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CHAPTER

26

26.1 INTRODUCTION

This chapter is intended primarily for engineers and designers

whose experience with vessels is primarily with metal equip-

ment. Those having experience with fiberglass equipment but not

with Section X [1] or RTP-1 [2] will also find this chapter useful,

but they may want to skim over the following sections on FRP2

technology.

Section X is part of the ASME Boiler and Pressure Vessel

(B&PV) Code and has been enacted into law in 37 jurisdictions in

the United States and Canada. Although the authors of RTP-1

wrote it so that it could be used as a Code, RTP-1 has not been

enacted into law anywhere; therefore, it is at present a voluntary

standard. Both standards govern vessels constructed of thermoset-

ting resin reinforced with glass fibers. In addition to glass fibers,

Section X also provides for vessels reinforced with carbon or

aramid fibers. The pressure scope of Section X is 15 psig to

15,000 psig internal pressure of which the upper limit depends on

the size and construction of the vessel. RTP-1 covers tanks and

vessels with design pressures 0–15 psig. Both standards have pro-

visions for vessels with external pressure from 0–15 psig.Neither RTP-1 nor Section X makes a good handbook or text-

book on FRP vessel design. This chapter is intended to serve as a

manual on the use of the documents. An engineer who specifies an

FRP vessel does not need to have the under-standing of FRP that

the vessel designer possesses. However, in specifying the vessel,

the engineer necessarily makes many design choices, for which rea-

son he or she should understand the rudiments of FRP technology.

Section 26.2 discusses the basics of FRP technology, particularly

aspects that might be foreign to metal-vessel engineers.

26.2 FRP TECHNOLOGY

The purpose of this section is to discuss technology used in

Section X and RTP-1 that may not be familiar to engineers anddesigners of metal vessels. This section describes the resins and

reinforcing fibers included in RTP-1 and Section X. The docu-

ments govern vessels built of epoxy, vinyl ester, polyester, furan

and phenolic resins reinforced with glass, and carbon and aramid

fibers. It also describes the following processes used to manufac-

ture RTP-1 and Section X vessels: contact molding, bag molding,

centrifugal casting, and filament winding. The joining of vessel

parts made by these methods is also discussed.

Stress analysis of FRP equipment involves lamination theory

and  plate-and-shell theory . Plate-and-shell theory is widely used

by metal-vessel designers and is therefore not discussed except

where it forms part of the bases for design examples. Lamination

theory is a branch of mechanics concerned with plates and shells

made of layered material, where the layers are bonded together,

but have different elastic properties. Lamination theory is essen-

tial to the engineering of FRP tanks and vessels but is not needed

to design and analyze metal equipment. Engineers familiar with

metal-vessel design are usually unacquainted with lamination the-

ory; therefore its rudiments are discussed. This chapter presents

the physical, intuitive basis for lamination theory and examples of 

its application, but not its mathematical development. Lamination

theory is used in both RTP-1 and Section X.

Acoustic-emission (AE) examination is another technology

widely applied to both new and in-service FRP tanks and vessels,

although not as widely to metal equipment. It is required for some

Section X vessels and is optional for RTP-1.

FIBER-REINFORCED PLASTIC

PRESSURE VESSELS AND

ASME RTP-1–REINFORCED

THERMOSET PLASTIC

CORROSION-RESISTANCE EQUIPMENTPeter Conlisk1 and Bernard F. Shelley

1 Late Peter J. Conlisk was the originator of this chapter for the 1st, 2nd and 3rd

editions. Bernard F. Shelley updated this chapter for the 4th edition.2 FRP is an acronym that stands for fiber-reinforced plastic; RTP is an acronym that

stands for reinforced-thermoset resin. Herein, FRP, RTP, and fiberglass are all used as

synonyms.

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26-2 • Chapter 26

26.2.1 FRP-Composite Materials

FRP-composite materials governed by Section X and RTP-1

consist of thermosetting plastic that is reinforced by glass, aramid,

or carbon fibers. The vast majority of FRP-composite tanks and

vessels use glass fibers. Thermosetting resins are viscous liquids

that can be cured to form rigid solids. The curing process is initi-

ated by the addition of a hardening agent, the use of catalysts and

initiators, the use of heat, or the use of a combination of chemical

agents and heat. Once cured, the now-rigid plastic cannot be melted

and rehardened, for which reason the vessel parts built of com-posites made with thermosetting resins cannot be welded together

but must instead be assembled by adhesive joints. Vessel parts are

built up layer by layer with glass fibers bound together with the

thermosetting resin. The layers are applied to molds or mandrels

by many processes that are described in this chapter.

The fiber reinforcement contributes structural performance

required of the vessel or tank. The fibers are the primary contribu-

tor of strength and stiffness of the vessel parts. Section X covers

FRP reinforced by E-glass, S-glass, or aramid and carbon fibers,

whereas RTP-1 covers FRP reinforced by either E-glass or S-

glass. The average diameter of a glass fiber is approximately

0.0005 in.; the diameter varies from 0.00025 in. to 0.00075 in.

Table 26.1 summarizes fiber properties.

Section X provides for five kinds of resin, each described asfollows:

Isophthalic Polyester This is the lowest cost system governed

by the ASME standards. Isophthalic polyester has good strength

and corrosion resistance and is therefore widely used for FRP

chemical-process equipment. It is cured at room temperature.

Vinyl Ester These resins combine both epoxy and polyester

technology. They have excellent corrosion resistance, strength, and

toughness, but they are more expensive than isophthalic poly-

esters. They can be cured at room temperature.

Chlorendic Bisphenol-A Fumerate These resins are used for

more exotic systems to improve corrosion resistance and high-temperature service and are therefore more expensive than vinyl

ester. They are cured at room temperature.

Phenolic These resins have better flammability properties (e.g.,

higher flame retardance and lower smoke emissivity) than the

other four families of resin. Phenolic composites are more brittle

than composites built with the other resins, and phenolic resins are

harder to process than the others. Phenolics are cured at room

temperature.

Epoxy There is wide range of epoxy resins available. Epoxy

composites typically are stronger than composites made with the

other resins and have good chemical resistance. They are usuallycured with heat.

Furan This is a liquid thermosetting resin in which the furan

ring is an integral part of the polymer chain made by the conden-

sation of furfuryl alcohol. Furan resins have excellent corrosion

resistance especially with fluids with organic contaminates. They

also provide higher temperature resistance than most polyester

resins. They are very brittle in nature, hard to handle and must be

post cured at elevated temperatures.

RTP-1 governs FRP made with isophthalic polyester, vinyl

ester, and chlorendic Bisphenol-A Fumerate resins; it does not

cover phenolic, furan or epoxy laminates.

The resin and glass are combined and applied to the vessel-part

mold in thin layers called laminae. Many laminae combine to form

the full-part thickness, and this “stack-up” or sequence of laminae iscalled a laminate. Laminae can be classified by the form of reinforc-

ing glass they contain. The common lamina types are as follows:

Mat Lamina Figure 26.1 shows a magnified view of this prod-

uct form. The mat commonly used in tanks and vessels weighs

either 0.75 oz/ft2 or 1.5 oz/ft2 and is supplied in rolls of various

widths. When it is combined with resin, applied to a mold, and

cured, a 1.5 oz/ft2 mat ply is typically 0.43 in. thick and is by

weight about 35% glass fiber.

Woven-Roving Lamina Figure 26.2 shows woven-roving rein-

forcing glass. There are five fiber bundles per inch in the vertical

FIG. 26.1 FIBERGLASS-REINFORCING MAT

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direction and four in the horizontal direction. The woven-roving

lamina weighs 24 oz/yd2 (2.7 oz/ft2).3 A typical specimen is 0.33 in.

thick and is by weight 50%–60% glass fiber.

Filament-Wound Lamina The following brief description of 

filament winding is taken from an article on the Composite

Fabricators Association Web site [3].What is filament winding? Filament winding has been com-

pared to “wrapping a whole bunch of string around a spool and

then taking the spool out late.” That’s a fairly simple analogy, but

it’s close to the mark. The spool essentially is the internal part,

referred to as the mandrel that forms the shape of the filament

wound structure. The string is the reinforcing fiber that is system-

atically wound around the mandrel until it totally covers the sur-

face area to a depth desired by the designer. In order to keep the

string in the place, the fiber reinforcement is saturated with the

glue, or resin, which eventually cures and binds the fibers in place.

A filament-wound lamina has all the fibers running in the same

direction. The fibers are continuous and are precisely placed by

the winding process. Therefore, they are more tightly packed than

the fibers in mat and woven-roving laminae. Filament-woundlaminae have a higher glass content than the other types—

60%–70% by weight. Figure 26.3 shows spools of glass-roving

laminae (bundles of individual fibers) that are used for filament

winding. About 5,000 individual fibers make up a strand that is

wound on the spool. The fibers are about 0.005 in. in diameter.

The roving bundles are applied at various wind angles, which are

the angles between the fiber and a line on the surface of the part

that is parallel to the axis of the cylinder being constructed.

C-veil, Carbon-Fiber Veil, and Nexus Lamina The corrosionresistance of the process surface of a laminate is often enhanced by

applying a corrosion barrier . Typically, the innermost surface con-

sists of a C-veil, carbon-fiber veil, or nexus ply followed by two or

three mat plies. A C-veil ply is a resin-rich layer about 0.01 in. thick 

and reinforced with a C-glass veil. Veil is a gauzy sheet of randomly

oriented C-glass fibers weighing about 0.1 oz/yd3.

The glass content is approximately 10% by weight. In a nexus

lamina, the C-glass veil is replaced by a thin, feltlike sheet made

from polyester fibers. Veil made from carbon fiber is also used,

and occasionally double C-veil or nexus layers are used.

Mat and veil-reinforced laminae are isotropic in the plane of the

laminate, whereas woven-roving and filament-wound piles are

3 For reasons unknown to the author, it is an industry practice to quote mat

weight in oz/ft2 and woven-roving weight in oz/yd2.

FIG. 26.2 WOVEN-ROVING REINFORCING GLASS

FIG. 26.3 SPOOLS OF CONTINUOUS ROVING

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26-4 • Chapter 26

orthotropic in both stiffness and strength. Tables 26.2, 26.3, and 26.4

each summarize the properties of the laminae discussed pre-viously.

Table 26.2 provides reinforcement weight, lamina thick-ness, and

glass content by weight of the six types. Table 26.3 lists the elastic

properties of the laminae; Table 26.4, the strength properties.

The principal direction of a lamina is the direction of the

fibers. For woven-roving laminae, the principal direction is either

fiber direction; in isotropic laminae, the principal direction is

arbitrary. In Tables 26.3 and 26.4, X refers to the principal direc-

tion and Y refers to the direction in the plane of the lamina per-

pendicular to X. Tables 26.3 and 26.4 provide room-temperature

properties for laminae made with Derakane 470 resin and with

the glass contents listed. Properties of laminae made with otherresins or glass content vary somewhat from those listed. At first

glance, it would seem that the woven-roving lamina is only

slightly anisotropic, as the moduli in the  X and Y directions are

not too different. However, in isotropic material the shear modu-

lus G is related to Young’s modulus  E and Poisson’s ratio v by

the following equation:

(26.1)

Suppose for simplicity that we wished to treat the woven-

roving lamina as an isotropic material and decided to set  E as the

G   = E 

2(1   + v)

average of the two Young’s moduli in the table and use the listed

value of Poisson’s ratio. Then,

psi(26.2)

This value for G is 3.06 times the actual value. The actual

woven-roving lamina is much more compliant for tensile strain at

45 deg. to the principal direction than the assumed isotropic

model. Some woven-roving laminae have the same Young’s modu-

lus in the principal directions; however, because of their low shear

modulus, they should be treated as orthotropic materials in thestress analysis. A common example of this kind of behavior is a

cloth handkerchief. It is much stiffer in the thread directions than

in the bias direction. Even though the tensile moduli in the thread

directions are roughly equal, the cloth is highly anisotropic.

The values in Table 26.4 are for the same laminae as in Table

26.3; laminae made with other resins and glass contents have

somewhat different strength properties. However, most other fea-

tures of Table 26.4, including mat lamina having higher tensile-

strength than compressive-strength properties, are common to all

the laminae allowed by Section X and RTP-1. Nonetheless, the

strength behavior is very different and more complicated than that

of ductile metals used in tanks and vessels. Strengths may or may

G   =2.71   * 106

2(1   + 0.15)= 1.18   * 106

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not be different in different directions. For example, the tensile

strength of mat laminae is the same in both directions, whereas

the tensile strength of filament-wound laminae is 32 times greater

in the fiber direction than it is in the cross-fiber direction. In some

laminae (such as mat or woven-roving), the compressive strength

in a given direction is less than the tensile strength. In filament-wound plies, the compressive strength is less than the tensile

strength in the fiber direction, but it is greater than the tensile

strength in the cross-fiber direction. There is no obvious general

relationship between shear strength and the other strength values.

Complicated elastic and strength properties make stress analy-

sis of FRP equipment more difficult and time-consuming than

analysis of metal equipment of similar complexity. Finite-element

methods make such stress analysis practical. Many commercially

available finite-element codes have layered composite-plate ele-

ments that employ lamination theory (to be described in Section

26.9.1) to form the stiffness matrices of the elements and also

provide lamina-by-lamina stress- and strain-field output. The

codes usually include failure criteria suitable for use with FRP

laminates, one of which—the Tsai-Wu Tensor Interaction Criterion(to be discussed)—is used by both RTP-1 and Section X. If an FRP

tank or vessel can be validly modeled by plate elements, finite-

element analysis is somewhat more expensive than analysis of a

comparable metal vessel, but not prohibitively so.

26.2.1.1 Notation for Laminate Sequences As stated previously,

a laminate is composed of a sequence of laminae. This paragraph

explains the common notations used for specifying a laminate

sequence or stack-up. “V ” designates a corrosion-veil lamina; “ M ,”

a mat lamina; “WR,” a woven-roving lamina; and “FW ´ a,” or“FW´ a,” a filament-wound lamina in which is the wind angle.A stack-up is described by combining these symbols; for example,

a

a laminate consisting of a veil ply, two mat plies, and three sets of 

alternate mat and woven-roving plies —finished by a mat ply—is

designated by “V , MM , 3( M , WR) , M.” A filament-wound laminate

0.46 in. thick, with a wind angle of 55 deg. and a standard corro-

sion barrier, is designated by V , 2 M , 9(FW 55 deg.). The lami-

nate has a veil and two mat plies for a corrosion barrier, followedby eighteen plies of 0.02 in. thick filament-wound layers with

alternate plies at 55 deg. and 55 deg.Table 26.5 lists the lamination sequences commonly used for

mat–woven-roving laminates, and Table 26.6 gives the drafting

symbols that specify the sequences. The assumptions made in

these tables are that veil plies are 0.01 in. thick, mat plies are

0.043 in. thick, and woven-roving plies are 0.033 in. thick. The

glass fiber in the mat plies weighs 1.5 oz/ft2, whereas the fiber in

the woven-roving plies weighs 24 oz/yd2.

The “ E ” plies in Table 26.5 are exotherm plies. Resin curing is

an exothermic reaction that generates enough heat to damage the

laminate if the laminate thickness is built too fast. To prevent this

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26-6 • Chapter 26

occurrence, the laminator pauses after the corrosion barrier is laid

down until the peak of the exothermic reaction occurs, after which

the laminate begins to cool. The laminator resumes activity until the

first E ply is reached; then waits again for the peak exotherm. (The

 E plies are ordinary mat plies.) Fabrication continues in this man-

ner, with a pause at each exotherm ply. To build thicker

mat–woven-roving parts, the laminator simply adds more 3( MR), M 

sequences, giving proper attention to the exotherm plies.

The ply thicknesses assumed in the foregoing paragraph are

typical of industry practice, but Fabricators may not use preciselythese values. Instead, they may use the values that their shops

actually produce. Because of these minor variations among

Fabricators, it is better to specify the laminate in a vessel part by

drafting symbols such as those in Table 26.6 rather than simply

giving the thickness and type of laminate. For example, an engi-

neer who wants to specify a mat–woven-roving laminate in.

thick would specify a V , 2 M , 3( MR) M stack-up in addition to

specifying the reinforcing glass weights.

26.3 FABRICATION METHODS4

Pressure-containing parts for RTP-1 and Section X, Class II

vessels are made by contact molding and filament winding. Partsfor Section X, Class I vessels are made by those two processes as

well, but also by bag molding and centrifugal casting. Section X,

Class III vessels are only made by filament winding over a metal-

lic or thermoplastic liner with polar boss openings. Each of these

methods is discussed in the following paragraphs.

38

26.3.1 Contact Molding

The following definition is from the glossary of Section X [1]:

Contact molding—a process for molding reinforced plastic in

which reinforcement and resin are placed on a mold—cure is

either at room temperature using a catalyst–promoter system

or by heat in an oven, and no additional pressure is used.

Contact molding includes two processes: the hand lay-up and the

spray-up. In the hand lay-up method, the mold is first prepared witha parting agent so that the resin does not adhere to the mold as it

cures. On head molds, wax-parting agents or a liquid such as

polyvinyl alcohol is used; on cylindrical mold, Mylar film is usually

used. A sheet of reinforcing material, such as a C-glass veil, is then

placed on the mold and wetted with catalyzed and promoted resin.

(Catalyst and promoter are added to all resins except epoxy so that

they will cure and become solids. A hardener may be added to the

epoxy, or it may be heat-cured.) The resin-wetted reinforcing mate-

rial is compacted and pressed to the mold by hand with a roller to

squeeze out excess resin and to remove air bubbles. Rollers resem-

ble paint rollers, except that the type used in this application is

metal with deep grooves about in. wide and in. deep, with a in.

pitch. Rollers vary from 2 or 3 in. to in. in diameter and from 3 in.

to 12 in. in width. After the first lamina is applied, the second andsubsequent plies are added the same way. Veil, mat, and woven-

roving plies are all applied by the hand lay-up method.

In the spray-up method, resin and reinforcing glass are applied to

the mold with a chopper gun. Figure 26.4 shows a schematic depic-

tion of a chopper gun. Four hoses carry fluids to the gun: an air

hose that powers the chopper and provides a stream of air for carry-

ing the chopped glass and resin to the mold; a resin hose; a hose

that conveys the catalyst and promoter to the gun; and a solvent

hose. A glass strand, which (as mentioned previously) contains

about 5,000 individual glass fibers, also enters the gun. In the gun,

the resin, promoter, and catalyst are mixed and then sprayed onto

the mold surface. At the same time, the roving strand enters the gun

and is chopped into lengths that vary from to 2 in., and the34

34

14

14

18

 In the FRP tank and vessel industry, the term Fabricator is used the same way

as  Manufacturer is in the metal vessel industry. The term  Manufacturer is usually

reserved for those who manufacture resin, reinforcing glass, and other components

supplied to the Fabricator.

FIG. 26.4 SCHEMATIC DIAGRAM OF A CHOPPER GUN

4

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chopped glass is also sprayed onto the mold at the same place as

the resin. The result is that a layer of resin-wetted glass fibers is

deposited on the mold. The mass of chopped glass fiber and cat-

alyzed and promoted resin is compacted with a roller, as in the

hand lay-up process. A lamina made this way is generally consid-

ered equivalent to a mat ply of the same thickness. When the opera-

tor pauses, even for a short time, he or she pumps solvent through

the gun to remove the resin. If this is not done, the resin—beingcatalyzed and promoted—would rapidly solidify and clog the gun.

Contact molding is used to make all pressure-containing parts,

including nozzles with flanges. It is versatile and requires only

inexpensive, simple tooling. However, it is also labor-intensive,

involving so much handwork that quality control is more difficult

than with more automatic processes.

26.3.2 Filament Winding

Figure 26.5 is a schematic diagram of filament winding. A band

of glass or other fiber roving is pulled from the creel through a resin

bath and wound onto the mandrel. For winding a cylindrical shell,

Mylar film is ordinarily used as the parting agent. The roving band is

2–6 in. or more wide, depending on the diameter of the part being

wound. Consider winding an 8 ft diameter vessel shell with a55 deg. wind angle. The roving band would be about 5 in. wide and

consist of 45 strands. (Nine strands per in. of width is typical.) Each

strand has about 5,000 individual fibers; thus the 5 in. band consists

of 225,000 fibers. The creel would hold 45 spools of roving. The

carriage feeding the band onto the mandrel moves axially along the

mandrel to maintain the proper wind angle. When the carriage

reaches the end of the mandrel, it reverses direction, laying down a

band with the opposite slope of the band put down on the first pass.

With a 55 deg. wind angle, the bands would form a helix on the

shell, with a pitch of 211.2 in.; therefore, the bands are widely

spaced. The carriage is carefully controlled so that on the third pass

(the second pass in the original direction), the band is next to the

band made on the first pass. Eventually this process results in the

covering of the mandrel with two plies of material: one with a windangle of 55 deg.; the other, 55 deg. The process continues untilthe desired thickness is built up. Laminate thickness increases quickly

enough during winding so that the process must be paused to let the

peak exotherm occur, just as in contact molding. After the exotherm

but before the winding is resumed, the laminator usually applies a mat

bedding ply, either by using the hand lay-up method or by using a

chopper gun. The laminate laid down at the ends while the carriage is

reversing has a variable wind angle (from 55 deg. to 0 deg.) as well as

variable thickness, for which reason the laminate is called the turn-

around zone. This portion is usually cut off and scrapped.

Filament-wound laminates have of a 60%–70% glass content

by weight, considerably higher than mat or mat–woven-rovinglaminates. Consequently, filament-wound laminates are stronger

and stiffer than the others. Because the process is more automated

than contact molding, the quality is more predictable. Once a

winding setup is working properly, the quality is more repeatable

and the quality control is easier than with contact molding.

Cylinders as small as 1 in. and as large as 80 ft are filament-

wound. Mandrels with either horizontal or vertical axes are used,

as are winders on which the mandrel is mounted so that it can be

rotated about more than one axis. These winders can produce ves-

sels complete with heads.

26.3.3 Bag Molding

Only Section X, Class I provides for bag molding. Qualification

of a Class I design is by destructive testing of a prototype. If theprototype satisfies Section X requirements, vessels identical to the

prototype may be built and receive an ASME RP Stamp. Design

qualification of Class II vessels is by mandatory design rules and

nondestructive acceptance testing. Class I rules are suitable for

mass-produced vessels, whereas Class II rules are used for one-of-

a-kind or limited-production equipment. The two classes are dis-

cussed more thoroughly later in this chapter.

Figure 26.6 sketches the bag-molding concept. The catalyzed

resin–glass mixture is applied to the inside of the mold, the bag is

inserted and pressurized, and the resin is cured either at room

temperature or by the application of heat. The resin–glass mixture

may be applied by contact molding; otherwise, the reinforcing

fibers may be a preform, a reinforcement that is preshaped to the

general geometry of the intended molded part, usually by lightpressing or by distribution of chopped fibers of a perforated for-

mer. It is used on more complex or deep-draw moldings to opti-

mize the distribution and orientation of the fibers [4]. The

Fabricator may also apply the resin and glass onto the bag and

FIG. 26.5 FILAMENT WINDING

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26-8 • Chapter 26

then insert the bag into the mold. Bag molding can produce parts

with a higher glass content than contact molding, as the

reinforcement–resin mass is compacted more during bag molding

than during the rolling step of contact molding. Thus bag-molded

parts are stronger and stiffer than contact-molded parts. In addi-

tion, bag molding can produce vessels with integral heads.

26.3.4 CENTRIFUGAL CASTING

Figure 26.7 is a schematic depiction of centrifugal casting.

Resin, resin catalyst and promoter, and glass fiber are all con-

veyed to a device that chops the glass and blends the ingredients;sprays them onto the inside of the mold. The mold rotates at a

high enough speed for the centrifugal force to press the

resin–glass mass against the mold. Either room- or elevated-

temperature curing may be used. Centrifugal casting produces

hollow cylindrical parts, such as vessel shells.

26.3.5 Joining Vessel Parts

The aforementioned processes produce vessel parts: shells,

heads, nozzles, and so on. Because the resins governed by theASME documents are all thermosets, once cured they will not melt

and solidify into good material. Thus vessel parts cannot be joined

by welding. The industry has developed adhesive-joint techniques

for assembling parts; these are discussed in this section.

Figure 26.8 shows the steps for making the type of butt joint

required by RTP-1 for making head-to-shell or shell-to-shell

girth joints. Bonders apply the structural overlay—also called

strap-ping—to the outside of the vessel, which is usually covered

with a film of wax. Air inhibits the cure of most resins used for

vessels, so the common practice is to coat the outside surface of a

part with resin that contains a small fraction of wax. The wax

floats to the surface, preventing the contact of air with the curing

resin and producing a wax film on the outside of the vessel. This

film would interfere with bonding to the surface, so it is thereforeremoved before a structural joint is applied. The bonder first sands

the surface to which the joint is to be applied with a coarse abra-

sive until the wax is removed and the glass fiber is exposed. The

 joint plies are then applied by the use of hand lay-up methods.

The joint may be of all-mat-ply construction or of alternate plies

of mat and woven-roving. If the joint is all mat, each ply overlaps

the preceding ply by in. If the joint is alternating mat and woven-

roving, the woven-roving plies are of the same width as the mat ply

underneath them, and each mat ply extends in. beyond the ply

beneath it. Steps (2) and (3) in Fig. 26.8 illustrate the application of 

the structural strapping. Peak exotherms are accommodated the

same way as in making laminates, as discussed previously. The

design rules in RTP-1 govern the thickness of the joint overlay;

their intention is for the joint laminate to be at least as strong as thestronger of the laminates in the parts being joined and for the over-

12

516

FIG. 26.7 CENTRIFUGAL CASTING

FIG. 26.6 BAG-MOLDING CONCEPT

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lay to be wide enough to provide adequate shear strength to carry

the load from the part to the joint overlay to the second part.

The final step (4) of Fig. 26.8 is to make a corrosion seal for the

 joint. This seal is made on the inner (process) surface, as shown in

Fig. 26.8, and the seal is a minimum of two plies of 1 mat with an

additional C-veil or nexus veil on the inside. The innermost mat play

is at least 3 in. wide, the next ply extends at least in. beyond the

first, and the veil ply extends at least in. beyond the mat plies.

The joint is applied to cured FRP parts. Therefore, the bond

between the joint and the parts is adhesive; it is not the molecular

bond that forms when the parts are cured. Adhesive bonds are notas strong as molecular bonds, but they are strong enough to pro-

vide safe joints as long as the requirements of the applicable

ASME Standard are satisfied.

Figure 26.9 illustrates the bell-and-spigot joint, another design

detail provided by RTP-1. This joint is used to assemble shell seg-

ments or to join the head and shell. The first step in making the

 joint is to fit and hold the parts, which is ordinarily done with fix-

tures. The next step is to apply the resin putty as shown in Fig.

26.9. The resin putty is made of the same resin as the parts being

 joined and is thickened with particulate-mineral filler. Recall that

the strapping is put in place and then compacted with a roller. The

resin putty serves as a foundation for the application of the struc-

tural strapping—that is, something to press the roller against.

Finally, the corrosion seal is installed.Figure 26.10 illustrates a Section X, Class II butt joint—a vari-

ation on the RTP-1 butt joint shown in Fig. 26.8 —that constitutes

a head-to-shell joint, although the detail also applies to shell-girth

 joints. The difference between the RTP-1 joint and the Section X

 joint is that the parts to be joined are scarfed first, as in steel weld-

ing, and then the structural overlay is applied. Rules for dimen-

sions of the joint are given in Section X, Article RD-1175 [1].

Both RTP-1 and Section X use the same styles of joints for

attaching nozzles to shells or heads. Figure 26.11 shows one type

of joint —a penetrating nozzle —in which the nozzle neck pro-

trudes inside the shell or head to which it is attached. The nozzle

neck–flange assembly is first attached to the head or shell with

12

12

12

fixtures or with a few dabs of hot-melt adhesive to hold the nozzle

in place while the attachment laminate is applied. Next, the resin

putty is placed as shown in Fig. 26.11 to provide a base for the

structural attachment layers. Finally, the structural overlay is

installed. Either RTP-1 or Section X, whichever applies, governs

the dimensions of the overlay. Flanges are attached to nozzle

necks by similar joints, and the reinforcing pad is added to mini-

mize stress intensification caused by cutting the hole in the shell

or head on which the nozzle in installed. Reinforcing-pad dimen-

sions are given in Section X or RTP-1, as applicable.

FIG. 26.8 RTP-1–STYLE BUTT JOINT

FIG. 26.9 BELL-AND-SPIGOT JOINT

FIG. 26.10 SECTION X–STYLE BUTT JOINT

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26-10 • Chapter 26

26.4 STRESS ANALYSIS OF FRP VESSELSSimpler RTP-1 or Section X, Class II vessels can be

designed by using design rules found in the ASME Standards,

although many configurations are not governed by these

rules. Both Section X and RTP-1 provide for design-by-stress

analysis, which covers such configurations. Two factors com-

plicate the stress analysis of FRP vessels compared to metal

vessels:

(1) Vessel parts are made of layered composites, in which the

layers have different elastic and strength properties, causing

each layer to have its own stress distribution.

(2) Each type of layer has five distinct strength properties,

which complicates the failure criterion.

This section discusses how these complications are treated.

Lamination analysis provides a way of dealing with the first

complication of the preceding list. Most tanks and vessels have

geometries that allow for valid analysis by the plate-and-shell

theory, which is true of both FRP and metal equipment. A fun-

damental assumption in the theory is that the variation of strain

through the thickness of a part is linear, or that the “plane sec-

tions remain plane”—an idea that Fig. 26.12 illustrates. Sketch(1) of Fig. 26.12 depicts an undeformed cross section of a lami-

nate with eight laminae. The vertical lines represent the edge

view of planes in the laminate. If an in-plane force were

applied to the laminate, it would deform as shown in sketch (2):

stretching in the load direction and contracting in the other two

directions. The vertical planes would move apart but still

remain parallel. If pure bending were applied, the situation

would be as shown in sketch (3): the vertical planes would

rotate, but remain in plane. Strain in the cross section therefore

varies linearly in the direction normal to the plane of the lami-

nate. The same two kinds of deformation can occur simultane-

ously from loading normal to the page and also as a result of 

twisting; however, the variation of the strain is still linear in the

normal direction.The foregoing assumption about strain is called the Kirchoff 

hypothesis and is fundamental to plate-and-shell theory. It is as

true when applied to FRP laminates as when it is applied to plates

made of homogeneous, isotropic material. In an FRP laminate,

each lamina has a linear stress–strain law, but each type of lamina

has different elastic properties and therefore a different linear

stress–strain law, although the lamina stresses can be computed

FIG. 26.11 PENETRATING-NOZZLE-INSTALLATION-LAMINATE OVERLAYS

FIG. 26.12 PLANE SECTIONS REMAINING PLANE

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FIG. 26.13 NORMAL STRESS IN LOAD DIRECTION FOR EXTENSIONAL STRAIN

from the strain. Lamination theory, a branch of mechanics that

treats this situation, is used to formulate the relationship between

the strain in a plate or shell and the force and moment resultants

in the solid.

As an example of the results of lamination theory, consider the

stress distribution in a 7-ply mat–woven-roving laminate 0.271 in.

thick subjected to a tensile force resultant of 500 lb/in. in the princi-

pal direction of the woven-roving plies. The laminate constructionis given in Table 26.7. In a homogeneous plate, the stress would be

500/0.271 1,845 psi, but because the two types of ply in the lam-inate have different elastic properties, the stress is not constant

through the thickness. (Note: please see Table 26.3 for the lamina

properties used in this example.) Figure 26.13 plots the normal

stress in the load direction. Figure 26.14 graphs normal stress in the

direction perpendicular to the load. The strain constitutes the uni-

form extension in the load direction and the Poisson’s ratio con-

tractions in the perpendicular direction. Figure 26.13 shows that

the stress in the 4-mat plies is the same (1,235 psi) and that the

stresses in the woven-roving plies are equal at 2,904 psi but

higher than the stress in the mat plies. Stress in the woven-roving

plies, although higher because they are stiffer than the mat plies,

are under the same strain. Both stresses are considerably different

from the stress that would occur in a homogeneous laminate—

1,845 psi.

In a homogeneous laminate, stress would vanish in the cross-

load direction. However, again because of different elastic proper-

ties, the Poisson’s contraction induces stress in the cross-fiber

direction, as shown in Fig. 26.14. Stress in the mat plies is 175 psi

tension; in the woven-roving plies, it is 303.4 psi compression.

The force resultant from these stresses is 0.As a second example, consider the same laminate subjected to a

22.58 in.-lb/in. bending moment. In a homogeneous laminate, the

maximum bending stress is given by the following familiar equation:

(26.3)

Figure 26.15 shows that the stresses for laminae 1, 2, and 3 are

1171.4 psi, 1860.2 psi, and 391.5, respectively, all in compression.

The stress in lamina 4 vanishes, whereas the stress in laminae 5,

6, and 7 are symmetric to laminae 3, 2, and 1, respectively, but are

tensile instead of compressive. Note that the maximum bending

stress is not in the extreme fiber. Figure 26.16 gives the ply stresses

in the cross-load direction. In this case, the neutral bending plane is

s   =6 M 

t 2  =

6   * 22.58

0.2712  = 1,845

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26-12 • Chapter 26

FIG. 26.15 NORMAL STRESS FROM BENDING LOAD IN BENDING DIRECTION

FIG. 26.16 NORMAL STRESS DISTRIBUTION IN DIRECTION PERPENDICULAR TO BENDING

FIG. 26.14 NORMAL STRESS PERPENDICULAR TO LOAD DIRECTION FOR EXTENSIONAL STRAIN

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at the middle plane, but that is only because this laminate is sym-

metric about the middle plane.

If a veil and 2-mat corrosion barrier were added, the laminate

would no longer be symmetric and the neutral bending surface

would not coincide with the middle surface. Furthermore, there

are laminates where the neutral plane for bending in one direction

does not coincide with the neutral bending plane for bending in

the perpendicular direction. Fortunately, modern engineering soft-ware provides practical ways of treating these complexities.

Engineers analyzing structures built of ductile metals often use

either the von Mises or the Tresca criterion to decide whether a

state of stress is excessive. But in general, an FRP lamina has five

independent strength properites, as discussed in Section 26.2.1.

The Tsai-Wu quadratic interaction criterion is in general use for

layered-composite materials; it represents a generalization of the

von Mises criterion [5] and provides a strength criterion for FRP.

Both RTP-1 (in paragraph M3-530) and Section X (in para-

graph RD-1188.5) use the same form of the Tsai-Wu quadratic

interaction criterion. The purpose of the criterion is to distinguish

between stress states that overload any lamina and stress states

that are acceptable. Both standards employ strength ratios for this

purpose. The equations that state the quadratic interaction criterionin terms of a strength ratio may be written as follows:

(26.4)

where

S  xx  the normal stress in a principal direction of the lamina inquestion

S  yy the normal stress in the other principal directionS  xy the shear stress in the plane of the lamina

 R the strength ratio

The other parameters are defined in terms of the five lamina

ultimate strengths, as follows:

(26.5)

where

 X and X c the tensile and compressive strengths in the  x direction, respectively

Y , Y c the tensile and compressive strengths in the y direc-tion, respectively

S u the shear strength

Given the five strength values and a stress state, that is, a set of 

values for S x, S y, and S xy, equation (26.4) can be solved for  R.

This equation is quadratic in R and therefore has two roots for R:

one positive, the other negative. If the positive root is greater than

 F  y   =1

Y -

1

Y c

 F  xy   = -1

22 F  xx F  yy  F  x   = 1

 X -

1

 X c

 F  xx   =1

 XX c F  yy   =

1

YY c  F ss   =

1

S u2

+  R(F  x S  xx   + F  yS  yy)   - 1   = 0

 R2(F  xx S  xx 2

+ 2F  xyS  xx S  yy   + F  yyS  yy2

+ F ssS  xy2 )

a value stipulated in Section X or RTP-1 for the layer in question,

the stress state in the layer is acceptable; however, if the positive

root is less than the stipulated value, the stress state is excessive

and not allowed.

The physical meaning of R is that if all three stresses are multi-

plied by R, the ply is just at the point of failure. Thus  R is like a

safety factor; the greater  R, the farther from failure the lamina is.

Because the five lamina strength values are different for differentlamina types, and also because the stress varies from lamina to

lamina, the criterion is applied to each layer separately.

Finite-element stress analysis of FRP tanks and vessels take

more time than analysis of metal equipment of comparable con-

figuration. Instead of inputting one or two sets of isotropic material

property values for the entire vessel, the analyst must input a set

of orthotropic values for each type of laminate in the vessel.

Furthermore, instead of simply inputting a plate thickness for

each vessel part of different thickness, the analyst must input an

entire lamination sequence for each part and must also sift

through the stress distribution in each lamina. For example, if a

vessel shell consists of twelve plies of material, the analyst

must check the stress distribution in every ply instead of one

bending and one membrane stress distribution for the entirepart.

Modern finite-element software makes stress-distribution check-

ing a practical task. The analyst can set up a set of material con-

stants for each lamina type in the vessel and then refer to the

property set when he or she inputs data that defines the lamination

sequence. Many software systems that have a capability for

layered-composite plate elements provide efficient ways for

specifying stack-ups and also provide ways of finding the most

highly stressed lamina without the analyst having to view the

stress distribution in every lamina. The Algor post-processor, for

example, produces a “worst-ply” plot. The program makes color-

contour plots of the reciprocal of the strength ratio, where the

value plotted is the worst 1/  R for any lamina at that point on the

vessel. Using this plot, the analyst can quickly isolate areas (if there are any) where the strength criterion is violated; then, he or

she looks at individual ply plots in those areas to isolate the loca-

tions and plies where stress is excessive. Other software systems

have other ways of filtering the voluminous stress output pro-

duced by composite-element calculations.

A simpler strength criterion is being introduced into the current

edition of RTP-1, ASME RTP-1-2011. The criterion is intended

for details of design and construction for which no rule is provided

in Subpart 3A, but for which other recognized engineering formulas

exist. They may be accepted by comparing calculated stress with

ultimate laminate strength to establish a minimum design factor.

Other recognized formulas include stress calculations presented in

various sections of the ASME pressure vessel codes, formulas

included in the non-mandatory appendices of RTP-1, and welldocumented formulas presented elsewhere.

Combined flexural and membrane stress must comply with the

following inequalities:

(26.6)

and

smc

St

+sfc

Sf 

…1

F10

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26-14 • Chapter 26

(26.7)

Where

calculated maximum sustained membrane stress calculated maximum sustained flexural stress calculated maximum combined intermittent and

sustained membrane stress

calculated maximum combined intermittent andsustained flexural stress

St ultimate tensile strengthSf  ultimate flexural strength

F10 design factor for sustained loads 10F5 design factor for sustained loads 5

Examples of sustained stress are hydrostatic stress and design

pressure stress. Examples of loads that induce intermittent stress

are wind, earthquake and loads from personnel standing on a ves-

sel. In the two inequalities, maximum stress means the stress with

the largest absolute value. Absolute values of stress are used in

the inequalities.

Quadratic Interaction Damage Criterion Section X, in a pre-

vious edition, Peter Conlisk introduced a new strength criterion

based on acoustic emission measurements of FRP samples which

define the lowest stress at which significant damage occurs. The

required tests are defined by Article RT-8 in Section X. For contact

molded laminates, flexural and shear tests are required. For fila-

ment wound laminates, a sample filament wound cylinder must be

tested. The values upon which the criterion is based are:

Rd damage criterion stress ratio 1.25Sd damaged based design value with respect to shear stress in

the plane of the laminate.

Xd tensile and compressive damage based design value in thex (strong) direction

Yd tensile and compressive damaged based design value inthe y (weak) direction

damage criterion design factor 0.75 stress in the lamina material direction x at the point and

lamina under investigation

stress in the lamina material direction y at the point andlamina under investigation

in-plane shear stress at the point and lamina under investigation

The Quadratic Interaction Design Criterion is:

ss

sy

sx

°

sfi

smi

sf c

smc

smi

St

+sfi

Sf 

…1

F5 (26.8)

This criterion is scientifically better than the others in the two

standards, but it is just now being introduced into use.

26.5 SCOPES OF SECTION X AND RTP-1

This section discusses the scope of both Section X and RTP-1.

The scope of Section X is discussed first, followed by that of 

RTP-1.

26.5.1 Scope of Section X

Section X has two classes of vessels: I and II, both of which

differ in scope. In brief, the classes are distinguished as follows:

(1) Class I vessel designs are qualified through possibly

destructive fatigue and pressure testing of a prototype.

Vessels similar to the prototype may then be built and the

ASME Code Symbol RP applied, but the prototype itself,however, may not receive the Code Symbol RP.

(2) Class II vessel design is qualified through mandatory design

rules and nondestructive acceptance testing, which includes

an acoustic-emission (AE) examination.

(3) Class III vessel designs require advanced stress analysis

including ASME Section VIII, Div. 3 analysis for the metal-

lic bosses at each end. Futher the designs are qualified

through possible destructive fatigue and pressure testing of 

a prototype like class I but in addition are subject to addi-

tional prototype testing including flaw, permeability, boss

torque test, penetration and environmental testing. Finally

an acoustic emission test is performed during the final

hydrotest to further ensure the production vessel is of sound

design. At the present time Class III vessels are limited tothe stationary storage of hydrogen gas.

Table 26.8 gives the pressure scope for Class I vessels.

Vessels with only polar-boss openings must satisfy the follow-

ing requirements to be eligible for the higher pressure scope:

(1) openings shall be centered on the axis of rotation;

(2) openings shall be of the polar-boss type wound in place on

the axis of revolution;

(3) the boss diameter shall not exceed half the vessel inside

diameter; and

(4) the filaments shall not be cut.

 Rd2

°2  c asx

Xdb 2 - sxsy

XdYd+ asy

Ydb 2 + ass

Sdb 2 d   … 1

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COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 26-15

The pressure scope for Class II vessels is more complicated,

depending on the size of the vessel. As is discussed below, Section

X vessels must be between 6 in. and 192 in. in diameter. There

are two methods for design calculations: Method A that uses

design rules like Section VIII, Division 1, and Method B that

provides for design by stress analysis. Vessels designed by

Method A are limited to 100 psi internal design pressure and 144 in.

diameter.

Vessels designed by Method B rules shall have pressure and

diameter restrictions as follows:

1. The algebraic product of the internal pressure in psig and the

diameter in inches shall not exceed 14,400 lb/in (Equation

26.9).

2. The maximum internal pressure shall not exceed 250 psig.

3. The maximum inside diameter shall not exceed 192 in.

Vessels may be designed using a combination of Methods A

and B. For such vessels the maximum design pressure is limited

to 100 psig with a maximum inside diameter of 144 in. Vessels

designed by either Methods A or B are limited to a maximum

external pressure of 15 psig.

(26.9)

where

P is the design pressure in psi and

 D is the diameter in in. These rules are expressed by Figure

26.17

The maximum external design pressure for Class II vessels is

15 psig.

The pressure scope for Class III vessels shall not be less than

3000 psig nor more than 15000 psig. The outside diameter of the

P   =14400

 D

liner is further limited to 100 inches and the burst pressure of the

liner shall not exceed 10% of the burst pressure of the vessel.

The design temperature of Section X vessels must not exceed

250ºF or 35ºF less than the maximum-use temperature of the

resin, whichever is less. The maximum design temperature of 

Section X, Class III vessel shall be at least 35°F below the

maximum-use temperature of the resin but in no case shall it

exceed 185°F. The minimum design temperature is –65°F. The

maximum-use temperature of a resin is either the glass-transition

temperature (TG) or the heat-deflection (also called heat-distortion)

temperature, whichever the Fabricator and resin supplier prefer.

When a polymer is cooler than its TG, it is rigid and hard; when

it is hotter than TG, it is rubbery. The Section X resins are used

below the TG, whereas other resins (such as tire rubber) are used

above it. The elastic modulus of Section X resins drops orders of 

magnitude at and above the TG [6]. The heat-deflection tempera-

ture is the temperature at which a specified bar specimen deflects

0.01 in. when loaded as a simple beam to a constant 264 psi (see

ASTM D 648, Test Method for Deflection Temperature of 

Plastics under Flexural Load , for details). It is usually measured

for resin castings, not laminates [7]. For the resin used in Section

X, the TG and heat-deflection temperatures are approximatelyequal. The temperature scope applies to both Class I and Class II

vessels.

Vessels fabricated under Section X intended for Section IV

potable-water use are limited to applications permitted herein.

The vessels are limited to internal pressure only with a maximum

allowable working pressure (MAWP) of 160 psig. The maximum

allowable temperature used shall be 210ºF [8].

The following classes of vessels are exempted from the scope

of Section X [9].

(1) Pressure containers, which are integral parts of rotating or

reciprocating mechanical devices (e.g., pumps, compressors,

turbines, generators, engines, and hydraulic or pneumatic

FIG. 26.17 INTERNAL PRESSURE SCOPE FOR SECTION X VESSELS

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26-16 • Chapter 26

cylinders) where the primary design considerations and or

the stresses are derived from the functional requirements of 

the device.

(2) Piping systems in which the primary function is to transport

fluids from one location to another within a system of which

it is an integral part.

(3) Piping components, such as pipe, flanges, bolting, gaskets,

valves, expansion joints, fittings, and pressure-containingparts of other components (e.g., strainers) and devices that

are used for mixing, separating, snubbing, distributing and

metering, or controlling the flow, provided the pressure-

containing parts are generally recognized as piping compo-

nents or accessories.

(4) Vessels that have any part of their shells, heads, nozzles, fit-

tings, or support laminates heated above the aforementioned

maximum temperature allowable.

(5) Vessels having an inside diameter or maximum internal

cross-sectional dimension not exceeding 6 in. without any

limitation of the length of the vessel or pressure.

(6) Pressure vessels for human occupancy.

(7) Vessels intended to store, handle, transport, or process

lethal fluids.

The jurisdiction of Section X vessels includes only the vessel

and integral communication chambers; it terminates where

(1) the external piping is connected to the vessel at the threaded

first joint, the first circumferential adhesive-bonded joint,

and the face of the first flange in bolted flanged connections;

or where

(2) the lugs, skirts, and other supporting structures are joined

directly to a vessel at the first joint or connection beyond the

vessel, but the attachment of the supporting structure to the

vessel is included in the scope.

Section X vessels are limited to those constructed of thermoset-

ting epoxy, polyester–vinyl ester, furan or phenolic resins rein-forced by glass, or carbon or aramid fibers.

26.5.2 Scope of RTP-1

The pressure scope of RTP-1 is simpler than that of Section X

and applies to stationary vessels used for the storage, accumula-

tion, or processing of corrosive and other substances at pressures

not exceeding 15 psig external and/or 15 psig internal above any

hydrostatic head. The maximum temperature within the scope of 

RTP-1 is not defined. RTP-1, Article 1-130 states only that

applications above 180F require that the designer recognizes

and accounts for possible reduced mechanical properties at

the elevated temperature and possibly decreasing mechanical

properties with time as a consequence of thermal and chemi-

cal exposure. Such elevated temperature applications require

special design attention, and consultation with the Resin

Manufacturer is essential.

In this connection, it should be noted that RTP-1 requires a

Registered Professional Engineer experienced in the design of RTP-1

vessels to certify the design, including the design temperature(s).

Certain types of FRP equipment are excluded from the scope of 

RTP-1. They are as follows:

(1) vessels with an internal design pressure in excess of 15 psig;

(2) hoods, ducts, and stacks;

(3) fans and blowers;

(4) vessel internals, such as entrainment separators and

packing-support plates;

(5) pumps;

(6) piping; and

(7) underground, fully buried closed vessels

The geometric jurisdiction is similar to Section X. RTP-1

includes the following:

(1) Where external piping is to be connected to the vessel,

(a) the first threaded joint for screwed connections;

(b) the face of the first flange for bolted connections; and

(c) the vessel side sealing surface for proprietary connections

or fittings.

(2) The vessel attachment joint when an attachment is made to

either the external or the internal surface of the vessel.

(3) Covers for vessel openings such as manholes and

hand-holes.

(4) The vessel side sealing surface for proprietary fittings

attached to the vessels for which rules are not provided by

RTP-1, such as gages and instruments.

RTP-1 vessels are limited to those constructed of thermosettingpolyester or vinyl ester, each reinforced by glass fibers.

26.6 DESIGN QUALIFICATIONS OFSECTION X AND RTP-1 VESSELS

This section discusses design qualification of Section X and

RTP-1 vessels. Design qualification of Section X, Class I vessels

is by destructive testing. Qualification for Class II vessels requires

design calculations and a successful AE examination. RTP-1 ves-

sel designs are qualified by design computations and, in some

cases, by proof testing.

26.6.1 Section X, Class I Design Qualifications

No design calculations are required for Section X, Class I

vessels. Section X does contain Nonmandatory Appendix AA

(Suggested Methods of Preliminary Design for Class I Vessels), but

the Fabricator is not obligated to use it. The Fabricator must build a

prototype of a new design and subject it to a cyclic and a qualifica-

tion pressure test. Table 26.9a summarizes these requirements.

The pressure qualification test is a type of hydrostatic pres-

sure test. Filament-wound vessels and pipes tend to “weep” at

pressures considerably less than their burst pressures, that is,

test liquid oozes through the laminate and beads on its surface,

possibly at pressures well below bursting. When this occurs, it

is sometimes difficult to pump the liquid into the test piece

quickly enough to attain the desired test pressure, for which

reason Section X permits the use of a flexible bladder inside the

vessels during the pressure qualification test to attain the quali-

fication pressure. No leakage may occur during cyclic testing,

nor may a liner or bladder be used that is not part of the vessel

design.

When a prototype vessel satisfies these requirements, a vessel

identical to it may be built and marked with the ASME RP Code

Symbol. It may not, however, receive a Code Stamp. Section X

provides a thorough set of quality assurance requirements to

ensure that production vessels are essentially identical to the suc-

cessful prototype vessel. These requirements are discussed in the

forthcoming paragraphs.

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26.6.2 Section X, Class II Design Qualifications

Class II requirements are more similar to those of other sections

of the Code. Section X, Class II requires design computations and

a hydrostatic test, the latter part of an AE examination that is

required for all Class II vessels. Unlike other Code sections, the

Fabricator is required to develop materials’ data for his or her

design calculations. A Registered Professional Engineer must cer-

tify that the design calculations satisfy Section X.

Manufacturers of metal vessels build them of plate and othermetal-product forms that are made of standardized alloys.

Therefore, it is possible to make a compilation of materials’ data,

such as from Section II, Part D of the Code, and use it as input for

design calculations. However, that approach is not useful for FRP

vessels. Fabricators combine resin and fiber reinforcement to pro-

duce vessel components, with results that differ among them.

Neither the Resin Manufacturer nor the Fiber Manufacturer has

control of these differences and therefore cannot certify any par-

ticular set of properties for a cured laminate. Section X requires

Fabricators to measure mechanical properties of the laminates

that they produce for use in design computations.

Section X provides two kinds of design calculation: method A

and method B. Method A is design-by-rule analysis, in which the

thicknesses of the pressure-containing parts are given by simple

mathematical expressions in terms of design pressure, dimensions

of the part, and elastic constants of the laminate of which the part is

made. The properties used in method A are effective elastic con-

stants of the laminate taken as a unit, not the elastic properties of 

the individual laminae comprising the laminate. To provide material

data for a particular design, the Fabricator must measure the elastic

properties of each type of lamina he or she intends to use in the ves-

sel. The design-basis lamina must be composed of the same resin

and reinforcing fiber that will be used as well as the same catalyst,

promoter, and other additives. Based on the lamina properties, the

design engineer uses lamination theory to calculate the elastic

constants of the laminate. Section X, Article RD-12 contains the

lamination theory equations that are used, which are usually volu-

minous and possible to perform with a pencil, some paper, and a

slide rule, although ordinarily commercial software is used. It is the

responsibility of the Registered Professional Engineer who certifies

the design to establish that the software used in the design gives

identical results to the equations in Section X. Figure 26.18 shows

the components for which method A rules exist and indicates the

article giving the rule for a particular component.

Method B governs design-by-stress analysis. A set of thicknessesfor vessel parts is chosen and the stress fields are calculated

throughout the vessel for that choice as well as for all relevant

load combinations. The strength criterion specified by Section X

is applied to determine whether the computed stresses satisfy the

criterion. Section X, Article RD-1188 uses a form of the Tsai-Wu

criterion. Given the strain fields in a vessel for a particular load

combination, Section X lays out a procedure for calculating the

strength ratios, but it does not specify how the analysis to deter-

mine the strain fields should be implemented.

FIG. 26.18 SECTION X, CLASS II, METHOD

B COMPONENTS

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26-18 • Chapter 26

Section X, Nonmandatory Appendix AC (Discontinuity Stresses

for Class II Method B Vessels) discusses discontinuity stress analy-

sis, although very few engineers today use discontinuity analysis,

for it has been largely supplanted by finite-element analysis—the

way most method B calculations are done. The Code does not pro-

vide rules for deciding whether a given analysis is valid; that is the

responsibility of the Registered Professional Engineer.

No vessel can be designed entirely by method A; every vesselcontains supports, for which method A lacks rules. (The same

comment is true of Section VIII, Division 1.) Article RD-1150

requires that design calculations be provided for internal and

external attachments such as supports. Using a combination of 

methods A and B is allowed. There is a very important paragraph

in the preface that states,

The Code contains mandatory requirements, specific prohibi-

tions, and nonmandatory guidance for construction5 activities.

For the Code does not address all aspects of these activities and

those aspects which are not specifically addressed should not be

considered prohibited. The Code is not a handbook and cannot

replace education, experience, and engineering judgment . The

phrase engineering judgment refers to technical judgmentsmade by knowledgeable designers experienced in the applica-

tion of the Code. Engineering judgments must be consistent

with Code philosophy and such judgments must never be used

to overrule mandatory requirements or specific prohibitions of 

the Code.

In the spirit of this paragraph, Article RD-1186 on attachments

states that the effect of local structural discontinuities from small

attachments need not be included in the stress analysis of the ves-

sel if, in the opinion of the registered Professional Engineer, they

are insignificant. Thus the engineer may design as many compo-

nents as possible with the simple rules of method A and supple-

ment these calculations with method B stress analysis, as needed.

He or she may use this experience and informed judgment to

accept some design details without analysis. Section X, Class II

provides a practical, reliable way to design FRP vessels. The AEexamination demonstrates the structural integrity of the vessel.

Section 26.7 presents a design example that has all the compo-

nents shown in Fig. 26.18.

26.6.3 Section X, Class III Design Qualifications

Design calculations are required for Section X, Class III ves-

sels. Section X, Appendix 8 does not contain mandatory design

rules but does refer to non-linear stress analysis as a basis for

designing the structural walls of these vessels. In addition limits

are placed on the maximum fiber stress of 28.5% for glass fibers

and 44.4% for carbon fibers of the tensile strength of the fibers.

The metallic end bosses are to be designed using applicable

ASME Section VIII, Division 3 rules. The fabricator must build a

prototype of a new design and subject it to a cyclic and qualifica-

tions tests as shown in Table 26.9b. The User must provide a

Users Design Specification which enumerates the service condi-

tions for the vessel. In addition a minimum 20 year cycle life is

mandated for this type of vessel.

Since the Class III vessel contains a either a metallic or thermo-

plastic liner, no leakage is permitted during the hydrostatic, cyclic

or volumetric expansion tests.

5 The term construction, as used in this Foreword, is an all-inclusive term that comprises materials, design, fabrication, examination, inspection, testing, certification, and

pressure relief.

TABLE 26.9b SECTION X, CLASS III QUALIFICATION TESTS

Qualification Test Criteria

Hydraulic Pressure 1.25 × Design Pressure & held for 30 min-no leaks

Hydraulic Expansion 1.25 × Design Pressure and expansion limited to 110%

Hydraulic Burst Failure pressure to be at least 3.5 × design pressure for glass fibers and 2.25 × design pressure for

carbon fibers

Cyclic Fatigue Cycle from 10% of design pressure to design pressure for a minimum of 2.6 × the design cycle life

without leakage or failure

Creep Vessel shall be pressured to 1.25 × design pressure at 185°F and held for 2000 hr then subject to a leak

and burst test and satisfy the criteria for the leak and burst test.

Flaw Two vessels are tested with two longitudinal flaws cut into shell. One is subject to a burst test and the

other to a fatigue test. The burst test shall be a minimum of 2 times design pressure and the fatigue

test shall last a minimum of 1000 cycles without leakage.

Permeation(for non-metallic liners only)

Vessel shall be filled with 5% hydrogen and 95% nitrogen, placed in a sealed container and monitoredfor 500 hours leak rate to be less than 0.15 std/cc per hour per liter of vessel volume.

Torque Boss fittings shall be tighted to 150% for specified torque and a leak test at design pressure conducted

without leaks or damage to the threads.

Penetration Vessel is pressurized to design pressure and subject to an impact from an armor piercing bullet of

0.3 in. dia or greater. at 45 degrees to the sidewall without rupture.

Environmental The vessel shall be impacted in 5 spots along the shell by a pendulum with an impact energy of 22.1 ft-lbs

then subject to exposure for 48 hours with sulfuric acid, sodium hydroxide, gasoline, ammonium

nitrate and windshield washer fluid. The vessel is cyclic pressurized from 10% of design pressure to

125% design pressure for 3000 cycles then held at 125% design pressure without leaks or rupture.

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COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 26-19

Finally an acoustic emission examination is performed during

the hydrostatic testing of the production vessel with acceptance

criteria given in para. 8-620(b)(7)(e).

When a prototype vessel satisfies these requirements, a vessel

identical to it may be built and marked with the ASME RP Code

symbol stamp. It may not, however, receive a Code Stamp unless

it passes the quality control requirements to ensure the produc-

tion vessels are essentially identical to the successful prototypevessel.

26.6.4 Design Qualifications of RTP-1 Vessels

Design qualifications of RTP-1 vessels resemble those for

Section X, Class II. The RTP nomenclature is slightly different:

Subpart 3A design is analogous to the method A design in Section

X and Subpart 3B is analogous to the method B design. Part 3 of 

RTP pertains to design; Subparts 3A and 3B are subsets of Part 3,

the former covering design-by-rule analysis, the latter covering

design-by-stress analysis.

Figures 26.19 and 26.20 sketch the components for which

Subpart 3A rules are available. The notes on the drawings refer to

the articles in RTP-1 that cover the indicated detail. The “NM”

notes—for example, the note indicating the footprint load on thetop of the vessel in Fig. 26.20—refer to nonmandatory provisions.

That means that RTP-1 may be satisfied by using the component

design in the NM article, although the provision is not compulsory.

RTP-1 introduced a new pressure containing component: flat

sandwich plates with balsa cores. Non-mandatory Appendix NM-

15 “Flat Cored Plate Design.” Mandatory Appendix M-13 “Balsa

Wood Receiving and Inspection Procedures” provide quality

assurance requirements for the balsa.

RTP-1 defines the footprint load as a 250 lb vertically down-

ward load that is distributed uniformly over a 16 in.2 compact 

area, an area with an aspect ratio close to 1.0 (e.g., a circle or

square). The footprint-load requirement is intended to prevent

damage to the vessel if someone stands on it, such as the time

when the piping is connected to a nozzle on the top head.Because RTP-1 vessels may have very low design pressures, the

footprint-load requirement may dictate the thickness of a top

head. Although the collection of components covered by

Subpart 3A is more complete than the method A collection in

Section X, neither has the variety available in Section VIII,

Division 1.

Material properties for design are treated differently in Subpart

3A than they are in Section X. RTP-1 requires the results of 

mechanical properties tests on samples cut from complete lami-

nates, as opposed to tests on individual laminae. The propertytests must be run on all types of laminates used.

The strength criterion required by Subpart 3B rules, like

method B in Section X, is based on the Tsai-Wu quadratic

interaction criterion. However, there are differences in the way

the criterion is applied.

Sections 26.7–26.10 provide a series of design examples illus-

trating design calculation and specification of all the components

shown in Figs. 26.19 and 26.20.

26.6.5 Design Qualification Overview

Design qualification in Section X Class I is empirical, based

on a thorough prototype testing. Class II design is based partly

on calculation, partly on testing. Material testing provides material

properties, calculation establishes the part dimensions andthicknesses, and an AE examination gives an experimental verifi-

cation of the design. Section X, Class III design is based on

advanced stress analysis and thorough prototype testing with the

additional requirement of a an AE examination to verify the

design during the hydrostatic test of the production vessel. RTP-1

design is based either entirely or largely on measured material

properties and calculation, and it does not require hydrostatic

testing of vessels with design pressures less than 0.5 psig and

diameters not exceeding 12 ft For larger vessels or those with

design pressures greater than 0.5 psig, a hydrostatic test is

required. All three methods are based on long experience and pro-

duce safe, reliable vessels.

FIG. 26.19 AVAILABLE DESIGN BY SUBPART 3A

COMPONENTS (CHART 1 OF 2)

FIG. 26.20 AVAILABLE DESIGN BY SUBPART

3A COMPONENTS (CHART 2 OF 2)

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26-20 • Chapter 26

26.7 SECTION X EXAMPLE: DESIGNSPECIFICATION

Section X, Article RG-310 states the requirement for a Design

Specification as follows in a single paragraph:

The User, or an agent acting in his behalf, requiring that a vessel

be designed, fabricated, tested and certified to be a vessel comply-

ing with this Section, shall provide or cause to be provided forsuch a vessel information as to operating conditions, including

intended use and material compatibility with the contents, in

such detail as will provide the basis for design, material selec-

tion, fabrication, and inspection in accordance with this Section.

This information will be designated hereinafter as the Design

Specification.

Figure 26.21 is a sketch of a Section X vessel suitable for use

in a Design Specification. The vessel is a reactor with internal

design pressure of 40 psig that will be filled with 1.2 specific

gravity liquid coincident with the internal design pressure. The

empty reactor will also be subjected to 10 psig external pressure.

The design temperature is 150F for both internal and externaldesign pressures. Acme 105 vinyl ester resin, reinforced by glass

fibers, is determined to be suitable for the liquids the User intendsto process in the reactor. The User desires the Fabricator to

choose the brand of reinforcing glass fiber. The contents are cor-

rosive, so the User requires a conventional-veil-ply and 2-mat-ply

corrosion barrier. In addition, the User requires a visual inspection

level 2. (Visual inspection and other quality control provisions are

discussed later in this section.)

Many FRP vessels require corrosion barriers, but Section X

does not provide rules for their construction (although it does

allow their use). Section VIII treats liners the same way. For

example, many steel vessels have rubber liners that are

required to prevent excessive corrosion. Without the proper

design and installation of the liners, these vessels would not be

safe and reliable. Section VIII leaves the task of design and

installation to the Manufacturer, and similarly, Section X

leaves the task of design and installation of corrosion barriers

to the Fabricator. The nontreatment of liners and corrosion bar-

riers is a good example of the following statement from the

preface of Section X:

The Code does not address all aspects of these activities and

those aspects which are specifically addressed should not be con-

sidered prohibited.

Table 26.10 is an example of a Design Specification for aSection X vessel. The first set of entries gives the vessel designa-

tion in addition to the names, addresses, telephone numbers, and

e-mail addresses of the User, the User’s Agent, and the individual

who prepared the Design Specification.

The final version of the Design Specification is often a collab-

oration between the User and the Fabricator. However, the

Design Specification is a key part of the User’s request for quota-

tion. Thus, so that the Fabricator’s bids are comparable, it is wise

for the User to develop a complete, thorough Design

Specification.

In this example, the User has chosen the resin and therefore

accepts responsibility for compatibility of the resin with vessel

contents. If the User had wished the Fabricator to select the

resin, the User would have needed to make a complete disclo-sure of the vessel contents, including any changes in the contents’

composition during the chemical reactions occurring in the ves-

sel. It is obvious that the person who selects the resin must

understand what the vessel will contain, but sometimes Chemical

Manufacturers regard such information as proprietary. If they want

to keep the composition of the contents secret, they must choose

the resin themselves.

Because the reactor will be installed indoors, there are no snow,

rain, or wind loads. Unprotected FRP is subject to damage from

the ultraviolet radiation of the Sun. Therefore, if the vessel will be

stored outdoors for a long period before it is installed, the User

would need to inform the Fabricator. The Fabricator would then

recommend an ultraviolet inhibitor for the final coat of resin or a

pigmented-gel coat on the outside of the vessel.The User’s Design Specification should contain any informa-

tion necessary to the Fabricator but not governed by Section X.

For example, the corrosion barrier should be specified, and

although tolerances on nozzle locations are important as well,

they are not provided in Section X and should thus be included in

the Design Specification. Scheduling, shipping, delivery, pay-

ment, and other commercial arrangements must be worked out

and possibly documented in the Design Specification.

Nozzle elevations are measured from the bottom of the skirt. It

is tempting to reference them from the bottom tangent line, but

that location is not easily located in a finished FRP vessel.

Consider Fig. 26.10, which shows a head-to-shell joint. The thick,

bulging joint overlay conceals the exact location of the tangent

line.Section X, Class II vessels are required to satisfy visual inspec-

tion criteria, but they apply only to the structural part of the lami-

nate. A visual inspection of defects, such as pits and bubbles, are

at least as important in the corrosion barrier; however, Section X

does not cover them, for which reason the User’s Design

Specification should provide criteria for such an inspection.

Article 6-940 and Table 6-1 of RTP-1, however, do contain such

criteria that are suitable for use with Section X equipment. The

User could reference the RTP-1 provisions in the Design

Specification.

All too often, a User’s Design Specification lists several national

standards on FRP equipment, such as RTP-1, Section X, ASTMFIG. 26.21 SECTION X DESIGN EXAMPLE

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COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE • 26-21

pipe-and-tank standards, and the now-obsolete National Bureau of 

Standards’ PS15-69 document. The User’s standard imposes all of 

them on the same vessel and states something to the effect of “in

case of conflicts among these standards, the most stringent shall

apply”—practice that invites chaos. In the author’s experience,

RTP-1 for tanks and low-pressure vessels and Section X for higher-

pressure vessels, together with a good User’s Design Specification,

shall suffice.

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26-22 • Chapter 26

26.8 SECTION X: EXAMPLE DESIGNCALCULATIONS

Design calculations for the vessel in the Design Specification of 

Table 26.10 are presented in the following paragraphs. Table 26.11

lists the design calculations and the section numbers of this chap-

ter where they are presented.

The vessel will be constructed of mat–woven-roving laminate.

Section X requires the use of lamina properties coupled with

lamination analysis to determine the laminate properties for use in

method A design. (See Table 26.3 earlier in the chapter for a listof mat- and woven-roving lamina properties.) They were used

together with the lamination theory equations in Section X, Article

RD-12 to obtain the mechanical properties of the mat–woven-

roving laminate listed in Table 26.12. In that table and in the

design formulas that follow, the following symbols are used:

 E 1 the axial tensile modulus E 2 the hoop tensile modulus

 E 1f  the axial flexural modulus E 2f  the hoop flexural modulus

v1 Poisson’s ratio for stress in x direction and contraction in y direction

v2 Poisson’s ratio for stress in y direction and contraction in x direction

v1f  Poisson’s ratio for bending stress in  x  direction andcontraction/expansion in y direction

v2f  Poisson’s ratio for bending stress in  y direction andcontraction/expansion in x direction

Section X, Class II does not allow the thickness of the corro-

sion barrier to be considered as contributing to structural strength.

Therefore, even though the vessel would have a corrosion barrier,

it is not included in the forthcoming calculations.

26.8.1 Component Pressures

The internal pressure used in design computations for each

component is the sum of the design pressure and the hydrosta-

tic pressure at the component. This pressure is given by the

following

P Pd  h (26.10)

where

Pd  the design pressure y the weight densityh the vertical distance of the component to the surface of the

liquid contents

The distance of h is measured to the centerline of nozzles in the

shell, to the deepest point on nozzles in the heads, to the bottom

tangent line of the shell, to the location where the heads and shell

abut for the joints, and to the deepest points in the heads. The

weight density, , is the product of the specific gravity and theweight density of water, which is 0.0361 lb/in.3; thus 0.0433lb/in.3. The external pressure is the same for all components —10

psig. Table 26.13 lists the internal pressures.

26.8.2 Top and Bottom Heads

To safely resist internal pressure, Section X requires that the

thickness of a 2:1 ellipsoidal head be at least equal to t as given

by (RD-1173.1):

(26.11)

where

 E the lesser of E 1 and E 2 from Table 26.12 1.666 106 psi

P the component pressure given in Table 26.13 41.34 psig(top head)

 D the inside diameter of the head 96 in.

When these values are inserted in the equation (26.11), the

result is t 1.191 in., which is similar to an equation in SectionVIII, Division 1, except for the 0.6 knockdown factor in the

denominator. In this case, however, the allowable stress has been

replaced by 0.001E, which is 1,666 psi. The head must a