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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. 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.
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: 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. Again, the HSLA steels demonstrate some exceptions to these general rules.
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: 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. Testing for mechanical properties. A6 specifies the general location of the specimens. This affords a check on uniformity within a heat. Specification A20 also specifies the location from which the specimens are to be taken.
Repair of surface imperfections and the limitations on repair of surface imperfections are more restrictive in A20 than A6. Residual stresses will be reduced by this procedure. This treatment hardens and strengthens the steel and is normally followed by tempering. This temperature normally lies between F and F. 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 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 , if the designer has selected a Charpy V Notch value of "x" ft.
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. 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.
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. 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.
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.
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. 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. 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. 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. 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. 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 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.
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: In addition, the basic API Standard and AWWA Standard 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. The other design methods are based on refined procedures that take into account plate grade, service temperature, thickness and higher standards 7 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.
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. 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.
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: 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.
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. 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.
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.
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. 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.
API 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 D 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. 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 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.
AWWA 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 tanks a. 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. These loads are considered to be the pressure caused by a wind velocity of MPH. 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. 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. Seismic - Because of their flexibility, flat-bottomed cylindrical steel tanks have had an excellent safety record in earthquakes. Prior to the Alaskan earthquake of , 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.
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.
Seismic probability maps of the United States can be found in each. If applicable, local conditions should be investigated.
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.
Because of proportionately large loss of section by corrosion on small areas, it is recommended that no anchor bolt be less than 1. 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 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 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. 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.
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.
If corrosion allowance is necessary it should be added in accordance with the respective standard. If corrosion allowance is necessary for roof supporting structural members, it should be added in accordance with the respective standard. 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: 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: 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. 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 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.
API 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. Structural members shall have a minimum thickness of 0. 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.
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. Spacing on inner rings does not exceed 5. 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 Because molasses is heavier than water, the full design stress is present in service.
However, the addition of a corrosion allowance is required when warranted by service conditions. Self-Supporting Roofs - Self-supporting cone, dome or umbrella roofs shall conform to the appropriate requirements of API unless otherwise specified by the purchaser.
Accessories API 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 Ibs. 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. 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 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 , a lower design stress should be considered for the same reasons as given under "Molasses Tanks. 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 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. Molasses Tanks - Molasses presents no unusual problems other than the fact that its specific gravity is about 1. It is quite common to require 13 AWWA Standard exceeds the following values and may in some cases be unsatisfactory below these limits: 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. 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. Inasmuch as all welds create locally high residual stresses, all brackets, welding lugs, etc. 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.
Anyone dealing with tanks should obtain a copy of the complete standard. 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 Appendix C includes steels of significantly higher strength levels and correspondingly higher design stress levels. This introduces new design problems. For example, for A steels, the permissible design stress of 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. 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 A 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. 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. 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. 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: 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.
The maximum slenderness ratio Ur for roof support columns shall be Roof support columns shall be designed as secondary members. Roof trusses, if any, shall be placed above the maximum water level in climates where ice may form. 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: 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. The purchaser shall specify pipe connections, 15 3. 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. 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 D 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. 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.
The overstress in the shell would be minimal. The equation for outflow vent capacity is: Notice that hp in the above equation is the full liquid height above the design point rather than h - 1 as used in API The calculation for ring five top ring is: Ring 5 will be increased to 0.
Shell stability is calculated using the basic equation: 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. 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 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.
See table 3A-1 for shell thicknesses before and after minimum thickness and wind stability adjustments. For 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: 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. For the seismic shear a simple calculation of 0. 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. The minimum required coefficient of friction against sliding is: This coefficient is well below established values which range as high as 0.
The wind moment at the base of the shell is calculated: The value of WL is based upon a bottom plate width L that will carry the resisting contents and is calculated by the equation: The following design example covers the API tank. A detailed example is in the API Appendix. The thickness calculations for rings 1 and 2 are shown in figure 3A 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: The design method considers two response modes of the tank and contents: 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 equation for overturning due to seismic loading applied to the bottom of the shell is: Since H calculates less than the shell height, calculate a transposed shell height using the equation: 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 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. 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, The stiffener ring required section modulus is calculated by the equation: The shell is now stable for a design wind velocity of mph.
A qualified ,geotechnical engineer should be retained to conduct the subsurface exploration and to make specific recommendations concerning: 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: A factor of safety of 3.
A factor of safety of 2. 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 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 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 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.
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: Direct hoop tension resulting from the lateral earth pressure on the inside face of the ringwall.
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. 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. For wall-like ringwalls the area of vertical reinforcement provided should not be less than 0.
The area of hoop reinforcement provided should not be less than 0. 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 for details of recesses at flush type cleanouts. References, Part III 1. Bottom of excavation should be level. Remove any unsuitable material and replace. 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 "". Type 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.
It is used under conditions too severe for Type , such as mineral acids phosphoric acid, sulfuric acid , strong organic acids oxalic, formic, etc.
The five stainless steels most generally used as plate material for construction of liquid storage tanks are Types , L, , L and S. The last is not recognized as standard by American Iron and Steel Institute. The chemical compositions of these types are listed in Table and their mechanical properties are listed in Table 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 The five types fall within two categories: 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 F temperature range for sufficient time see Figure 5.
If the degree of precipitation is severe - Le. 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. 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. Even these should be carefully investigated to establish such a need before the additional expense of the L grades is incurred. Types and 0. 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. This is represented by the distance from O to B. Therefore, the observer at A with the black axes notices their clock as reading the distance from O to A while they observe the clock moving relative him or her to read the distance from O to B.
Due to the distance from O to B being smaller than the distance from O to A, they conclude that the time passed on the clock moving relative to them is smaller than that passed on their own clock. A second observer, having moved together with the clock from O to B, will argue that the other clock has reached only C until this moment and therefore this clock runs slower.
The reason for these apparently paradoxical statements is the different determination of the events happening synchronously at different locations. Due to the principle of relativity, the question of who is right has no answer and does not make sense. Relativistic length contraction means that the proper length of an object moving relative to an observer is decreased and finally also the space itself is contracted in this system.
The observer is assumed again to move along the ct -axis. The second observer will argue that the first observer has evaluated the endpoints of the object at O and A respectively and therefore at different times, leading to a wrong result due to his motion in the meantime.
If the second observer investigates the length of another object with endpoints moving along the ct -axis and a parallel line passing through C and D he concludes the same way this object to be contracted from OD to OC. Each observer estimates objects moving with the other observer to be contracted. This apparently paradoxical situation is again a consequence of the relativity of simultaneity as demonstrated by the analysis via Minkowski diagram.
For all these considerations it was assumed, that both observers take into account the speed of light and their distance to all events they see in order to determine the actual times at which these events happen from their point of view. Another postulate of special relativity is the constancy of the speed of light. It says that any observer in an inertial reference frame measuring the vacuum speed of light relative to himself obtains the same value regardless of his own motion and that of the light source.
This statement seems to be paradoxical, but it follows immediately from the differential equation yielding this, and the Minkowski diagram agrees.
It explains also the result of the Michelson—Morley experiment which was considered to be a mystery before the theory of relativity was discovered, when photons were thought to be waves through an undetectable medium. That means any position on such a world line corresponds with steps on x - and ct -axes of equal absolute value. From the rule for reading off coordinates in coordinate system with tilted axes follows that the two world lines are the angle bisectors of the x - and ct -axes.
That means both observers measure the same speed c for both photons. Further coordinate systems corresponding to observers with arbitrary velocities can be added to this Minkowski diagram. For all these systems both photon world lines represent the angle bisectors of the axes. The more the relative speed approaches the speed of light the more the axes approach the corresponding angle bisector. The scales on both axes are always identical, but usually different from those of the other coordinate systems.
Straight lines passing the origin which are steeper than both photon world lines correspond with objects moving more slowly than the speed of light. If this applies to an object, then it applies from the viewpoint of all observers, because the world lines of these photons are the angle bisectors for any inertial reference frame. Therefore, any point above the origin and between the world lines of both photons can be reached with a speed smaller than that of the light and can have a cause-and-effect relationship with the origin.
This area is the absolute future, because any event there happens later compared to the event represented by the origin regardless of the observer, which is obvious graphically from the Minkowski diagram. Following the same argument the range below the origin and between the photon world lines is the absolute past relative to the origin. Any event there belongs definitely to the past and can be the cause of an effect at the origin.
The relationship between any such pairs of event is called timelike , because they have a time distance greater than zero for all observers. A straight line connecting these two events is always the time axis of a possible observer for whom they happen at the same place. Two events which can be connected just with the speed of light are called lightlike. In principle a further dimension of space can be added to the Minkowski diagram leading to a three-dimensional representation.
In this case the ranges of future and past become cones with apexes touching each other at the origin. They are called light cones. Following the same argument, all straight lines passing through the origin and which are more nearly horizontal than the photon world lines, would correspond to objects or signals moving faster than light regardless of the speed of the observer. Therefore, no event outside the light cones can be reached from the origin, even by a light-signal, nor by any object or signal moving with less than the speed of light.
Such pairs of events are called spacelike because they have a finite spatial distance different from zero for all observers. On the other hand, a straight line connecting such events is always the space coordinate axis of a possible observer for whom they happen at the same time. By a slight variation of the velocity of this coordinate system in both directions it is always possible to find two inertial reference frames whose observers estimate the chronological order of these events to be different.
Therefore, an object moving faster than light, say from O to A in the adjoining diagram, would imply that, for any observer watching the object moving from O to A, another observer can be found moving at less than the speed of light with respect to the first for whom the object moves from A to O. The question of which observer is right has no unique answer, and therefore makes no physical sense.
Any such moving object or signal would violate the principle of causality. Also, any general technical means of sending signals faster than light would permit information to be sent into the originator's own past.
In the diagram, an observer at O in the x - ct system sends a message moving faster than light to A. But B is in the past relative to O. The absurdity of this process becomes obvious when both observers subsequently confirm that they received no message at all, but all messages were directed towards the other observer as can be seen graphically in the Minkowski diagram.
Furthermore, if it were possible to accelerate an observer to the speed of light, their space and time axes would coincide with their angle bisector. The coordinate system would collapse, in concordance with the fact that due to time dilation , time would effectively stop passing for them.
These considerations show that the speed of light as a limit is a consequence of the properties of spacetime, and not of the properties of objects such as technologically imperfect space ships.
The prohibition of faster-than-light motion, therefore, has nothing in particular to do with electromagnetic waves or light, but comes as a consequence of the structure of spacetime. When Taylor and Wheeler composed Spacetime Physics , they did not use the term "Minkowski diagram" for their spacetime geometry. When abstracted to a line drawing, then any figure showing conjugate hyperbolas, with a selection of conjugate diameters, falls into this category.
The momentarily co-moving inertial frames along the world line of a rapidly accelerating observer center. The vertical direction indicates time, while the horizontal indicates distance, the dashed line is the spacetime trajectory "world line" of the observer. The small dots are specific events in spacetime.
If one imagines these events to be the flashing of a light, then the events that pass the two diagonal lines in the bottom half of the image the past light cone of the observer in the origin are the events visible to the observer. The slope of the world line deviation from being vertical gives the relative velocity to the observer.
Note how the momentarily co-moving inertial frame changes when the observer accelerates. Media related to Minkowski diagrams at Wikimedia Commons. From Wikipedia, the free encyclopedia. Redirected from Loedel diagram. Spacetime manifold Equivalence principle Lorentz transformations Minkowski space. Introduction to general relativity Mathematics of general relativity Einstein field equations. Introduction to gravitation Newton's law of universal gravitation.
Four-vector Derivations of relativity Spacetime diagrams Differential geometry Curved spacetime Mathematics of general relativity Spacetime topology.
Retrieved 19 November A Most Incomprehensible Thing: Various English translations on Wikisource: Mechanics and Thermodynamics illustrated ed. Special Relativity for Beginners: A Textbook for Undergraduates. The Theory of Relativity. Proceedings of the American Academy of Arts and Sciences. Archives des sciences physiques et naturelles supplement. The Lorentz—Einstein transformation and the universal time of Ed.
The Electromagnetic Field Reprint of ed. See Google books, p. A simplified approach to Einstein's theories. University of California Press. Archives des sciences physiques et naturelles. Special Relativity Reprint of ed. See also Reprint of third edition at Google books, p. Elemente der Relativitätstheorie [ Elements of the theory of relativity ].
Anales de la sociedad cientifica argentina. American Journal of Physics.
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