

~ "'-.s' 6' "'" ~ t'-...

L

A l~ .2

~

~

~ :! L

'J

I

'\

'"""

I 1)4 lYe 'ta 3/4 SHELL THICKNESS. t. IN INCHES

IZO

\

"z~

l:re

~

o~

"-

/

I¥'

k-

"-, ~

~

@

120';

I II 1/ / / / // fa: 7 1.09 =~

/

/

L

/

h.DD I Rlt-GS

150·

//

L

\. \

~

-:l

• . I~

..,

/

V.17

~

~

T~~

PL

_'T~r~ foil'.-:-~

~

-

./

~

~(2 ..

A _

Lt.: f'-

-.

""':::

6"

~

1-

,

~

80

~

90

40

50

,,,,,-

'" """" '"

...

60 7o

,~

~:~ ~" ~~~

"'-,

~I~

"\ ~.s I'Z'

.'" '\~

~ 110 12-'

~ 1.~:

"\

I...,

.25

30

~ ,"'~ " "'-

~ ~O

W to)

·r 20

~ ~, .........

4'"

:r:

AT P~TS

./'

"'ADO Rlt-GS AT SU PPORT ~

~ 30 ~ .........

~

/

/e-I~~ "LRf A~ 16... ~ ADD ~INCS AT ... ...... SUPPORT / \ V NOT ~r ~ .2.4 / / VA"! .. fr;~ ~ BE V /,. ~6~ ~~.5 ify PPORT ED CJ-I ~ TWO SADO "-ES / / "CtJE ....K ~AO/

\

~ ~~

~a

BASIS OF' DESIGN A-265 CRADE C CARBON STEEL LIQUIO WT. - . 42 LBS PtR. CU. F'T EX AMPLE SHOWN BY ARROWS R - 5'} USE 120" SADOLES L- 80' A = R/2 OR LESS t • 3/;' CHECK HEAD PL THK

Ve:

/e = II o~ .Izi

IZO·

\~

........

IV:2

I

~

80


- 8R + 1Ot) 2t2

or

S3

=4t(b

0 - 12KaQR, if L * < 8R + 1Ot) Lt2

• Note: For multiple supports: L = Twice the length of portion of shell carried by saddle. If L ~ 8R use 1st formula.

It seems reasonable to allow this combined stress to be equal to 1.50 times the tension allowable provided the compressive strength of the material equals the tensile strength. In the first place when the region at the horn of the saddle yields, it acts as a hinge, and the upper portion of the shell continues to resist the loads as a twa-hinged arch. There would be little distortion until a second paint near the equator started to yield. Secondly; if rings are added

40

to reduce this local stress, a local longitudinal bending stress occurs at the edge of the ring under pressure. 5 This local stress would be 1.8 times the design ring stress if the rings were infinitely rigid. Weld seams in the shell should not be located near the horn of the saddle where the maximum moment occurs.

EXTERNAL LOADS Long vessels with very small tlr values are susceptible to distortion from unsymmetrical external loads such as wind. It is assumed that vacuum relief valves will be provided where required; so it is not necessary to design against a full vacuum. However, experience indicates that vessels designed to withstand 1 lb. per sq. in. external pressure can successfully resist external loads encountered in normal service. Assume the external pressure is 1 lb. per sq. in. in the formulas used to determine the sloping portion of the external pressure chart in the current A.S.M.E. Unfired Pressure Vessel Code. Then when the vessel is unstiffened between the heads, the maximum length in feet between stiffeners (the heads) is given approximately by

L +

213H

r(n-- a: .. lIINa:cosa::1 _

' - -_ _~

r

r

When the head stiffness is utilized by placing the saddle close to the heads, the tangential shear stresses cause an additional stress in the head which is additive to the pressure stress. Referring to Section G-G of Fig. 6-4, it can be seen that the tangential shearing stresses have horizontal components which would cause varying horizontal tension stresses across the entire height of the head if the head were a flat disk. The real action in a dished head would be a combination of ring action and direct stress; however, for simplicity the action on a flat disk is considered reasonable for design purposes. Assume that the summation of the horizontal components of the tangential shears is resisted by the vertical cross section of the flat head at the center line, and assume that the maximum stress is 1.5 times the average stress. Then the maximum additional stress in the head in lb. per sq. in. is given by

= 30 ( 8rth

1t -

)

SIN~COs.d

Figure 6-8 indicates the saddle reactions, assuming the surfaces of the shell and saddle are in frictionless contact without attachment. The sum of the assumed tangential shears on both edges of the saddle at any point A is also shown in Fig. 6-8. These forces acting on the shell band directly over the saddle cause ring compression in the shell band. Since the saddle reactions are radial, they pass through the center O. Taking moments about point 0 indicates that the ring compression at any pOint A is given by the summation of the tangential shears between a and . This ring compression is maximum at the bottom, where = 1t. Again, a width of shell equal to 5t each side of the saddle plus the width of the saddle is assumed to resist this force. See Appendix B. Then the stress in lb. per sq. in. due to ring compression is given by

ADDITIONAL STRESS IN HEAD USED AS STIFFENER

S4

Ii" C.O$$

RING COMPRESSION IN SHELL OVER SADDLE

= E Yif( i)2 52.2

£( ,.. 00.".

This stress should be combined with the stress in the head due to internal pressure. However, it is recommended that this combined stress be allowed to be 25 0/0 greater than the allowable tension stress because of the nature of the stress and because of the method of analysis.

When ring stiffeners are added to the vessel at the supports, the maximum length in feet between stiffeners is given by

L - 2A

=

Figure 6-8. Loads and reactions on saddles.

Yif( i)2 52.2

= E

MAl(

S5

=

0

(

t(b+ 10t)

1t -

1 + cos a ) a + sin a cos a

or

S5

=

K5 0 t(b + 10t)

The ring compression stress should not exceed one-half of the compression yield pOint of the material.

WEAR PLATES The stress may be reduced by attaching a wear plate somewhat larger than the surface of the saddle to the shell directly over the saddle. The thickness t used in the formulas for the assumed cylindrical shell thickness may be taken as (t1 + t2) for S5 (where t1 : shell thickness and t2 = wear plate thickness), provided the width of the added plate equals at least (b + 10t1) (see Appendix B).

sin2 a ) a + sin a cos a

or

41

The thickness t may be taken as (t1 + t2) in the formula for 52, provided the plate extends rl10 inches above the horn of the saddle near the head, and provided the plate extends between the saddle and an adjacent stiffener ring. (Also check for 52 stress in the shell at the equator.) The thickness t may be taken as (t1 + t2) in the first term of the formula for 53, provided the plate extends rl10 inches above the horn of the saddle near the head. However, (t12 + t22) should be substituted for t2 in the second term. The combined circumferential stress (53) at the top edge of the wear plate should also be checked using the shell plate thickness t1 and the width of the wear plate. When checking at this point, the value of K3 should be reduced by extrapolation in Fig. 6·7 assuming e equal to the central angle of the wear plate but not more than the saddle angle plus 12°.

..... 1l.

H[ [ "IN.

Mcp = Or { ~ - sin 2nn sin 13 cos c!> [3/2 + (It -

Mp

n

2(1 - cos

13)

cos

cos

p may be found by statics and is given by

P p

P

-

0 [ nn

p sin p

_ cos

2(1 - cos p)

p] _

cos P (Mp + Mt) r(1 - cos p) or

Pp

p]+

r(1 - cos P}

= K6 Or

n Knowing the moments Mp and Mf, the direct load at

Knowing the maximum moment MJ3 and the moment at the top of the vessel, Mf, the direct load at the point of maximum moment may be found by statics. Then the direct load at the horn of the saddle is given in pounds by

-

13) cot III }

For the range of saddle angles considered, M~ is maximum near the equator where = p. This moment and the direct stress may be found using a procedure similar to that used for the stiffener in the plane of the saddle. Substituting p for and K6 for the expression in the brackets divided by 21t, the maximum moment in each ring adjacent to the saddle is given in in .-Ib. by

n

p

10'

shown in Section A·A. Conservatively, the support may be assumed to be tangential and concentrated at the horn of the saddle. This is shown schematically in Fig. 6·9; the resulting bendingmoment diagram is also indicated. This bending moment in in.·lb. at any pOint A above the horn of the saddle is given by

When the saddles must be located away from the heads and when the shell alone cannot resist the circumferential bending, ring stiffeners should be added at or near the supports. Because the size of rings involved does not warrant further refinement, the formulas developed in this paper assume that the added rings are continuous with a uniform cross section. The ring stiffener must be attached to the shell, and the portion of the shell reinforced by the stiffener plus a width of shell equal to 5t each side may be assumed to act with each stiffener. The ring radius is assumed equal to r. When n stiffeners are added directly over the saddle as shown in Fig. 6·4 (e), the tangential shear distribution is known . The equation for the resulting bending moment at any point was developed previously, and the resulting moment diagram is shown in Fig. 6-6. The maximum moment occurs at the horn of the saddle and is given in in.-Ib. for each stiffener by M J3 .;... - K6Or -

(} sin

-

Figure 6-9. Circumferential bending-moment diagram, stiffeners adjacent to saddle.

DESIGN OF RING STIFFENERS

n Pf) = Q [

.;1t

= K7 Q n

Then the maximum combined stress due to liquid load in each ring used to stiffen the shell at or near the saddle is given in lb. per sq. in. by S6 = - !5.zQ ± K60 r

(MJ3 - M1)

or

na

PJ3 = K7 Q

n

nllc

where a = the area and lIe = the section modulus of the cross section of the composite ring stiffener. When a ring is attached .to the inside surface of the shell directly over the saddle or to the outside surface of the shell adjacent to the saddle, the maximum combined stress is compression at the

If n stiffeners are added adjacent to the saddle as shown in Fig. 6-4 (b), the rings will act together and each will be loaded with shears distributed as in Section a-a on one side but will be supported on the saddle side by a shear distribution similar to that 42

th = thickness of head, in. b = width of saddle, in. F = force across bottom of saddle, lb. S1, 8 2, etc. = calculated stresses, lb. per sq. in. K1, K2, etc. = dimensionless constants for various support conditions. M4>, M~, etc. = circumferential bending moment due to tangential shears, in.-Ib. 8 = angle of contact of saddle with shell, degrees.

shell. However, if the ring is attached to the opposite surface, the maximum combined stress may be either compression in the outer flange due to liquid or tension at the shell due to liquid and internal pressure. The maximum combined compression stress due to liquid should not exceed one-half of the compression yield point of the material. The maximum combined tension stress due to liquid and pressure should not exceed the allowable tension stress of the material.

(3

= (. 180

Each saddle should be rigid enough to prevent the separation of the horns of the saddle; therefore the saddle should be designed for a full water load. The horn of the saddle should be taken at the intersection of the outer edge of the web with the top flange of a steel saddle. The minimum section at the low pOint of either a steel or concrete saddle must resist a total force, F, in pounds, equal to the summation of the horizontal components of the reactions on one-half of the saddle. Then

=Q

[ 1

+ cos (3 - 112 sin2(3 ] (3 + sin (3 cos (3

~

a =

180

2

+

Q) 6

= ~ ( 58

180 12

+ 30 ). 2~

= arc, in

7t -

~( ~ + 180

2

JL) = the central angle, in radians, 20

from the vertical to the assumed point of maximum shear in unstiffened shell at saddle. = any central angle measured from the vertical, in radians. p = central angle from the upper vertical to the point of maximum moment in ring located adjacent to saddle, in radians. E = modulus of elasticity of material, lb. per sq. in. Ilc = section modulus, in. 3 n = number of stiffeners at each saddle. a = cross-sectional area of each composite stiffener, sq. in. pP' p~ = the direct load in lb. at the point of maximum moment in a stiffening ring.

= KaQ

The effective section resisting this load should be limited to the metal cross section within a distance equal to r/3 below the shell. This cross section should be limited to the reinforcing steel within the distance r/3 in concrete saddles. The average stress should not exceed two-thirds of the tension allowable of the material. A low allowable stress is recommended because the effect of the circumferential bending in the shell at the horn of the saddle has been neglected. The upper and lower flanges of a steel saddle should be designed to resist bending over the web(s), and the web(s) should be stiffened according to the A.I.S.C. Specifications against buckling. The contact area between the shell and concrete saddle or between the metal saddle and the concrete foundation should be adequate to support the bearing loads. Where extreme movements are anticipated ·or where the saddles are welded to the shell, bearings or rockers should be provided at one saddle. Under normal conditions a sheet of elastic waterproof material at least V4 in. thick between the shell and a concrete saddle will suffice.

Bibliography 1. Schorer, Herman, "Design of Large Pipe Lines," A.S.C.E. Trans., 98, 101 (1933), and discussions of this paper by Boardman, H.C., and others. 2. Wilson, Wilbur M., and Olson, Emery D., "Test of Cylindrical Shells," Univ. III. Bull. No. 331. 3. Hartenberg, R.S., "The Strength and Stiffness of Thin Cylindrical Shells on Saddle Supports," Doctorate Thesis, University of Wisconsin, 1941. 4. Zick, L.P., and Carlson, C.E., "Strain Gage Technique Employed in Studying Propane Tank Stresses Under Service Conditions," Steel, 86-88 (Apr. 12, 1948). 5. U.S. Bureau of Reclamation, Penstock Analysis and Stiffener Design. Boulder Canyon Project Final Reports, Part V. Technical Investigations, Bulletin 5.

Nomenclature

= load on one saddle, lb. Total load = 20. = tangent length of the vessel, ft. = distance from center line of saddle to tangent line, ft. H = depth of head, ft. R = radius of cylindrical shell, ft. Q

L A

Appendix The formulas developed by outline in the text are developed mathematically here under headings corresponding to those of the text. The pertinent assumptions and statements appearing in the text have not been repeated .

r = radius

=

= ~ ( .!!

central angle from vertical to horn of saddle, in degrees (except as noted).

radians, of unstiffened shell in plane of saddle effective against bending.

7t -

t

~) = 2

DESIGN OF SADDLES

F

-

of cylindrical shell, in. thickness of cylindrical shell, in.

43

Maximum Longitudinal Stress

The bending moment in ft.-lb. at the mid-span is

Referring to Fig. 6-3, the bending moment in ft.-lb. at the saddle is

20 L

+ 4H

2Q [(L - 2A)2 _ 2HA _ A2 R2 - H2 ] L + 4H 8 3 2 + 4 3

[2HA + A2 _ R2 - H2] = 3 2 4

3 OA

OL 4

[1 ___-_Z_+_R_2_~_L_H_2_ ]

1 +~ 3L Referring to Section A-A of Fig. 6-4 the centroid of the effective arc = r sin d. If - a) shown in Section A-A or G-G of Fig. 6-4 or in Fig. 6-S. Then _

~ cI> 0 ~ a

sin 2 1t,

(

~ P ( cos ~0

.

2r3 [ 1. sin cos + 1. EI 2 2

r3 [

a - sin a cos a ) ,dcI>2 _ 1t - a + Sin a cos a

EI

45

_

P )2 r3 d = P EI

_ sin

2 sin cI> sin B + sin2 B] B=

B

sin pcps

B2

P+ P_ 2

.0

sin2

P

p]

~

VALUES OF

H/L

= .10

H/L

= .05

HfL

=

~ ~

~

=

R

H

.~ ~ ~ ~

t;:~

KI

v/

v"}

~v

0"

"-. .... ......... .........

•8

........

, ....

.6

-" ........ .......

#

0

K~",0

'"

I. o

K, .8

oj

6

.

-...-;.~ ,

Iff:"r:-

~~

-

.2

J

I. 2

,.'7

~ ..ft!tvr:

.4

J

,,~y ~

~o/

+.

= 3 sin J3 + cos J3 - 1/4 ( cos ·cI> -

sin _ cI> _ sin cI> cos cI>

rtB

~4

2

+

4

sin2 _ sin

2

~

~ (24) -

2 sin 4> - sin 4>

P cos P _

+

Y = ( cos 4> -

given by

M - cos

+

The distance from the neutral axis to pOint A is

r2dcI> =

- 2 cos 4> - 4> sin 4» ] d4>

+ 4> cos - 2 cos 2 cI> - cI> sin cI> cos cI> -

Si~ J3 (2

_

U1

~ cos ~ ]

~

= -.SL

Mi

=

0

The moment about the horizontal axis is

Mh

~ B_

Then the indeterminate moment is

2

[ cI> _ sin cI> _ sin + cos cI> 2 2 Or2 rtE!

d

+

=

[

46

2

~2 sin cI> ~

) x

~

~ )2 + 2 cos2 B

]}

~cosll+1-2(~y

.

4 - 6 (

= ~;

This is the mrXimum when

+

+

hi

(hi

h)

h,

+

h7

+ ~l + 2 (h2 +

hi

+ ~ + hll].

+ ~) + h2 + h) + h. + h~ + ~ + h1 + ha].

+

+ h2 + h3 + ~ + h, + ~ + h7 + h. + 11,].

+ 1.1

4 (hi

h lO)

+

Area

=

d [ \.1 (hi

+ 11,) + hz + h3 + h. + h, + h6 + h1 + hI].

When the ends arc nol curved. but are the straight lines hi and ~ then.

Area

Trapezoidal Rule:

Area = d [0.4

hlo

(110 +

=!! ["" +

Durand's Rule:

Area

Simpson's Rule:

When the ends are curved. ho and hlO are zero and cancel out of fonnulas.

The given figure has been divided into ten strips of width, d; the ordinates are ho to h lO .

Divide the plane surface into an even number of parallel strips of equal width .

IRREGULAR PLANE SURFACE

o

a::

::J ....

()

OJ

a.. X·

::J

Cl)

» 1:) 1:)

Appendix B. (Cont'd)

Thin Wall Sections (Dimensions are to Center of Wall)

A

= rrdt

I

= rrd 3 t 8

S = rrd 2 t 4

- -- t

r

= O.355d

b

=d

A = 4dt

d

3

I = 2d t

b

3 r

-

- -.

= 0.408d

d>b

-t

A = 2(b

-

~

d

r--

+ d)t

2

I 1-1 = d 6 t (3b + d)

b

SI_l

= d; (3b + d)

r

= O.289d ~~ ... rJF+(T

I-I

Sector of thin annulus 2

A = 2a.Rt

Il~j::

R·

(1 - Si~ a) Y2 = R (-Si: a - cos a) y1 = R

,

~ I

2

A-6

-.....J

l> ,

.r--

c- >-,

n

V

M , '~

q

;'" ------1:,

.

'

w

v

q

u

t

me"

e

m

Pb

e

0, -A,

p n.

= area of circle-area of segment. m n p

~i\'ell in tahles

the quotient of

~: C

h~'

the coenirimt

·.,'J'J

pu

Circular Lune, m p n s

Area = segment. m p n-segment. m s n.

v Q w).

se~ent. t

Circular Zone, t u w V

+ art'a of !:t'~ent .

= b x ex coeff. = U9 x :1.52 x 0,5.12 = 3.%56.

Area = area of cirde-(area of

Area

are obtained by interpolation . Example-Gin"n: rise = 1.-19 and chord = 3.52. .' rb"",U9_ 3.52 - 0 .... ~ .... ,. C ()(' fljalrnt -- 0-"1') . /J-_.

Intermediate coefficients for values of? not .civen in tahl('S C

~iv('n opposite

Given: rise. b. and chord. c. Area = product of ril'C and chord. h x c. multiplied

Circular Segment, from Table II page 284

Coefficient by interpolation = 0 .371233. Area = d 2 x coeff. = 25.9-1629 x 0.371233 = 9.6321.

are obtained by interpolation. Example-Given : ric;e = 2; 16 and diameter = 5~y'!. b d =27 J6 +5~~ =0.178528.

Intermediate coefficients for values of ~ not

Given: rise. b. and diameter. d = 2r. Area = square of diameter. d 2• multiplied by the coefficient d\'en . • fb oPPOsite the quotient 0 d '

Circular Segment, from Table I, pages 282 and 283

Area

Circular Segment, m q n, greater than half circle

2

Area = area of sector. m 0 n p-area of triangle. m 0 n (IenRth of arc. m p n. x radius. r)-(radius. r.-rise. b)x chord . r

Circular Segment, m p n, less than half circle

in degrees.

= 0.0087266 x square of radius, rl. x angle of arc, m

Area = ~'l (length of arc, m p n )( radius, r) _ f . 1 arc, n:' p n, in degrees - area 0 ClrC e x 360

mBn

P

Circular Sector, m 0 n p

AREA OF CIRCULAR SECTIONS

o ng .

P

log = 0.9942997

b

= 0.2485749

v',2 - Ir + y - bl2

x

1

-;3

1.50211501

0 .0322515, log

= 2.5085500

0.1013212. log = 1.0057003

~

" = 3.14159265359.

= 0.4971499

110

"

=

57.2957795. log

= 1.7511226

0.0174533.1011 = 2.2418774

0.SM11H. log

= 1.7514251

- Are. of Segment nop

180

x rl

- A,e. of tri.ngle ncp

.Jf =

log

Jlo x rZ x .,

x

llength of .rc nop x rl - x (, - bl 2

= A,e. of Circle

=

= chord b = rise = A,e. of Sector ncpo

= 0.0017268

= Area of Circle

= rt Uength of arc nop

angle ncp in deg,e.s

.,

=

1.27324 side of square 0.78540 diamate, of circle 1.41421 slda of squa,e 0.70711 diameter of circle

, = ,adius of ci,cle

Area of Segment nsp

0.3183099. log

4

2raln2~ = ' +.,-~ b-r+~

Not,, : logs of f,actlons such a.1 :5028501 .nd 2.5085500 ma., .Iso be w,itten 9.5028501 - 10 .nd 1.501550 - 10,espectlvely.

1.7724539. log

,,2

~

2

= 2,sln~ , - ~v'4,2 - c2 = .!.tan~ 2 4

2v'2br - b2

4b2 + c2 --I-b-

A,ea 0' Secto, ncpo

Are. of Segment nop

, = ,adlus of elrcle

= 0.017483 r A'

~ = 57.2957I a

180"

~

6.283111' = 3.14159 d 0.31831 clrcumfe,ence 3.14159,2

VALUES FOR FUNCTIONS nF 1T

= 31.0062767. log = 1.4914496 ~

= 9 .1169604-4.

v;- =

... 3

... 2

•

c

CIRCULAR SEGMENT

®

CIRCULAR SECTOR

Side of square in.."ibed in circle

~;~~~:~~:~j~l~e~~~~=~:;a:':~~~ua,e

Diameter of circle of equal pe'lphery as squa,e

b

Rise

., =

C

Cho,d

=

A' =

Radius,

Angle

A,c

Ci,eumf ..,ence Oiamete, A,ea

PROPERTIES OF THE CIRCLE

en ct> en

-6'

a.. m

::J

Q,)

en

ct>

(")

....,

()

o-+.

en

ct>

.-+

ct> ....,

"0

-0 ....,

o

X ()

a..

::J

ct>

l> "0 "0

Appendix D. Surface Areas and Volumes

SURFACES AND VOLUMES OF SOLIDS CI RCULAR RI NG (TORUS) D and R = Mean Diameter and Mean Radius, respectively, of Ring d and r = Mean Diameter and Mean Radius, respectively. of Section Surface = ,/!,2 Dd = 4,/!,2Rr ,/!,2 Volume = 2,/!,2Rr2 = "4 Dd 2

I

4·R?l I I

1 - - - - - - - - -1- - - - - - - - - - - - - - - - - - - - - - - - - - PRISMOID End faces are in parallel planes. Volume =

l

6 (A + A' + 4M), where

l = perpendicular distance between ends A.A' = areas of ends M = area of mid section, parallel to ends

UNGULAS FROM RIGHT CIRCULAR CYLINDER I.

(As formed by cutting plane oblique to base) Base, abc, less than semicircle; Convex Surface = h[2re- (d X length arc abc)] + (r-d)

= h [~eL-(d X area Base, abc, = semicircle; Convex Surface = 2rh Volume

II. Ill. I

I

I

,,I _L

Volume = J r 2h Base, abc, greater than semicircle (figure); Convex Surface = h [2re + Cd X length arc abc)] + ~ + d)

Volume = h [~e3 + (d X area base abc) + (r + d) Base, abc, = circle, oblique plane touching circumference. Convex Surface = '/!'rh Volume = Y2'/!'r2h Base. abc. = circle, oblique pl~ne entirely above (figure) Convex Surface = 2'/!'r X Y2 (h, minimum + H, maximum) Volume = '/!'r2 X Y2 (h, minimum + H, maximum)

J

, ~

base abe)] + (r - d)

IV. V.

ANY SOLID OF REVOLUTION Let abcd represent the generating section about axis A·A of solid abef. Let g at distance h from A-A be the center of gravity of abed. Let aO be the angular amount of generating revolution. Then Total Surface of solid abef = (2'/!'ha + 360) X perimeter abed Volume of solid abef = (2'/!'ha + 360) X area abed For complete revolution (2'/!'ha + 360) = 2'/!'h

A-a

I

»

(0

$

,.

,

t'

I

L

~~--+--->i

1{

-+-1---

~----c----->t

.--r /

Q

~--eL-->i ---,r

...-'....... ~,'f'

L=SJ[

I

'J!/

.,;.,

~

: ::L

----:-S

1

a:

::J ......

(')

o

o

X

a.

::J

CD

"0 "0

Appendix E.

M·ISCELLANEOIJS FORIUULAS 7. Heads for Horizontal Cylindrical Tanks:

1. Area of Roofs. UmbrelJa Roofs: ciiamf"trr or tank in feet.

o=

Hemi·ellipsoidal /leads have an ellipsoidal rross section, usually with minor axis equal to one half the major axis-that is. depth 1,4 D, or more.

=

=0.842 D' (when radius = diameter) 0.882 D' (when radius = 0.8 diameter)

Surface area . in 1. { square feet f

=

Conical Roof.: Surface area in} { square feet

= 0.787 D' (when pitch is % in 12) = 0.792 D' (when pitch is Ilh in 12)

2. Average weights. -490 pounds per cubic foot-specific gra\'ity 7.85

Steel

Wrought iron -485 pounds per cubic fOOl-specific gravity 7.7i

-450 pounds per cubic foot-specific gravity 7.21

Cut iron

1 cubic foot air or gu at 32- F., 760 m.m. barometer cular weight x 0.0027855 pounds.

3. Expansion in steel pipe feet per

}OO

= mole·

=

0.78 inch per 100 lineal degrees Fahrenheit chan~e in temperature

Dished or Basket Heads consist of a spherical segment nor· mally dished to a radius equal to the inside diameter' of the tank cylinder (or within a range of 6 inches plus or minus) and connected to. the straight cylindrical flange by a "knuckle" whose inside radius is usually not less than 6 per cent of the inside diatneter of the cylinder nor less than 3 times the thick· ness of the head plale. Basket heads closely approximate hemi· ellipsoidal heads. Dumped Heads consilit of a spherical segment joining the tank cylinder directlY without the transition "knuckle." The radius = D. or less. This type or head is used only for pressures of 10 pounds per square inch or less, ex{'eptin~ where a com· pression ring is placed at the junction of head and shell. Surlace Area 0111 eads: (7a) Hemi.ellipsoidal Heads:

= 0.412 inch per mile per de~ree Fahrenheit tempera·

S = 'Ii' R' [l + KI(2-K)) S = surface area in square feet

ture chan~e.

R K

4. Linear coefficients of expansion per degree increase in temperature:

Per Degree Fahrenheit STRUCTURAL STEEL-A-7 70 to 200 ° F .............. 0.0000065

Per Degree Centigrade

0

21.1 0 to 93°C ............. .

0.0000117

STAINLESS STEEL-TYPE 304 32 ° to 932 OF ...•........... 0.0000099 0° to 500°C .............. .

0.0000178

ALUMINUM -76° to 68°F .............. 0.0000128 -60° to 20°C ............. .

T= 6PD

=

S working preuure in pounds per square inch

= diameter of cylinder in feet S = allowable unit working stress in pounds per square inch =

(7d Bumped Heads: 5 = .. Rr (1 K') S, R, and K as in formula (7a)

+

0/ Head$:

(7d) Hemi-ellipsoidal Heads: R

K

= radius of cylinder in feet = ratio of the depth of the head (not including the Onnj:e) to the ' radius of the cylinder ~lraight

(7e) Dished or Basket Heads: Formula (7d) gives volume within practical limits.

(70 Bumped Heads:

D

T

(7b) Dished or Basket Heads: Formula (7a) gives surface area within practical limits.

\' = %,.. K R"

5. To determine the net thickness of shells for horizontal cylindrical pressure tanks:

P

ratio of the depth o( the head I not including the straight fIanj:e) to the radius of the cylinder

The above formula isnol exact but is within limits of practical accuracy_

Yolume 0.0000231

= radius of cylinder in feet

=

V = Y2 .. K RI (1 + % K'l V, K and R as in formula (7dl

Net thickness in inches

Resulting net thickness must be corrected to gross or actual thickness uy dh'iding by joint efficiency.

6. To determine the net thickness of heads for cylindrical pressure tanks: ' (6a) Ellipsoidal or Bumped Heads:

Note: K in aLove formulas may ue determined as follows: Hemi·ellipsoidal heads-K is known Dished Heads-K MR mR R

= radius of knuckle in feet = radius of cylinder in feet MR

.\1 - I f

S

For IlIlmpf>d hf'ao".

T, P and" D as in formula 5

2m)

= principal radius of head in feet

-

T= 6PD

= M- V (M-l) (M + 1 = [M- V W-IJ

Bumped Heads- K

_ mR

m-lf m = 0

(6b) Dished,or Basket Heads:

T = 1O.6P(MR)

8. Total Volume of a Sphere:

s

T, S lind P as in formula 5 MR

= principal radiuo:; of head in feet

Resulting net thickness of heads i~ both net and gross thick. nen if one piece seamless heads are used, otherwise net thick· ness must be corrected to Jrro'lS thickness as above. Formula~ 5 and {, mu!"t often he modified to comply with various en~ineerin~ codes, and state and municipal reftUlalions. Calculated ~O8!l plate thickneuet are sometime. arbitrarily increased to provide an additional anowance (or corrosion.'

A-10

V = total volume D = diameter of sphere in feet V = - 0.523599 D3 Cubic Feet V = -0.093257 D3 Barrels of 42 U.S. Gallons Number of barrels of 42 U.S. Gallons at any inch in a true sphere (3d-2h) h2 X .0000539681 where d is diameter of sphere and h is depth of liquid both in inches. The desired volume must include appropriate ullage for the stored liquid.

=

Appendix E. (Cont'd)

MISCELLANEOUS FORMULAS (CONTINUED) 9. Total volume or length of shell in cylindrical tank with ellipsiodal or hemispherical heads: V

Total volume

L

Length of cylindrical shell

KD

Depth of head

V

= '7iD2 (L +

L

=

4

(V

1'/3 KD

-

10. Volume or contents of partially filled horizontal cylindrical tanks: (lOa) Tank cylinder or shell (straight portion only)

R2L[(;8~O)

Q

- sin

Note: To obtain the volume or quantity of liquid in partially filled tanks, add the volume per formula (lOa) for the cylinder or straight portion to twice (for 2 heads) the volume per formula (lOb), (I0e) or (lOd) for the type of head concerned.

11. Volume or contents of partially fined herni-ellipsoidal heads with major axis vertical:

e cos e ]

Q

partially filled volume or contents in cubic feet

R

radius of cylinder in feet

L

length of straight portion of cylinder in feet

Q

v R

The straight portion or flange of the heads must be considered a part of the cylinder. The length of flange depends upon the diameter of tank and thickness of head but ranges usually between 2 and 4 inches. a A ~

Cos

e

= =

~

a ratio 1 - ~. or

Q R-a

R

= degrees

partially filled volume or contents in cubic feet

V

total volume of one head per formula (7d)

a

R= ~

R

radius of cylinder in feet

1Y2 V A (l - Y.l

a

~2)

.

KR =

a

~ KR = depth of liquid in feet

a ratio

"