WITH CLOSURES
h real need for the use of formed on
cal vessels arose the development of the power steam boiler early in the nineteenth century. a result of the frequent occurrence of boiler explosions, the British House of Commons in 1817 made the recommendation that the heads of cylindrical boilers be hemispherical (12). Since then a wide variety of formed closures termed “heads” have been developed, standardized, and extensively used in the fabrication of process pressure vessels. The development of the thermal cracking process in the petroleum industry during the period from 1915 to 1930 resulted in the con-struction of thousands of pressure vessels with formed heads operating in the range of from 100 to 400 psi. The of these early vessels usually were of the torispherical-dish type with a small knuckle radius.
The first formed heads were of a small size and were hand-forged by “bumping out” a flat plate. One of early American steel producers, Lukens Steel Company, in 1885 formed a 5-ft-diameter dished head by digging a hole in the ground to the approximate radius of the dish and bumping the heated plate into the by the use of mauls. Since then of forming heads have been highly developed by the use of dies and forging and spinning techniques. Figure 5.1 shows a photograph of the world’s largest flanging machine spinning a head with a 20 ft, 6 in.
diameter.
5 . 1 G E N E R A L
Development of Welded The early
thermal-cracking of industry used
pressure vessels in which the formed were to
shell. These the of leakage
around the heads. AI tempts to correct this were made by means of fillet welding the plate edges seal welding the rivet heads. These vessels often were not satisfactory unless the fillet welds were made so large that the loads were carried by the fillet. welds rather than the rivets. When it was realized that the welds were carry ing the loads rather than the rivets, a large number of vessels for low-pressure service (walls less than 1 in. thick) were fabricated entirely by oxyacetylene The limitations of the welding at this time, in particular the
of the bare electrode welds, made the construc-tion of heavy-walled vessels impracticable. With the development of flux-coated electrodes ductile welds were possible. This development resulted in practical
of riveted-fabrication techniques for pressure-vessel service.
5.1 b Use of Formed Heads. Cylindrical vessels with formed heads are used for a wide variety of applications in which cylindrical tanks with flat bottoms cannot be used.
These applications can be grouped into three (1) use, (2) pressure consideration, and (3) size limitations.
Processing equipment such as distillation columns, desorption units, packed owers, evaporators, crystallizers, and heat exchangers are essentially cylindrical vessels hav-ing formed heads plus other required functional parts.
If the working pressure of the process vessel is to be her than atmospheric pressure, formed heads are usually used to close the vessel.
In general, all cylindrical vessels requiring a working pressure in vapor space of lb in. gage or more are fabricated with formed heads. Large-diameter
Fig. 5.1. World’s largest machine spinning a head 20 ft, 6 in. in outside diameter. (Courtesy of Steel Company.)
flat-bottomed, cone-roofed storage vessels are limited to pressure in the vapor of only a few ounces.
cylindrical vessels with flat bottoms and siderably smaller diameters may operate under allowable working pressure of several pounds per square inch if a domed or umbrella roof is used. Equipment designed to operate under less than atmospheric pressure will also require the use of formed heads. Small horizontal storage vessels supported off the ground are usually fabricated with formed heads although flat ends of heavy plate are
I imes used.
Vertical versus Horizontal Vessels. In general, he functional requirements of the vessel determine whether the vessel shall be vertical or horizontal. For example, tilling columns and packed towers, which utilize the force
gravity for phase separation, require vertical installation.
Heat exchangers and storage vessels may be either vertical or horizontal. In the case of heat exchangers, the selection is often controlled by the routing of the fluids and transfer considerations. In the case of storage vessels, the installation location is important. If the vessel is to be installed outdoors, the wind loads on vertical vessels may impose the necessity of heavy foundations to prevent
For this reason, horizontal storage vessels are
usually more economical. However, important con-siderations such as available floor space or ground area, head room, and maintenance may be deter-mining factors.
5.2 MATERIAL SPECIFICATIONS
Vessels with formed heads are most commonly fabricated from low-carbon steel wherever corrosion and temperature considerations will permit its use because of the low cost, high strength, ease of fabrication, and general availability of mild steel. Low- and high-alloy steels and nonferrous metals are used for special services.
The steels commonly used fall into two general
tions: (1) the steels specified by the code for unfired pressure vessels often referred to as “boiler-plate steels, of or quality; and (2)
grade steels, some of which are permitted by the above code in certain applications and which arc widely used the construction of storage vessels under specifications given in API Standard 12 C (2). The design of vessels accordance with the code for unfired pressure
vessels is treated in Chapter 13, which includes a description of the materials and specifications. The discussion in this
chapter will be restricted to those used in the
tion of vessels with formed ends not requiring fabrication in accordance with these codes.
Comparison of Specifications for Structural- and Boiler-quality Steel Plates. Structural-quality steel rather than boiler-plate-quality steel is used in the fabrication of many vessels with formed heads because of economic con-siderations and its availability. Both types of steel are available in the “killed and the “semikilled or rimmed quality. A “killed steel is one completely deoxidized by the addition of aluminum, silicon, or manganese at the time of the casting of the ingot. The purpose of killing is to minimize the interaction of carbon and oxygen and to reduce the formation of blow holes. A completely killed steel requires “hot capping,” more time in the soaking pit, and more time for the ingot heating. “Hot capping is, the use of an insulated mold on top of the ingot mold to hold a molten reservoir of metal for feeding the ingot as it shrinks on solidifying. A partially killed or rimmed steel is a partially deoxidized steel. An ingot of rimmed steel has a high-purity, low-carbon steel rim from which it obtains its name. Fully killed structural steels have no advantages boiler-plate steel because of their high cost and limited availability.
One of the major differences between boiler-plate steel and structural-plate steel is the quality control dictated by the number and severity of test requirements. As far as chemical requirements are concerned, the principal differ-ence expressed by ladle analysis is the more
limit placed on phosphorus and sulfur for boiler-plate steels.
The thickness tolerances are the same for boiler-plate steels and structural steels when plates are ordered to a given thickness. The physical tests are the same for both steels except for the number of tests and the stipulated loca-tion for test specimens. Structural-quality plate steels require only two tension and two bend tests from each heat
metal which may contain over 100 tons. Flange-quality boiler-plate steel requires one tension and one bend test from each plate rolled. Firebox-quality boiler-plate steel requires two tension tests and one bend and one homo-geneity test from each plate as rolled. There are also minor differences in the methods permitted for repairing surface defects in the slabs prior to rolling.
Boiler-plate steel such as SA-285 flange quality and box quality had mill quality extras of $0.40 and $0.50 per 100 lb respectively as of January 1956 (see Appendix C).
Other boiler-plate steels such as SA-212 and SA-201 had mill quality extras of from $1.20 to $1.55 per 100 lb, depend-ing upon thickness and grade. Killed steels had mill extras of $0.65 per 100 lb. The use of structural-grade steels results in the minimum of quality-extra charges, and the use of these steels is justified whenever permissible. In selecting steels for pressure-vessel fabrication to satisfy code requirements, Chapter 13 should be consulted.
Types of Structural-steel Plates. The most widely available types of plain-carbon structural-steel plates are listed (67) in ASTM-A6-54T. Those most suitable for vessel construction are A-7, A-113, A-131 and A-283.
Specification ASTM-A6-54T gives the general requirements such as permissible variations in dimensions and weight, methods of testing, correcting of defects, and rejection (67).
Proportioning and Head Selection for Cylindrical Vessels with Formed Closures
ASTM-A-7, A-283, Grade C, and A-283, Grade D are the most commonly used plain carbon steels in the construction of storage vessels and are widely used for vessels with formed heads, especially the steel designated as A-283, Grade C. Steel A-283-54 is of the structural quality intended for general applications. It is available in four grades, A, B, C, and D, having minimum tensile strengths of 45,000, 50,000, 55,000 and 60,000 psi respectively, as given in Table 5.1. This steel is available in thicknesses up to and including 2 in., but its use in vessels designed to code specification is limited to thicknesses up to and including in. Grades A and B are primarily used in severe cold-forming applications where high ductility is of prime importance and tensile strength is a minor considera-tion. On the other hand, Grade D does not have sufficient ductility for easy shell and head forming and is not as easily
welded as Grade C. As a result, Grade C is the most widely used structural-quality plate steel for vessel construction.
The major. portion of all oil-storage tanks, elevated tanks, water standpipes, and other varieties of tanks of all descrip-tions, involving both dishing and rolling, are constructed of ASTM-A-283, Grade C.
Steel A-7 is intended for use in the construction of bridges and buildings and for general structural purposes. It has physical properties identical to A-283, Grade D. These steels are the same whether made by the open-hearth or electric-furnace processes. However, steel A-7 is also made by the acid-Bessemer process, and steel made by this process is not recommended for vessel construction. Steel A-7 is available in all standard thicknesses, and its use is permitted . in vessels designed to present code specifications and having shell thicknesses up to and including in., providing the steel has properties equivalent to A-283, Grade D.
Steel ASTM-A-113-55 is a structural steel used for the construction of locomotives and railroad cars except where boiler plate is required. It is made by either the open-hearth or the electric-furnace process and is available in nearly all standard thicknesses. This steel is made in 3 grades, A, B, and C. Steel A-113-55, Grade B has prop-erties approximately midway between those of steels A-283-54, Grades C and B, as shown in Table 5.1. Note that the grade specifications for tensile strength for the A-113 steels run in the reverse order of the grade specifications for A-283 steels. There is no particular advantage to using this steel in preference to A-283 steels except when it is more readily available. It may be used for vessels designed to present code specifications with the same limitations as for A-283 grade steel.
Steel ASTM-A-131-55 is an improved structural steel intended primarily for use in ship-construction. Formerly, the specifications for this steel were essentially the same as
for A-7 and A-283, Grade D. To improve the quality of ship-hull steels, the specification was changed in 1950 in order to include an increase in quality specifications with increasing thicknesses. This logical requirement of . increased quality with increased thickness warrants
con-sideration of this steel as a material of construction for heavy-vessel fabrication. For this steel there is a limitation on the maximum percentage of carbon and a range of from
0.60 to 0.90 manganese for all plates thicker than in.
- - - - - - - - l - - - r - - - - - --
Steel
Table 5.1. 1955 ASTM Steel Specifications (67)
Max % %
Min Yield Thickness Min Min % S
Point, Available, Elone.. in.. Elone.. in.. C (ladle)
psi in. (ladle)
45,000 to 55,000 24,000 2 50,000 to 60,000 27,000 2 55,000 to 60,000 30,000 2 60,000 to 72,000 33,000 2 60,000 to 72,000 33,000 15 58,000 to 71,000
* See text for limitations.
32,000 and less
32,000 to 1
32,000 1 and over
Also, for plates having a thickness of 1 in. or more, a require-ment of 0.15% to silicon is specified. In addition, it is stipulated that this steel be manufactured to have an inherent fine-grained structure. This steel is available in a wide range of thicknesses and is of higher quality than A-7 but presently is not permitted in the construction of vessels designed to meet unfired-pressure-vessel codes. The addi-tional quality requirements for heavier plates of this steel will increase its cost and may thereby eliminate any savings from using it instead of boiler-plate steels.
Other structural-quality steels listed in ASTM designa-tion A-6-54T are A-8, A-94, A-284, and A-242. Steel A-8 is a to nickel steel containing a maximum of carbon and having a tensile strength of from 90,000 to 115,000 psi. It is intended for use in main stress-carrying structural members. The nickel addition results in liner, stronger, and tougher pearlite than is found in plain carbon steel and appreciably increases the yield point, fatigue limit, and impact strength. The difficulties of welding this steel plus the cost extras for nickel addition precludes its use for vessel construction. Steel A-94 is a structural silicon steel containing a maximum of 0.40% carbon and a minimum of 0.20 silicon and having a tensile strength of from 80,000 to 95,000 psi and a minimum yield point of 45,000 psi.
This steel may be eliminated from consideration for vessel construction on the basis of welding and the cost extras for fully killed steel. Steel A-284 is a low- and intermediate-strength carbon-silicon steel containing from
0.10% to silicon and having tensile strengths of from 50,000 to 60,000 psi depending upon the grade. The steel is coarse-grained and requires heat treating for grain refinement. The presence of the silicon tends to dissociate carbides to form soft graphite thereby weakening the welded joints. For these reasons and because this steel is a fully killed steel and therefore involves cost extras, it is not economical to use it for vessel construction.
Steel A-242 is a low-alloy structural steel intended marily for use as a stress-carrying material of structural members when saving in weight and atmospheric-corrosion
27 30 no 0.04 0.05
resistance are important. Thicknesses are limited to not under in. and not over 2 in. It contains a maximum of manganese and a maximum of carbon.
This steel has a yield point of 50,000 psi for thicknesses of from to in., 45,000 for thicknesses of to in.
and 40,000 for thicknesses of to 2-in. in comparison to a yield point of 30,000 psi for A-283, Grade C. For the plates thick and less this represents an increase of
or more in yield strength. Using the same design factor of safety based on yield point results in a proportional decrease in metal thickness required to resist a given load.
In designs in which stress rather than elastic stability or brittle fracture is controlling, the use of steel rather than a plain carbon steel such as A-283, Grade C may result in a saving. See Table 3.2 for specifications for this steel and Chapter 3 for further discussion of its use.
5 . 3 P R O P O R T I O N I N G O F V E S S E L S W I T H F O R M E D HEADS
In general, the cost of a vessel may be considered to be proportional to the weight of the steel used in its construc-tion. It would therefore appear that for storing a fluid under uniform pressure a vessel having the minimum surface area and thickness per unit volume would be the most eco-nomical. A spherical vessel has the minimum surface area per unit volume and the minimum shell thickness for a given pressure and volume. If the cost of fabrication were not a prime consideration, the most economical shape for a vessel would therefore appear to be a sphere. However, the fabrication costs of spherical vessels are so great that their use is limited to special applications. Cylindrical vessels are more easily fabricated, in the majority of cases are con-siderably simpler to erect, are readily shipped, and are therefore more widely used in the process industries.
For a simple cylindrical vessel with formed heads, the . optimum ratio of length to diameter, L/D, is a function of the cost per unit area of the shell and the formed heads.
More complex vessels such as distillation columns, heat exchangers, and evaporators have additional parts such as
Proportioning and Head Selection for Cylindrical Vessels with Formed Closures
D i m e n s i o n s f o r a 2 : 1 e l l i p s o i d a l d i s h e d h e a d .
trays in distillation columns and tube bundles in heat exchangers which must also be considered in determining the optimum proportions.
The proportioning of a simple vessel may be based either on the cost per pound of the material or the cost per unit area of the material. In Chapter 3 the proportioning of flat-bottomed, cylindrical, cone-roofed tanks was based on the cost per unit area because land and foundation costs, which are important for such vessels, can best be considered on a unit-area basis. In addition, the cost of coned roofs and flat bottoms are relatively constant on a unit-area basis for large-diameter tanks. However, cylindrical tanks with formed ends for various pressure services have wide variations in thickness and therefore vary in cost per unit area. The cost of land area and foundations is usually a minor consideration for such vessels. Therefore, is more advantageous to consider the cost of shell and heads in terms of unit rather than in terms of unit area.
5.30 Equations for Optimum Proportions of Vessels with Elliptical Dished Heads.
VOLUME RELATIONSHIPS. A cylindrical vessel closed at dished heads has a volume equal to the volume of the cylindrical section plus twice the vol-ume contained in one of the heads. The volvol-ume contained in a head can be expressed in terms of a cylinder of equiva-lent volume having the same inside diameter as the cylin-drical section of the head. Figure 5.2 is a cross section of . . . . . an ellipsoidal head having a 2: 1 ratio.
for the volume relationships for a ellipsoidal head are as follows.
The equation of au ellipse is:
For a 2: 1 ellipsoidal dished head a = 2b Substituting we obtain:
Expanding we obtain:
+ =
Solving for we obtain:
Differential volume,
= A dy = dy Integrating we obtain:
of an equivalent cylinder is:
= where H = length of cylinder
Equating we obtain:
3 3
Thus the volume of IWO ellipsoidal heads having a ratio of 2.0 is:
Therefore, the the vessel is:
where = length of the vessel, line tangent line, between heads, feet.
Solving for L, we obtain:
COST RELATIONSHIPS. The diameter of a circular plate required for forming an ellipsoidal head is approximately greater than the internal diameter of the finished ves-sel (103). Also, the cost of the formed heads is approxi-mately greater than the cost of the steel from which they are formed. This increase in cost results from cost extras for circular plates and the cost of forming and
machining. Let .
= cost of fabricated shell, dollars per pound
= cost of fabricated shell, dollars per pound