FRP Analysis in Caesar-II

Technical Discussions TSO=Torsional Stress, Outside

Pipe Stress Analysis of FRP Piping Underlying Theory The behavior of steel and other homogeneous materials has been long understood, permitting their widespread use as construction materials. The development of the piping and pressure vessel codes (Reference 1) in the early part of this century led to the confidence in their use in piping applications. The work of Markl and others in the 1940’s and 1950’s was responsible for the formalization of today’s pipe stress methods, leading to an ensuin g diversification of piping codes on an industry by industry basis. The advent of the digital computer, and with it the appearance of the first pipe stress analysis software (Reference 2), further increased the confidence with which steel pipe could be use d in critical applications. The 1980’s saw the wide spread proliferation of the microcomputer, with associated pipe stress analysis software, which in conjunction with training, technical support, and available literature, has brought stress analysis capability to almost all engineers. In short, an accumulated experience of close to 100 years, in conjunction with ever improving technology has led to the utmost confidence on the part of today’s engineers when specifying, designing, and analyzing steel, or ot her metallic, pipe. For fiberglass reinforced plastic (FRP) and other composite piping materials, the situation is not the same. Fiberglass reinforced plastic was developed onl y as recently as the 1950’s, and did not come into wide spread use until a decade later (Reference 3). There is not a large base of stress analysis experience, although not from a lack of commitment on the part of FRP vendors. Most vendors conduct extensive stress testing on their components, including hydrostatic and cyclic pressure, uni-axial tensile and compressive, bending, and combined loading tests. The problem is due to the traditional difficulty associated with, and lack of understanding of, stress analysis of heterogeneous materials. First, the behavior and failure modes of these materials are highly complex and not fully understood, leading to inexact analytical methods and a general lack of agreement on the best course of action to follow. This lack of agreement has slowed the simplification and standardization of the analytical methods into universally recognized codes BS 7159 Code Design and Construction of Glass Reinforced Plastics Piping (GRP) Systems for Individual Plants or Sites and UKOOA Specification and Recommended Practice for the Use of GRP Piping Offshore being notable exceptions. Second, the heterogeneous, orthotropic behavior of FRP and other composite materials has hindered the use of the pipe stress analysis algorithms developed for homogeneous, isotropic materials associated with crystalline structures. A lack of generally accepted analytical procedures has contributed to a general reluctance to use FRP piping for critical applications. Stress analysis of FRP components must be viewed on many levels. These levels, or scales, have been called Micro-Mini-Macro levels, with analysis proceeding along the levels according to the "MMM" principle (Reference 4).

CAESAR II User's Guide

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Technical Discussions

Micro-Level Analysis Stress analysis on the "Micro" level refers to the detailed evaluation of the individual materials and boundary mechanisms comprising the composite material. In general, FRP pipe is manufactured from laminates, which are constructed from elongated fibers of a commercial grade of glass, E-glass, which are coated with a coupling agent or sizing prior to being embedded in a thermosetting plastic material, typically epoxy or polyester resin. This means, on the micro scale, that an analytical model must be created which simulates the interface between these elements. Because the number and orientation of fibers is unknown at any given location in a FRP sample, the simplest representation of the micro-model is that of a single fiber, extending the length of the sample, embedded in a square profile of matrix.

Micro Level GRP Sample -- Single Fiber Embedded in Square Profile of Matrix

Evaluation of this model requires use of the material parameters of: 1.

the glass fiber

2.

the coupling agent or sizing layer normally of such such microscopic proportion that it may be ignored

3.

the plastic matrix

It must be considered that these material parameters might vary for an individual material based upon tensile, compressive, or shear applications of the imposed stresses, and typical values vary significantly between the fiber and matrix (Reference 5): Young's Modulus Ultimate Strength Material

tensile (MPa)

Coefficient of Thermal Expansion

tensile (MPa)

m/m/ºC

Glass Fiber 72.5 x103

1.5 x 103

5.0 x 10-6

Plastic Matrix

.07 x 103

7.0 x 10-6

2.75 x 103

The following failure modes of the composite must be similarly evaluated to:

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§

failure of the fiber

§

failure of the coupling agent layer

§

failure of the matrix


Technical Discussions §

failure of the fiber-coupling agent bond

§

failure of the coupling agent-matrix bond

Because of uncertainties about the degree to which the fiber has been coated with the coupling agent and about the nature of some of these failure modes, this evaluation is typically reduced to: §

failure of the fiber

§

failure of the matrix

§

failure of the fiber-matrix interface

You can evaluate stresses in the individual components through finite element analysis of the strain continuity and equilibrium equations, based upon the assumption that there is a good bond between the fiber and matrix, resulting in compatible strains between the two. For normal stresses applied parallel to the glass fiber:

ef = em = saf / Ef = sam / Em saf = sam Ef / Em Where:

ef = Strain in the Fiber e = Strain in the Matrix saf = Normal Stress Parallel to Fiber, in the Fiber Ef = Modulus of Elasticity of the Fiber

sam = Axial Normal Stress Parallel to Fiber, in the Matrix Em = Modulus of Elasticity of the Matrix Due to the large ratio of the modulus of elasticity of the fiber to that of the matrix, it is apparent that nearly all of the axial normal stress in the fiber-matrix composite is carried by the fiber. Exact values are (Reference 6):

saf = sL / [f + (1-f)Em/Ef ] sam = sL / [fEf /Em + (1-f)] Where:

sL = nominal longitudinal stress across composite f = glass content by volume


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Technical Discussions The continuity equations for the glass-matrix composite seem less complex for normal stresses perpendicular to the fibers, because the weak point of the material seems to be limited by the glass-free cross-section, shown below:

Stress Intensification in Matrix Cross-Section

For this reason, it would appear that the strength of the composite would be equal to that of the matrix for stresses in this direction. In fact, its strength is less than that of the matrix due to stress intensification in the matrix caused by the irregular stress distribution in the vicinity of the stiffer glass. Because the elongation over distance D1 must be equal to that over the longer distance D2, the strain, and thus the stress at location D 1 must exceed that at D 2 by the ratio D2/D1. Maximum intensified transverse normal stresses in the composite are:

Where:

sb = intensified normal stress transverse to the fiber, in the composite s = nominal transverse normal stress across composite nm = Poisson's ratio of the matrix Because of the Poisson effect, this stress produces an additional following:

s'am equal to the

s'am = Vm sb

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Technical Discussions Shear stress can be allocated to the individual components again through the use of continuity equations. It would appear that the stiffer glass would resist the bulk of the shear stresses. However, unless the fibers are infinitely long, all shears must eventually pass through the matrix in order to get from fiber to fiber. Shear stress between fiber and matrix can be estimated as

Where:

tab = intensified shear stress in composite T = nominal shear stress across composite Gm = shear modulus of elasticity in matrix Gf = shear modulus of elasticity in fiber Determination of the stresses in the fiber-matrix interface is more complex. The bonding agent has an inappreciable thickness, and thus has an indeterminate stiffness for consideration in the continuity equations. Also, the interface behaves significantly differently in shear, tension, and compression, showing virtually no effects from the latter. The state of the stress in the interface is best solved by omitting its contribution from the continuity equations, and simply considering that it carries all stresses that must be transferred from fiber to matrix. After the stresses have been apportioned, t hey must be evaluated against appropriate failure criteria. The behavior of homogeneous, isotropic materials such as glass and plastic resin, under a state of multiple stresses is better understood. Failure criterion for isotropic material reduces the combined normal and shear stresses ( sa, sb, sc, tab, tac, tbc) to a single stress, an equivalent stress, that can be compared to the tensile stress present at failure in a material under uniaxial loading, that is, the ultimate tensile stress, Sult. Different theories, and different equivalent stress functions f( sa, sb, sc, tab, tac, tbc) have been proposed, with possibly the most widely accepted being the Huber-von Mises-Hencky criterion, which states that failure will occur when the equivalent stress reaches a critical value the ultimate strength of the material:

seq = Ö{1/2 [(sa - sb)2 + (sb - sc)2+ (sc - sa)2 + 6(tab2+ tac2+ tbc2)} £ Sult This theory does not fully cover all failure modes of the fiber in that it omits reference to direction of stress, that is, tensile versus compressive. The fibers, being relatively long and thin, predominantly demonstrate buckling as their failure mode when loaded in compression.


933

Technical Discussions The equivalent stress failure criterion has been corroborated, with slightly non-conservative results, by testing. Little is known about the failure mode of the adhesive interface, although empirical evidence points to a failure criterion which is more of a linear relationship between the normal and the square of the shear stresses. Failure testing of a composite material loaded only in transverse normal and shear stresses are shown in the following figure. The kink in the curve shows the transition from the matrix to the interface as the failure point.

Mini-Level Analysis

Mini-Level Analysis Fiber Distribution Models Although feasible in concept, micro level analysis is not feasible in practice . This is due to the uncertainty of the arrangement of the glass in the composite the thousands of fibers that might be randomly distributed, semi-randomly oriented, although primarily in a parallel pattern, and of randomly varying lengths. This condition indicates that a sample can truly be evaluated only on a statistical basis, thus rendering detailed finite element analysis inappropriate. For mini-level analysis, a laminate layer is considered to act as a continuous hence the common reference to this method as the "continuum" method, material, with material properties and failure modes estimated by integrating them over the assumed cross-sectional distribution, which is, averaging. The assumption regarding the distribution of the fibers can have a marked effect on the determination of the material parameters. Two of the most commonly postulated

934


Technical Discussions distributions are the square and the hexagonal, with the latter generally considered as being a better representation of randomly distributed fibers. The stress-strain relationships, for those sections evaluated as continua, can be written as:

eaa = saa/EL - (VL/EL)sbb - (VL/EL)scc ebb = -(VL/EL)saa + sbb/ET - (VT/ET)scc ecc = -(VL/EL)saa - (VT/ET)sbb + scc/ET eab = tab / 2 GL ebc = tbc / 2 GT eac = tac / 2 GL Where:

eij = strain along direction i on face j sij, tab = stress (normal, shear) along direction i on face j EL = modulus of elasticity of laminate layer in longitudinal direction VL = Poisson’s ratio of laminate layer in longitudinal direc tion ET = modulus of elasticity of laminate layer in transverse direction VT = Poisson’s ratio of laminate la yer in transverse direction GL = shear modulus of elasticity of laminate layer in longitudinal direction GT = shear modulus of elasticity of laminate layer in transverse direction These relationships require that four modules of elasticity, EL, ET, GL, and GT, and two Poisson’s ratios, VL and V, be evaluated for the continuum. Extensive research (References 4 - 10) has been done to estimate these parameters. There is general consensus that the longitudinal terms can be explicitly calculated; for cases where the fibers are significantly stiffer than the matrix, they are: EL = EF f + EM(1 - f) GL = GM + f/ [ 1 / (GF - GM) + (1 - f) / (2GM)] VL = VFf + VM(1 - f) You cannot calculate parameters in the transverse direction. You can only calculate the upper and lower bounds. Correlations with empirical results have yielded approximations (Reference 5 and 6): ET = [EM(1+0.85f 2) / {(1-VM2)[(1-f)1.25 + f(EM/EF)/(1-VM2)]} GT = GM (1 + 0.6Öf) / [(1 - f)1.25 + f (GM/GF)] VT = VL (EL / ET) Use of these parameters permits the development of the homogeneous material models that facilitate the calculation of longitudinal and transverse stresses acting on a laminate layer. The resulting stresses can be allocated to the individual fibers and matrix using relationships developed during the micro analysis.


935


Macro-Level Analysis

Macro to Micros Stress Conversion

Where Mini-level analysis provides the means of evaluation of individual laminate layers, Macro-level analysis provides the means of evaluating components made up of multiple laminate layers. It is based upon the assumption that not only the composite behaves as a continuum, but that the series of laminate layers acts as a homogeneous material with properties estimated based on the properties of the layer and the winding angle, and that finally, failure criteria are functions of the level of equivalent stress. Laminate properties may be estimated by summing the layer properties (adjusted for winding angle) over all layers. For example

Where: ExLAM = Longitudinal modulus of elasticity of laminate tLAM = thickness of laminate Ek = Longitudinal modulus of elasticity of laminate layer k Cik = transformation matrix orienting axes of layer k to longitudinal laminate axis C jk = transformation matrix orienting axes of layer k to transverse laminate axis tk = thickness of laminate layer k After composite properties are determined, the component stif fness parameters can be determined as though it were made of homogeneous material that is, based on component cross-sectional and composite material properties. Normal and shear stresses can be determined from 1) forces and moments acting on the cross-sections, and 2) the cross-sectional properties themselves. These relationships can be written as:

saa = Faa / Aaa ± Mba / Sba ± Mca / Sca sbb = Fbb / Abb ± Mab / Sab ± Mcb / Scb scc = Fcc / Acc ± Mac / Sac ± Mbc / Sbc tab = Fab / Aab ± Mbb / Rab

936


Technical Discussions tac = Fac / Aac ± Mcc / Rac tba = Fba / Aba ± Maa / Rba tbc = Fbc / Abc ± Mcc / Rbc tca = Fca / Aca ± Maa / Rca tcb = Fcb / Acb ± Mbb / Rcb Where:

sij = normal stress along axis i on face j Fij = force acting along axis i on face j Aij = area resisting force along axis i on face j Mij = moment acting about axis i on face j Sij = section modulus about axis i on face j

tij = shear stress along axis i on face j Rij = torsional resistivity about axis i on face j Using the relationships developed under macro, mini, and micro analysis, these stresses can be resolved back into local stresses within the laminate layer, and from there, back into stresses within the fiber and the matrix. From these, the failure criteria of those microscopic components, and hence, the component as a whole, can be checked.

Implementation of Macro-Level Analysis for Piping Systems The macro-level analysis described above is the basis for the preeminent FRP piping codes in use today, including Code BS 7159 (Design and Construction of Glass Reinforced Plastics Piping Systems for Individual Plants or Sites) and the UKOOA Specification and Recommended Practice for the Use of GRP Piping Offshore. BS 7159

BS 7159 uses methods and formulas familiar to the world of steel piping stress analysis in order to calculate stresses on the cross-section, with the assumption that FRP components have material parameters based on continuum evaluation or test. All coincident loads, such as thermal, weight, pressure, and axial extension due to pressure need be evaluated simultaneously. Failure is based on the equivalent stress calculation method. Because one normal stress (radial stress) is traditionally considered to be negligible in typical piping configurations, this calculation reduces to the greater of (except when axial stresses are compressive): (when axial stress is greater than hoop) (when hoop stress is greater than axial) A slight difficulty arises when evaluating the calculated stress against an allowable , due to the orthotropic nature of the FRP piping normally the laminate is designed in such a way to make the pipe much stronger in the hoop, than in the longitudinal, direction, providing more than one allowable stress. This difficulty is resolved by defining the allowable in terms of a design strained, rather than stress, in effect adjusting the stress allowable in proportion to the strength


937

Technical Discussions in each direction. In other words, the allowable stresses for the two equivalent stresses above would be (ed ELAMX) and (ed ELAMH ) respectively. In lieu of test data, system design strain is selected from Tables 4.3 and 4.4 of the Code, based on expected chemical and temperature conditions. Actual stress equations as enumerated b y BS 7159 display below: 1.

Combined stress straights and bends:

sC = (sf 2+ 4sS2)0.5

ed ELAM

or

sC = (sX2 + 4sS2)0.5 ed ELAM Where: ELAM = modulus of elasticity of the laminate; in CAESAR II, the first equation uses the modulus for the hoop direction and in the second equation, the modulus for the longitudinal direction is used.

sC = combined stress s• = circumferential stress = s•P +

s•B

sS = torsional stress = MS(Di + 2td) / 4I

sX = longitudinal stress = sXP +

sXB

s•P = circumferential pressure stress = mP(Di + td) / 2 td

s•B = circumferential bending stress = [(Di + 2td) / 2I] [(Mi SIF•i)2 + Mo SIF•o)2] 0.5 for bends, = 0 for straights MS = torsional moment on cross-section Di = internal pipe diameter td = design thickness of reference laminate I = moment of inertia of pipe m = pressure stress multiplier of component P = internal pressure Mi = in-plane bending moment on cross-section SIF•i= circumferential stress intensification factor for in-plane moment M = out-plane bending moment on cross-section SIF•o = circumferential stress intensification factor for out-plane moment

sXP = longitudinal pressure stress = P(Di + td) / 4 t d

938


Technical Discussions sXB = longitudinal bending stress = [(Di + 2td) / 2I] [(Mi SIFxi)2 + Mo SIFxo)2]0.5 SIFxi = longitudinal stress intensification factor for in-plane moment SIFxo = longitudinal stress intensification factor for out-plane moment 2.

Combined stress branch connections:

sCB = ((s•P + sbB)2 + 4sSB2)0.5 £ ed ELAM Where:

sCB = branch combined stress s•P = circumferential pressure stress = mP(Di + tM) / 2 tM

sbB = non-directional bending stress = [(Di + 2td) / 2I] [(Mi SIFBi)2 + Mo SIFBo)2]0.5

sSB = branch torsional stress = MS(Di + 2td) / 4I tM = thickness of the reference laminate at the main run SIFBi = branch stress intensification factor for in-plane moment SIFBo = branch stress intensification factor for out-plane moment 3.

When longitudinal stress is negative (net compressive):

s• - V•x sx £ e• ELAM• Where: V•x = Poisson’s ratio giving strain in longi tudinal direction caused by stress in circumferential direction

e• = design strain in circumferential direction ELAM•= modulus of elasticity in circumferential direction


939

Technical Discussions BS 7159 also dictates the means of calculating flexibility and stress intensification (k- and i-) factors for bend and tee components, for use during the flexibility analysis.

940


Technical Discussions BS 7159 imposes a number of limitations on its use, the most notable being: the limitation of a system to a design pressure of 10 bar, the restriction to the use of designated design laminates, and the limited applicability of the k- and i- factor calculations to pipe bends (that is, mean wall thickness around the intrados must be 1.75 times the nominal thickness or less).

This code appears to be more sophisticated, yet easy to use. We recommend that its calculation techniques be applied even to FRP systems outside its explicit scope, with the following recommendations: §

§

§

Pressure stiffening of bends should be based on actual design pressure, rather than allowable design strain.

Design strain should be based on manufacturer’s test and experience data wherever possible (with consideration for expected operating conditions). Fitting k- and i- factors should be based on manufacturer’s test or analytic data, if available.

UKOOA

The UKOOA Specification is similar in many respects to the BS 7159 Code, except that it simplifies the calculation requirements in exchange for imposing more limitations and more conservatism on the piping operating conditions.


941

Technical Discussions Rather than explicitly calculating a combined stress, the specification defines an idealized envelope of combinations of axial and hoop stresses that cause the equivalent stress to reach failure. This curve represents the plot of: (sx /

sx-all)2 + (shoop / shoop-all)2 - [sx shoop / (sx-all shoop-all)] £ 1.0 Where:

sx-all = allowable stress, axial shoop-all = allowable stress, hoop The specification conservatively limits you to that part of the curve falling under the line between sx-all (also known as sa(0:1) ) and the intersection point on the curve where shoop is twice sx-(a natural condition for a pipe loaded only with pressure), as shown in the following figure.

An implicit modification to this requirement is the f act that pressure stresses are given a f actor of safety (typically equal to 2/3) while other loads are not. This gives an explicit requirement of: P des £ f 1 f 2 f 3 LTHP Where: P des = allowable design pressure f 1 = factor of safety for 97.5% lower confidence limit, usually 0.85 f 2 = system factor of safety, usually 0.67 f 3 = ratio of residual allowable, after mechanical loads = 1 - (2

sab) / (r f 1 LTHS)

sab = axial bending stress due to mechanical loads r = sa(0:1)/sa(2:1)

sa(0:1) = long term axial tensile strength in absence of pressure load sa(2:1) = long term axial tensile strength under only pressure loading LTHS = long term hydrostatic strength (hoop stress allowable) LTHP = long term hydrostatic pressure allowable

942


Technical Discussions This has been implemented in the CAESAR II pipe stress analysis software as: Code Stress

sab (f 2 /r) + PDm / (4t)

Code Allowable

£

(f 1 f 2 LTHS) / 2.0

Where: P = design pressure D = pipe mean diameter t = pipe wall thickness K and i-factors for bends are to be taken from the BS 7159 Code, while no such factors are to be used for tees. The UKOOA Specification is limited in that shear stresses are ignored in the evaluation process; no consideration is given to conditions where axial stresses are compressive; and most required calculations are not explicitly detailed.


943


FRP Analysis Using CAESAR II Practical Applications CAESAR II has had the ability to model orthotropic materials such as FRP almost since its inception. It also can specifically handle the requirements of the BS 7159 Code, the UKOOA Specification, and more recently ISO 14692. FRP material parameters corresponding to those of many vendors’ lines are provided with CAESAR II. You can pre-select these parameters to be the default values whenever FRP piping is used. Other options, as to whether the BS 7159 pressure stiffening requirements should be carried out using design strain or actual strain can be set in CAESAR II’s configuration module as well.

944




945

Technical Discussions Selecting material 20 — Plastic (FRP) – activates CAESAR II’s orthotropic material model and brings in the appropriate material parameters from the pre-selected materials. The orthotropic material model is indicated by the changing of two fields from their previous isotropic values: Elastic Modulus (C) changes to Elastic Modulus/axial and Poisson's Ratio changes to Ea/Eh*Vh/a. These changes are necessary because orthotropic models require more material parameters than do isotropic. For example, there is no longer a single modulus of elasticity for the material, but now two: axial and hoop. There is no longer a single Poisson’s ratio, but again two: V h/a (Poisson’s ratio re lating strain in the axial direction due to stress-induced strain in the hoop direction) and V a/h (Poisson’s ratio relating strain in the hoop direction due to stress-induced strain in the axial direction). Also, unlike isotropic materials, the shear modulus does not follow the relationship G = 1 / E (1- V ), so that value must be explicitly input.

To minimize input, a few of these parameters can be combined due to their use in the program. Generally, the only time that the modulus of elasticity in the hoop direction or the Poisson’s ratios is used during flexibility analysis is when calculating piping elongation due to pressure (note that the modulus of elasticity in the hoop direction is used when determining certain stress allowables for the BS 7159 code): dx = (sx / Ea - Va/h * shoop / Eh) L Where: dx

946

= extension of piping element due to pressure


Technical Discussions sx

= longitudinal pressure stress in the piping element

E

= modulus of elasticity in the axial direction

Va/h

= Poisson’s ratio relating strain in the axial direction due to stress-induced strain in the hoop direction

shoop = hoop pressure stress in the piping element Eh

= modulus of elasticity in the hoop direction

L

= length of piping element

This equation can be rearranged, to require only a single new parameter, as: dx = (sx - Va/h

shoop * (Ea / Eh )) * L / Ea

In theory, that single parameter, Vh/a is identical to (Ea / Eh * Va/h) giving: dx = (sx Vh/ashoop) * L / Ea The shear modulus of the material is required in ordered to develop the stiffness matrix. In CAESAR II, this value, expressed as a ratio of the axial modulus of elasticity, is brought in from the pre-selected material, or can be changed on a problem-wise basis using the Special Execution Parameter (see "Special Execution Parameters" on page 287) dialog box accessed by the Environment menu from the piping spreadsheet (see figure). This dialog box also shows the coefficient of thermal expansion (extracted from the vendor file or user entered) for the material, as well as the default laminate type, as defined by the BS 7159 Code: §

§

§

Type 1 – All chopped strand mat (CSM) construction with an internal and an external surface tissue reinforced layer. Type 2 – Chopped strand mat (CSM) and woven roving (WR) construction with an internal and an external surface tissue reinforced layer. Type 3 – Chopped strand mat (CSM) and multi-filament roving construction with an internal and an external surface tissue reinforced layer.

The latter is used during the calculation of flexibility and stress intensification factors for piping bends. You can enter bend and tee information by using the auxiliary spreadsheets.


947

Technical Discussions You can also change bend radius and laminate type data on a bend by bend basis, as shown in the corresponding figure.

Specify BS 7159 fabricated and molded tee types by defining CAESAR II tee types 1 and 3 respectively at intersection points. CAESAR II automatically calculates the appropriate flexibility and stress intensification factors for these fittings as per code requirements. Enter the required code data on the Allowables auxiliary spreadsheet. The program provides fields for both codes, number 27 – BS 7159 and number 28 – UKOOA. After selecting BS 7159, CAESAR II provides fields for entry of the following code parameters: SH1 through SH9 = Longitudinal Design Stress =

ed ELAMX

Kn1 through Kn9 = Cyclic Reduction Factor (as per BS 7159 paragraph 4.3.4) Eh/Ea = Ratio of Hoop Modulus of Elasticity to Axial Modulus of Elasticity K = Temperature Differential Multiplier (as per BS 7159 paragraph 7.2.1)

948


Technical Discussions After selecting UKOOA, CAESAR I I provides fields for entr y of the following code param eters: SH1 through SH9 = hoop design stress = f 1 * LTHS R1 through R9 = ratio r = ( sa(0:1) / sa(2:1)) f 2 = system factor of safety (defaults to 0.67 if omitted) K = temperature differential multiplier (same as BS 7159) These parameters need only be entered a single time, unless they change at some point in the system.

Performing the analysis is simpler than the system modeling. evaluates the operating parameters and automatically builds the appropriate load cases. In this case, three are built: §

§

§

Operating includes pipe and fluid weight, temperature, equipment displacements, and pressure. This case is used to determine maximum code stress/strain, operational equipment nozzle and restraint loads, hot displacements, and so forth. Cold (same as above, except excluding temperature and equipment movements). This case is used to determine cold equipment nozzle and restraint loads. Expansion (cyclic stress range between the cold and hot case). This case may be used to evaluate fatigue criteria as per paragraph 4.3.4 of the BS 7159 Code.

After analyzing the response of the s ystem under these loads, CAESAR II displa ys a menu of possible output reports. Reports may be designated by selecting a combination of load case and results type (displacements, restraint loads, element forces and moments, and stresses). From the stress report, you can determine at a glance whether the system passed or failed the stress criteria.


949

Technical Discussions For UKOOA, the piping is considered to be within allowable limits when the operating stress falls within the idealized stress envelope this is illustrated by the shaded area in the following figure.

Conclusion A pipe stress analysis program with wor ldwide acceptance is now available for evaluation of FRP piping systems as per the requirements of the most sophisticated FRP piping codes. This means that access to the same analytical methods and tools enjoyed by engineers using steel pipe is available to users of FRP piping design.

References 1.

Cross, Wilbur, An Authorized History of the ASME Boiler an Pressure Vessel Code, ASME, 1990

2.

Olson, J. and Cramer, R., "Pipe Flexibility Analysis Using IBM 705 Computer Pro\-gram MEC 21, Mare Island Report 277-59," 1959

3.

Fiberglass Pipe Handbook, Composites Institute of the Society of the Plastics Indus\-try, 1989

4.

Hashin, Z., "Analysis of Composite Materials a Survey," Journal of Applied Mechanics, Sept. 1983

5.

Greaves, G., "Fiberglass Reinforced Plastic Pipe Design," Ciba-Geigy Pipe Systems

6.

Puck, A. and Schneider, W., "On Failure Mechanisms and Failure Criteria of Filament-Wound Glass-Fibre/Resin Composites," Plastics and Polymers, Feb. 1969

7.

Hashin, Z., "The Elastic Moduli of Heterogeneous Materials," Journal of Applied Mechanics, March 1962

8.

Hashin, Z. and Rosen, B. Walter, "The Elastic Moduli of Fibre Reinforced Materials," Journal of Applied Mechanics, June 1964

9.

Whitney, J. M. and Riley, M. B., "Elastic Properties of Fiber Reinforced Composite Materials," AIAA Journal, Sept. 1966

10. Walpole, L. J., "Elastic Behavior of Composite Materials: Theoretical Foundations," Advances in Applied Mechanics, Volume 21, Academic Press, 1989 11. BS 7159: 1989 British Standard Code of Practice for Design and Construction of Glass Reinforced Plastics GRP Piping Systems for Individual Plants or Sites. 12. UK Offshore Operators Association Specification and Recommended Practice for the Use of GRP Piping Offshore., 1994

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FRP Analysis in Caesar-II

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