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
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a en
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>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
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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
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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
<
17.83 ft
Therefore, only one stiffener ring is required. Place the stiffener ring at the mid-point of the transposed shell height. This location on the actual shell may be found by back calculating through the transposed shell heights. By inspection one can determine that the stiffener ring will be located on ring 4, 12.67 ft from the top of the shell or 27.0 ft. from the bottom. The stiffener ring required section modulus is calculated by the equation: Z = 0.0001 0 2 H (3-15) Z = 0.0001 X (150)2 x 12.67 = 28.5 in3 The configuration of the stiffener ring may take on many different shapes at the preference of the purchaser or supplier. The shell is now stable for a design wind velocity of 100 mph. The wind loads on the API 650 tank are identical to the AWWA tank; therefore, the resulting wind shear and moment at the bottom of the API 650 tank are the same as the AWWA tank.
APPENDIX B - TANK FOUNDATIONS Soils Investigation The subgrade of a potential tank site must be capable of supporting the weight of the tank and contained fluid. A qualified ,geotechnical engineer should be retained to conduct the subsurface exploration and to make specific recommendations concerning: the type of foundation required, anticipated settlements, allowable soil bearing and specific construction requirements. The ultimate soil bearing capacity should be determined using sound principles of geotechnical engineering. The following minimum factors of safety should be applied to the ultimate bearing capacity when determining the allowable soil bearing: 1. A factor of safety of 3.0 for normal operating conditions. 2. A factor of safety of 2.25 during hydrotest. 3. A factor of safety of 2.25 for operating conditions plus the maximum effect of wind or seismic forces. An allowable soil bearing based solely on the above factors of safety may result in excessive total settlements. If required, these factors of safety should be increased in order to limit the anticipated total settlements to acceptable values. Factors of safety larger than the above minimums are also required by certain codes and standards, such as AWWA 0100. Factors of safety lower than the above minimums
Shear = 113,386 Ibs. Moment = 2,383,778 ft-Ibs. The ratio, C =2M/dw, calculates to be 0.094 < 0.666; therefore, no anchors are required to resist overturning due to wind. The roof framing scheme will change significantly from the AWWA design since the maximum rafter spacing at the shell cannot exceed 2 x pi (6.28 ft) and the maximum rafter spacing between inner rafters cannot exceed 5.50 ft. For this example consider twelve girders and outer columns, 48 inner rafters and 84 outer rafters. Consider 25 PSF snow load and 7.65 PSF dead load. Using identical design procedures as the AWWA 0100 design and API 650 allowable stresses, we will choose the following roof framing members: Inner rafters = W12 x 14 Outer rafters = W12 x 14 Girders = W16 x 31 Center column = 12" dia. sch 20 Outer columns = 8" dia. sch 20 18
3/16" ROOF PL LAP WELDED TOP SIDE ONLY
.. (Y)
~ RING 5
C'\J
".-.
RING 4
.-. I
RING 3
"
0
(/)
0 "It
W
RING 2
l.:J
I
Z .....
a::
RING 1
I.
('\J
"'.....
If)
.1
150'-0
1/4'BOTTOM PL LAP WELDED TOP SIDE ONLY Figure 3A·1 -
Flat Bottom Tank
b.) ADJUSTED FINAL THICKNESSES FOR STATIC HEAD AND WIND STABILITY (AWWA DESIGN)
a.) CALCULATED SHELL THICKNESSES FROM STATIC HEAD ONLY (AWWA DESIGN) RING #
THICKNESS
MATERIAL
RING #
THICKNESS
MATERIAL
5
0.1547"
A36
5
0.3125"
A36
4
0.3152"
A36
4
0.3152"
A36
3
0.3942"
A573GR70
3
0.4758"
A36
2
0.5273"
A573GR70
2
0.5273"
A573GR70
1
0.6603"
A573GR70
1
0.6603"
A573GR70
Table 3A·1 -
Shell Plate Thicknesses
19
R
=
42'-61 36 RAFTERS R
= 2'-4
Figure 3A·2 -
~
72 RAFTERS
1/2
Framing Layout -
AWWA
NON-UN I FORM LOAD .
UNIFORM LOAD (INCLUDES RAFTER
~T.)
Rl
R2
DESIGN LENGTH
Figure 3A-3 -
Typical Rafter Loading
______ REACTIONS FROM INNER RAFTERS _..--....L..--.-_-..---L---..-_--.---L---..,..._--.--..I.---._______ REACT IONS FROM OUTER RAFTERS GIRDER DEAD LOAD
Figure 3A·4 -
Typical Girder Loading 20
J\)
.....&.
iJ iJ
Z
1>
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 <=
2.0 OK
RING NO.2
=
=
DESIGN: D 150.000 H 31.542 G = 1.000 S = 28000. CA Td = 2.6*D*{H -l)*G/S + CA = 0.4254 + CA = 0.4879 TX = 2.6*D*{H-X/12)*G/S
= 0.0625
TU 0.4254 0.4116 0.4121
X3 23.872 23.482 23.495
23.872 23.482 23.495
X3 23.062 22.711 22.723
23.062 22.711 22.723
TL K 0.5362 1.2606 0.5362 1.3028 0.5362 1.3013 TX = 0.4121 + CA =
C 0.1211 0.1390 0.1384 0.4746
X2 45.847 52.595 52.369
Xl 26.607 28.571 28.506
'
X
TX 0.4116 0.4121 0.4121
DESIGN: PARA. 3.6.4.5 RATIO = 95.500/[SQRT (6*0*0.5362) I = 4.3471 T2 = Tx + (T1 - Tx)* (2.1 - 4.3471/1.25) = 0.2410 T2D = 0.4121 + CA HYDROTEST: D = 150.000 H = 31.542 n = 2.6*D*(H -l)*G/S = 0.3970 TX = 2.6*D*{H -Xl12)*G/S TU 0.3970 0.3851 0.3854
TL K 0.5005 1.2606 0.5005 1.2998 0.5005 1.2985 TX= 0.3854
G = 1.000
C
0.1211 0.1377 0.1372
X2 45.846 52.127 51.924
S
= 30000.
Xl 26.202 28.036 27.977
X
HYDROSTATIC: PARA. 3.6.4.5 RATIO = 95.500/[SQRT(6*D*0.5005)] = 4.4997 T2 = TX + (Tl - TX)*{2.1 - 4.4997/1.25) = 0.2128 T2T = 0.3854 MINIMUM DESIGN THICKNESS
= 0.4746
USE: 0.475 IN. A573 70
FIGURE 3A-7 -API 650 VARIABLE POINT CALCULATIONS
22
TX 0.3851 0.3854 0.3854
THICKNESS 0.3125" 0.3125" 0.3750" 0.4750" 0.5990"
RING # 5
4 3 2 1
TABLE 3A-2 -
Wtr Wtr Wtr Wtr Wtr SUM
MATERIAL A36 A36 A573GR70 A573GR70 A573GR70
ADJUSTED FINAL THICKNESSES (API 650 DESIGN) (ring 5) (ring 4) (ring 3) (ring 2) (ring 1) OF Wtr
FIGURE 3A-8 -
= = = = = = =
95.50 INCHES 95.50 60.54 33.61 18.79 303.94 INCHES 25.33 FEET
TRANSPOSED SHELL HEIGHT (API 650 DESIGN)
may be considered when actual experience with similar - tanks and foundations at a particular site indicates that satisfactory performance can be expected.
Tank Grade The tank grade (surface which supports the tank bottom) can be constructed of earth materials provided the subgrade beneath the tank bottom is capable of supporting the weight of the contained fluid. The tank grade usually consists of a 4" sand cushion placed over properly compacted fill or soil. It is recommended that the finished tank grade be constructed at least 6 inches above the surrounding ground surface and be crowned from its outer periphery to its center. A slope of 1 inch to 10 feet is suggested. The sand should be clean and free of corrosive elements. Care should be taken to exclude lumps of earth or other deleterious materials from ' coming into contact with the bottom. These materials can cause electrolytic action that will result in pitting of the bottom plate. If the sand cushion is placed on top of crushed rock fill, the rock should be carefully graded from coarse at the bottom to fine at the top. If this is not done, the sand will percolate down through the voids in the coarser rock. An excellent tank grade can also be obtained by substituting about 1112 inches of asphalt road paving mix for the sand cushion. This material is available from ready mix plants in many sections of the country. It is very important that the paved tank
grade be constructed level and to the proper profile, particularly near the shell. Once the asphalt has set up, it is extremely difficult for the tank builder to correct inaccuracies by taking down the high and filling in the low spots. Drainage is important both from the standpoint of soil stability and bottom corrosion. Good drainage should be provided under the tank itself and in ' the general area around the tank. Where the terrain does not afford natural drainage, proper ditching around the tank may help to correct the deficiency.
Foundations The shell of a flat bottom tank can be supported on a compacted granular berm, concrete ringwall or concrete slab foundation. Local soil conditions, tank loads and the intended use of the tank will determine which of these foundations is suitable for a particular site. Tanks that require anchor bolts must be supported, by ringwall or slab foundations. Granular Berm Foundation - When a qualified geotechnical evaluation concludes that it is unnecessary to construct a ringwall or slab foundation, the shell can be supported by a granular berm foundation. The berm should be constructed of well graded and properly compacted stone or gravel. The berm should extend a minimum of 3 feet beyond and 2 feet inside the tank shell as shown in Figure 38-1. The berm should be level to within + 1/8 inch in any 10 feet of circumference and to within ± 1/2 inch in the total circumference. Adequate drainage 23
The top of the ringwall should be smooth and level to within ± 1/8 inch in any 30 feet of circumference. No point on the total circumference should vary more than ± 1/4 inch from the specified finish elevation.
away from the berm must be provided to prevent erosion of the berm under the shell. Alternatively, a welded or bolted steel grade band can be used to retain the outer portion of the berm.
Slab Foundation - When the subgrade beneath the tank bottom cannot adequately support the weight of the contained fluid, a slab foundation is required. The area of the slab must be sufficient to produce a soil bearing (due to the total weight of the tank, foundation and contained product) less than the allowable soil bearing. The depth to the bottom of the slab will depend on local conditions and must be sufficient to place the bottom of the slab below anticipated frost penetration and within the specified bearing strata. The detailed design of the slab and requirements for the materials, construction and testing should be in accordance with the American Concrete Institute's Building Code Requirements for Reinforced Concrete (ANSIIACI 318).
Concrete Ringwall Foundation - When suitable bearing is not available at the surface, but is available at a reasonable depth below the surface, a ringwall foundation should be considered. The depth of the ringwall will depend on local conditions and must be sufficient to place the bottom of the ringwall below anticipated frost penetration and within the specified bearing strata. As a minimum, the bottom of the ringwall should be located 2 feet below the lowest adjacent finish grade. The width of the ringwall must be sufficient to produce a soil bearing less than the specified allowable soil bearing. As a minimum, the ringwall width should be 1 foot. The inside horizontal projection (inside the tank shell) should be no less than 4 inches. The ringwall must be reinforced to resist the following forces: 1. Direct hoop tension resulting from the lateral earth pressure on the inside face of the ringwall. Unless substantiated by proper geotechnical analysis, the lateral earth pressure should be assumed to be 30 0/0 of the vertical pressure due to the contained fluid and the soil weight. 2. Bending moment resulting from the uniform moment load. The uniform moment load is due to the eccentricities of the shell and pressure loads relative to the centroid of the soil bearing stress. The pressure load is due to the fluid pressure on the inside horizontal projection of the ringwall. 3. Bending, torsion and shear resulting from lateral, wind or seismic, loads. A rational analysis, which includes the effect of the foundation stiffness, should be used to determine the soil bearing stress distribution and the above internal design forces. The area of reinforcement provided must be sufficient to resist the above forces and should not be less than the following minimums. These minimums are intended to prevent excessive cracking due to shrinkage and temperature. 1. For wall-like ringwalls the area of vertical reinforcement provided should not be less than 0.0015 times the horizontal cross-sectional area of the ringwall. 2. The area of hoop reinforcement provided should not be less than 0.0025 times the vertical crosssectional area of the ringwall. The detailed design of the ringwall and requirements for the materials, construction and testing should be in accordance with the American Concrete Institute's Building Code Requirements for Reinforced Concrete (ANSIIACI 318). Recesses shall be provided in the concrete ringwall for flush type cleanouts, drain off sumps and any other appurtenances that require recessing. Refer to API 650 for details of recesses at flush type cleanouts.
References, Part III 1. API Standard 650 Welded Steel Tanks for Oil Storage, Division of Refining, American Petroleum Institute, Eighth Edition, November 1988. 2. AWWA Standard 0100-84 Welded Steel Tanks for Water Storage, American Water Works Association. 3. Manual of Steel Construction, American Institute of Steel Construction, Inc., Ninth Edition. 4. "Oil Storage Tanks", The Prince William Sound, Alaska, Earthquake of 1964 and Aftershocks, Volume II, Part A, U.S. Dept. of Commerce, 1967. 5. "Fluid Mechanics", Dodge & Thompson.
24
Figure 38-1 -Example of Foundation with Crushed Stone Ringwall from API 650, Eighth Edition, November 1988 4' MIN. OF COMPACTED CRUSHED STONE, SCREENINGS, FINE GRAVEL, CLEAN SAND, OR SIMILAR MATERIAL
"II
3' MIN.
2' MIN.
SLOPE IF PAVED SLOPE :::' ,"
..
!
...
!
. ...
. !
!
,
""
COARSE STONE OR COARSE GRAVEL 11 MAX. SIZE
~1 1
THOROUGHLY COMPACTED FILL OF FINE GRAVEL, COARSE SAND, OR OTHER SUITABLE MATERIAL
Note: Bottom of excavation should be level. Remove any unsuitable material and replace. with suitable fill, thoroughly compacted.
Figure 38-2 - Example of Concrete Ringwall Foundation 1/21 THICK (MIN) ASPHALT - IMPREGNATED BOARD (OPTIONAL)
Z 0-<
~
.
II
II II
4' MIN. OF COMPACTED CRUSHED STONE. SCREENINGS, FINE GRAVEL, CLEAN SAND. DR SIMILAR MATERIAL SLOPE
FINISH GRADE
\D
MATERIAL AND FILL, z
...... ~
ru REINFORCEMENT AT BOTH FACES FOR RINGWALL WIDTHS EXCEEDING 12 INCHES. CLOSED STIRRUPS MAY BE REQUIRED FOR SHEAR AND/OR TORSION.
II' MIN:.I
25
Part IV Stainless Steel Tanks for Liquid Storage Introduction
Type 304
t the present time, the only rules for stainless . steel storage tanks are given in Appendix Q of API Standard 620(1) which covers lowpressure tanks for liquefied hydrocarbon gases, particularly liquefied ethane, ethylene, and methane, at a minimum temperature of - 270F. Rules for the design and construction of pressure vessels including stainless steel vessels - are given in the ASME (2) Boiler and Pressure Vessel Code, Section VIII, Division 1 and Division 2, Pressure Vessels. In the following discussion rules are presented for design and construction of stainless steel tanks at atmospheric pressures. These rules are not intended to cover storage tanks which are to be erected in areas subject to regulations more stringent than specified in the following pages. These rules are recommended only insofar as they do not conflict with local requirements.
Possessing corrosion resistance, strength and fabricability, this is the general purpose stainless steel, long known as "18-8". Attesting to its wide usage is the fact that it accounted for 35% of all stainless steels produced in the United States in 1980. Type 304 is extensively specified for food handling and storage, dairy equipment, nuclear fluids, and in general most applications where even small amounts of corrosion product would be intolerable.
A
Type 316 Containing higher nickel than Type 304, and 2-30/0 molybdenum, Type 316 possesses greatly improved resistance to corrosion by pitting. It is used under conditions too severe for Type 304, such as mineral acids (phosphoric acid, sulfuric acid), strong organic acids (oxalic, formic, etc.) and halides in various dilutions.
FACTORS AFFECTING SELECTION OF STAINLESS STEEL
Types 304L and 316L
There are a total of 62 stainless steel compositions that are recognized as standard by the American Iron and Steel Institute (3), as well as commercially available proprietary compositions. The five stainless steels most generally used as plate material for construction of liquid storage tanks are Types 304, 304L, 316, 316L and 410S. The last is not recognized as standard by American Iron and Steel Institute. The chemical compositions of these types are listed in Table 4-1 and their mechanical properties are listed in Table 4-2. The selection of a particular type of stainless steel for a given corrosive environment often follows extensive study of comparative data, and sometimes even pilot or service testing. However, a general understanding of the corrosion resistance capabilities of the five stainless steels, in terms of their relative resistance to various common media, is shown in Table 4-3. The five types fall within two categories: namely, Types 304, 304L, 316 and 316L are in the chromium-nickel group, while Type 410S is in the straight chromium group.
Containing 0.03% maximum carbon, these are the low carbon counterparts of Types 304 and 316. The lower the carbon content, the less the chromium carbide that can be formed. Chromium-nickel stainless steels form a grain boundary chromium-carbide precipitate when heated in the 800-1650F temperature range for sufficient time (see Figure 4-1) (5). If the degree of precipitation is severe - Le. the grains are completely surrounded - there may be a loss of corrosion . resistance in aggressive media such as hot, oxidizing acids (e.g. strong nitric acid), iron or copper sulfates in hot dilute sulfuric acid, and air-saturated hot sulfuric acid. Such aggressive corrosion conditions do not normally exist in storage tanks. Intergranular corrosion attack used to be a common occurrence when the stainless steels contained up to 0.12% carbon (as in Type 302, for example). This was enough carbon to remove considerable chromium from solution during welding cycles, causing mild to heavy carbide preCipitation in the weld heat-affected zone. Corrosive attack would 27
be evident in this zone, if the environment was severe. This situation resulted in widespread specifying of low carbon (0.03 0/0 maximum) stainless steels, but it should be understood that there are relatively few situations where the L grades are actually required for storage vessels. Even these should be carefully investigated to establish such a need before the additional expense of the L grades is incurred. Types 304 and 316 (0.08 0/0 maximum carbon) can, in many cases, be welded free of carbide precipitation. If a small amount does develop, it may be unaffected by the liquid being stored, except possibly as indicated above. It should be noted here that galvanized material or other zinc products welded to stainless steel will cause intergranular cracking. In general, the L grades should be used when and only when - it is ascertained that conditions will be present, which are conducive to intergranular attack on as-welded 0.08 0/0 maximum carbon stainless steel (see Figure 4-1). The general corrosion and pitting resistance of the L grades is not better than their higher carbon counterparts in the annealed condition; nor is there any advantage in weldability or fabricability.
failure of life of the vessel is very dependent on temperature, concentration of chloride and stress. Increased values in each case will shorten the life of the vessel. 4. While Types 304 and 316 are both susceptible to hot chloride stress corrosion cracking, Type 316 under similar service conditions. tends to give better life ·than Type 304. 5. Because of variation in fabrication and service stresses, it is frequently difficult to predict the life of an austenitic stainless steel vessel in hot chloride-containing media.
STAINLESS STEEL PLATE Manufacture Stainless steel plate is defined as a flat rolled or forged product, 3/16 inch (4.76 mm) and over in thickness, and 10 inches (254 mm) and over in width (3). It is formed in the same type of equipment as utilized for carbon steel plate, although production allowances must accommodate the much greater hot strength of stainless steel over carbon and low alloy steels. In producing plate, care is taken to attain the good surface condition that is essential to corrosion resistance. The first of several surface cleaning operations occurs at the slab stage, where the 4 to 10-inch-thick bloomed slab is ground or scarfed overall to remove not only the scale but some of the underlying base metal as well. The slab is then cut to size, yielding the ordered plate size, reheated and hot rolled. The plate is then annealed, and again cleaned of scale by either a chemical solution or mechanical means, or both. During the hot rolling, high pressure water jets and other mechanical devices are employed to assure that the refractory scale is not rolled into the surface. Light gauge plate (3/16 inch and 114 inch thick) can be rol/ed in coils up to 60 inches wide on continuous mills. This product normally has improved surface, gauge accuracy and offers greater flexibility in length.
Type 410S This straight-chromium stainless steel is not subject to the above form of carbide precipitation. It finds use where moderate corrosion resistance is needed, and slight product contamination is not critical (see Table 4-3). The low carbon (0.08 0/0 maximum) results in a tough plate product which avoids formation of the less-tough metallurgical structures possible in high-strength, low-alloy steels.
Stress Corrosion Cracking Another phenomenon associated with the chromiumnickel stainless steels Types 304, 304L, 316 and 316L, is stress corrosion cracking. By definition, stress corrosion cracking involves the combined action of a tensile stress and a corrosive medium. Aside from some ultra-pure metals, most commercial metals are subject to this phenomenon in certain specific environments. While the initial reaction may be one of great concern, it should be emphasized that throughout industry there are numerous applications of stainless steel in environments where stress corrosion cracking does not occur or which have been engineered to avoid stress corrosion cracking. Although stress corrosion cracking is not fully understood, there are some general guidelines that can be related to stainless steels: 1. The form of stress corrosion usuaUy found in the AISI 300 stainless steels is related to exposure to hot chloride-containing corrosive media. 2. At temperature much below 160 of, stress corrosion failures are not very likely to occur. 3. At temperatures exceeding 160 o F, the time to
Forming Press brake flanging or bending, and roll bending are the most widely used cold forming operations performed on stainless steel plate. Type 410S has cold forming characteristics similar to carbon and low alloy steels in the 35,000-50,000 psi yield strength range. The chromium-nickel stainless steels (Types 304, 304L, 316, 316L), on the other hand, work-harden quite rapidly with increasing plastic deformation. As the steel increases in strength with increased deformation, the bending forces exerted by the forming equipment rise commensurately. The most noticeable effect of work hardening is the greater degree of springback, compared with carbon steel. Dies for brake bending and rolls for roll bending must overbend the stainless steel to compensate for the springback. In brake bending, 28
requirements, finishing may include a final polishing to produce the brightest surface possible. Various cleaning practices are summarized in ASTM A380 (6) and more comprehensively described in ASTM Special Technical Publication 538 (7).
bending to a smaller radius can compensate for the greater springback.
Cutting Most stainless steel plates are cut by tank fabricators with the plasma arc process. Thin plates can be sheared. Thicker plates can be cut by saw cutting or abrasive wheel cutting. Gas-oxygen (oxy-gas) is also applicable if used in conjunction with iron powder. Stainless steel cannot be cut by conventional flame cutting, but in some cases may be cut and beveled with the carbon-arc gouge if the cut edges are ground to remove oxides.
FACTORS AFFECTING TANK DESIGN Th,e design rules and details of API Standards 650 (8) and 620 (1) are applicable for stainless steel tanks at atmospheric pressure with certain exceptions. In the following. discussion, the design stresses recognize the increased toughness of stainless steels over carbon steels and the low yield! tensile ratios of Types 304, 304L, 316 and 316L. The increased toughness permits designing to a higher proportion of yield strength, but the lower yield strength introduces the problem of permanent strain. Section VIII of the ASME Code (2) recognizes the strain by stating two allowable design stresses for the austenitic stainless steels. The higher stresses are related to the following footnote to the ASME table of stresses: "Due to the relatively low yield strength of these materials, these higher stress values were established at temperatures where the short time tensile properties govern to permit the use of these alloys where slightly greater deformation is acceptable. These higher stress values exceed 62112 percent but do not exceed 90 percent of the yield strength at temperature. Use of these stress values may result in dimensional changes due to permanent strain. These stress values are not recommended for flanges of gasketed joints or other applications where slight amounts of distortion can cause leakage or malfunction." After consideration of the allowable design stresses of the ASME Code and the API Standards, the following stress basis is suggested for stainless steel tanks at atmospheric pressure: a. The design basis for shells where permanent strain ~ .05 0/0 is acceptable is the lesser of: Sd = .8 x .3 x Ft see Table 4-5(a) b. The design basis for shells where permanent strain ~ .1 % is acceptable is the lesser of: Sd = .9 x . .3 x Ft see Table 4-5(b) = min. yield strength where F t = min. tensile strength Sd = design stress c. Because the lower carbon grades (Types 304L, 316L) usually exhibit yield strengths at room temperature greater than the specified minimum value, the allowable stress for 100 0 F has been based only on the tensile factor. d. Where a lower level of permanent strain is desirable such as mentioned above for gasketted joints or other applications where slight amounts of distortion can cause leakage or mechanical malfunction see Table 4-5(c) for values.
Welding Gas metal arc and ' submerged arc welding are highproduction methods and are usually used in the down hand position, fully automated. Both give deep penetration and, for high volume welding that can be positioned, are the lowest cost methods for joining plates. A modification of gas metal arc called interrupted (or pulse) arc welding is useful for butt, fillet, and lap welding. Shielded metal arc~ welding is widely used for all types of stainless steel welding, particularly where automatic welding is impractical. Advantages are low cost equipment and mobility. Disadvantages are slow speeds and high labor cost for skilled operators. An essential requirement for any '!Velding method is clean edges (and near-edge areas) prior to welding. Contaminants, whether organic or inorganic, can cause problems when they decompose in the arc heat. The oxide film on stainless steel surfaces is very refractory and reduces the wetting action between parent and weld metal. The filler metals for welding stainless steels are listed in Table 4·4. When stainless steel is welded to carbon or low alloy steels, Type 309 electrodes are normally used.
Cleaning and Passivation
'Yor
These two terms are actually synonymous if the word clean is strictly interpreted to mean "the complete removal of all contaminating materials from the stainless steel surface". If the surface is clean, it will self passivate. Iron particles and!or oil are the contaminants most generally encountered, and to the extent that they are present some surface staining or rusting may occur. Whether such an occurrence is serious or not depends on the requirements of the application which can range from "food quality surfaces" to simply "retention of structural strength". Prevention of contamination is to be preferred over removal of contaminants. A main source of contamination due to iron particles results from comingling plate fabrication operations involving carbon steel and stainless steel. Another source is the existence of weld scale or weld spatter, which can only be removed by energetic chemical or mechanical means. In extremely demanding
'Yor
'Y
29
e. The yield values at temperature can be obtained from table AHA2 of ASME Section VIII, Div. 2. The allowable stresses listed in Table 4-5, a, b, and c, result from these bases, with the higher stresses for the austenitic grades taking into account the greater deformation of item b above. Table 4-5(b) should be the default basis unless directed otherwise for shells and Table 4-5(e) should be used for flanges. The design thickness for each shell course can be calculated by the formula in API Standard 650, modified by the allowable stress and joint efficiency: t = (2.6) (D) (H-1) (G) + C (E) (1000S d ) where: t = minimum thickness, in inches C = an additional thickness required for corrosion allowance (rarely if ever required) D = nominal diameter of tank, in feet. This shall be the centerline diameter of the shell plates, unless otherwise specified by the purchaser H = height, in feet, from bottom of course under consideration to top of top angle, or to bottom of any overflow which limits tank filling height G = specific gravity of liquid to be stored, but in no case less than 1.0 Sd = maximum allowable stress in ksi. Values tabulated in Table 4-5, a or b E = 1.0 if tank is radiographed in accordance with section 6 = 0.85 if tank is radiographed in accordance with A.5.3 = 0.7 if tank is not radiographed. This value shall be given as part of the buyers' specifications Stainless steel separation pads (or poison pads) should be considered at points where carbon steel is welded to the stainless steel tank to avoid carbide precipitation. Typical areas for this would be anchor bolts and support brackets. The recommended nominal thickness of shell plates should not be less than th~,,~; based on construction minimums:
Standard 650 Tank Shells", presented in May, 1963, to the API Division of Refining. For the design of shells under external load (small negative pressures) the designer should refer to ASME Section VIII or Part III of "Design of Plate Structures" (11). For the design of structural members, the designer should refer to the Stainless Steel Cold-Formed Structural Design Manual (10).
NOTE: Roof designs for stainless steel tanks may be done in a similar manner as that outlined in part III for carbon steel tanks but normally all .structural units will need to be fabricated in custom shapes. A lighter gage, lighter than .17 allowed in API 650 for carbon steel structural units, may be used to accommodate forming.
FACTORS AFFECTING FABRICATION & CONSTRUCTION Before proceeding with any fabrication or construction of a stainless steel tank, satisfactory weld procedure qualifications should be performed in accordance with all the essential variables of Section IX, Welding Qualifications, of ASME Boiler and Pressure Vessel Code, including conditions of postweld heat treatment or the omission of postweld heat treatment. Requirements and restrictions for postweld heat treatment are described in ASME Section VIII. Materials that would require postweld heat treatment should not be used for storage tanks designed by the rules in this manual. All austenitic chromium-nickel alloy steel welds, both butt and fillet, between plates exceeding 3/4 inch nominal thickness, shall be examined for detection of cracks by the liquid penetrant method, before the hydrostatic test of the tank. All cracks shall be eliminated. Butt-welded joints in Type 410S welded with electrodes that produce an austenitic chromiumnickel weld deposit shall be radiographed when the thinner plate at the welded joint exceeds 1112 inches. Referring to Part AM of ASME Sect VIII Div 2 it will be noted that both values of thermal conductivity (TC) and thermal diffusivity (TO) (given in Btulhr ft OF and ft 2 /hr respectively) are considerably lower (about 2 to 1) for stainless compared to carbon steel, which indicates that heat (from welding) is not conducted away or diffused as rapidly with stainless steels and therefore distortion is likely unless design steps are taken to assure that nozzle location (with respect to vertical and horizontal seams) should be thought out. Also the tolerances given in API 650 for banding and peaking may not be achievable for stainless steel shells. For the design of stainless steel tanks at refrigerated temperatures, the designer is referred to Appendix Q "Low-Pressure Storage Tanks for Liquefied Hydrocarbon Gases" of API Standard 620. This subject is beyond the intended scope of this discussion.
Nominal Tank Nominal Plate Diameter Thickness Smaller than 50' 3/16" 50' to 120' excl. 1/4" 120' to 200' incl. 5/16" Over 200' 3/8" Throughout this design procedure it shall be remembered that Young's Modulus for stainless steel is less than that of carbon steel. Therefore designs for compression and stability should consider this fact. Normally the tank shell should be designed to resist the design wind velocity given in the customer's specifications. API Standard 650 provides rules for stiffening tank shells. The background for the API rules was given in a paper, "Stability of API 30
FIGURE 4-1
1652
900 0.080
,,
............
;'
I
800
1472
700
1292
U
o.
!! ::I
eK
'"~
0
::l
! 8.
E
E
~
~
600
1112
500
932
10aec.
1min.
1Omln.
1hr.
10 hrs.
1OOhrs.
1OOOhrs.
TIme
Time required for formation of carbide precipitation in stainless steels with various carbon contents. Carbide precipitation forms in the areas to the right of the various carbon-content curves. ·W ithin time-periods applicable to welding, chromium-nickel stainless steels with 0.05% carbon would be quite free from grain boundary precipitation. (5)
31
10.000hrs.
TABLE 4-1 - STAINLESS STEELS COMMONLY USED FOR CONSTRUCTION OF LIQUID STORAGE TANKS (4) COMPOSITION, PERCENT ASTM Type
UNS No.8
Carbon max.
Manganese max.
Phosphorus max.
Sulfur max.
Silicon max.
304
(830400)
0.08
2.00
0.045
0.030
. 1.00
304L
(830403)
0.03
0.045
2.00
0.030
1.00
Chromium
Nickel
18.00 ~ 20.00 18.0020.00
12.00
B.OO10.50
B.OO-
Other Elements N 0.10 Max. N 0.10 Max.
316
(831600)
0.08
2.00
0.045
0.030
1.00
16.00 18.00
10.00 14.00
2.00-3.00 Molybdenum N 0.10 Max.
316L
(831603)
0.03
2.00
0.045
0.030
1.00
16.0018.00
10.00 14.00
2.00-3.00 Molybdenum N 0.10 Max.
4108
(S41 008)
O.OB
t.OO
0.040
0.030
1.00
11 .50 13.50
0.60 (max)
aUnified Numbering System, originated by ASTM and 8AE, developed to provide a single orderly system for designating commercial metals and alloys.
TABLE 4·2 - MECHANICAL PROPERTIES OF STAINLESS STEELS COMMONLY USED FOR CONSTRUCTION OF LIQUID STORAGE TANKS (4) ASTM Type
UNS No.
Tensile Strength, min ksi MPa
Yield Strength, min MPa ksi
C
Hardness, max RBc Bhn b
304
(830400)
75
515
30
205
40
202
92
304L
(S30403)
70
485
25
170
40
183
88
316
(831600)
75
515
30
205
40
217
95
316L
(S31603)
70
485
25
170
40
217
95
4108
(841008)
60
415
30
205
22.0
183
88
a Elongation in 2 inches (50.8 min) b
Elongation,8 min Percent
Brinell Rockwell-B
32
TABLE 4·3 - RELATIVE CORROSION RESISTANCE OF STAINLESS STEELS ,COMMONLY USED FOR CONSTRUCTION OF LIQUID STORAGE TANKS ASTM Type
UNS No.
Mild Atmospheric and Fresh Water
304
(S30400)
X
X
304L
(S30403)
X
316
(S31600)
316L 410S
Atmospheric Industrial Marine
Chemical Oxidizing
Salt Water
Mild
-
-
X
-
X
X
-
X
X
-
X
X
-
X
X
-
X
(S31603)
X
X
X
X
X
X
X
(S4100B)
X
-
-
-
X
-
-
Note: X's indicate environments to which the various stainless steels may be considered resistant.
TABLE 4-4 - TYPICAL FILLER METALS FOR WELDING STAINLESS STEELS Base Metal
Electrodes (AWS)
Type 304
E30B-15 or 16; ER30B; E30BT-2
Type 304L
E30BL-15 or 16; ER30BL; E30BT-2
Type 316
E316-15 or 16; ER316; E316T-2
Type 316L
E316L-15 or 16; ER316L; E316T-2
Type 410S**
E410*-15; ER410*; E410T*-2
*Type 410 electrodes must be specified to O.OB% maximum carbon in all cases. * * It is permissible (and often desirable) to weld Type 410S with austenitic (chromium-nickel) electrodes.
33
Reducing
TABLE 4·5 - ALLOWABLE STRESSES FOR TANK SHELLS OF STAINLESS STEEL Minimum Yield, KSI
Minimum Tensile, KSI
100°F
200°F
300°F
400°F
500°F
600°F
304a
30.0
75.0
22.5
20.0
18.0
16.6
15.5
14.6
304 b
30.0
75.0
22.5
22.5
20.3
18.6
17.5
16.4
304La
25.0
70.0
21.0c
17.0
15.3
14.0
13.0
12.4
304Lb
25.0
70.0
21.0c
19.2
17.2
15.8
14.7
14.0
316a
30.0
75.0
22.5
20.6
18.6
17.1
15.9
15.0
316 b
30.0
75.0
22.5
22.5
21.0
19.3
17.9
16.8
316La
25.0
70.0
21.0c
16.9
15.1
13.8
12.7
12.0
316Lb
25.0
70.0
21.0C
19.0
17.0
15.5
14.3
13.5
410S a
30.0
60.0
18.0
18.0
18.0
18.0
18.0
18.0
Type
For Metal Temperatures Not Exceeding
Note: a, b, & c explained on page 32.
34
TABLE 4-S(a) - ALLOWABLE STRESSES FOR TANK SHELLS OF STAINLESS STEEL Limiting % Strain O.OS%
=
Minimum Yield, KSI
Minimum Tensile, KSI
100°F
304
30
75
22.5
20
304L
25
70
21
316
30
75
316L
25
4108
30
Type
For Metal Temperatures Not Exceeding 400°F
500°F
600°F
18
16.6
15.5
14.6
17
15.3
14
13
12.4
22.5
20.6
18.6
17.1
15.9
15
70
21
16.9
15.1
13.8
12.7
12
60
18
18
18
18
18
18
200°F
300°F
TABLE 4-S(b) - ALLOWABLE STRESSES FOR TANK SHELLS OF STAINLESS STEEL Limiting % Strain 0.10/0
=
Minimum Yield, KSI
Minimum Tensile, KSI
100°F
200°F
300°F
400°F
500°F
600°F
304
30
75
22.5
22.5
20.3
18.6
17.5
16.4
304L
25
70
21.0
19.2
17.2
15.8
14.7
14.0
316
30
75
22.5
22.5
21.0
19.3
17.9
16.8
316L
25
70
21.0
19.0
17.0
15.5
14.3
13.5
Type
For Metal Temperatures Not Exceeding
TABLE 4-S(c) - ALLOWABLE STRESSES FOR FLANGES OR GASKETTED JOINTS OF STAINLESS STEEL Limiting % Strain = 0.01 % per 62.50/0 Fy Yield Strength limit Minimum Yield, KSI
Minimum Tensile, KSI
100°F
200°F
300°F
400°F
500°F
600°F
304
30
75
20.0
16.7
15.0
13.9
12.9
11.5
304L
25
70
16.7
14.3
12.8
11.7
10.9
10.3
316
30
75
20.0
16.7
15.0
13.9
12.9
11.5
316L
25
70
16.7
14.3
12.8
11.7
10.9
10.3
4108
30
60
18
18
18
18
18
18
Type
For Metal Temperatures Not Exceeding
35
TABLE 4-6 FACTORS FOR LIMITING PERMANENT STRAIN IN HIGH-ALLOY STEELS1
References, Part IV 1. API Standard 620 - Recommended Rules for Design and Construction of Large, Welded, LowPressure Storage Tanks; Division of Refining, American Petroleum Institute, Eighth Edition, June 1990. 2. American Society of Mechanical Engineers, 1980. 3. "Steel Products Manual - Stainless and Heat Resisting Steels", December 1974, American Iron and Steel Institute. 4. ASTM Designation A240-80b (ANS G81.4) Standard Specification for Heat-Resisting Chromium and Chromium-Nickel Stainless Steel Plate, Sheet and Strip for Fusion-Welded Unfired Pressure Vessels. 5. Svetsaren English edition 1-2; 1969, p. 5. 6. ASTM Designation A380-78 (ANS G81.16) Standard Recommended Practice for Cleaning and Descaling Stainless Steel Parts, Equipment and Systems. 7. ASTM S.T.P. 538 "Cleaning Stainless Steel" includes ASTM A380 and 22 papers presented at a symposium. 8. API Standard 650 - Welded Steel Tanks for Oil Storage; Division of Refining, American Petroleum Institute, Eighth Edition, November 1988. 9. ASTM Designation A370-77 (ANS G60.1) Standard Methods and Definitions for Mechanical Testing of Steel Products. 10. "Stainless Steel Cold-Formed Structural Design Manual - 1974 Edition", American Iron and Steel Institute. 11. "Desig,('l of Plate Structures", Vol. 2, AISI/SPFA, 1991. 12. Steel Products Manual - Plates; Rolled Floor Plates: Carbon, High Strength Low Alloy, and Alloy Steel, January 1979.
Limiting Permanent Strain, 0/0
Factors
0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01
0.90 0.89 0.88 0.86 0.83 0.80 0.77 0.73 0.69 0.63
NOTE: (1) Table 4-6 lists multiplying factors which, when applied to the yield strength values shown on Table AHA-2, will give a value that will result in lower levels of permanent strain. If this value is less than the design stress intensity value listed in Table AHA-1, the lower value shall be used.
Other Information on Corrosion "Corrosion Resistance of the Austenitic ChromiumNickel Stainless Steels in Chemical Environments", The International Nickel Co., April 1970, 16 pages. "Selection of Stainless Steels", American Society for Metals, 1968, 82 pages. "Corrosion Engineering", G. Fontana and N.D. Greene, McGraw-Hili Book Co., 1967. "The Possibility of Service Failure of Stainless Steels by Stress Corrosion Cracking", J.E. Truman and H.W. Kirkby, Metallurgia, August 1965.
36
Steel Plate Engineering Data-Volume 2
Useful Information on the Design of Plate Structures Revised Edition-' 1992
Published by AMERICAN IRON AND STEEL INSTITUTE With cooperation and editorial collaboration STEEL PLATE FABRICATORS ASSOCIATION, INC. Revised December 1992
Acknowledgements or the preparation of the original version of this te.ch.nical publication, the American Iron and Steel Institute initially retained Mr. I.E. Boberg and later obtained the services of Mr. Frederick S. Merritt. For their skillful handling of the assignment, the Institute gratefully acknowledges its appreciation.
F
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 this publication. Appreciation is expressed to the American Institute of Steel Construction, American Petroleum Institute, the American Society of Mechanical Engineers, Business Communications, Inc., Chicago Bridge and Iron Company, Pitt-Des Moines, Inc., U.S. Army Mobility Equipment Command, and the American Water Works Association for their constructive suggestions and review of this material. Much of the illustrative and documentary material in this manual appears through their courtesy.
American Iron and Steel Institute The material presented in this publication has been prepared in accordance with recognized engineering principles and Is for general information only. This Information 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 patent or patents. Anyone making use of this Information assumes all liability arising from such use.
AMERICAN IRON AND STEEL INSTITUTE 1101 17th Street, N.W., Suite 1300 Washington, D.C. 20036-4700
December 1992
jj
Introduction olume 1 of this series, "Steel Tanks for Liquid Storage," deals with the design of flat-bottom, cylindrical tanks for storage of liquids at essentially atmospheric pressure. Steel plates, however, are used in a wide variety of other structures, such as pipe, penstocks, pressure vessels, stacks, elevated tanks, and bulk storage tanks. These structures present special problems in design and detail, the answers to which are not readily available without searching a number of sources. Volume 2 gives useful information to aid in design of such structures.
V
Scope Volume 2, "Useful Information on the Design of Plate Structures," does not cover in depth the design of any particular structure. For example, design of stacks involves problems of vibration that are beyond the scope of this volume. Similarly, design of pressure vessels requires a detailed knowledge of ASME, state and, sometimes, city codes. Designers should work with the applicable code. Any attempt to summarize pressure-vessel codes could be misleading and even dangerous, because of constant revision and updating by the various regulatory bodies. There are, however, many facets of plate design that are generally applicable to many types of structures. Information on these is not now conveniently collected in one source. Drawing on many sources, this volume offers such information and discusses some of the more commonly encountered problems. Included is an outline of membrane theory, data for weld design, commonly used details, plus data and mathematical tables useful in design of steel plate structures. The intent is to include information principally pertinent to plate structures. For convenience of users of this volume, some data readily available elsewhere, particularly in mathematical tables, has been incorporated. Volume 3, "Welded Steel Pipe," and Volume 4, "Penstocks and Tunnel Liners," of this series treat these applications in detail and are available from Steel Plate Fabricators Association, Inc.
iii
Contents Part Part Part Part Part Part Part Part Part Part
I II III IV V VI VII VIII IX X
Flat Plates ................................. 1 Large Diameter Plate Tubular Columns .......... 7 External Pressure on Cylinders ............... 11 Membrane Theory .... . . . . . . . . . . . . . . . . . . . . .. 17 Self-Supported Stacks . . . . . . . . . . . . . . . . . . . . . . . 27 Supports for Horizontal Tanks and Pipe Lines ... 35 Anchor Bolt Chairs .......... . .......... . ... 49 Design of Fillet Welds . . . . . . . . . . . . . . . . . . . . . .. 53 Inspection and Testing of Welded Vessels ...... 63 Appendices ........ '....................... 65
v
Part ' l Flat Plates lat plates are used in many conventional structural forms, such as plate girders, built-up columns, or component parts of trusses. Such uses are well covered in standard texts or handbooks and are not discussed in this volume. Instead, Part I will cover applications in steel tanks.
The mode of support and manner of loading specified must be complied with if the stresses are to be realized. No commercial edge fastening will correspond exactly with the theoretical conditions. The exact restraint of the edge, where bending is of prime importance, will depend on the rigidity of the support, the flexibility of any gaskets used, the position of the bolting circle and the spacing of the bolts therein, as well as the tightness with which the joint is bolted up. When membrane action is of importance, the degree of bolting up and the ability of the reinforced opening to resist slight deformations under radial tensions will largely determine the exact stress in the plate and the corresponding deformation. The bending moment at the edge is of less importance than at points where plate resistance depends primarily on bending. In view of these remarks, the conditions "Fixed" and "Supported" serve as guides to the possible range of stress and deflection.
F
Bending Stresses and Deflections Used as a membrane, as in the shell of a tank, a steel plate is a very efficient member. In contrast, a flat plate in bending normal to its plane is inefficient. Circumstances, nevertheless, sometimes dictate the use of a ' flat-walled tank because of space limitations, or the storage of a corrosive liquid may dictate use of a grillage-supported bottom to facilitate inspection. In such cases, a stiffened flat surface is indicated. On the next page, formulas are given for calculating the maximum bending stresses and maximum center deflections of certain flat plates. These formulas have been derived from various sources, the most important being based on an analytical derivation from elastic theory. However, those relating to three classes of elliptical plates and to certain others with a central applied load are less rigid in their derivation though sufficiently reliable for the use of the designer. It must be remembered that all formulas apply to materials such as steel, for which Poisson's ratio is 0.30. The inherent limitations of these formulas must be kept in mind. It is assumed that tensions in the plane of the plate appropriate to membrane action are small or negligible compared with the stresses due to bending. In general, the deflection must be small compared with the plate thickness if this is to be true. For greater deflections, other more complicated formulas must be used in whose derivation both membrane and bending action are considered. The formulas given may yield reliable working stresses yet be absolutely unreliable in calculating the load at failure and the corresponding deflection, particularly in the case of materials which elongate materially before failure, or which assume a dished form under load through initial stressing beyond the elastic limit. In general it must not be expected that these formulas will yield stresses accurate to better than 5 0/0.
Notation a
= length,
A
=
b
= length,
8 81 82
E f
Fy H
Ls n
p P 1
in., of semi-minor axis of supporting ellipse for elliptical plates length, in., of semi-major axis of supporting ellipse for elliptical plates
in., of short side of rectangular plate at supports
= length, in., of long side of rectangular plate or side of square at supports = factor for stress in uniformly loaded, fixededge, rectangular plates (Tables 1A and 18) = factor for stress in uniformly loaded, simply supported, rectangular plate (see Tables 1A and 18) = modulus of elasticity, psi = maximum fiber stress in bending, psi = specified minimum yield strength, psi = uniform load, ft. of water = stiffener spacing, in. = alA or bIB = uniform load or pressure, psi = concentrated load, lb.
r r'
R S
~
<1> <1>1
<1>2
<1>3
plate approaches a catenary between supports, the support spacing is given approximately by the following formula:
radius, in., of central loaded area = i~side knuckle radius, in., for flat, unstayed, circular plates = radius, in., to support for circular plates = spacing, in., of adjacent staybolts at corners of square plates = plate thickness, in. = center deflection, in., of plate relative to supports = factor for stress in circular flanged plate (see Table 1A) = factor for deflection of uniformly loaded fixed-edge, rectangular plates (see Tabl~s 1A and 1 B) = f~ctor for deflection of uniformly loaded, simply supported rectangular plates (see Tables 1A and 1B) = factor for deflection of fixed-edge, rectangular plates subjected to central concentrated load (see Tables 1A and 1B)
Ls =
(54,0:0
/2 ) ,12
Ls
(1-3)
112
= 900 1- = 2,076 1P
(1-4)
H
Figure 1-2 gives graphical solutions for Eqs. 1·3 and 1-4. For the catenary approach, it is essential that a lateral force of 10,OOOt be resisted at the peripheral support. Since this is not always practicable, application of the catenary approach is limited. Similarly, it should not be used where pressure is reversible or where deflection is objectionable. In the above discussion, only plate stresses have been considered, and it is assumed that any welded plate joints will develop the full strength of the plate including appropriate joint efficiencies. Also, the stiffener system should be in accordance with accepted structural design principles. Protection against brittle failure of a structure sho~ld be considered at the time of design. Since environmental extremes, design detail, material selection, fabrication methods and inspection adequacy are all interrelated in protecting a structure from such failure, these factors should be evaluated.
(1-1)
For convenience in connection with tank bottoms, the load can be expressed in feet of water, rather than psi, in which case:
Ls = ( 124,6 15 t2) 1/2 H
2;')
Because of the approximate nature of the solution, a conservative value for f is indicated. Assu~ing f = 10,000t and E = 29,000,000 psi for mild carbon steel, the equation becomes:
One of the most commonly encountered conditions is a uniformly loaded flat plate supported on uniformly spaced parallel stiffeners. In the absence of any code or specification requirement, assume an allowable bending stress equal ~o 3/4 of the specified minimum yield stress value In the plate for determination of stiffener spacing Ls, in. The plate stress can be obtained from the formula in Table 1A for the case of a rectangle b x B, where B = CD and b is taken as Ls. Thus, for the fixed condition (continuous over the supports), the maximum permissible spacing of stiffeners becomes:
Ls =
~(
(1-2)
Figure 1-1 gives graphically stiffener spacing determined from Eqs. 1-1 and 1-2 for an allowable bending stress of 27,000 psi (i.e. Fy =36,000 psi). If deflection exceeds t12, the plate will tend to act as a membrane in tension and exert a lateral pull on the outside support that must be taken into account. An alternative solution, therefore, is to assume that yielding does occur at the support and the plate acts as a catenary between supports. At intermediate supports, the tension in the plate will be balanced; but at the outside support, restraint must be provided to· resist that tension. This is not always easily accomplished. When the span is such that the profile of the
2
• • • •I I I
CONTINUOUS BEAM 50 45
-..... (1)
co
Note: Plate figured .. a oontlnuoua beam with a unit II.reaa of 27,000 pel In bending. May be uaed for other II.reaaea by varying H directly with unit strea•.
t = 5/16"
35
~ \t- 30 o ..... (1)
25
- 20 (1)
u..
J:
...
"C
co 15 (1)
J:
10 5
, , , I I I I I I
40
'-
0 10
15
20
25
30
35
40
45
50
55
Support Spacing, Ls (in)
Figure 1-1. Stiffener Spacing for Flat Plate Acting as Continuous Beam.
CATENARY ACTION 50 10,000 t - - I - - _......- - i Ls
45
-..... 4035 ~~_~
__
~~~_~~~~_ _~_ _ _~~~~on~~~~.(~~) ~ ~.(9~)
CO
~
\t-
O
..... (1) (1)
~
J:
...
"C CO
(1)
.........
Caution: UN thla graph only to determine limiting value. for comparison.
'(1)
~--- ~f-: l~, O~O
t = 7116"
30
NOTE: Platea IIgured .. a catenary at 10,0001 tension. End. must be reatralned and capable of taking a horizontal pull par Inch of 10,000 time. thlckneea.
t
25
= 1/2"
20 15
J:
10 5 0 10
15
20
25
30
35
40
45
50
55
Support Spacing, Ls (in)
Figure 1-2. Stiffener Spacing for Flat Plate with Catenary Action.
I
60
,3
60
Table 1-1A. Flat Plate Formulas Poisson's Ratio = 0.30 SHAPE
Loading
f
Fixed
R2 -r t
0. 75P
Uniform p
Circle Radius
R
Fixed Supported
1.43 [,og IO
(-~)+0.11 (fi)
P-;r
3
a P2
Supported 0.420
Central concen· trated p
Fixed
Supported
4
P
""1
13.1
P
2
0.42n + n + 2.5
Fixed
b2 B) p -
Uniform '
Supported
b2 B2 p...:...
(p) a
7
5~3
Supported
0.308
Fixed
n = a/A Ap;Jroximate Fits n == 1, load over 0.01 %of area
Uniform
p
Uniform
2
~
¢(p) -b 3 E t3
p
P 1.582" t
Staybolts spaced at corners of square of sideS
0 .228
0.0138
t
.!.. +cP
O. '2S
S2
2t
E 78 ~)
t)K E
t3
E7
0.0284 (p) S4
1+~R
2
Fits n = 1 and n = 0 =
.
n ApproxlnJ(lte
t
f max. center of side
t
4
0.0443
PT
(R -~
(E.) £3 E
t
p
depend 2 on Bib. See Table 1 B. b . B = n Approximate
Fitsn = 1 andn = 0
2
0.287 p 2
Supported
¢2 and 8
B
t
_12 B'l
P 1.32"2 t
¢) and 8 I depend on B/b . See Table 1 B.
b
p-
Fixed
Fastened to shell
(!)-;;4
t
Central concen· trated P
Fits n :.: 0 and n == 1 n - alA Approximate Fi ts n = 0 and n = 1 Load over 0.01 % of area
(p) b ¢ -2 E t3
P
6
a Exact n=A SOlution n = ~ Approximate
..
¢I
-;r
1 + 2.4n 2
4
E -;r
t
7
Square
Circular Flanged
1.365
uniform over circle, radius r. Center Stress As above Center Stress
t
t
4 .00 P 1 + 2n2
Fixed
Supported
Flat Stayed Plate
£t. t3
t2
p
BXB
0 .55 (p) E
t2
Rect.angle Central concen· trated P
K3
*
t
50
4
...
0.22(1.) E
3n 4 + 2n 2 + 3
max . at edge
f max. at center
2
+ n2 + 1
3n 4 + 2n2 + 12.5
Uniform P
BXb b
Pit 2
a2
6 3n + 2n2 + 3 4
p
a<
J
2
1.43'~OglO(;!r 0.334 + 0.06(~)2J ?'
Uniform
Ellipse 2A X 2a A
2
P
Fixed
f
O:.695(£~ E t3
1.24pt
Remarks
R4 (~) ?
0.17
R2
Supported Central concen· trated P on r
Center Deflection ~ In .
Maximum Fiber Stress, psi
Edge Fixation
f max. of center As above. Deflection nearly exact . Approximate for J; area of contact not too small. If plate as a whole de· forms, superimpose the stresses and deflections on those for plate flat when loaded. ¢varies with shell and joint stiffness from 0.33 to C.38 Knuckle 8adius, r'
J]
*Formula of proper form to fit circle and infinite'rectangle as n varies from 1 to O. tFormulas for load distributed over 0.0001 plate area to match circle when n for stress when n = O. Stress is lower for larger area subject to load.
=1. They give reasonable values
tFormulas of empirical form to fit Hutte values for square when n = 1. They give reasonable values when n =O. Assume load on 0.01 of area. Apparent stresses only considered. These formulas are not to be used in determining failure.
4
• •
Table 1-1 B. Flat-Plate Coefficients Stress Coefficients - Circle with .Concentrated Center Load
rlR
• • • •I I
• • • • • • • •
1.0
0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
Fixed l
0.157
1.43
1.90
1.57
1.65
1.75
1.86
2.00
2.18
2.43
2.86
Supported 2
0.563
1.91
1.97
2.05
2.13
2.23
2.34
2.48
2.66
2.91
3.34
3.0
4.0
5.0
Stress and Deflection Coefficients - Ellipse
1.0
Ala
1.2
1.4
1.6
1.8
2.0
2.5
1.42 0.322
1.54 0.350
1.63 0.370
1.77 1.84 0.402 0.419
1.91 0.435
1.95 0.442
2.00 0.455
00
Uniform Load' Fixed. Stress 3 0.75 Deflection 4 0.171
1.03 1.25 0.234 1.284
Uniform Load Supported 5 1.24
1.58
1.85
2.06
2.22
2.35
2.56
2.69
2.82
2.88
3.00
Central Load Fixed 6 Supported'
3.26 3.86
3.50 4.20
3.64 4.43
3.73 4.60
3.79 4.72
3.88 4.90
3.92 5.01
3.96 5.11
3.97 5.16
4.00 5.24
2.86 3.34
Stress and Deflection Coefficients - Rectangle
" 1.0
1.25
Stress 8 1 Stress 82 4 1 + 2n2 5.3 1 + 2.4n2
0.308 0.287
0.399 0.454 0.376 0.452
1.33
1.75
1.56
2.09
Deflection 4>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
For Fy
For Fy> 34 ksi tiRo Range (}L tiRo $ 0.0035372 Formula (2-4) 0.0035372 ~ tiRo < 0.012 13.86 + 1771.2 tiRo tiRo ~ 0.0125 36
FS = 2 C'c = ""'2 1(2Elo L
K", = 1-0.5
(2-6)
(2-7)
C'C)2 = 0.5 (KUr
Kef>
Proposed Revision to AWWA Standard 0100-84. AISC 1989 Specification for Structural Steel Buildings - Allowable Stress Design and Plastic Design
when KUr~ C'c
(~~r
when KUr
~
when KUr
(2-8)
< C'c
(2-9)
25
AISC Some of the formulas in the AISC Specifications are presented in terms of Dclt. Those formulas, when shown below, have been converted to tiRo terms, so they are not in the exact same form as those in the specification. Members subjected to both axial compression and bending stresses should be proportioned to satisfy the combined stress requirements of the A'ISC specification. The combined stress formulas are not presented here so must be obtained from the AISC specification. . The AISC specification contains no recommendations for allowable stresses when tiRo < Fy16500. For Fy 16500 ~ tiRo < Fy 11650 Fb = 331 tiRo + 0.40 Fy Fa = smaller of the value obtained from formula 2·10 or
[
1 - (KUr)21 F 2Ce2 Y
J
when KUr
.§. + 3(KUr) _ (KUr)3 3
8Ce
12 1[2E or 23(KUr)2
(2-10)
< Ce
(2-11 )
8Ce3
h KU > C w en r e
(2-12)
8
• • • • • •I ~
20 18
AISC-
16
~
~ ./"
---- ---- . /V
14 12 Fa (ksi) 10
---- -----
~
k"
./
8 6
I
4
" "-PR OPOSE DAVM
/'
A
/
/ oV 2
o
0.004
0.008
I II
• • ,• • • • • •
~
0.012
0.016
0.02
t/ Ro
KUr
= 0, Fy = 30 ksi Figure 2-1
".
\ )'.
22
20
A1SC
18
-----
16 14
Fa 12 (ksi) 10
~
8 6
I
4
2
o
l( o
/
/'
A
~
----------
~
~
!-""
~ -/~
V i'-Pf ~OPos r-DAWV JA
/ -
L
0.004
0.008
0.012
t/ Ro
KUr
= 0, Fy = 36 ksi Figure 2-2 9
0.016
0.02
.>
• • •I •I C • • • • • •II • •
Part III External Pressure on Cyli nders ________________________
ylindrical vessels subjected to external pressure must be designed as tubular columns to resist axial loads imposed on the heads. In addition, circumferential stiffeners may be required to prevent buckling of the shell due to radial pressure.
Is
I~
L
Ls
N
= external pressure, psi
Pa
= allowable external
pressure, psi For a vessel with atmospheric pressure inside, and greater than atmospheric pressure outside, p and ' Pa refer to the gage pressure outside the tank. For a vessel with atmospheric pressure outside and a partial vacuum inside, p and Pa refer to the partial vacuum inside the tank, in psi, taken as a positive number. For vessels which are simultaneously exposed to a partial vacuum inside and greater than atmospheric pressure on the outside, P and Pa should be taken as the maximum difference in the inside and outside absolute pressures. t = minimum thickness, in., of cylindrical plate; or for determining stiffener spacing, average thickness, in., of unsupported shell between stiffeners; or for short spans, thickness, in., of middle quarter of span t1 = weighted average thickness, in., of shell between end stiffeners !l = Poisson's ratio = 0.30 for steel
Notation
A As B Do Ro E F Fa h
p
= strain factor (see Fig. 3-1)
= cross-sectional area, sq in., of stiffener = allowable pressure factor (see Fig. 3-1) = outside diameter, in., of cylinder plate
= outside radius, in., of cylinder = modulus of elasticity, psi = safety factor wlrespect to predicted failure = allowable unit stress, psi = height or length, in., of cylindrical shell between end stiffeners = required moment of inertia of the stiffening ring cross section about its neutral axis parallel to the axis of the shell, in.4 = required moment 'of inertia of the combined ring-shell cross section about its neutral axis parallel to the axis of the shell, in.4 = design length, in., of cylinder = largest of following: Distance between head bend lines plus onethird depth of each head if there are no stiffener rings Greatest distance center to center between any two stiffener rings Distance from first stiffener to head bend line plus one-third depth of head = half the distance, in., from center of stiffener to next stiffener or line of support on one side . plus half the distance, in., to next stiffener or line of support on the other side = number of complete waves into which stiffener ring will buckle = number of waves into which unstiffened shell between end stiffeners will buckle
Types of Pressure Vessels With respect to the spacing and sizing of stiffeners, cylindrical vessels may be grouped into three general classifications: A. Vessels designed for an external (or internal) pressure greater than 15 psi. These are usually subject to the rules of ASME Code. The code provides a safety factor of 3 for stiffener spacing based on buckling of the shell between stiffeners. B. Vessels subject to both axial and radial/oads and designed to operate at 15 psi or less. These are not always specified to be in accordance with code rules. When the external pressure approaches the upper limit or the pressure cycle alternates between internal and external, the stiffener design might best be in accordance with code rules with a minimum safety factor of 3. For less severe conditions, some designers have reduced the safety factor to 2112 with successful results. C. Storage tanks of large diameter. These are 11
If A from Step 4 is to the left of the applicable material/temperature line, then use: _ 2AE Pa - 3(Oclt) (3-2)
sometimes subjected to relatively static, small, external pressures that are radial only. Examples are earth pressure on buried tanks, or granular or liquid pressure on the inner shell of a double-walled tank. In such cases, successful results have been achieved with the stiffener design based on a safety factor of 2. It should be noted that the ASME code as well as most of the experimental and analytical shell buckling information aVpilable are for a uniform round shell with uniform static loading. In the case of a buried or submerged horizontal tank, or a vertical tank subjected to wind loading, the external pressure will vary around the periphery of the tank. In the case of a partially buried vertical tank, varying compaction and soil conditions may cause the external pressure to vary in an irregular way around the tank. Wind or water currents may produce dynamic effects which would present problems in the analysis. Any such variation in the loading, or any significant deviation from a true circular shape, may result in bending stresses in the cylindrical shell and stiffeners, which are not accounted for by the following analysis. Additional investigation may be required in these cases. The selection of the factor of safety in all cases should take into account the consequences associated with a failure of the structure, as well as the accuracy of the analysis and accuracy and duration of the loadings. Caution should also be exercised in applying ASME design equations to shells which do not meet ASME tolerances.
When t may be determined by factors other than external pressure, then, for known values of Pa and Do, and a known or assumed value of t, factor Bean be determined from Eq. 3-1. The steps outlined above can be reversed to determine stiffener spacing from the corresponding UDo ratio obtained from the chart. ASME also provides charts for steels of other strengths, as well as other metals and alloys. Where pressure-vessel codes apply, reference should be made to the latest edition of the code. Sizing the stiffener rings as prescribed by ASME is done as follows: The required moment of inertia should not be less than: (3-3) or:
s
Design of Pressure Vessels
A.
Step 6. Step 7.
Using the value of A from Step 4, enter the applicable material chart in Fig. 3-2. Move vertically to the material/temperature line for the maximum design temperature. From this intersection, move horizontally to the right and read value of B. Compute the allowable external pressure from the following formula: Pa =
4B 3Delt
= DQ 2Lsft + A/LJA 10.9
(3-4) The width of shell contributing to the combined moment of inertia (Is') should not be greater than 1.10 VDot. Assume that half the width lies on each side of the centroid of the ring, except that there should be no overlap of effective widths between two adjacent stiffeners. The procedure for stiffener design is as follows: Step 1. Assuming the shell has been designed, Do, Ls and t are known. Assume a stiffener section and determine its area, As, and moment of inertia, Is. Then calculate B vom pDQ ] B = 3/4 [ t + AILs (3-5) Step 2. Enter the right-hand side of chart on Fig. 3-2 at the computed value of B. Step 3. Follow horizontally to the design temperature line. Step 4. Move vertically to the bottom of the chart and read the value of A. Step 5. Calculate required value of Is from Eq. 3-3 or I~ from Eq. 3-4. Step 6. If Is required is greater or substantially less than Is provided, assume a new section and repeat the steps. Step 7. If the value of B in Step 3 is below the left end of the applicable material temperature line, then use A = 2BIE. Type B. Non-Code Vessels Subject to Both Axial and Radial Loads. For pressure vessels, stiffener design might best be in accordance with code rules with a minimum safety factor of 3. Code charts, however, do not include Delt ratios greater than 1,000 whereas many non-code vessels are of .reJatively large diameter and have Delt ratios greater than 1,QOO. In such cases, internal pressure often controls shell thickness. But even small external pressures may require stiffeners because of the large diameter.
Design of types A, Band C vessels is discussed in the following: Type A. ASME Code Rules. To serve as an illustration, Figs. UCS 28.1 and 28.2 and UGO-28.0 have been reproduced here as Figs. 3-1 and 3-2. These charts are used to determine shell thickness of cylindrical and spherical vessels under external pressure when constructed of carbon steel having a yield strength of 30,000 to 38,000 psi. The procedure for using the chart is as follows: Step 1. For the assumed t, determine ratios UDo and Delt. Step 2. Enter left-hand side of Fig. 3-1 at the value of UD o. Step 3. Move horizontally to the line representing Delt. Step 4. From this intersection move vertically downward to determine the value of factor Step 5.
I'
(3-1)
12
\
20.0 11.0
0 \
.•
\t\.lH-4-+,,-+1H-+-R--t-IrHH--+++++HH-H-+t-t-tt--r-t-t-t-ttt-t-t-rr-t-tt-rtM1tt-H
16.0 ~ - \-~-+-~44H+-I-l-+++-+-+-+H-HH++-+-+-+-H-tt-+-H-H-t1-t--t-1-t-i-tt--HH-tttt1
(
,
14.0 12.0 10.0 9.0
f
8.0
7.0
\ K.~\->\J.lr-\Hi~ \fH\-Ht-HH-+-H-+-1H-+H-H-tt-H-tH-tt-T-H-t-ttt1---Ht-Ht-HH1t1rt1 \
...\ I ~\ ~ ~\ 0
~
o
~
~ .. \
5.0
~
\
~O .'O~"" \
,
3.5
0
~
;
3.0
.
.
~
2.5 -
~
~
2.0
~..
I I I
•I
~
r\\ \ 1\
\ 1\ \
\
\
\
\
1\
\
\~
\
\
~
\
1.2
1
\
\ 1\ \
\ \
\
r\ \. i\ \ \
~ \
.90 \
\
1\ \ \
r"\
\
\
1\
\
\ \
r"\
1\
r\
\
\ \
\.
\
\ \ \
\
~-:.. \
1\ \ .I ~ \ \: L 240'
1\
\
\"\
\
'.)~
~~ \,.;
\
"\ \
I\
~\O
r\ r\ \
\
\ \
\
r\ \
"\
\
\J
\
\
\
1\ \ \ \
1\ \
[\
I\.
~ \
\
\ \
I\. i\
\
\
\
1\
i\ \ \ \
\
\
1\
~_
~'.-
\
['\0
\ I\. \ \ J\ \ \ \ I ~ .60 t--+-+-+-+--I-t-+-~~-+-+-1f-l.cf-~\H--H.:-IH-l~\:-:4.~~~:-+--*+.1f+P+--+-~I~\~~+.-1=+W-i
\ \ \ \ \ , 1\ \ \ \ \ \ \~ .50 t--+-+-+-+--+-""';-+-H~\-f-1~~\r-+-1Ito\+TI\+-!-l+--+'-I\-1\r-+-Jod--''r-\.-+--+\M-!\o~\r-+--''r-T-I\~ ' ~",_..
i
1\ \ \ \' r \ \ . . . . . -"" 'Jt-+-+-+-I-+-+-+-+-Hf-1l,,,,,~~--j-J~.,\~.,,,+-,,~\..:Ir4-l,-\+--4\-1I~ \~,\+l-1M1\-PI\~\-+-l\-f\M\~i-\~'-PI!li \
.4Q
.J5
. ,
\
:::
1
~
\
\
"\
\
•
1\ ~ \.
\
1\ \ \
i\
1\:\ \ \ [\ \. \ \ \\ \r\ "
1\ \ 1\,
\
r\
\
:\ \..
\1\
\r\i\ \ '\ \1\ i\ \[\ \ \ \\ '\ \ \'\ \ \ \ 1\
\\ ~ 1\1\ \
\1\ \\
.20 .18 . \6
1\
:)~J
\.~
~y/
~~'Z "\' \ \ '\ . V. 0
I:'
,, i\ 1\ \ r\ \ .1. t--t-+-+-+-~H-H-T+-+--+-I~~+-+-+rHflt-~~+-+-4r-++*+~~-+--f-Il'o,~~
.12
NOTE: Sec hble UGO·28.0 10' ubulM nlun
_\
1\
I\.
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.10
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\
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\ \
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1\ \ \ I\.
\ i\
f'
\
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r\ \
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\ \ r\ \
\
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1\
\
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\\
\'\
\. \
~
\
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\
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,I
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1\
~ r\ 1\
\ \ \. \
r\ \
I\"
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\ \ \ \
1\ \
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' 1\
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.80 .10
1\
\ \ 1\.\
\ \
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\ ~
1 \ \ _\ \
\
\
\
I\.
\
1.0
"\
1\
\ \
1.4
\
\
\
\ \ 1\ r\ r\
r\ \ ~ \ i\.
\
\
\
:::
·to
~
~~
-~
\ \
\
, • r\
--:
\
"\
,%\ \
\ 1\
'\
~~,\ 1\
\ i\
\
6.0 r-" _ '0
(
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\
\ \
\
I\. \ \ \~ .\
f\ 1\
I\.
t\ \
N
\~ _}:'~'
\ " !\'\
::~!=:~~=~:~~~\~v.~X~\~~~~~~~t§ t--:t-+-+-+-+-H-+-H+--+-+--1H--+-+++I\'%~-~1\~~~~~~~~ ~~=t~:~ I 1\1 Il\ l\ I "I "\J I'\. Lf'.
.010 .060 t-+-+-+-+-+-t-+-+-H+--I-+--1I-+--+-+++t,1 }J
\
I -\
I'
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
~~
.,;'"
/,
./
~
.........
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'
.,..,.
L.-""
11
....... ,.,.
~
...".
.... i-'~
I I
....
-,.,-
.......
l,......- ........
~i'"
I
I
-~ ....
:...--~
~
.E • 29.0 x 10e ......... ...... I E. 27.0 x 10e
.....-
20,000 18.000
I
up to :lOOF ~-
/ ---. l..- I--
I
--;;.;,.
./
'1:
3
4 5 6789
.OO(X)1
a: u
0
~
< u..
::3.500 l-
3.000
r;
~
2.500
(A~
2
7.000 6.000
4.000
{/, '1/ ......
......... I: ~,
'h
/,
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
"
.......
---
........
;;;;;;--
:-.-
~"...,.
-,...
..... ~
~-
...
20,000 18.000
V?OO F-
~~
16,000
----- ,.,.'" -
... V
...". ~
... ...V
.............
...-
•
-
I
I I
I
I
~I
~
I
800 FII
J900 F_
~
----
104,000 12.000
~
............. ,...
;;.ii"
:1" 5 6789 .0001
rh
:/.
0
7.000
u..
6.000
.... .;'
5.000
~
4.000 3.500
'Ii'
3.000
~ '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 1R2<1>2 + 2T2 2R,cJ>,
=
"2
"2
Equating the two: P.R2 2.R1<1>1 =
2T1 ,R2<1>2 + 2T2 2R1<1>,
"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.:: ,'')
",,)
<.;WI :;/:
LINE OF SUPPORT
'J
X
:',:, ::,:,)" ',,;
:',<,,:' :',::, ':','
:;,: '
.. :
~;)}
1::
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
<
"~
"'" ""'~
''""'"'" '" '"
9o I00 II
o
12 o
~13
,.
Figure 6-2. Location and type of support for horizontal pressure vessels on two supports.
SELECTION OF SUPPORTS
should be increased for extremely heavy vessels, and in certain cases it may be desirable to reduce this width for small vessels. Thin-wall vessels of large diameter are best supported near the heads provided they can support their own weight and contents between supports and provided the heads are stiff enough to transfer the load to the saddles. Thick-wall vessels too long to act as simple beams are best supported where the . maximum longitudinal bending stress in the shell at the saddles is nearly equal to the maximum longitudinal bending stress at mid-span, provided the shell is stiff enough to resist this bending and to transfer the load to the saddles. Where the stiffness required is not available in the shell alone, ring stiffeners must be added at or near the saddles. Vessels must also be rigid enough to support normal external loads such as wind. Figure 6-2 indicates the most economical locations and types of supports for large steel horizontal pressure vessels on two supports. A liquid weight of 42 lb. per cu. ft. was used because it is representative of the volatile liquids usually associated with pressure vessels.
When a cylindrical vessel acts as its own carrying beam across two symmetrically' placed saddle supports, one-half of the total load will be carried by each support. This would be true even if one support should settle more than the other. This would also be true if a differential in temperature or if the axial restraint of the supports should cause the vessel acting as a beam to bow up or down at the center. This fact alone gives the two-support system preference over a multiple-supporting system. The most economical location and type of support generally depend upon the strength of the vessel to be supported and the cost of the supports, or of the supports and additional stiffening if required. In a few cases the advantage of placing fittings and piping in the bottom of the vessel beyond the saddle will govern the location of the saddle. The pressure-vessel codes limit the contact angle of each saddle to a minimum of 120 0 except for very small vessels. In certain cases a larger contact angle should be used. Generally the saddle width is not a controlling factor; so a nominal width of 12 in. for steel or 15 in. for concrete may be used. This width
37
t ;t
(a) UNSTIFFENED SHELL
~
3H
T
r", I
\
I
\
I
Q Qd
A(~)
I
... /
, I
i
(b) SHELL STIFFENED BY RINGS ADJACENT TO SADDLE B
4
:
;'
~
,~ (~ +:.»
(1-+1)
SECT A·A
!
B4
I. (QL)(~-<4~ 1.~1 _ 1.<4H L
A-
-
i
(I ~
l Cl.) LO .... OS ~ AtACTIO. NS
ASSUMED TANGENTIAL SHEAR STRESS
RING
!
(e) SHELL STIFFENED BY RING IN
Q (~)
PLANE OF SADDLE
~l+T
X
(d) SHEAR DIAGRAM SADDLE AWAY FROM HEAD
(b)
MOMEWT OIAGA.......
IN
'T.- Las
(e) SHELL STIFFENED BY HEAD
10
Figure 6·3. Cylindrical shell acting as beam over supports. Where liquids of different weights are to be stored or where different materials are to be used, a rough design may be obtained from the chart and this design should be checked by the applicable formulas outlined in the following sections. Table 6-1 outlines the coefficients to be used with the applicable formulas for various support types and locations. The notation used is listed at the end of the paper under the heading Nomenclature.
MAX_ OSlNa (
~-;;-;-
a-SlNu
. -.
cos. ) cos.
+ SiNo
SECTC·C
Figure 6·4. Load transfer to saddle by tangential shear stresses in cylindrical shell. just as though the shell were split along a horizontal line at a level above the saddle. [See Fig. 6-4 (a)]. If this effective arc is represented by 2A (A in radians) it can be shown that the section modulus becomes:
MAXIMUM LONGITUDINAL STRESS The cylindrical shell acts as a beam over the two supports to resist by bending the uniform load of the vessel and its contents. The equivalent length of the vessel (see Figs. 6-2 and 6-3) equals L + 4H13, closely, and the total weight of the vessel and its contents equals 20. However, it can be shown that the liquid weight in a hemispherical head adds only a shear load at its junction with the cylinder. This can be approximated for heads where H ~ R by representing the pressure on the head and the longitudinal stress as a clockwise couple on the head shown at the left of Fig. 6-3. Therefore the vessel may be taken as a beam loaded as shown in Fig. 6-3; the moment diagram determined by statics is also shown. Maximum moments occur at the midspan and over the supports. Tests have shown that except near the saddles a cylindrical shell just full of liquid has practically no circumferential bending moments and therefore behaves as a beam with a section modulus lie = 1tr2t. However, in the region above each saddle circumferential bending moments are introduced allowing the unstiffened upper portion of the shell to deflect, thus making it ineffective as a beam. This reduces the effective cross section acting as a beam
lie
= 1tr2t
A + sin A cos A - 2 Sin: A ) u
It (
Si~ ~
- cos
~)
Strain gage studies indicate that this effective arc is approximately equal to the contact angle plus onesixth of the unstiffened shell as indicated in Section A-A of Fig. 6-4. Of course, if the shell is stiffened by a head or complete ring stiffener near the saddle the effective arc, 2A, equals the entire cross section" and lie = 1tr2t. Since most vessels are of uniform shell thickness, the design formula involves only the maximum value of the longitudinal. bending stress. Dividing the maximum moment by the section modulus gives the maximum axial stress in lb. per sq. in. in the shell due to bending as a beam, or
S1
=
± 3K1QL 1tr2t
K1 is a constant for a given set of conditions, but actually varies with the ratios AIL and HIL ~ RIL for different saddle angles. For convenience, K1 is plotted in Fig. 6-5 against AIL for various types of saddle supports, assuming conservative vafues of
38
1.6
/
1.4
~/ ? lv~ «
1.2
-........
~ ~«;
K, .8
"'{<
-Y
~«;
..... ~
.6
".:>
~vv
of?
'-....
by (0/2 + ~/20) or (1t - a) as shown in Section A-A of Fig. 6-4. The summation of the vertical components of these assumed shears must equal the maximum total shear. The maximum tangential shear stress will occur on the center side of the saddle provided the saddle is beyond the influence of the head but not past the quarter point of the vessel. Then with saddles away from the heads the maximum shear stress in lb. per sq. in. is given by
/
0
~~
,;::.f? -::i
1.0
v
"re
4'
~ ~~17 ~
i'--.!!'lyG
~'f:f:€
.4
~~
o
S 2
= K2Q (L rt
L
+
2A ) 4H
3 o
.02
.04
.06
.08
.10
-.12 '
.14
.16
.18
.20
.22
.24
Values of K2 listed in Table 6-1 for various types of supports are obtained from the expressions given for the maximum shears in Fig. 6-4, and the appendix. Figure 6-4 (f) indicates the total shear diagram for vessels supported on saddles near the heads. In this case the head stiffens the shell in the region of the saddle. This causes most of the tangential shearing stress to be carried across the saddle to the head, and then the load is transferred back to the head side of the saddle by tangential shearing stresses applied to an arc slightly larger than the contact angle of the saddle. Section C-C of Fig. 6-4 indicates this shear distribution; that is, the shears vary as the sin 4> and act downward above angle a and act upward below angle a. The summation of the downward vertical components must balance the summation of the upward vertical components. Then with saddles at the heads the maximum shear stress in lb. per sq. in. is given by 8 2 = K2 Q
RATIO A
T
Figure 6-5. Plot of longitudinal bending-moment constant, K1 •
H = 0 when the mid-span governs and H = R when the shell section at the saddle governs. A maximum value of RIL = 0.09 was assumed because other factors govern the design for larger values of this ratio. As in a beam the mid-span governs for the smaller values of AIL and the shell section at the saddle governs for the larger values of AIL; however, the point where the bending stress in the shell is equal at mid-span and at the saddle varies with the saddle angle because of the reduced effective cross section. Fig. 6-SA in App. 8 gives acceptable values of K1 • This maximum bending stress, S1' may be either tension or compression. The tension stress when combined with the axial stress due to internal pressure should not exceed the allowable tension stress of the material times the efficiency of the girth joints. The compression stress should not exceed one half of the compression yield point of the material or the value given by S1
~(
E..) 29
rt
in the shell, or
in the head. Values of K2 given in Table 6-1 for different size saddles at the heads are obtained from the expression given for the maxim.um shear .stress in Section C-C of Fig. 6·4 and the appendix. The tangential shear stress should not exceed 0.8 of the allowable tension stress.
(tlr) [2 - (2/3) (100) (tlr)]
.
which is based upon the accepted formula for buckling of short steel cylindrical columns. * The compression stress is not a factor in a steel vessel where tlr~ 0.005 and the vessel is designed to be fully stressed under internal pressure.
CIRCUMFERENTIAL STRESS AT HORN OF SADDLE
·See also par UG·23 (b) ASME Code Section VIII Div. I.
TANGENTIAL SHEAR STRESS
In the plane of the saddle the load must be transferred from the cylindrical shell to the saddle. As was pointed out in the previous section the tangential shears adjust their distribution in order to make this transfer with a minimum amount of circumferential bending and distortion. The evaluation of these shears was quite empirical except for the case of the ring stiffener in the plane of the saddle. Evaluation of the circumferential bending stresses is even more difficult. Starting with a ring in the plane of the saddle, the shear distribution is known. The bending moment at any point above the saddle may be computed by any
Figure 6-4 (d) shows the total shear diagram for vessels supported in saddles away from the heads. Where the shell is held round, the tangential shearing stresses vary directly with the sine of the central angle 4>, as shown in Section 8-8 of Fig. 6-4, and the maximum occurs at the equator. However, if the shell is free to deform above the saddle, the tangential shearing stresses act on a reduced effective cross section and the maximum occurs at the horn of the saddle. This is approximated by assuming the shears continue to vary as the sin 4> but only act on twice the arc given
39
• • IZO
----------~,~___
- - - Ut
I , O~
.. ..
0' .0 I
o
/
.. '
ISO·
SH[L~
v.. sr Irr(~o
~tL~
UII"
'H"
(D
//
120·
V/
11O·
o
..5 " ...TIO
~
,,-
Figure 6·7. Plot of circumferential bendingmoment constant, K3 • Figure 6-6 Circumferential bending-moment diagram, ring in plane of saddle.
near the horn of the saddle. Because of the relatively short stiff members this transfer reduces the circumferential bending moment still more. To introduce the effect of the head the maximum moment is taken as
of the methods of indeterminate structures. If the ring is assumed uniform in cross section and fixed at the horns of the saddles, the moment, M\f)' in in.-Ib. at ,any point A is given by:
~~
cos <1> + ' cI> sin cI> 2 2
M\f) = Or { 1t
f3
Mp = K3Qr where K3 equals K6 when AIR is greater than 1. Values of K3 are plotted in Fig. 6-7 using the
+
assumption that this moment is divided by four when
AIR is Jess than 0.5.
cos P _ 1 (cos cI> - ~) x 2413
9[
The change in shear distribution also reduces the direct load at the horns of the saddle; this is assumed to be 0/4 for shells without added stiffeners. However, since this load exists, the effective width of the shell which resists this direct load is limited to that portion which is stiffened by the contact of the saddle. It is assumed that St each side of the saddle acts with the portion directly over the saddle. See Appendix B. Internal pressure stresses do not add directly to the local bending stresses, because the shell rounds up under pressure. Therefore the maximum circumferential combined stress in the shell is compressive, occurs at the horn of the saddle, and is due to local bending and direct stress. This maximum combined stress in lb. per sq. in. is given by
4-6(T)'+2COS2B]}
Si~ Pcos f3
+ 1 - 2(
Si~ PY
This is shown schematically in Fig. 6-6. Note that 13 must be in radians in the formula. The maximum moment occurs when = 13. Substituting f3 for <1> and K6 for the expression in the brackets divided by 1t, the maximum circumferential bending moment in in.-Ib. is
Mp
= K6 0r
When the shell is supported on a saddle and there is no ring stiffener the shears tend to bunch up near the horn of the saddle, so that the actual maximum circumferential bending moment in the shell is considerably less than Mp, as calculated above for a ring stiffener in the plane of the saddle. The exact analysis is not known; however, stresses calculated on the assumption that a wide width of shell is effective in resisting the hypothetical moment, M p, agree conservatively with the results of strain gage surveys. It was found that this effective width of shell should be equal to 4 times the shell radius or equal to one-half the length of the vessel, whichever is smaller. It should be kept in mind that use of this seemingly excessive width of shell is an artifice whereby the hypothetical moment Mp is made to render calculated stresses in reasonable accord with actual stresses. When the saddles are near the heads, the shears carry to the head and are then transferred back to the saddle. Again the shears tend to concentrate
S3
=-
4t(b
0 - 3K30, if L>- 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 <1>. 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 <5 equals any central d angle measured from the bottom, the moment of inertia is
2f3t
§: (
cos2 0 - 2 cos 0 Si: /1 +
Si~/
) do
where
A
1
4A nr2t [ L
= nr2t, and = 3K10L
- H2 1 + 2 R2 L2
(
]
d + sin d cos d _ 2 sin2 d ] d [ sin d - cos <5 d
= 30L
)
- - - - = - - - 4 ~L
K1 =
)
1 + 4H 3L
Tangential Shear Stress Section a-a of Fig. 6-4 indicates the plot of the shears adjacent to a stiffener. The summation of the vertical components of the shears on each side of the stiffener must equal the load on the saddle Q. Referring to Fig. 6-4 (d) the sum of the shears on both sides of the stiffener at any point is Q sin c'Phtr. Then the summation of the vertical components is given by 2
~ 1t 0 ~
Then the stress in the shell at the saddle in lb. per sq. in. is given by S1
_ 4 ~ L
nr2t
The section modulus for the tension side of the equivalent beam is r2t
(
51
=
Si~/1
L2 1 + 4H 3L
The section modulus
2r3t [1/2 sin <5 cos <5 + Q _ 2sin <5 sin d + sin2 d <5]~ = 2 d d2 0 f.lt [sin /1 cos /1 + /1 - 2
1 + 2 R2 .- H2
=
0
sin 2 rd nr
= 20 1£
.[
_ sin
c'P cos c'P] 1£
2
2
=0
0
The maximum shear stress occurs at the equator when sin = 1 and K2 = 1/1£ = 0.319. ~ Section A-A of Fig. 6-4 indicates the plot of the shears in an unstiffened shell. Again this summation of the vertical components of the shears on each side of the saddle must equal the load on the saddle. Then the total shear at any point is
R2 - H2
(1 _ __-_I_+_---'=-2A...:..::L"---_) x 1 + ~ 3L
o
sin r(n - a + sin a cos a) and the summation of the vertical components is given by or
0 sin 2, rd ~ a r(n - a + sin a cos a)
2 ~n
S1 = 3K1 0L nr2t
=
where
1t( Si:/1
- cos /1 )
. 2 K, = [ /1 + sin d cos d - 2 Sind d
[
~
1 (
o[
- sin cos ]1£ = 0 n - a + sin a cos a a The maximum shear occurs where c'P = a and K2 = _ _ _s,;:..i..;,..;.n..,.;:a..:...-_ _ n -a + sin a cos a
1 X
~ + R22AL .- H2 ) 1
Section C-C of Fig. 6-4 indicates the shear transfer across the saddle to the head and back to the head side of the saddle. Here the summation of the vertical components of the shears on arc a acting downward must equal the summation of the vertical
1 - _L +-4H
3L 44
component of the shears on the lower arc acting upward. Then
~
2
ao -~~--=--!.0 sin2 <1>, rd<1>,
~
1t -
2~ [
1[
2
a
Q sin 2 = a + sin a cos a)
(1t -
~in ex cos ex
ex +
o[
][
COS
4>2 ] :
cos <1> + cos a - a + sin a cos a
= ]
1t -
The ring compression becomes a maximum in the shell at the bottom of the saddle. Or if
0
o[
a - sin a cos a ] [<1>2 _ sin <1>2 cos <1>2] 1t 1t - a + sin a cos a 2 2 a
1 + cos a ] a + sin a cos a
1t -
Then
Finally
Q (a
- sin a cos a) =
Q (a
+ cos a ] - a + sin a cos a
- sin a cos a)
1t
1t
The maximum shear occurs when cI>2 = a and
K2
=
sin a [ 1t
1t
Design of Ring Stiffeners; Stiffener in Plane of Saddle
a - sin ~ cos a ] - a + Sin a cos a
Referring to Fig.6~6, the arch above the horns of the saddle resists the tangential shear load. Assuming this arch fixed at the top of the saddles, the bending moment may be found using column analogy. If the arch is cut at the top, the static moment at any pOint A is
Circumferential Stress at Horn of Saddle See under the heading Design of Ring Stiffeners.
Additional Stress in Head Used as Stiffener Referring to Section G-G of Fig. 6-4, the tangential shears have horizontal components which cause tension across the head. The summation of these components on the vertical axis is
~a Q
sin cI>, cos cI>, rdcI>1 -
~ 1t Q
sin cI>2 cos cI>2 [
~ 0 1tr
~ a 1tr
-
sin a cos a ] sin a cos a rd<1>
20 [<1>, _ sin <1>, cos cI>,] a = 2
[
~ +
or 1t
~
1tr
a
-
a [
1tr
~ <1> Q sin <1>, rd<1>, = _ ~
a)
=
1tr
o sin2 <1>2
(1t -
Q {[ sin2 cI>1]a _ [ 2
1t
0
1t
Ms
1t
a - sin ~ cos a ] [Sin 2 cI>2]1t} - a + Sin a cos a 2 a
=
!
2
<1»
d,
[ - COS'V1 "" - cos Sin . 2 "" 'V1 + 2
sin sin cos
0,: [
sin2 a ) 1t - a + sin a cos a
- sin If>, cos If>, cos If> - sin 2 <1>, sin
0
-_ -Or
=
2
~
1t
a - sin ~cos a ] rdcI>2 1t - a + Sin a cos a
o(
= Or ~ If> (sin If>,
_ <1>1 sin ] <1> 2 0
1
1
1 -
cos 4> -
~ sin 4> 1
Then the Ms lEI diagram is the load on the analogous column. The area of this analogous column is
Then assuming this load is resisted by 2rth and that the maximum stress is 1.5 times the average
8,
84 = K4 0
= 2 ~P -'- dcI> = gfu: ~o EI
EI
rth where
K4 = -s3 ( 1t -
The centroid is sin P/J3" and the moment of inertia about the horizontal axis is
sin2 a ) a + sin a cos a
Ih = 2
Wear Plates The ring compression at any point in the shell over the saddle is given by the summation of the tangential shears over the arc = (cI> - 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/
<-v.6/
k
~
""-
"'J
~
~ "- ,"J
,"'-...
~
~~ ~
'""::'-~""-'"''"""'" a""""~V"'""'0"'~8 '""""~" "~O ~
~
"-
~
"
"'-
A
L
"-
~
AOQf2~
'"'"
"YV
----- -
.4 2 0
~
~
"- ""- "-", ,~
"- ,~ ,"'- ,~ "\,......... ,"'- ,"- ~,
(J
VALUES OF
I. 4
V
,~'t;
~~/
........
1,
V
:
1.2
V
V
/
1.4
l.O
?P .~ .~ .~
V V /--"V V V V V V V V V V V V V V ,/' ~ 5- ::::--V / ~- :/V V '/ ~ t/ Y ~ ;:, ~
VV VVV /" ~V ~ ::/ ~ / V / -:/ -:/ /
-
0
.~ ~
0>
IV V V V V
WHEN
..........
~ ......
"'-
................
.........
~. "'
R = 2H
WHEN
Figure 6-SA. Plot of longitudinal bending-moment constant K , "
~; [ ~ sin Bcos J3
The load on the analogous column is
q
= 2 ~ ~ Ms rd = 20r2 ~ ~ ( ~
0
= 20r2
q
rtE!
~ sin <1»
1 - cos -
reEl ~ 0
EI
[2~
- 3 sin
~
+
]~
- Or3
= - 2 ~ ~ M.s ( ~ 0 EI
~~
rtfl ~ 0
cos -
~
)
M.nr. = Or { 2p Ih
3
S~2 ~ + BS~2 ~
- 12 sin2 p + 2p2 sin 2p ] } ~2 - 2 sin2 ~
Si~ B ) "
Finally, the combined moment is given by
=-
Ms + M;
= Or { re
cos cI>
+.
= 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
- Or3 [ 2 sin cI> - cos
+
The distance from the neutral axis to pOint A is
r2dcI> =
- 2 cos 4> - 4> sin 4» ] d4>
+ 4> cos <1»
~
9 _ ] p 0
]j!
2~
~ sin ~ cos ~
4r
- 3 sin p
rt
L [ 9~ sin p cos p + 3P2
[ 2 cos cI> - 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
Mp
2
1t
The summation of the horizontal components of the radial reactions on one-half of the saddle shown in Fig. 6-8 must be resisted by the saddle at = 1t. Then this horizontal force is given by
~ cos ~ + ~ ~ +
p sin p -
= Or
Design of Saddles
then
4
4
~
F = ~. 1t O( - cos sin + cos p sin <1» rd = ~ p r(1t - ~ + sin ~ cos ~)
o[ Finally
o[
Because of the symmetry the shear stress is zero at the top of the vessel; therefore, the direct load in the ring at the top of the vessel, Ptl may be found by taking moments on the arc ~ about the horn of the saddle. Then
(1 - cos
~)rPt = Or [ ,1t
P - 0 [ 1 t -
1t
-
1 - cos
Psin p 2( 1 - cos ~)
]
~
-
~2 sin ~
= Or (1
Then
- cos
] - (Mp - MJ
1t
Psin p 2(1 - cos ~)
-
cos P (M - MJ r(1 - cos B) Il
where
Psin B 2(1 - cos B)
cos
B] +
P-
P+
1/2 sin2 p ] sin ~ cos ~
P-
P+
1/2 sin2 p sin ~ cos ~
After the article had been published, certain refinements seemed desirable; therefore, the following has been added to take greater advantage of the inherent stiffness of these vessels. The methods outlined in the paper will give conservative results. The effective width of shell has been limited to 10t in order to prepare the chart of Fig. 6-2. It has been shown 5 that this effective width may be taken as 1.56 Yrf. That is, where 5t each side of the saddle or stiffener has been used, the more liberal value of 0.78 vff each side could be used. The values plotted in Fig. 6-5 for K1 cover conservatively all types of heads· between H = 0 and H = R. More liberal values are given in Fig. 6-5A for hemispherical and 2 to 1 ellipsoidal heads for values of HIL between 0 and 0.1. The minimum values of K1 given in Table 6-1 have not been listed for specific values of AIL and HIL; so they are conservative. Specific minimum values of K1 may be read from Fig. 6-5A.
or
K7 = -1t1 [
=
~
Appendix B
~) -(Mp - MJ
cos B ] +
P ]1t
The bending at the horn would change the saddle reaction distribution, and increase this horizontal force.
Substituting the value above for Pt , and solving for Pp gives
PIl = Q [
K8 =1 + cos 1t -
. 1 (M MJ - r( 1 - cos ~) Il-
1t
1 + cos 1t -
The direct load, PIl , at = ~, the point of maximum moment may be found by taking moments about the center. Then
r(PI} + Pt)
112 sin2 - cos cos 1t - ~ + sin ~ cos ~
cos P (Mil - MJ Qr(1 - cos P)
If the rings are adjacent to the saddle, K6 and K7 may be found in a similar manner, except that the static structure would become the entire ring split at the top and loaded as indicated in Fig. 6-9.
47
Part VII ~nchor
Bolt
Chairs~~~~~~~~~_ w
W
hen anchor bolts are required at supports for a shell, chairs are necessary to distribute the load to the shell. Small tubular columns (less than 4 ft in diameter) may be an exception if the base plate is adequate to resist bending. Otherwise, chairs are always needed to minimize secondary bending in the shell. For flat-bottom tanks, choose a bolt circle to just barely clear the bottom without notching it. For other structures, follow the minimum clearances shown in Fig. 7-1 a. The designer must evaluate anchor bolt location for interference with base or bottom plate.
W = total load on weld, kips per lin. in. of weld WH = horizontal load, kips per lin. in. of weld Wv = vertical load, kips per lin. in. of weld
= top-plate length, in., in radial direction
c
= top-plate thickness, in.
d
= anchor-bolt diameter,
e
= anchor-bolt eccentricity, in.
e min
= 0.886d
f
= distance, in., from outside of top plate to
e
= cone angle, degrees, measured from axis of cone
Z
= reduction
Critical stress in the top plate occurs between the hole and the free edge of the plate. For convenience we can consider this portion of the top plate as a beam with partially fixed ends, with a portion of the total anchor bolt load distributed along part of the span. See Fig. 7-2.
in.
s = ~2 (0.375g fc
+ 0.572, based on a heavy hex nut clearing shell by 1/2 in. See Table 7-1
c = [ :, (0.375g - 0.22d) ]1/2
fmin = dl2 + 118 g = distance, in., between vertical plates (preferred g = d + 1) [Additional distance may be required for maintenance.]
= chair height,
i
= vertical-plate thickness, in. = vertical-plate width, in. (average width for tapered plates) = column length, in. = bottom or base plate thickness, in.
k L
m p
Chair must be high enough to distribute anchor bolt load to shell or column without overstressing it. If the anchor bolt were in line with the shell the problem would be simple - the difficulty lies in the bending caused by eccentricity of the anchor bolt with respect to the shell. Except for the case where a continuous ring is used at the top of chairs, maximum stress occurs in the vertical direction and is a combination of bending plus direct stress. Formulas which follow are approximations, based on the work of Bjilaard.
load, kips; or maximum allowable anchor-bolt load or 1.5 times actual bolt load, whichever is less
R
= nominal shell
radius, in., either to inside or centerline of plate (radius normal to cone at bottom end for conical shells)
s
= stress at point, ksi
t
= shell or column thickness, in.
(7-2)
Chair Height
= design
= least radius of gyration, in.
(7-1 )
Top plate may project radially beyond vertical plates as in Fig. 7-1d, but no more than 1/2".
in.
r
- 0.22d)
or
edge of hole
h
factor
Top Plate
Notation a = top-plate width, in., along shell b
= weld size (leg dimension), in.
s
=
pet2 .[ 1.32 Z
1.43 ah2 + (4ah2).333
Rt 49
+ .031 ] (7-3) t'Rf
Table 7-1. Top-Plate Dimensions
Anchor Bolt Nut
Based on anchor-bolt stresses up to 12 ksi for 11/2-in.-dia. bolts and 15 ksi for bolts 1% in. in diameter or larger; higher anchor bolt stresses may be used subject to designer's decision.
d + t)Hole dia
~ H-:; ~" r: " -
--,.--+-....~,-:"'..
J
-
c
001,.
Top Plate Dimensions, in.
~TI---r-..:;---L---_~
~~
d 1112 13/4 2 2114
el
(d) Conical Skirt
Figure 7-1. Anchor-Bolt Chairs.
r---j
-L'I ,-\
I
,J
I
r
41/2 4% 5 5114
1.B7 2.09 2.30 2.52
p
0.734 0.919 1.025 1.145
19.4 32.7 43.1 56.6
~
Vertical Side Plates Be sure top plate does not overhang side plate (as in Fig. 7-1d) by more than 1/2" radially. Vertical-plate thickness should be at least jmin = 1/2" or 0.04 (h - c), whichever is greater. Another requirement is jk~ P125, where k is the average width if plate is tapered. These limits assure a maximum Ur of 86.6 and a maximum average stress in the side plates of 12.5
To.ol load
H
rcA)'-.. ~J
2112 23A 3 3114
Bolt Load, kips
emin Cm/n
I
,
d /
"L
a
If chair height calculated is excessive, reduce eccentricity e, if possible, or use more anchor bolts of a smaller diameter. Another solution is to use a continuous ring at top of chairs. ' If continuous ring is used, check for maximum stress in circumferential direction, considering the ring as though it were loaded with equally spaced concentrated loads equal to Pe/h. Portion of shell within 16t either side of the attachment may be counted as part of the ring. (Refer to Fig. 7-3) Note that the base plate or bottom is also subjected to this same horizontal force, except inward instead of outward. This is true even if a continuous ring is not used around the top of the chairs - but it should never cause any very high stresses in the base, so we do not normally check it. However, it is a good thing to keep in mind in case you have a very light base ring.
.c
(c) Flat Bottom Tank
'lil 1 11fo 1114
~l=d+ 1
and where earthquake or winds over 100 mph must be considered. Maximum recommended chair height h = 3a.
(b) Vertical Column or Skirt
(a) Typical Plan & Outside Views
f
I..J
~
Po,Holly Fixed Ends
Figure 7-2. Assumed Top-Plate Beam. Where: Z
= _____1..:...;.~0_ _ _ __
,1~ (
7f +
(7-4)
1.0
Maximum recommended stress is 25 ksi. This is a local stress occurring just above the top of the chair. Since it diminishes rapidly away from the chair, a higher than normal stress is justified but an increase for temporary loads, such as earthquake or wind is not recommended. The following general guidelines are recommended.
.,
Minimum chair height h =6", except use h =12" when base plate or bottom plate is 3/8" or thinner
Figure 7-3. Chair with Continuous Ring at Top. 50
ksi, even assuming no load was transmitted into the shell through the welds.
Assembly of Chair For field erected structures, ship either the top plate or the entire chair loose for installation after the structure is sitting over the anchor bolts. _ Where base plate is welded to skirt or column in shop, attach side plates in the shop and ship top plate loose for field assembly. See Fig. 7-4. Where base or bottom plate is not welded to shell in the shop, as for flat-bottom tanks and single pedestal tanks, shop attach side plates to top plates and then ship the assembly for field installation. When you do this, weld both sides at top of side plates so shrinkage will not pull side plate out of square. See Fig. 7-5. Welds between chair and shell must be strong enough to transmit load to shell. 1/4" minimum fillet welds as shown in Figs. 7-4 and 7-5 are nearly always adequate, but you should check them if you have a large anchor bolt with 'a low chair height. Seal welding may be desired for application in corrosive environments. Assume a stress distribution as shown in Fig. 7-6 as though there were a hinge at bottom of chair. For the purpose of figuring weld size, the base or bottom plate is assumed to take horizontal thrust only, not moment. Note that loads are in terms of, kips per inch of weld length, not in terms of kips per square inch stress. Critical stress occurs across the top of the chair. The total load per inch on the weld is the resultant of the vertical and horizontal loads.
Figure 7-6. Loads on Welds. Formulas may also be used for cones, although this underrates the vertical welds some. Wv
WH = W
=
P
(7.;5)
Pe
(7-6)
a + 2h
ah + 0.667h 2
= y'Wv
+
Wtt
(7-7)
For an allowable stress of 13.6 ksi on a fillet weld, the allowable load per lin. in. is 13.6 x 0.707 = 9.6 kips per in. of weld size. For weld size w, in., the allowable load therefore is 9.6w
~
W
(7-8)
Design References H. Bednar, "Pressure Vessel Design Handbook", 1981, pp. 72-93. M.S. Troitsky, "Tubular Steel Structures", 1982, pp. 5-10 - 5-16. P.P. Bjilaard, "Stresses From Local Loadings In Cylindrical Pressure Vessels," ASME Transactions, Vol. 77, No.6, 1955. P. Buthod, "Pressure Vessel Handbook," 7th Edition, pp. 75-82.
Figure 7-4. Typical Welding, Base Plate Shop Attached.
-:&16
Figure 7-5. Typical Welding, Base or Bottom Field Attached. 51
, • • •D •
Part VIII Design of Fillet Welds
•
esign of butt welds is closely controlled by weld details and jOint efficiencies clearly specified in various codes and specifications. Design of fillet welds, however, is not so clearly outlined. The following pages are intended to fill the gap. While referring to the following pages and designing fillet welds, the designer is encouraged to keep in mind actual shop and field welding practice and the quality of fillet welds that can consistently be expected. The size and length of the weld as well as the allowable stresses used in their design should reflect the actual shop and field welding and not necessarily the value used here . Size of an equal-leg fillet weld is the leg width W of the largest 45° right triangle which fits in its cross section. They are referred to by their leg sizes, such as a 1/4 in. fillet weld.
following: 1. Use of 45° (equal leg) fillet welds whenever possible 2. Minimum size of fillet 3. Lower cost of down welding position 4. Locate weld to eliminate eccentricity 5. Balanced welds to control distortion 6. Avoid locating welds in highly stressed areas 7. Readily accessible Use the smallest size of fillet permitted (see Fillet Weld Limitations). Flat fillets 5/16" and smaller are normally made in one pass and are more economical than larger fillets. Generally, the fillet with the least cross-sectional area is the most economical. Increasing the size of a fillet weld from 1/4" to 3/8" more than doubles the amount of filler metal, but the strength only increases 500/0. A gap also requires additional filler metal.
I
Figure 8-1. Fillet-Weld Sizes (Leg Dimensions) . .
~
I
,
Size of an unequal length fillet weld is described by the leg lengths of the largest right triangle which fits in its cross section, such as a 3/8" by 1/2" fillet weld. The strength of a fillet weld is assumed to equal the allowable shearing stress times the throat area of the weld. The throat area of a weld is the length of weld times the theoretical throat distance, which is the shortest distance from the root of the weld to the theoretical weld's surface. Some codes, however, define the throat distance differently. AWWA defines the throat as .707 times the length of the shorter leg of the fillet weld. AISC distinguishes between welding processes to be used when determining throat distances (e.g. AISC 1.14.6.2). The designer should check to see what code, if any, applies to the work. In these papers, however, the fillet weld throat dimension for an equal-leg fillet is assumed to be the leg length times 0.707 (i.e. cos 45°).
" triangle volumes
9 triangle volumes
13 friangle volumes
Figure 8·2. Volumes of 1-ln. Long Welds. Flat welding position is the most economical and overhead the least. For example, the relative costs of 3/8" fillets for different positions are: lap flat flat fillet vertical fillet overhead fillet
1000/0 11 00/0 240 0/0 250 0/0
The costs can vary according to weld procedure used. Specify shop welding whenever practical. The fitted-up material can normally be repositioned easier in the shop.
Types of Fillet Welded Joints Single-fillet welded joints Strength depends on size of fillet. Do not use when tension due to bending is concentrated at root of weld.
Economy of Welding Economical design of fillet welds includes the
53
Allowable Loads on Fillet Welds
Do not use for fatigue or impact loading. Difficult to control distortion.
Stress in a fillet weld is assumed as shear on the throat area, for any direction of applied load. Many codes express the allowable shear stress for fillet welds in psi on the throat area. It is more convenient, however, to express the strength of fillet welds as allowable load f, kips per lin. in. for 1" fillet. The following formula may be used to convert allowable shear stress on throat area to allowable load for 1" fillet with equal leg lengths:
Figure 8·3. Types of Single Fillet Welds.
Double-fillet welded joints Used for static loads. Economical when fillet size is 1/2" or less. Lap joint maximum strength in tension when length of lap equals at least 5 times the thickness of thinner material.
Figure
8~4.
f
= 0.707
x allowable shear stress, ksi
(8-1)
Since transverse welds are stronger than parallel (or longitudinal) welds some codes permit different allowable stresses for them. API 620 6th Edition and AWWA D100-84 are two codes that have different allowable stresses for the two types of welds. API 650 8th Edition and AISC 9th Edition, however, make no distinction between transverse welds and parallel welds and use the same allowable stress for both. The designer is cautioned to check which code applies to the work at hand as well as the most recent edition of the code to see if their approach to these types of stresses has changed. In the following pages, however, for the sake of completeness, a distinction will be made between the two types of stresses, fp and ft. When a jOint has only transverse forces applied to the weld, use the allowable transverse load ft. If only parallel forces are applied to the weld, use the allowable parallel load fp• If one of the forces is parallel and the other forces are transverse, use the allowable transverse load when the resultant force is found from Eq. 8-3. New specifications on allowable stress for fillet welds are given in Section 8 of the latest revision of AWS Structural Welding Code, 01.1. Current AISC specifications also refer to: 1. allowable stress at weld for both weld metal and base metal 2. minimum length of fillet weld 3. minimum size of fillet weld 4. maximum size of fillet weld 5. end returns or "boxing of welds" 6. spacing of welds 7. fatigue loading of welds
Types of Double Fillet Welds.
Double-fillet welded corner joint Complete penetration and fusion. Used for all types of loads. Economical on moderate thickness.
Figure 8·5. Corner Joint. Welds transmit forces from one member to another. They may be named according to the direction of the applied forces. Parallel welds have forces applied parallel to their axis. Fillet weld throat is stressed only in shear. Parallel welds may also be called longitudinal welds.
Figure 8-6. Parallel Weld.
Notation
Transverse welds have forces applied at right angles to their axis. Fillet weld throat has both shear and normal (tensile or compressive) stresses. Transverse welds are about 33 0/0 stronger than parallel welds.
A
= cross-section area, sq. in., of member transmitting load to weld
Aw = length, in., of weld b
= length,
C
= distance, in., from neutral axis to outer parallel surface or outer point
in., of horizontal weld
= horizontal component of c, in. C v = vertical component of c, in. d = depth, in., of vertical weld f = allowable load on fillet weld, kips per lin. in. per in. of weld size
Ch
Figure 8·7. Transverse Weld.
54
r
fb fp
= bending stress, ksi = allowable parallel load on
ft
=
f to
= =
I 10 Ix Iy J
= = = =
Jw
=
L M
=
n
p
= =
Q
= =
r
=
S
=
Sw = t
T
v
=
= =
w W = Wb = Wh = Wq = Ws = Wsa = Wt =
Wv = x
y
= =
Fillet weld size w, in., is found by dividing the force W, kips per lineal inch, on the weld by the allowable load f (kips per lin. in. for 1" fillet) for the weld. W=W (8-2) f
fillet weld, kips per lin. in. per in. of weld size allowable transverse load on fillet weld, kips per lin. in. per in. of weld size torsional stress, ksi moment of inertia, in.4, of member transmitting load to weld or of weld subjected to torque moment of inertia about 0 axis, in.4 moment of inertia about x axis, in.4 moment of inertia about y axis, in.4 polar moment of inertia, in.4, of member transmitting load to weld polar moment of inertia, in. 3, of weld lines subjected to torque column length, in. bending moment, in.-kips number of plate sides welded or number of welds loaded allowable concentrated axial load, kips statical moment of area, in.3, above or below a point in cross section, about neutral axis least radius of gyration, in. section modulus, in.3, of member transmitting load to weld or of weld subjected to moment section modulus, in.2, of weld lines subjected to bending moment plate thickness, in., or thickness, in., of thinnest plate at weld torque, in.-kips vertical shear, kips fillet weld size (leg dimension), in. total load on fillet weld, kips per lin. in. of weld bending force on weld, kips per lin. in. of weld horizontal component of torsional force on weld, kips per lin. in. of weld longitudinal shear on fillet weld, kips per lin. in. of weld average vertical shear on fillet weld, kips per lin. in. of weld actual shear on fillet weld, kips per lin. in. of weld torsional load on fillet weld, kips per lin. in. of weld vertical component of torsional force on weld, kips per lin. in. distance from y axis to vertical weld distance from x axis to horizontal weld
Table 8-1. Formulas for Force on Weld Type of Loading
Common Design Formula for ormulas for Force on Weld
. Stress, psi
Tension or Compression
Vertical
Shoar
Bending
Torsion
Longi~udinal
Shear
P A
V A
K/Kips per In.
w
p
- Aw
v w-s~
M
5
Tc
T
w _ Tc t
Jw
YQ
tr
Force W on a weld depends on the loading and shape of the weld outline. Table 8-1 shows the.. basic formulas for determining weld forces for various types of loads. Combining forces: There may be more than one force on the weld, such as bending force and shear force. It is usually easier to determine each force independently and then combine vectorially to obtain a resultant force. All forces which are vectorially added must occur at the same position in the weld. Be sure to find the position on the welded connection where the combination of forces will be maximum. To simplify calculations increase parallel forces by the ratio ftlfp before combining to account for the lower allowable parallel shear stress specified by some codes.
Combined Loads on Welds It is necessary to designate the size and length of fillet welds. Since neither are known, it is usually simpler to assume the length and then calculate the size.
55
w =
~ = ~ = 0.25" Use 1/4" fillet f
9.6
Weld volume = (1/4)2 x 12.5 = 0.39 cu. in. 2
w
TryA w2 =5+5=10" W2
=~
W2
=
Aw2
Figure 8·8. Forces on Weld Combined.
=
~ = 0.312"
Use 5/16" fillet
9.6
Use 1/4" fillet on three sides because of less weld volume. Check fillet size (see Fillet Weld Limitations).
(8-3) Shear load is considered uniformly distributed over the length of weld. Force formula Ws = VIAw from Table 8-1 gives average shear force. Use average shear force when combining with bending force or torsional force. However, if the average shear force about equals or exceeds the bending or torsional force, determine the actual shear force distribution to aid in locating the maximum combined force. The actual shear force per weld at any point can be determined from:
Refer to Fig. 8-8 for explanation of W1 , W2 ,and W3 • The total force shall be determined in accordance with the applicable code. Simple tension or compression loads: The force W, kips per inch of weld, is the load P divided by the length Aw of weld. As shown in Table 8-1 the tensile or compressive force on a weld is: W=
f
10
Weld volume = (5/16)2 x 10 = 0.49 cu in. 2
To determine the resultant force for combined forces, use Eq. 8-3. If only two forces exist, use 0 for one force.
W = tfW 1 2 + W2 2 + [ W3 (ft lfp)1 2
~
= ~ = 3.0 kips per lin. in.
P Aw
(8-4)
(8-5)
With this force W, the required fillet weld is calculated from Eq. 8-2. Example: Find size of fillet welds for the connection shown in Fig. 8-9. Assume Aw + 2112 = 12112".
=5
For example, the average shear force and actual shear force distribution are compared for a rectangular member in Fig. 8-10.
+ 5
mox .hear force
lf2 ~ ~I~~·:1·¥ t
W
1 'to-
.ectlon thru member at weld
30,000 lb.
Figure 8..9. Tension-Member Connection 1 •
= ~ = 2.4 kips per lin.
Average shear force Ws
=~ Aw
Wsa at 1
in.
12.5
= VQ = nl
VQ tQ 2 4
2
(t1~)
Wsa at 2 = VQ = ~ = 0 nI nI
=
actual
.hear forc.
diagram diagram
Figure 8·10. Shear Distribution at Welds.
Referring to API 650 the allowable basic shearing stress of an E60 electrode fillet weld is 13.6 ksi. f = (.707)(13.6 ksi)(1 inch weld) = 9.6 kips/inch/1 inch weld
W = ~ Aw
avg
.hear force
=
1AISC for E60 electrodes would give f (.707)(.3)(60) 12.7 ksi shear stress with max shear stress on base metal of .4 yield of base metal.
=
JL.
(8-6)
2d
= 3V
= 1.5Ws
(8-7)
4d (8-8)
Bending or torsional load may be applied to the same weld outline.
56
Table 8·2. Properties of Weld Outlines (Treated as a Line)
r Bending and shear load on a weld
Torsional and shear load on a weld
Bending (abollt x-x axi s)
Outl ine of Welded Joint
dG-- x ..Jt.. d[+-+x
Weld outline
Figure 8-11. Moment and Torque on Weld.
l
[1F~~,Y-
d
I
_..J.
~;2(b+dl
d(3b l + d2 ) 6
J
Sw • bd
2 l J w • b{b + 3d )
w
3
w
..
6
-'--j
b
(8-9)
J w " 12 in.'
2 S .. -d
dE.:--x t71 j
d'
d in.:Z Sw - 6
~
In the figure with the bending load, the weld must transfer the same stress as in the member at the connection. This stress can be determined using the common formula for bending stress.
Torsion
). ~(4b + d)
S (
w top
6 d' (4b,. d' • Sw(bott)· 6(2b+d) J w
~l.6b2dl 12(b
+d)
2[b+d) -_._---+._---------_ ... _......_._--_.._-
In the connection with the torsional load, the weld wants to rotate or twist about the center of gravity of the weld group. The stress in the weld can be found from:
Ef
(max forc:e at botl)
y'"
d
x
I
---:t .
S
w
r.
bd+ -d' 6
b+d
.J x- 2L
(8-10)
~
d~y
However, before using these formulas, it is necessary to determine the section modulus S or polar moment of inertia J of the weld without knowing its width (size). A simple way to determine the section modulus or polar moment of inertia of the weld is to treat the weld as a line. The property, such as section modulus S, of any thin area is equal to the property of the section when treated as a line Sw times its thickness w.
_'d y
2
Y-t+"2tJ
-
b
r-1
dEUx dE-6-
(8-11 )
x
~
(:2b· d)' b'(b.d)'
- --I w,.. .-- 12 2b + d --.- ...-----_..
S ( ) d(2b+d) w top" 1 d2 (2b+d) J (b+2d)' _d'(b+d)l b+ 2d Sw(bott)- 3(b:d) w 12 D
fmox force ot Dott)
d2 Sw - bd +3
s • 77d w
4
l
J
.. (b +d)' w
J w
6
_ 77d' 4
Revised and expanded outline properties given in Lincoln Electric pub· lication 0810.17. Solutions to Design of Weldments. p. 3.
The common formula for bending stress can now be used to find the bending force on the weld. Bending and shear forces on a welded connection are combined vectorially after determining each force
(8-12)
independently from Eqs'. 8-12 and 8-6. Determine the combined force Won the weld using Eq. 8-3. Make sure you have found the position on the welded connection where the combination of forces will be maximum. See Fig. 8-10 for shear force distribution. Calculate the required weld size from Eq. 8-2.
Properties of sections treated as lines for typical weld outlines are shown in Table 8-2. The method for determining these properties is given later. When designing welds using the line method, select the weld outline with care. Several combinations of line welds will produce the required property Sw or J w ' However, select the weld outline where the weld distribution is consistent with the load distribution in the member at the connection. For non-circular members (such as beams, channels, etc.) resisting torsion loads, transverse forces on the weld are present in addition to parallel forces computed from Tc/Jw. These transverse forces are the result of the non-circular cross section warping and should not be neglected.
Figure 8·12. Bending and Vertical Shear on Welds.
57
Example: Find size of fillet weld on clip loaded as shown in Fig. 8-13. Use f t = 8.9 kips per lin. in. and fp = 6.4 kips per lin. in. from API 620. Assume length of fillet = 10" (5" each side)
4k
Sw from Table 8-2
= cJ2 = 52 = 8.33 sq. in. 3
Bending force Wb =
3
M = Sw
4 x 3 8.33
= 1.44 kips per lin. in. Avg shear force Ws
Figure 8-14. Torque and Shear on Welds.
= Aw X = ..i. 10
= .40 kips per lin.
The horizontal torsional force component is
in.
Wh
= If.Jt.
(8-14)
Jw
The vertical torsional force component is
Wv
Figure 8-13. Loaded Clip. ft fp
= (.707) (12.6 ksi) (1
= (.707) (9.0 ksi) (1
inch weld) inch weld)
Resultant force W =
= B.9
kips/inch/1 inch weld inch weld
Wb 2 + [ Ws ( :; )
(8-15)
Jw
Equation 8-3 can now be used to find the resultant force on the weld. Increase the forces parallel to the weld at the point considered by ftlfp before combining. The required fillet size is calculated from Eq. 8-2.
= 6.4 kips/inch/1
y'
= B2n
r
Example: Find fillet size for connection 2
3"
0/1.44 + [ 0.40 ( ::: ) ]'
Fillet size
= 1.544 kips per I.in. w = W = 1.544 = .173" ft
3*"
Sk shown in Fig. 8-15. Use ft lin. in.
in.
= fp = 9.6
kips per
8.9
Use 3,/16" fillet
w
Note that the designer is still cautioned to check the shear capacity of the plate.
C
h
~~u>l
Torsional and shear forces on a welded connection are combined vectorially after determining each force independently from Eq. 8-6 and the torsional force formula
cg
-J '
(8-13) .
(b)
"i
Figure 8-15. Loaded Bracket. From Table 8-2,
Maximum torsional force occurs at the most distant
x
weld fiber measured from the center of gravity of the weld outline. This distance to the outer fiber is c in Eq. 8-13. The direction of the ,torsional force Wt may be other than horizontal or vertical. By resolving the torsional force into vertical and horizontal components, the problem of combining forces is simplified. Resolve the torsional force into components by using the horizontal and vertical components of dimension c as indicated by Eqs. 8-14 and 8-15.
=
Jw =
b2
2 _ _ = 0.75" = _ _3_ 2b + d 2 x 3 + 6
(2b + c/)3 _ b2 (b + d)2 2b + d 12
= (2
x 3
12
58·
+
6)3 _ 3 2 (3 + 6)2
2 x 3 + 6
= 83.25
in.3
Find components of maximum torsional force at 1. Cv = Ch
T
3"
=3
-
x = 2.25"
By Eq. 8-14, the horizontal component of torsional force is
Wh =
Figure 8-16. Examples of Built-up Members. Longitudinal shear force at any position along the length of beam is calculated from
IQv. Jw
= 5{3.75 +
2.25) (3) 83.25
=
Wq
=
VQ
(8-16)
, ni
Longitudinal shear force may vary along the length of the beam. The vertical shear diagram for the beam can be used as a picture of the amount and location of welds between flange and web.
1.08 kips per lin. in.
NOTE: (3.75 + 2.25) is the distance from the point load to the centroid of the weld.
t
By Eq. 8-15, the vertical component of torsional force is
Wv = IQb.
~
,
1 L
~
til"" 11111\ Seom 3
Seam 2
Seam 1
Jw
~
= 5(3.75 + 2.25)(2.25) 83.25 = 0.810 kips per lin. in.
Figure 8-17. Shear in Beams.
Find average vertical shear force:
Ws
Notice there is no shear in the middle portion of beams 1 and 2; therefore, little or no welding is required in this portion. When there is a difference in shear along the length of beam, as in beam 3, the welding could vary in this same ratio along the length of beam. This is why continuous welding is sometimes used at the ends of beams and reduced size or intermittent fillet welds used throughout the rest of the beam;
= - V = - -5- 3 + 6 + 3
Aw
= 0.416 kips per lin. in. Combine forces using Eq.8-3.
W = y(00810 + 0.416)2 + [ 1.08 (
~::
)] 2'
Built-up members subject to axial compression: Welds joining the component parts of a built-up compression member, such as a cone roof tank column, are also stressed in longitudinal shear. Determine this longitudinal shear force Wq from Eq. 8-16 using the shear V at any position along the member as given by Eq. 8-17 or 8-18.
= 1.635 kips per lin. in. Calculate weld size using Eq. 8-2. W
= W f
= 1.635 = 0.17" 9.6
Use 3/16" fillet.
Built-up members subject to bending: Welds attaching the flange to the web are stressed in longitudinal shear and must be adequate to transfer the calculated longitudinal shear force. "Note that if we had been using API 620 where ft = 8.9 kips per lin. in. and fp = 6.4 kips per lin. in., this equation would be
(::!)
= 0.01P for Ur < 60
(8-18)
Also at each end of a built-up compression member, use a total length of continuous fillet weld equal to the maximum width or depth of the member or 4", whichever is greater. Fillet weld size at any position along the beam or column is determined from Eq. 8-2 with the longitudinal shear force Wq at the same position.
Welds in Built-up Members
(.810 + .416)2 + [ 1.08
(8-17)
V
Check fillet size (see Fillet Weld Limitations).
W =
V = 0.02P for Ur> 60
r
W
= W =
f
59
~ fp
(8-19)
Table 8-3. Length and Spacing of Intermittent Welds Continuous Welds 0/0
Length of Intermittent Welds and Distance Between Centers, In.
60 57 50 44 43 40 37 33 30 25 20 16
3-5 2-4
Maximum clear space between intermittent fillet welds depends on the component parts of the built-up member. The clear space between welds must be close enough to prevent local buckling of the component parts when the loading develops the full strength of the built-up member.
4-7 4-8 4-9
3-6 ,
Example: Find size and spacing of fillet weld joining plate and angle of built-up member shown in Fig. 8-19. Use ft = 8.9 kips per lin. in., fp = 6.4 kips per lin. in.
3-7 2-5
4-10 3-8 3-9 3-10 3-12
2-6 2-8 2-10 2-12
4-12
O'170 kips ~er ft
~ 7.33'
~...Ili:. O.612"E~1 ..
1.575" .~ 2" x ,~ .. x 3/16"
~
"
Use intermittent fillet welds when the calculated leg size is smaller than the minimum specified in Table 8-5. The calculated size divided by the actual size used, expressed in percent, gives the length of weld to use per unit length: 0/0
Intermittent weld lengths and distances between centers for given percentages of continuous welds are shown in Table 8~3. 12"
12"
r
2".J
6"
Vi
2-12
~
~2"
~2"~&
•• r
W
012=W
6"
12"
I L
~.I
&
l-2"
Shear diagram for beam shows that welding for longitudinal shear could be reduced in center portion of beam. Because the vertical shear is small, design the welds for maximum shear throughout the length of beam. The longitudinal shear force is
W = VQ = 0.623(0.1875)6(0.518) q nI 1(1.094)
_~
= 0.332 kips per lin. in.
9
The continuous weld size required is
..r .....
w
Figure 8-18. Spacing of Intermittent Welds.
Minimum size fillet from Table 8-5 is 3/16".
Compression
rolled shape flange
24"
plate flange
22t (12" max)*
rolled shape flange
24"
continuous weld
= 0.052
0.1875
Table 8-4. Maximum Clear Space Between Intermittent Fillet Welds (Carbon Steel BUilt-up Members)
Tension
6.4
(Use fp because longitudinal shear force is parallel to weld.)
0/0
24t (12" 'max)*
= ~ = 0.332 = .052 fp
Minimum length of fillets for intermittent welds is 2" or 4w, whichever is greater. Selecting the longest fillet possible is usually the most economical. However, do not exceed the maximum clear space between fillets in Table 8-4.
plate flange
• 0.623 kips
Figure 8-19. Plate Girder.
= calculated leg size (continuous) x 100 (8-20) . actual leg size (intermittent)
,6 6 ·b ~I .p...
0.17(7.33) 2
x 100
= 27.70/ 0
Minimum length fillet permitted for intermittent welds is 2". Maximum clear space between fillets is, from Table 8-4, 22 x 3/16 = 4.1". Maximum spacing with 2" fillet = 2" + 4.1" = 6.1" . Use 2" - 6" intermittent fillet on one side. This provides 33 0/0 (Table 8-3) continuous weld which is more than adequate to transfer the calculated longitudinal shear.
Fillet Weld Limitations
* Many of the built-up members we use have an assumed flange. This
Minimum size fillet: The calculated weld size may be small. To eliminate cracks resulting from rapid cooling, it is best not to put too small a fillet on a thick plate. Follow Table 8-5 for minimum sizes.
flange, usually part of a roof, bottom or shell, may be partially restrained from local buckling when the maximum load is applied. When the built-up member has restraint on the flange, the clear space between fillet welds could be increased to about 32t maximum.
60
3 d - w1y -
From handbook,
Table 8-5. Minimum Size Fillets
12
When w is small, let Iy = 0
Thickness' ~ ~
>
Minimum Leg Size Of Fillet2
J
3/16" 1/4"3 114"3,4
112" 3/4" 3/4"
Jw
b
b
~
'2
'2
Ix
-,-_x
E=~31-:1'~o Ix w
of roll.d
lec:tion
max fillet· t
(8-22)
12
= 10
+ Ay2 = 0 + wby2
S
= wby2
= Ix
-:- y
= wby
Treated as a line, then Sw = ~ = by about x axis
w
Minimum length of fillets for strength welds: 11/2" or 4w, whichever is greater (Use 2" or 4w for intermittent welds)
(8-23)
From handbook 3 - wb IY -
Spacing of Fillet Welds: 1. When bars or plates are connected only by a set of parallel longitudinal fillets, the length of those welds should not be less than the perpendicular distance between those two welds. 2. When fillet welds are used for end connections, the distance between them must not be greater than 8 inches unless transverse bending is otherwise prevented.
12
J
= Ix
+ Iy
= wby2
+ wb
3
12
Treated as a line, then J w = ,{ = by2 +
w
l!!...
(8-24)
12
By adding the properties of the two basic lines in Figs. 8-21 and 8-22, properties for other straight line outlines may be determined. For example, find Sw and J w for the outline in Fig. 8-23:
Determining Weld Outline Properties Properties Sw and J w of a weld outline when treated as a line are nearly equal to the section modulus or polar moment of inertia divided by the width w of the weld. When w is small, say 100/0 of d, the error is usually less than 10/0. The properties Sw and J w in Table 8-2 are determined as follows: From handbook
y
w
Figure 8-22. Horizontal Weld.
y
Figure 8-20. Weld Size Limited to Plate Thickness.
x
= ,{ = s!!..
j
t
1x"-- -wcJ3 12 S = Ix -:- Q 2
+ 0
12
I
max fill.t - t
= wcJ3 12
From handbook, for a horizontal 3 weld, 10 = w b
o
Maximum size fillet for strength welds:
~dg •• fPI.t.
+ ~
Treated as a line, then
1Thickness of thicker part to be joined, 2Leg size of fillet need not exceed thickness of thinner part to be joined. 3A minimum fillet of 3/16" is acceptable provided 200°F preheat or surface examination of the weld (PT,MT) is performed. 4AWS 01.1-82 or AISC require a.minimum 5/6" fillet.
dge
=~
= wcJ2 6
Treated as a line by dividing by w, then Sw = ~ = cJ2 about x axis (8-21) w 6
II
Figure 8-21. Vertical Weld.
]I
Figure 8-23. Combination of Welds. 61
Ix
=2
wcJ3 + 2 (Wby2) 12
= wcJ3
Cautionary Note
+ 2wby2
6
Some designers and engineers are not aware of a form of cracking called lamellar tearing, which can occur beneath highly stressed T-joints in steel plate. Plate forced to deform plastically in the thruthickness direction by welds which are large, mUltipassed, and highly restrained can decohere at a plane of microscopic inclusions. A crack may then progress from plane-to-plane in a terrace-like fashion. While lamellar tearing is not frequent, even one incident has the potential of becoming a serious problem. Since there are means to minimize the hazard, it behooves the engineer to take every precaution by optimizing joint design and welding procedure selection. Where these factors cannot be controlled, it may be necessary to use special steels. The reader is referred to the following sources for guidance in designing against lamellar tearing: 1. Engineering Journal, Third Quarter, 1973, Vol. 10, No. 3, pages 61-73. American Institute of Steel Construction, Inc., 1221 Avenue of the Americas, New York, New York 10020 2. Bibliography on Lamellar Tearing, Welding Research Council Bulletin 232. Welding Research Council, 345 East Forty-Seventh Street, New York, New York 10017
When y = Q,
2
Ix
+ wbcJ2 = wd2 (d + 3b) 626
= wcJ3
3 _ wb wb3 - 0 + 21y 12 6
Sw =
(iL) 1.. = 2wcJ2 (d + 3b) w d 6wd
= cJ2 + bd about x axis 3
Jw
= .i.... = Ix
= b3
+ Iy = wcJ2 (d + 3b) + wb 3
w
w
(S-25)
+ 3bd2 + cJ3
6w (S~26)
6
62
Part IX Inspection and Testing of Welded Vessels necessary for the test is accomplished by means of a vacuum box placed on the top side. This box has a glass top and is open on the bottom. The portion of the weld to be inspected is brushed with a soapy solution, the box is fitted over it, and a vacuum created in the box. The weld is inspected through the glass top for leak-indicating bubbles.
treatise on the subject of defects in welded vessels and their detection is beyond the scope of this work. But an acquaintance with some of the available inspection and testing tools may serve to dispel the mystery of unfamiliar terms. In the interest of economy, the refinement of inspection and testing must be in tune with the degree of perfection necessary for various classes of work. For example, a pressure vessel storing a lethal substance, or one constructed of a special material known to be crack sensitive, may require as a minimum that 1000/0 of all main joints be radiographed. On the other hand, simple structures such as oil and water tanks, constructed of readily weldable materials, usually require only spot examination. In general, it is safe and wise to follow the inspection requirements of the applicable codes. First, let us distinguish between hydrostatic or overload testing to demonstrate strength or liquid tightness, and inspection to determine weld quality.
A
Inspection for Weld Quality Prior to the beginning of any welding, weld qualification and welder certification tests should be performed. These tests insure that the type of welds proposed are adequate for the application and that the workers proposed to be used are capable of applying the required welds. VISUAL INSPECTION is usually the first stage in the inspection of a finished weld, regardless of any other tool that may be employed. Visual inspection can determine conformity with specifications as to dimensional accuracy, extent, etc. It can also reveal noticeable surface flaws, such as obvious cracks, . surface porosity, undercutting of parent metal, etc. In some types of work, visual inspection is the only inspection performed; e.g., welds subjected only to compression as in a tubular column, or low-stressed fillet welds. But for most important structures, further inspection is usually required for the main joints, on which the strength of the structure depends. Some of the more commonly used methods are described below. RADIOGRAPHY is an inspection method that shows the presence and nature of macroscopic defects or other discontinuities in the interior of welds. Just as in the case of medical X-rays with which we are all familiar, radiography utilizes the ability of X-rays or gamma rays to penetrate objects opaque to ordinary light. Radiograph films can reveal slag (non-metallic) inclusions, porosity or gas pockets, cracks, lack of fusion, inadequate penetration, and even surface defects, such as undercut. However, welds are rarely perfectly free of all minor defects nor do they need to be. As a result, the inspector must have a good background of experience in reading films, and a knowledge of standards. The various construction codes, such as AWS and ASME, define limits of acceptability. MAGNETIC PARTICLE INSPECTION is an aid to
Testing for Strength and Tightness Required overload tests are clearly outlined in the various governing codes. Whenever the structure itself, its supports, and foundation conditions will permit, the overload test is usually hydrostatic, i.e., the structure is full of water when the overload,if any, is applied. For the water and oil tanks of Volume 1, no overload can be applied other than that inherent in any difference between the specific gravity of water and that of the product to be stored in service. The normal cone roof will withstand pressures only slightly greater than the weight of the roof plates. It will not withstand hydrostatic pressure due to overfilling. Hence, the water test level is limited to the top capacity line. The testing of the flat bottom, however, may warrant brief comment. The liquid tightness of a flat bottom is usually demonstrated by means of a soap bubble test. A soapy liquid is brushed on the weld and a small differential positive pressure created on the opposite side of the plate. Leaks in the weld will be indicated by bubbles as the air passes through the leak. Since the bottom of a tank is inaccessible from the underside, the differential pressure
63
When a FLUORESCENT PENETRANT is used, the indications will fluoresce when exposed to near ultra violet or black light. DYE PENETRANT utilizes visible instead of fluorescent dyes. As the dye penetrant rises from the flaw by capillary action, it stains the developer (usually a chalky substance) and clearly marks the flaw. ULTRASONIC INSPECTION requires a. great deal of explanation for even a rudimentary understanding of how it works. Briefly, ultrasonic testing makes use of an electrically timed wave of the same nature as a sound wave, but of. a higher frequency, hence the name ultrasonic. The sound wave or vibrations are propagated in the metal being inspected and are reflected back by any discontinuity or density change. The search unit contains a quartz or similar crystal, which can be moved over the surface much like a doctor's stethoscope. The search unit applies energy to the metal surface in short bursts of sound waves for a very short, controlled period of time. The crystal then ceases to vibrate for a sufficient period of time to receive the returning echoes. The reflected signals are indicated on a cathode ray tube or oscilloscope. From the reflection or oscilloscope pattern, a trained operator can determine the distance to the discontinuity and some measure of its magnitude. Ultrasonic testing is a valuable tool for certain applications. But it must be used only by an operator skilled in the interpretation of the reflection patterns. In addition to the above methods the following can be used: Eddy Currents, Acoustic Emission, Video Enhancement, Ultrasonic Holography, and Neutron Radiography. Only technically qualified personnel should use these methods.
visual inspection for surface defects too fine to be detected by the naked eye, plus those that lie slightly below the surface. With special equipment, more deeply seated discontinuities can be detected. The method is applicable only to magnetic materials. It will not function on non-magnetic materials such as the austenitic stainless steels. The basic principle involved is as follows: When a magnet,ic field is established in a ferro magnetic materiai containing one or more discontinuities in the path of the magnetic flux, minute poles are set up at the discontinuities. These poles have a stronger attraction for magnetic particles than the surrounding surface of material. Normally the area to be inspected ' is magnetized between two "prods" by introducing high amperage current or some other convenient means. Then the area is covered with a powder of finely divided magnetic particles " These form a visible pattern of any discontinuity due to the stronger attraction at those points. LIQUID PENETRANT INSPECTION is another method for detecting surface discontinuities too small to be readily seen by the naked eye. It is particularly useful on non-magnetic materials where the magnetic particle method is ineffective. The method utilizes liquids with unusual penetrating qualities, which, when applied to a previously cleaned surface, will penetrate all surface discontinuities. The surface is then cleaned of all excess penetrant and a developer applied. Penetrant that has entered a crack or other discontinuity will seep out, make contact with the developer and indicate the outline of the defect. There are two principal types of penetrant used;
64
Part X Appendices A. B. C. D. E. F. G.
Trigonometry Elements of Sections Properties of Circles and Ellipses Surface Areas and Volumes Miscellaneous Formulas Properties of Roof and Bottom Shapes Columns for Cone Roof Framing - Flat Bottom Storage Tanks H. Conversion Factors Specific Gravity and Weights of Various Liquids A.P.1. and Baume Gravity and Weight Factors Pressure Equivalents Wire and Sheet Metal Gages
65
A-1 A-2 A-7 A-8 A-10 A-12 A-13 A-15 A-17 A-18 A-18 A-19
Appendix A. Trigonometry
TRIGONOMETRIC FORMULAS Radiul AF
-1
TRIGONOMETRIC FUNCTIONS
- aln l A + COil A - lin A cOlec A - COl A lec A - tan A cot A
~/{a
H
"/~F
Sine A
COl A - c;c;s;cA 1 - COtA -
Coaine A
_ ain A _ _1_. _ lin A cot A _" 1-1lnl A _ AC ,t an A lee A
Tangent A
_~_-1--linAaecA COl A
- FO
cot A
COl A Cotangent A - lin A -
1
iiriA -
-HG
COl A cOlee A
1
tan A
Secant A
COl A tan A - " 1-COI I A - BC
-AD
- 8i'n'A - CciI"A cot A - COl A -
COlecant A
1
-AG
i'i'nA
.~~~
RIGHT ANGLED TRIANGLES
~ c
-
CI - b l
-
el
-
CI -
al
+ b2
al b
a
Abe
l
al
Required
Known
A
b
a, b
tan A -
a, C
aln A-!. C
•
B
I
a
~ a
tan B COl B
900-A
A, b
900-A
b tan A
A, e
900 -A
cain A
•
a
a cot A
1-
~ C
ab
ii"nA b COl A
K _ ~ (I - a) (1:- b) (I - c)
2 a l cot A --2bltan A --2CI lin 2 A 4
C COl A
a+b+c 2
T .,,~
"ca=;;.
-..!. C
OBLIQUE ANGLED TRIANGLES"
Are.
""'ii'+'b'i
A, •
Abe
c
b
8 1 -
bl + cl
bl -
a l + c. - 2 ac COl B
cl
a l + bl
-
-
-
2 be COl A
2 ab COl C
- "._... Required
Known A 'A, b,e
tan
1
2' A
--I
B
C
1
tan "2 B.
-
tan
K
K
I-a
I-b
C
2' C-
Are. " I (I-a) (I-b) (I-C)
K
.-=c 1SOO-(A+B)
a, A, B a, b, A
b
1
alnB-~ a
a lin B
atin C
Iin'A
ai'ftA btln C lin B
.,b.C tan A .' a lin C b-aeol C
" a l +b2-2ab COl C
A-1
ab aln C --2-
N
l> ,
_J..
SQUARE
IJ
d
-
~
Axis of moments through center
RECTANGLE
Axis of moments on diagonal
11
c
cent.~
Axl, of moments on base
SQUARE
Axl, of moments through
SQUARE
= d2
=~ 12
Vz
d2
=i
=
= bel
Z
r
S
"
= bell
"i v'12
=~ II
12
!l!!!
= 2~
I '"
e
A
3
2c3
=
Z
v'12
r",i
IIVz
5 "'~
I
c
A
Vi
r =..L
3
5" ~
I" ~ 3
c " d
A
"
z =~
d
=
.288675 d
3\12
'" ...!!!.
= .288675 d
'" .117851 dl
.707107 d
.577350 d
..Iff = .288875 d
=~ 6
r"
5
I" ~ 12
2
d2
c " If
A
.235702 dl
PROPERTIES OF GEOMETRIC SECTIONS
_J..
c
A"la of momenta through center
HOLLOW RECTANGLE
throu.h center of gravity
RECTANGLE A... of mom.nta any line
11..1. of momenta on elleton.'
RECTANGLE
lUj
AJd. of mom.nta on .....
ftECTANGLE
Z
S
It
8
A
•
A
I
It
-
bel
-
.lnSiOd
2
+ d' COl'.)
+ d COl •
-
+dl
bldl'
.W'
b,eI,'
-4-
12A
~- .bldll
COl'.
+ d l cOla.) + d coe a) 12
bld l l 12
-----ed
bd l
bel' -
2"
d
bd- bid.
~ b l ain'.
bel (b l aln l • I (b lin.
bd (b' a'n'. 12
b aln •
+dl)
bel
e (b l
bel
01
,01 b l + d l
bldl
bid' I (b i .+ dl )
01 b l + d'
bel
.[f
d
bell
-,-
bel'
-,-
d
bel
PROPERTIES OF GEOMETRIC SECTIONS
3
en
::J
O·
r-t
n
en en
0
en
-
r+
::J
en
m en
CD
x·
en :J a.
l> ~ ~
»
W
d,
1
i _ _ _ _ _ _ _*..
I
!"2
t
!-
d,----~-t-
Y
t--+-------+·-"T<.::......
TRIANGLE Alii, of momlnta on b...
AIlII 01 mom.nta through center of gravity
TRIANGLE
c,
1 !i+--3:-J..! I "
1..
.. ~
Axil :!~:,.r::~~~!n;OUgh b~ t
UNEQUAL RECTANGLES
b
LB
d
i
ll f
Axil of moment. through center 01 gravity
EQUAL RECTANGLES
•
A
•
C
A
z
s
C
A
Z
S
A
b (d - dtl
-
-
eI.')
bty
I
~ ta)
Sa
-
CaI
+ ~ + bataYa
bat,-
Cd -
~.
II _r:-
~'"
~.
..
~ 2
;231102 II
-.4OI:MI II
YTi -
d
24"
bd'
""38*
bd'
T
2d
2
~
1-("-(~)]
_II 1"A
I C _
bt'
A
+ bat, + b, ta
~ bt'
bt
"4 lel 2
It
dl)
d' - d,s
1 12(d -
J
b (d' -;; d,l) S
b(d';;d,,)
2
~
- ----r2 +
_
PROPERTIES OF GEOMETRIC SECTIONS
I
-1
..
_of _?j-l
through cent"
HOllOW CIRCLE Axl. of moments
-- ~--
HALF CIRCLE Axis of moments through center of gravity
d
[6I Axi. 01 moments through center
CIRCLE
Axi, of moment, through center of grnitv
TRAPEZOID
_
-: :
2" '"
d
,,:4 '" .049081d4
R
= .785l98R4
'" "': '" "R2 '" .785l98dZ '" 3.141593R2
IIlb + b,) V 2 1b2 + 4 bb, + b 121
d
dZlb2+4bb,+b,21 12(2b + b,)
3111b + b,)
cP 1b2 + 4 bb, + b,Z)
3Ib+b,)
dl2b fbI)
dlb + b,1 -2--
z
.,
I
~
+ d,2 _
S
(
1
-~
)
'"
Rl 2.
,. R
%
h
~.
Ih2 - 141 13,,' - 4) ---
%
d,.'
.515517R
1.570791R2
.2M338 R
'" .190681 R3
... (: ~)".,.,", R
2
I
d,2
---.-
d
d4 -
.0490811d4 _ d,4)
.785398(d2 - d 12)
d,.) _.ota,75 32d
v dZ
-
d,.' 14 ..1d4 -
..(d4
d
T
•
~-~
.- :: 2
A :: ~
z
S
A
R
r-+
ci
:J
n 0
:J
"0 16
» ~ ~CO
d
_ "Rl _ _ S -_"CP i2"-7-·098115d3-.785398R3
A
A
PROPERTIES OF GEOMETRIC SECTIONS
~
I
»
I
.1....
....
"TI
4
J--
..ARABOLIC "'ILLET IN RIGHT ANGLE I
COMPLEMENT OF HALF PARABOLA
.-S---_---11~-1.
·~l
rJAP••
I
HALF PARABOl..A
I
..ARABOl..A
a ..
"
,4, .b' I':•• a
-
-
-
A m
It
-
-
It
•
I.
I,
n
m
-
-
I ..
A
-.!!.. .Ib 105
-
..
II
n -
1. tl 8
-./-;:
t
2YZ
t
...!.... ab a 10
2100
2100
11
it
~alb
4
.!.b
2.... 10
1
I ·b
...!.. 15 .b a
abl
...!!. 410
• • ab 17'5
fb
t
f·b
-T -
-
l
Ia
I,
n
m
A
Ia
-
..!!.. 175 a
I.
I,
2
fa .. ,a
-
m
A
tot
PROPERTIES OF GEOMETRIC SECTIONS
-,-'
-.,-no
"alb
16 1 16
1
+) 8 (1 - + )
(
_"ahl
= ab
'Z
.M
= b = R.
(T -~, - "(', --n)
H(:~»)
(-i--:')
(:6 - ~) (:6 - ~) _"alb
I
.hZ
alb
J,;""
4b
J,;""
4a
= 4~ "Ib
• •~
~ ".hZ
.3b
J,;""
4a
= ..!.2 "ab
6 (1 -: ) " "'(2--~ 3 16 -
A
I.
'3
lz
't
A
13
't '2
A
• To obtain p,operti.. 01 ha" cI,cle. quarte, ei,el. and ci,eular complement substituta a
• ELLIPTIC COMPLEMENT
4
·--~----r-~-~3
4
rn~
I
• QUARTER ELLIPSE
"' ~-----L____LI_-L3
I
• HALF ELLIPSE
PROPERTIES OF GEOMETRIC SECTIONS
0:
r-+
0 ::::s
()
-
to
0X
::::s
CD
» -0 -0
0,
»
z-z la axl. of minimum
y
I
4
Tran.v.rse force oblique through center of oravity
:.t
BEAMS AND CHANNELS
x
ANGLE
A.i, of moment. throuoh center of ,ravit)'
=
K
+ cl
Zib
abcdt
~
lw ..
,. I. cos29 +
Iv slnZ8 K lin29
.. sln2& + 'y cos28 + K lin 28
. , =(i tlb-XI.l+dxl-clx-tP) 'a
+ c)
Product of 1nertf8 about X-X lit y-y
21b
tlb + c). '" ~ Y ., d2 + at
48
12 + 82
,.
14 M
!.sI.... +.!-.. ) Iy ( I,.
I,. cos2. + Iy sln2a
...ln2. + 1y cosZ.
wh«e M I. banding moment due to forcs F.
..
,.
~
!1:r:.:..'='.:'Iv!"!':~::!"Z=::,:.t!'::'
~:
=
A
Iy-:-I,.
ZK
24
yUR
48
a2
AU2R,! + 821
Z4
= ~nR2Sin:z. =nR,Ztan.
AI6R2 - 821
!n82cot.
2 tan.
a
2 sin.
a
.. :(i tld-YI3+bY3-aIY-tI3)
,.
of sides
ZVR2 - R,2
= /6R2 -
=
tan Z&
" = '2
" =~
A
R,
R
180"
... xI. of momenta
through center
Number
REGULAR POLYGON
PROPERTIES OF GEOMETRIC SECTIONS AND STRUCTURAL SHAPES
S .a
3
= d [\.1 (110 +
hlo>
+
+
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<---"11---->:
I
{g
5
I
t\
i_
Ii
1f ~d~ ---r
~t' /~-----~~
I
tiI
I I
-----~-
r«---d--->1
I
I
tli
:f_
--!-
(i
I
,5
-f'
I
I
1
, --- -- y-
S
,
: ,
a
,
I
A.
I
----J,.-
~L
I
t)
r
@
_'L
I I
h
U
Ii<-d-->lr 1I'd'
2
CYLINDER
~.
above base
+ Base Area
Surface = Sum of surfaces of bounding planes wh Volume ~ ""6 (I + m + n)
WEDGE
+
Convex = !~ (d + d') = .~ (d + d') "4h' + (d=
FRUSTUM OF CONE
Total Surface = Convex Surface + ·4Volume = ~ d 2h = .~ d 2 "4s~ 12 24 h Center of Gravity above base = "4.
Convex Surface =
CONE ~2 ds = ~ "ar:t4tii 4 yd!
iii!)
Lateral Surface = s (Top + Base Perimeters) + 2 If a = top area and A = base area, Total Surface = Lateral Surface + (a + A) Volume = h (a + A + viA) +3 Center of Gravity = h (~~_-t-_A + 2 above base 4 a + A + "aA
FRUSTUM OF PYRAMID
Center of Gravity =
Volume = 3" X Base Area
h
Total Surface = Lateral Surface
Lateral Surface = ~ X Base Perimeter
PYRAMID
Lateral Surface = h X Base Perimeter Total Surface = Lateral Surface + (2 X Base Area) Volume = h X Base Area Center of Gravity above Base - ~
PRISM
Volume Cylinder. right or oblique = area of section at right angles to sides X length of side. b Center of Gravity above Base -
4
Total Surrace = rdh + '"2 Volume = .11' d'h
Convex Surface = lI'dh
SURFACES AND VOLUMES OF SOLIDS
t
I
II
____ '
~- - -
I
,
I
C- - -->1
, r'
I
,
~--
...
~
G[
__--'_~___ :1_
I
I
_td ______ i_
---1X ':d
Ii _-t_
~----D----->{
-+-1---
~----c----->t
.--r /
Q
~--eL-->i ---,r
...-'....... ~,'f'
L=SJ[
I
'J!/
.,;.,
~
: ::L
----:-S
1<-----<:----+1
I
I
I
h :-
l+---d---;:.l
:G
/2
)
4
3" Rr'
+. R (!lin·Ie)] -e-
Sin-'e=Angle. in radians. whose sine ... e
Wheree=
R ·-
"Rt - -if
4h,>~~-r'] Total Surface - Convex Surface + rrl ,..r'h . h Volume - T Center of GraVlty = 3 above bage
Convex Surface- ;~2[ (rl +
PARABOLOID
Use common or base 10. log.
4 Volume-311'R 1r
2.303r2 +e)] Surface = 11' [ 2R' + - -e- Iog. 1~
(1
ELLIPSOID (II. Revolution about conjugate axis)
Volume -
Surface - 211'r [ r
ELLIPSOID (I. Revolution about transverse axis)
Total Surface ... 2yrh + (c 2 + C lI'h Volume = 24 (Jet + 3c'1 + 4h2)
i
Convex Surface = 2rrh
SPHERICAL ZONE
Spherical Surface=2rrh=r(c2 +4h 2 ) + 4 Total Surface = Spherical Surface + (rc 2 + 4) Volume = ,.-h 2(3r - h)+ 3= ,..h(3c 2 + -lh2) + 2.1 Center of gravity above base of segment = h (4r- h) +4(3r- h)
SPHERICAL SEGMENT
h)
Center of Gravity _ ~(r above center of sphere - , - 2
Volum'C"= ~ 1I'r2h= 1rr2( (r- ~r'L..~2)
Total Surface = i (4h+c)
lI'r
SPHERICAL SECTOR
Surface = rd 2 = 4rr2 rd J 4 Volume = Ir = j 1I'r' Side of an equal cube = diameter of sphere X 0.806 Length of an equal cylinder = diameter of sphere X 0.6667 Center of Gravity of Half Sphere = ~r above spherical center
SPHERE
SURFACES AND VOLUMES OF SOLIDS
l>
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
"<
'">< '" >0:
(lIb) Lower Head:
. a ratio
a
Radius of cylinder
~
(lOb) Hemi-ellipsoidal Heads: Q 3;4 V ~2 (l - 1f3~)
Q
Total volume of one head per formula (7d)
01a) Upper Head:
.
R=
e =
= Partially filled volume or contents in cubic feet
in feet
R = depth of liquid in feet
a
Dished or Basket Heads: Formula (1 Ob) gives partially filled volume within practical limits, and formula (7d) gives V within practical limits.
OOd) Bumped Heads: Formula (lOb) gives partially filled volume within practical limits, and formula (7f) gives V.
1'/3 KD)
7i~2)
(l0e)
R = depth of liquid in feet
A-11
Q
1'h V A2 (1 -
A
a
1m
a
~ KR = depth of liquid in feet
= a ratio
Y.l~)
.....a. N
I
»
1.3
0+~)
or
--4-
3p O
+ 4.5pO
~;.60 (~ +f)
+1.950
0.20830
90 0
o
90 0
Belt line Stres s (pound s)
W
NOTE: All dimensions expressed in feet; H
Angle at edge
o
trX\~ -3
0+~)
0+~)
o 90 0
(0 2
4X2)
"X\:4 - T
+ 6p O -6 p O or
-2.60
+2.60
0.15630
0.14390
h
I
2
6p r
2.6r (H + h)
12r - 4h
8rh - 3h
5
±gh (roughly)
calculate sector - V
calculate angle
2"rh
calculate
h
0.0796WO
Height). load.
colculafe
O.3183W~r2 -~ o
calculate new calculate vol. on basis vol. V - vol.V (h _ x) & subtract
~
h
2.6 H Do
3h
-.-
2h
T
Dh
-2-
=water elev. above belt line (Shell =total load carried, including dead
) X2)1,trX\T l02 _ 3X 2 T
+f) 0
(0 2
3p O
(H
0.31250
Partial Volume within depth X (cu. ft.)
Stress due to Gas pressure "p" Ibs per Inch
Stress (water) Ibs. per inch
of Mass
V to Centroid
Prol. Ar.
0.19190
0.19640 2
0.26180 2
0.39270 2
Projected Area
0.28780
1.2110
1.3220
1.57080
Length of Arc
V to Centroid
"Do
-2-
1.0840 2
1.240'
1.5710'
Surface, sq. ft.
.
30 0
O.276W
0.04510
0.0560
38.67 0
0.198W
0.05960
0.07550
('.11950 2
1.0800
1.04720 0.09060 2
0.88220 2
0.53670'
0.071750'
0.17550
,
T
0.84180 2
0.40310 '
1.95840'h
0.97920'
1.30560'
1.95840'
Volume, gals.
7.833h 2 (3r-h)
0.1340
r -0
0.05390'
h
1.0472h 2(3r"':h)
•
0.26180 2 h
0.17450'
0.13090'
.
STD. UMBRELLA SHAPES
~y ~y I,
h
r
0
~~T~ H
h
0.26180'
o "4
Volume, cu.ft.
o
3"
o
2"
Depth or RI Ie
~~~~Yr\xrl
r ~E~~l r¢j~x ~~I~. SEGMENTAL
Appendix F. Properties of Roof and Bottom Shapes
90 0
o
0.45430
0.44640 2
1.66610'
90 0
o
0.66020
0.56390 2
1.96350·
2.44810'
2.07720 1
o 0.32720'
f·
0.27770'
0.7070
~
,
90 0
o
0.10000
0.12550 2
1.10430
0.92860 2
0.60590'
0.08100 J
0.1690
O.R.=O K.R. = .060
~~m 0
90° CONISPH. 60° CQNISPH F & 0 HEAD
, Appendix G. Columns for Cone Roof Framing - Flat Bottom' Storage Tanks Pipe Columns Column Length and Allowable Load
Pipe Dia
Sch Thickness
lIr
Max Length
40 .280 20 .250 40 .322 20 .250 40 .365 20 .250 40 .375 10 .250
180 175 180 175 180 175 180 175 180 175 180 175 180 175 180 175
33/-8 32/-9 44/-3 43/-3 44/-2 42/-10 55/-8 54/-1 55/-0 53/-6 66/-4 64/-6 65/-9 64/-0 83/-6 81/-4
6
8
10
12
16
A WWA DIOO-84 Column Formulas
p
=[
1
18 000
+
L2
Max Load @
lIr
kips
36.8 37.6 43.3 44.4 55.3 56.6 54.3 55.5 78.5 80.2 64.6 66.1 96.0 98.0 81.4 83.2
Weight Area Ih/ft sq. in.
I in.4
S
r
in. 3
in.
19.0
5.58
28.1
8.5
2.25
22.4
6.58
57.7
13.4
2.96
28.6
8.40
72.5
16.8
2:94
28.0
8.25
113.7
21.2
3.71
40.5
11.91
160.8
29.9
3.67
33.4
9.82
191.9
30.1
4.42
49.6
14.58
279
43.8
4.38
42.1
12.37
384
48.0
5.57
Maximum permissible slenderness ratios Llr shall be 175 for columns carrying roof loads only. ,' The maximum permissible compressive stress for tubular columns and struts shall be determined by the formula
The maximum permissible unit stress for structural columns shall be determined by the formula
A '
Properties
1
= Xy
P A
18000r2
in which X is the smaller of
or 15,000 psi, whichever is less. Where: P = the total axial load, in pounds. A = the cross-sectional area, in square inches. L = the effective length of the column, in inches. , = the least radius of gyration, in inches.
18000
L2
+--18 000,2
or 15 000 psi and
for values of tlR less than 0.015, and unity (1.00) for values of tlR equal to or exceeding 0.015. Where: P = the total axial load, in pounds. A = the cross-sectional area, in square inches. L = the effective length, in inches. , = the least radius of gyration, in inches. R = the radius of the tubular member to the exterior surface, in inches. t = the thickness of the tubular member, in inches (minimum allowable thickness is IA in.).
A-13
API Standard 650 The maximum allowable compression shall not exceed the following limits: For columns on cross-sectional area, when Llr $ 120 (See Note 1),
Crna = [ 1 When 120
< Llr $
Crna
=
2
(Llr) 34,700
]
(
33,000Y ) FS
131.7 (see Note 2),
(Llr) 2 34,700
33,OOOY ) FS ------~~~~~--~--~ 1.6 - (L;200r) [
1 _
]
(
When Llr> 131.7
crna
=
where: Crna = maximum allowable compression , in pounds per square inch. L = unbraced length of column, in inches. r = least radius of gyration of column, in inches. Y = 1.0 for structural or tubular sections having tlR values greater than or equal to 0.015
149,000,000Y (Llr)2[1.6 - (L;200r)]
Note 1: The allowable stresses, not including Y, are tabulated in AISC S 310-311. Specifications for the Design, Fabrication, and Erection of Structural Steel for Buildings (1969), Table 1-33, column headed "Main and Secondary Members." Note 2: The allowable stresses, not including Y, are tabulated in AISC S 310-11, Table 1-33, column headed , 'Secondary Members."
[
2~ (
;
)] [ 2 _
2~0 (
;)]
for tubular sections having t/R values less than 0.015. = thickness of the tubular section, in inches, less any specified corrosion allowance. (The minimum thickness, including any currosion allowance on the exposed side or sides ., shall not be less than 114 inch for main compression members or %6 inch for bracing or other secondary members.) R = outside radius of tubular section, in inches. FS = safety factor = ~ + Llr _ _ -l,;;(L;;..;.I:..t.r)_3_ 3 350 18,300,000 For main compression members, Llr shall not exceed 180.
A-t4
(]1
~
I
»
K mol cd
A
Symbol m kg s
SUPPLEMENTARY UNITS Quantity Unit Symbol plane angle radian rad solid angle steradian sr
joule watt
Unit newton pascal N/m2 N·m
J/s
J W
kg·m/s 2
Formula
Symbol N Pa
10 18 10 15 10 12 109 106 103 102 10 1 10- 1 10- 2 10- 3 10- 6 10- 9 10- 12 10- 15 10- 18
Prefix exa peta tera giga mega kilo hecto b deka b decib centib milli micro nano pico femto atto
E380-79 for more complete information on 51. Use is not recommended.
1 000 000 000 000 000 000 1 000 000 000 000 000 1 000 000 000 000 1 000000000 1000000 1000 100 10 0.1 0.01 0.001 0.000001 0.000 000 001 0.000000000001 0.000 000 000 000 001 0.000 000000 000 000 001
SI PREFIXES Multiplication Factor
Quantity area volume velocity acceleration specific volume density
f a
P
n
~
da d c m
h
k
M
T G
P
E
Symbol
DERIVED UNITS (WITHOUT SPECIAL NAMES) Formula Unit m2 square metre m3 cubic metre m/5 metre per second m/5 2 metre per second squared m 3 /kg cubic metre per kilogram kg/m 3 kilogram per cubic metre
force pressure, stress energy, work, quantity of heat power
Quantity
a Refer to A5TM
b
Unit metre kilogram second ampere kelvin mole candela
DERIVED UNITS (WITH SPECIAL NAMES)
length mass time electric current thermodynamic temperature amount of substance luminous intensity
BASE UNITS Quantity
(Metric practice)
WEIGHTS AND MEASURES International System of Units (SI)a
=
=
= =
Square feet .006944 1.0 9.0 272.25 43560.0
=
=
=
=
=
=
Feet .08333 1.0 3.0 16.5 660.0 5280.0
=
=
=
= =
Gills Pints 1.0 = .25 4.0 = 1.0 8.0 = 2.0 32.0 = 8.0
=
Pints Quarts 1.0 .5 2.0 1.0 8.0 16.0 51.42627 25.71314 64.0 = 32.0
4.0
Quarts .125 .5 1.0 4.0
=
=
=
Acres
=
Bushels .01563 .03125 .25 .80354 1.0
Cubic
Cubic Feet .01945 .03891 .31112 1.0 1.2445 ,
=
=
.000207 .00625 1.0 640.0
Gallons Feet .03125 = .00418 .125 .01671 .250 .03342 1.0 .1337 7.48052 = 1.0
U.S.
LIQUID MEASURE
=
Pecks .0625 .125 1.0 3.21414
DRY MEASURE
=
SQUARE AND LAND MEASURE Square Yards Sq. Rods .000772 .111111 1.0 .03306 30.25 1.0 160.0 4840.0 3097600.0 102400.0
=
=
.0000098 .0015625 1.0
Sq. Miles
LINEAR MEASURE Furlongs Miles Rods Yards .00012626 = .00001578 .02778 = .0050505 .00151515 .00018939 .0606061 .33333 .1818182 = .00454545 = .00056818 1.0 1.0 5.5 .025 .003125 1.0 .125 220.0 40.0 1760.0 = 320.0 8.0 = 1.0
AVOIRDUPOIS WEIGHTS Grains Drams Pounds Tons Ounces 1.0 .03657 .002286 .000143 = .0000000714 27.34375 = 1.0 .0625 .00000195 .003906 437.5 1.0 .0625 .00003125 16.0 16.0 1.0 .0005 7000.0 256.0 14000000.0 512000.0 32000.0 2000.0 1.0
SQ. Inches 1.0 144.0 1296.0 39204.0
Inches 1.0 12.0 36.0 198.0 7920.0 63360.0
WEIGHTS AND MEASURES United States System
en
o-,
.-+
n
Q)
11
:J
o·
en
Cb -,
<
:J
o
()
:r:
X
0..
:J
(1)
» "0 "0
m
~
I
»
Quantity
Multiply by
a
inch foot yard mile
2.204622 1.102 311 x 10- 3
kilogram
ounce (avoirdupois) pound (avoirdupois) short ton
35.273966 x 10-3
gram
cubic inch cubic foot cubic yard gallon (U.S. liquid) quart (U.S. liquid) gram kilogram kilogram
kilogram
in2 ft2 yd 2 mi2
m2
m2 m2 km2
mm 2
yd mi
ft
in
mm m m km
Ib av
oz av
9
kg kg
qt
in3 ft3 yd 3 gal
cubic miRimetre mm3 cubic metre m3 cubic metre m3 litre I I litre
square square square square acre acre
square millimetre square metre squ.are metre square kilometre square metre hectare
inch foot yard mile
28.34952 0.453592 0.907 185 x 103
1.056688
61.023759 x 10-6 35.314662 1.307951 0.264172
b16.387 06 x 103 28.31685 x 10-3 0.764555 3.785412 0.946353
1.550003 x 10-3 10.763910 1.195990 0.386101 0.247 104 x 10-3 2.471044
4.046873 x 0.404687 103
x 103
to obtain millimetre metre metre kilometre
ounce (avoirdupois) pound (avoirdupois) short ton
litre
cubic-millimetre cubic metre cubic. metre litre
cubic inch cubic foot cubic yard gallon (U.S. liquid) quart (U.S. liquid)
square millimetre square metre square metre square kilometre square metre hectare
b 0.092903
square foot square yard square mile (U.S. Statute) acre acre 0.836127 2.589998
b 0.645160
39.370079 x 10-3 3.280840 1.093613 0.621370
1.609347
b25.400 b 0.304800 b 0.914400
square inch
millimetre metre metre kilometre
inch foot yard mile (U.S. Statute)
Refer to ASTM E380-79 for more complete information on SI. b Indicates exact value.
Mass
Volume
Area
Length
SI C'ONVERSION FACTORSa
b
0.238846 0.277 778 x 10-6
joule joule
t"C = (tOF x 32)/1 .8 t~ = 1.8 x to C + 32 b
a
kW
W
W
kW.h
Btu
ft.lbf
J J J J
degree Celsuis degree Fahrenheit
radian degree
rad
ft.lbfls foot-poundforce/second eBritish thermal Btu/h unit per hour horsepower hp (550 ft .• lbl/s)
Refer to ASTM E380-79 for more complete information on SI. Indicates exact value. e International Table
degree Fahrenheit degree Celsius
Temperature
17.45329 x 10.3 57.295788
1.341022
kilowatt ree ddl ra Ian
3.412141
0.737562
kilowatt
0.745700
watt
foot-poundforce eBritish termal unit ecalorie kilowatt hour
joule joule joule joule
watt
watt
watt
kPa kPa
kPa
Ibf.ft
Ibf.in
Ibflin2 pound-force per square Inch foot of water (39.2 F) inch of mercury (32 F)
kilopascal kilopascal
0.293071
1.355818
0.947817 x 10-3 joule
foot-pound-force/ second eBritish thermal unit per hour horsepower (550 ft. Ibfls)
0.737562
joule
b
0.295301
kilopascal
1.355818 1.055056 x 103 4.186800 3.600 000 x 106
0.334562
kilopascal
foot-pound-force eBritish thermal unit ecalorie kilowatt hour
0.145038
2.98898 3.38638
6.894757
kilopascal
pound-force per square inch foot of water (39.2 F) inch of mercury (32 F)
kilopascal
pound-forceinch pound-forcefoot
0.737562
8.850748
newton-metre
newton-metre
N.m N.m
Ibf
newton-metre newton-metre
ounce-force pound-force
0.112985 1.355818
3.596942 0.224809
newton newton
N N
newton newton
to obtain
pound-force-inch pound-force-foot
0.278014 4.448222
by
ounce-force pound-force
Multiply
Angle
Power
Energy, Work, Heat
Pressure, Stress
Bending Moment
Force
Quantity
SI CONVERSION FACTORSa
a:
.-+
:J
o
(")
I
·x
0..
:J
Cl)
» '0 '0
Appendix H. (Cont'd)
SPECIFIC GRAVITY AND WEIGHTS OF VARIOUS LIQUIDS Liquid Acetaldehyde Acetic Acid Acetic Anhydride Acetone Aniline Asphaltum Bromine Carbon DisulfIde Carbon Tetrachloride Castor Oil Caustic Soda, 66% Solution Chloroform Citric Acid Cocoanut Oil Colza Oil (Rape Seed Oil) Corn Oil Cottonseed Oil Creosote Dimethyl Aniline Ether Ethyl Acetate Ethyl Chloride Ethyl Ether FOr"maldehyde HI Fuel Oil 1/2 Fuel Oil 1/4 Fuel Oil 1/5 Fuel Oil 1/6 Fuel Oil Furfural Gasoline (Motor Fuel) Glucose Glycerin Hydrochloric Acid, 43.4% Sol. Kerosene Lal~tic Acid Lard Oil Linseed Oil-Raw Linseed Oil-Boiled Mercury Molasses Naphthalene Neallfoot Oil Nitric Acid. 91 % Solution Olive Oil Peanut Oil Phenol Pitch Rosin Oil Soy Bean Oil Sperm Oil Sulfer Dioxide Sulfuric Acid. 87% Solution Tar Tetrachloroethane Trichloroethylene Tung Oil Turpentine Water (Sea) Water (0 0 C) Water (20 0 C) Whale Oil
At Tei!' of 0
7f,ecific
Weight in Lbs. per
ral:lly
u.s. Cal.
Weight in Lbs. ~er Cu. t.
64.4 68.0 68.0 68.0 68.0 68.0 68.0 68.0 68.0 59.0 68.0 68.0 68.0 59.0 68.0 59.0 60.8 59.0 68.0 77.0 68.0 42.8 77.0 68.0 60.0 60.0 60.0 60.0 60.0 68.0 60.0 77.0 32.0 60 . 0 68.0 59.0 59.0 68.0 59.0 68.0 68.0 68.0 59.0 68.0 59.0 59.0 77.0 68.0 68.0 59.0 59.0 80.0
0.783 1.049 1.083 0.792 1.022 1.1-1.5 3.119 1.263 1.595 0.969 1.70 1.489 1.542 0.926 0.915 0.921-0.928 0.926 1.040-1.100 0.956 0.708 0.901 0.917 0.712-0.714 1.139 0.80-0.85 0.81-0.91 0.84-1.00 0.91-1.06 0.92-1.08 1.159 0.70-0.76 1.544 1.260 1.213 0.82 1.249 0.913-{).915 0.93 0:942 13.595 1.47 1.145 0.913-0.918 1.502 0.915-0.920 0.917-0.926 1.071 1.07-1.15 0.98 0.924-0.927 0.878-0.884 1.363 1.834 1.2 1.596 1.464 0.939-0.949 0.87 1.025 1.00 0.998 0.917-0.924
6.52 8.74 9.0: 6.60 8.51 9.2-1i5 25.98 10.52 13.28 8.07 14.16 12.40 12.84 7.71 7.62 7.67-7.73 7.71 8.66-9.2 7.96 5.90 7.50 7.64 5.93-5.95 9.49 6.7-7.1 6.7-7.6 7.0-8.3 7.6-8.8 7.7-9.0 9.65 5.8-6.3 12.86 10.49 10.10 6.83 10.40 7.60-7.62 7.8 7.84 113.23 12.2 9.54 7.60-7.65 12.51 7.62-7.66 7.64-7.71 8.92 8.91-9.58 8.61 7.70-7.72 7.31-7.36 11.35 15.27 10.0 13.29 12.19 7.82-7.90 7.25 8.54 8.34 8.32 7.64-7.70
49 65 68 49 64 69-94 195 79 100 60 106 93 96 58 . 57 57-58 58 65-69 60 44 56 57 44-45
64.4
68.0 68.0 68.0 59.0 68.0 59.0 39.2 68.0 59.0
A-17
71
50-53 51-57 52-62 57-66 57-67 72 44-47 96 79 76 51 78 57 58 59 849 92 71 57 9.4 57 57 73 67-72 61 58 55 85 114 75 100 91 59 54 64 62.4 62.3 57
The parameters given are approximate for estimating purposes only. The properties of the stored liquid should be determined analytically and used in the final design.
Appendix H. (Cont/d)
A.P.I. AND BAUME GRAVITY AND WEIGHT FACTORS The relation of Degrees Baume or A.P.I. to Specific Gravity is expressed by the following formuJas: For liquids lighter than willer: Degrees Baume
= 140 - 130, G
Degrees A.P.I.
=~ G
131.5,
For liquids heavier tluJn water: Degrees Baume = 145 _ 145, G
=
= ~::-:--:::-_140_-:::-_-:130 + Degrees Baume G = -===:-:-~1~4_1._5~-:::-':"" 131.5 + Degrees A.P.I.
Formulas are based on the weight of 1 gallon (U.S.) of oil with a volume of 231 cubic inches at 60 degrees Fahrenheit in air at 760 m.m. pressure and 50 % humidity. Assumed weight of 1 gallon of water at 60° Fahrenheit in air is 8.32828 pounds.
G
G
To determine the resulting gravity by mixing oils of different gravities: D
= md.m++ndn
= Density or Specific Gravity of mixture Proportion of oil of d density = Proportion of oil of d density = Specific Gravity of moil ='Specific Gravity of n oil
D m~ n d1 d2
=...."....,.,,,...-..,,,,-._14_5-,,,...--..,. 145 - Degrees Baume
=
G Specific Gravity ratio of the weight of a given volume of oil at 60° Fabrehelt to the weight of the same volume of water at 6()0 Fahrenheit.
l
1
PRESSURE EQUIVALENTS PRESSURE lib. per sq. in.
= 2.31 ft. water at 60°F = 2.04 in. hg at 60 F = 0.433 lb. per sq. in. = 0.884 in. hg at 60 F = 0.49 lb. per sq. in. = 1.13 ft. water at ~F = lb. per sq. in. gauge (psig) + 14.7 0
1 ft. water at 600f
D
1 in. Hg at 6()OF lb. per sq. in. Absolute (psia)
l
A-18
Appendix H. (Cont'd)
WIRE AND SHEET METAL GAGES Equivalent thickness in decimals of an inch
GaOl No.
7/0 610 510 4/0 310 2)0 1/0
,
2
I·
3 4 5 6 7 8
9 10 l'
12
u.s. SUncWd
GalvaniUd
GaOl tor Uncoated
Sheet Gaoe lor Hot-Dlpped
Hot & Cold Zinc Coated Rolled Sheets' Sheets'
-
---
.2391
.2242 .2092 .1943 .1793 .1644 .1495
.1345 ,1196 ,1046
-
' ,'
--
-, .1661 .1532 ."382 .1233 ,1084
u.s. SWidard
USA Stut Wire Gaoe ,
A90 .46~
.430.394.362" .331 .306
.283 .2S~
"
.244.225& .207 .192
Gage No.
13 14 15 16 17 16 19 20 21 22
23 24 25 26 27 28
.1n
.162 .148,135 .120:106-
29
30
Galvanized Gaoo tor Sheet Gaoe Uncoated for Hot·Dipped Hot & Cold Zinc: Coated Rolled Sheets' Shoets'
.0897 .0747 .0673 .0598 .0538 .0478 .0418 .0359 .0329 .0299 .0269 .0239 .0209 .0179 .0164 .0149
-
USA Steel Wire Gaoe
.0934
.09~
.0785
.060 .072
.0710 .0635 .0575 .0516 .0456 .0396 .0366 .0336 .0306 .0276 .0247 .0217
.0202 .0167 .0172 .0157
.06~
.054 .048.041 .035-
-
--
--
&Rounded value. The steel wire gage has been taken from ASTM AS10 "General Require. ments for Wire Rods and Coarse Round Wire, Cartxm Steel", Sizes originally quoted to 4 decimal equivalent places have been rounded to 3 decimal places in accordance with rounding procedures of ASTM "Recommended Practice" E29. b
The equivalent thicknesses are for intonnation only. The product is commonly specified to decimal thickness, not to gage number.
A-19
~
IJ n IJ
