Implementation of Macro-Level Analysis for Piping Systems - CAESAR II - Help

CAESAR II Users Guide

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CAESAR II Version
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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 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 by 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

    sΦ = circumferential stress

    = sΦP + sΦB

    sS = torsional stress

    = MS(Di + 2td) / 4I

    sX = longitudinal stress

    = sXP + sXB

    sΦP = circumferential pressure stress

    = mP(Di + td) / 2 td

    sΦB = circumferential bending stress

    = [(Di + 2td) / 2I] [(Mi SIFΦi)2 + Mo SIFΦo)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

    SIFΦi= circumferential stress intensification factor for in-plane moment

    M = out-plane bending moment on cross-section

    SIFΦo = circumferential stress intensification factor for out-plane moment

    sXP = longitudinal pressure stress

    = P(Di + td) / 4 td

    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 = ((sΦP + sbB)2 + 4sSB2)0.5 £ ed ELAM

    Where:

    sCB = branch combined stress

    sΦP = 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):

    sΦ - nΦx sx £ eΦ ELAMΦ

    Where:

    nΦx = Poisson’s ratio giving strain in longitudinal direction caused by stress in circumferential direction

    eΦ = design strain in circumferential direction

    ELAMΦ= modulus of elasticity in circumferential direction

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.

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.

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 fact that pressure stresses are given a factor of safety (typically equal to 2/3) while other loads are not. This gives an explicit requirement of:

Pdes £ f1 f2 f3 LTHP

Where:

Pdes = allowable design pressure

f1 = factor of safety for 97.5% lower confidence limit, usually 0.85

f2 = system factor of safety, usually 0.67

f3 = ratio of residual allowable, after mechanical loads

= 1 - (2 sab) / (r f1 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

This has been implemented in the CAESAR II pipe stress analysis software as:

Code Stress

Code Allowable

sab (f2 /r) + PDm / (4t)

£

(f1 f2 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.