1 - CoolH2O Metric Total A4

CAESAR II Seminar COADE, Inc.

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Seminar Job: CoolH2O (metric) Fiberglass Cooling Water System Topics Addressed: Modeling of Fiberglass Pipe

BS 7159 Code/UKOOA Code FRP Configuration Options Static Seismic (IBC, uniform loads, load case builder) Use of CNODEs to displace anchors/restraints

Introduction:

This job consists of an FRP cooling water header, which decreases from 1800 mm diameter, to 1500 mm diameter, to 1200 mm diameter, to 1050 mm diameter as a succession of 750 mm diameter lines tap off of it. Modeling this job provides the opportunity for the user to explore the capabilities that CAESAR II offers for analyzing FRP pipe. Additionally, static seismic loads will be applied to this system, illustrating methods using uniform loads and load combinations.

Basics of Fiberglass Piping Analysis:

Stress analysis of Fiber Reinforced Plastic 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.

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 (called 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.

Typically, on a micro level, the following failure modes are evaluated:

1) failure of the fiber 2) failure of the plastic matrix 3) failure of the fiber-matrix interface

Generally, the glass fiber is found to be much stronger in tension than is the matrix, so most tension (along the axis of the fiber) is naturally taken by the fiber, rather than the matrix.


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Mini level analysis: 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 which may 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 element analysis inappropriate.

For mini-level analysis, a laminate layer is considered to act as a continuous material, with material properties and failure modes estimated by averaging them over the assumed cross-sectional distribution. 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 distributions are the square and the hexagonal, with the latter generally considered to be a better representation of randomly distributed fibers.

Use of these parameters permits the development of the homogenous material models which facilitate the calculation of longitudinal and transverse stresses acting on a laminate layer. Typical mini-level analysis shows that due to stress intensification and relative weakness of the matrix relative to the glass fibers, laminate layers are typically very strong only in a single direction i.e., the direction corresponding to the predominate alignment of the glass fibers.


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Macro level analysis: 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 homogenous 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.

Since individual laminate layers are usually strong only in one direction, they are wound upon each other at various angles to tailor the desired strength in various directions. Typically, for pipes, the laminate layers would be arranged in such a way that their strength in the hoop direction is approximately twice that in the axial direction.

Total laminate properties may be estimated by summing the layer properties (adjusted for winding angle) over all layers. For example:

ELAM|| = (1 / tLAM) (E||k Cik + Ek Cjk) tk k

Where: ELAM|| = 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 Cjk = transformation matrix orienting axes of layer k to transverse laminate axis tk = thickness of laminate layer k


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Once composite properties are determined, the component stiffness parameters may be determined as though it were made of homogenous material i.e., based on component cross-sectional and composite material properties, and interaction formulae for normal and shear stresses can be developed.

0

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3

4

5

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Combined Stresses and at failure: Araldite CY232

CAESAR IIs orthotropic model for piping systems:

CAESAR IIs orthotropic material model is activated through the selection of Material 20 FRP. The orthotropic material model is indicated by the changing of two fields from their previous isotropic values: "Elastic Modulus (C)" --> "Elastic Modulus/axial" and "Poissons Ratio" --> "Ea/Eh*Vh/a". These changes are necessary due to the fact that 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 -- Vh/a (Poisson's ratio relating strain in the axial direction due to stress-induced strain in the hoop direction) and Va/h (Poisson's ratio relating strain in the hoop direction due to stress-induced strain in the axial direction). Also, unlike with isotropic materials, the shear modulus does not follow the relationship G = 1 / E (1-V) as for metals, so that value must be explicitly input as well.


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In order 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 are 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 = (x / Ea - Vh/a * hoop / Eh) L Where:

dx = extension of piping element due to pressure x = longitudinal pressure stress in the piping element Ea = modulus of elasticity in the axial direction Vh/a = Poisson's ratio relating strain in the axial direction due to stress-induced strain in the hoop direction hoop = 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 = (x - hoop * (Ea / Eh * Vh/a)) * L / Ea Note, that in theory, that single parameter, (Ea / Eh * Vh/a) is identical to Va/h.

Requirements of the BS 7159 Code:

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; since 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):

eq = (x2 + 42) (when axial stress is greater than hoop) eq = (h2 + 42) (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 is resolved by defining the allowable in terms of a design strain d, rather than stress, in effect adjusting the stress allowable in proportion to the strength in each direction i.e., the allowable stresses for the two equivalent stresses above would be (d ELAMX) and (d 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.

Note that when longitudinal stress is negative (net compressive):

- Vx x ELAM

Where: Vx = Poissons ratio giving strain in longitudinal direction caused by stress in circumferential direction = design strain in circumferential direction ELAM = modulus of elasticity in circumferential direction


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(Note that CAESAR II prints a different allowable depending upon which stress calculation controls Hoop, Axial, or Compressive.)

The BS 7159 Code gives very explicit, and detailed, equations for stress calculations in straight pipe, bends, and tees.

The BS 7159 Code 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 Bend k- and i- Factors


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BS 7159 Tee i- Factors

Requirements of the UKOOA Code:

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 which cause the equivalent stress to reach failure. This curve represents the plot of:

(x / x-all)2 + (hoop / hoop-all)2 - [x hoop / (x-all hoop-all)] 1.0 Where:

x-all = allowable stress, axial hoop-all = allowable stress, hoop


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UKOOA Idealized Stress Envelope

The Specification conservatively limits the user to that part of the curve falling under the line between x-all (also known as a(0:1)) and the intersection point on the curve where hoop is twice x-(a natural condition for a pipe loaded only with pressure). 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 ab) / (r f1 LTHS) ab = axial bending stress due to mechanical loads r = a(0:1) / a(2:1) a(0:1) = long term axial tensile strength in absence of pressure load a(2:1) = long term axial tensile strength in under only pressure loading LTHS = long term hydrostatic strength (hoop stress allowable) LTHP = long term hydrostatic pressure allowable


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Note that this has been implemented in the CAESAR II pipe stress analysis software as:

Code Stress Code Allowable

ab (f2 /r) + PDm / (4t) (f1 f2 LTHS) / 2.0 Where:

P = design pressure Dm = 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.

Configuration Options for FRP Piping:

In this example, the material has the properties of Wavin 55o winding FRP pipe. These parameters are:

Ea = 12,000 MPa Eh = 20,400 MPa (Eh/Ea = 1.7) Ea/Eh Vh/a = 0.38 Density = 1849 kg/m3 CTE = 20E-6 mm/mm/oC Shear Modulus = 11,496 MPa Bend laminate type = Chopped strand mat with multi-filament roving construction

Use BS 7159 code Stiffen for actual pressure Strain Class 1 (Table 4.4: Mild chemical conditions, normal temperatures) Design Strain = 0.0018 (Table 4.3)

CAESAR IIs material database is not currently configured for orthotropic materials such as FRP. Therefore, CAESAR IIs orthotropic model must be triggered through use of Material 20 (FRP), with the material parameters entered explicitly. These parameters include:

Axial Modulus of Elasticity (Ea) (entered on spreadsheet) The Ratio (Ea/Eh)Vh/a (entered on spreadsheet) Pipe Density (entered on spreadsheet) Coefficient of Thermal Expansion (entered on Special Execution Parameters) Ratio of Shear Modulus (G) to Axial Modulus (Ea) (entered on Special Execution Parameters) FRP Bend Laminate Type (entered on Special Execution Parameters)

This may become tedious, especially if the same type of FRP material is used frequently. In this case, the appropriate material parameters may be entered in the CAESAR II Configure/Setup, to be used automatically whenever Material 20 is used.


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These parameters are entered using the FRP PROPERTIES tab of Configure/Setup. The configuration items are described below:

Use FRP SIF: If checked, and any code other than one specifically addressing FRP (such as BS 7159 or UKOOA) is in effect, all fittings will receive a fixed SIF of 2.3; if unchecked, the SIF will be calculated according to the instructions of the specified code. (Note: for BS 7159 and UKOOA, SIFs will be calculated as per the specified code, regardless of the setting of this directive.)

Use FRP Flexibilities: If checked, and any code other than one specifically addressing FRP (such as BS 7159 or UKOOA) is in effect, all bends will receive a fixed flexibility factor of 1.0; if unchecked, the flexibility factor will be calculated according to the instructions of the specified code. (Note: for BS 7159 and UKOOA, the flexibility factors will be calculated as per the specified code, regardless of the setting of this directive.)

FRP Property Data File: Selecting an FRP type from one of the ones listed reads in much of the associated material data.

BS 7159 Pressure Stiffening: The BS 7159 Code requires pressure stiffening based upon the design strain (i.e., as though the pipe were always fully pressurized). A more realistic approach may be to calculate pressure stiffening based upon the strain induced by the actual design pressure.


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FRP Laminate Type: This item is considered when calculating SIFs and Flexibility Factors of bends under the BS 7159 and UKOOA codes. Choices include:

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.

Exclude f2 from UKOOA bending stress: The UKOOA code is implemented in CAESAR II as:

ab (f2 /r) + PDm / (4t) (f1 f2 LTHS) / 2.0

There is some belief in the FRP community that the f2 (on the left side of the equation) is a mistake on the part of UKOOA, and should be excluded from the equation. Checking this directive implements the equation without the f2.

FRP Density: Self explanatory; can be read from an FRP file.

FRP Alpha (x E-06): The coefficient of thermal expansion, length/length/degree, multiplied by 1,000,000; can be read from an FRP file.

Axial Modulus of Elasticity: Self explanatory; can be read from an FRP file.

Ratio Shear Mod : Elastic Mod: Ratio of the FRP shear modulus to the axial modulus of elasticity; can be read from an FRP file.

Axial Strain : Hoop Stress (Ea/Eh*Vh/a): Ratio of the FRP axial modulus of elasticity to the hoop modulus of elasticity, all multiplied by Poissons ratio for strain in longitudinal direction due to stress-induced strain in circumferential direction; can be read from an FRP file.

For this example, choose the WAVIN55.FRP file, Actual Pressure, Laminate Type 3, and exclude f2.

Modeling the System:

The following issues are of specific interest during the modeling phase:

Element 10-20 originates at an anchor. The pipeline is 1800 mm diameter, with a non-standard 46 mm wall thickness.

The 1.5 mm corrosion layer should be entered here. This layer will always be used in the weight and thermal force calculations, but excluded from the pipe strength calculations.

Enter a temperature of 50C, representing the highest temperature that the cooling water may reach.

The bend at node 20 (as well as that at node 30) should be long radius, with two miter points. Note that the BS 7159 Code ignores the number of miters when calculating the bend SIF and flexibility factor.

Besides the anchor at node 10, there is a +Y (weight only) support at node 18 (the bend near point). Use a friction coefficient of 0.15 on all restraints, to represent plastic on steel/concrete.


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Entering Material 20 (FRP) brings in the material parameters entered in Configure/Setup. This can be verified by examining the material parameter section on the main spreadsheet and the Special Execution Options.

The applicable code is BS 7159. For SH1, the user must enter the allowable axial stress, which happens to be the Axial Modulus of Elasticity (1.2E4 MPa) times the design strain (0.0018), or 21.6 MPa. The Kn factors are fatigue factors they are used to divide the allowable SH1 in the presence of extreme cyclic loading (note that Kn is greater or equal to 1.0) (for this application, assume Kn1 is blank, or 1.0, indicating minimal cyclic loading). The field Eh/Ea indicates ratio of both the hoop modulus to the axial modulus, and the hoop allowable to the axial allowable (since the allowable is the design strain times the modulus of elasticity), in this case 1.7. K is the mean temperature multiplier, a factor by which the difference in temperature between the fluid the environment is to be multiplied (since FRP has natural insulating qualities). For liquids, BS 7159 dictates a K value of 0.85 (for gases K is 0.80).


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For water, fluid density of 1.0SG should be entered.

The branch connection at node 40 (as well as all other branches) is a BS 7159 Fabricated tee, modeled in CAESAR II as a reinforced tee (SIF type 1). Node 40 (along with nodes 60, 100, 120, 160, 180, 190, and 250) is supported by a +Y (weight only) support (with friction coefficient of 0.15). Note that BS 7159 reinforced tees assume a pad thickness equal to the pipe wall thickness, so enter that value for clarity.

The restraint at node 50 (as well as those at nodes 90, 110, 150, and 170) is combination guide and +Y (weight only) restraint (with friction coefficient of 0.15).

Elements 70-80 and 130-140 are modeled as reducers.

Element 190-220 is a branch off of the 1200 mm line. Its diameter and thickness should be changed to 1050 mm and 28 mm respectively. (The user may also consider modeling an X-From Offset of 600 mm here.)

The bends at nodes 250 and 260 should be modeled with 2 miter points.

Element 40-280 is a branch off of the 1800 mm line. Its diameter and thickness should be changed to 750 mm and 25 mm, respectively. (Offsets should be considered here as the actual flexible length of straight pipe [before the bend] 3600 mm is much smaller than the modeled length 4500 mm and therefore much stiffer. However, for this layout the effect is minimal [about 5% in terms of stress] and excluded for simplicity.) The bend at node 280 has 4 miter points.

After modeling the branch through node 300, that branch can be duplicated via the list processor 5 times (with the node increment set to 30, 60, 90, etc.). It is also necessary to change the branch intersection nodes to 60 (from 70), 120 (from 130), and 180 (from 190).


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Load Case Setup:

As mentioned earlier, the BS 7159 requirements dictate that only an Operating stress check be made, for that case where the worst stress (strain) is expected. In order to determine which type of load is causing any potential overstress, it may be convenient to build Sustained and Expansion cases as well:

1 W+T1+P1 (OPE) 2 W+P1 (SUS) 3 L1-L2 (EXP)

Results and Output Review:

Running this analysis shows that this system is overstressed at node 180 (the tee of the last 30 branch). The cause of this overstress can be determined by looking at the Code Compliance report, highlighting all three load cases. (Note for the Operating Case, CAESAR II prints a different allowable depending upon which stress calculation controls Hoop, Axial, or Compressive.)

From this, it is apparent that the failure is due to the thermal expansion load. This will have to be fixed.

Solving the Expansion Problem:

The philosophy behind solving expansion problems in a Fiberglass piping application is different from that in a steel piping application. For steel piping, the preferred hierarchy for solving such a problem is 1) adding flexibility through loops and bends, 2) using expansion joints, and 3) using restraints to re-direct growth to areas where it can be better handled. For Fiberglass applications, due to the relatively low modulus of elasticity of Fiberglass, the lack of significant flexibility provided by FRP bends, and the potential problems involved in the joining of FRP sections, the hierarchy is exactly the opposite. The preferred method is to use axial restraint to force the thermal expansion into compression (in this case,


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the line must be adequately guided); the next preference is to use expansion joints; and the last resort is to use expansion loops.

In this case, the amount of expansion at node 180 can be approximately halved by adding an axial (Z-direction restraint) at node 110. Re-running the analysis with this modification causes the system to now pass the code check:


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The UKOOA Code:

As noted earlier, CAESAR II offers two different fiberglass piping codes BS 7159 and UKOOA. Some people prefer the UKOOA code, since it often requires a smaller wall thickness than does BS 7159. This belief can be verified (at least for this particular analysis) by rerunning this system under the UKOOA code.

Upon selection of the UKOOA code, the fields of the Allowables auxiliary screen change:

For SH1, the user must now enter f1 x LTHS at the 2:1 stress condition. This may be obtained from vendor data; in the case of the Wavin 55 material, it is available from the graph of the combined stress failure envelope, as shown below. Note that the axes have been switched (axial stress on the horizontal axis) on this graph relative to the traditional UKOOA envelope format, so the desired 2:1 position is now identified as R = 0.5. Likewise, the values in this graph include the service factor f2, which can be eliminated by dividing the values on the outer curve by 0.67. This gives a f1 x LTHS value of 125 N/mm2, or 18125 psi. An alternative means of getting this value is to find the value given by the vendor for the long term Hydrostatic Design Basis; again, for this case 125 N/mm2.


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R1 represents the ratio of the allowable axial stress at the 0:1 stress condition to that at the 2:1 stress condition. For this material, this ratio appears to be approximately 41/42, or 0.97.

F2 is the system factor of safety, which is usually taken as 0.67.

K is the BS 7159 mean temperature multiplier, which for liquids, should be 0.85.


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Re-analyzing the system with the UKOOA code shows that the system is now stressed to a much lower level perhaps to a large extent because this code does not require SIFs at tees. But also remember, UKOOA does not necessarily handle compressive loads well!.


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Static Seismic Using the International Building Code:

This cooling water system is located in a seismically active region, so it must also be designed to withstand earthquake loads. For this analysis, the International Building Code, 2000 Edition shall be considered to be in effect. We will assume that this installation is located in Site Class D (Stiff soil profile), in El Centro, California. (For Site Class Definitions, refer to IBC Table 1615.1.1.) The structure in which this system is operating has an average roof height of 12 meters.

Section 1621 of the IBC gives the Architectural, Mechanical and Electrical Component Seismic Design Requirements, to which piping must be designed. This Section defines two types of loading that the piping system must be designed for: inertial and relative displacements. Note that the effects of the seismic relative displacements shall be considered in combination with displacements caused by other loads that means that they shall be treated as secondary loads, rather than primary loads.

Inertial Loads:

Section 1621.1.4 defines a horizontal seismic acceleration factor to be applied uniformly throughout the structural mass. This acceleration factor, aH, is defined as:

aH = [(0.4 ap SDS) / ( Rp / Ip)] (1 + 2 z / h], but:

aH 1.6 SDS Ip, and:

aH 0.3 SDS Ip

Where:

ap = Component amplification factor, from Table 1621.3 = 1.0 for pipes

SDS = Design elastic response acceleration at short period, from Section 1615.1.3

Rp = Component response modification factor, from Table 1621.3 = 2.5 for Limited deformability piping systems

Ip = Component importance factor, from Section 1621.1.6 (1.5 for life-safety components, hazardous material containing, or storage racks in occupancies open to the general public; 1.0 for all others)

= 1.0

z = Height in structure at point of attachment = 6.25 m (average of elevation of all 8 connections)

h = Average roof height of structure = 12.5 m

Section 1617.1 implies that a vertical acceleration be considered as well. This acceleration factor, aV, is defined as:

aV = 0.2 SDS

From Section 1615.1.3:

SDS = 2/3 SMS


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Where:

SMS = Maximum considered earthquake spectral response accelerations for short period, from Section 1615.1.2

From Section 1615.1.2:

SMS = Fa SS

Where:

Fa = Site coefficient defined in Table 1615.1.2(1)

SS = Mapped spectral accelerations for short periods, from Section 1615.1

The global coordinates of this piping system on the coast near Los Angeles are 33.9083 latitude and -118.41045 longitude.

Below is an extract from (NEHRP/FEMA) Map 5, Maximum Considered Earthquake Ground Motion for the Southern California Area of 0.2 sec Spectral Response Acceleration (5% of Critical Damping) Site Class B: These maps are also available on-line at http://eqhazmaps.usgs.gov/index.html. The area of interest lies within the circle.

This map shows that the short period acceleration is between 1.75 and 1.90 gs. This would be the maximum horizontal acceleration of an oscillator tuned to a period of 0.2 seconds during a seismic event that has a 2% chance of occurring within the next fifty years.

34 Lat.

-119 Long.

-118 Long.

34 Lat.


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Using the software and data shipped with IBC to collect SS (1.765g) & Fa for Site Class D (1.00):

L.A. Refinery Date and Time: 5/6/2005 2:13:18 PM MCE Ground Motion, - ,Conterminous 48 States Latitude =,33.90833,Longitude =,-118.41045 Period,MCE Sa (sec),(%g) 0.2 ,176.5,MCE Value of Ss, Site Class B 1.0 ,067.2,MCE Value of S1, Site Class B Spectral Parameters for , Site Class D 0.2, 176.5, Sa = FaSs, Fa = , 1.00 1.0, 100.8, Sa = FvS1, Fv = , 1.50

Note: Be sure to use collect design accelerations or MCE ground motions and not probabilistic ground motions.

Values for Fa are listed in Table 1615.1.2(1). Here, Fa is 1.0:

Therefore:

SMS = Fa SS = 1.0 x 1.765g = 1.765g

SDS = 2/3 SMS = 2/3 x 1.765g = 1.18g

So the appropriate seismic acceleration is:

aH = [(0.4 ap SDS) / ( Rp / Ip)] (1 + 2 z / h) = [(0.4 x 1.0 x 1.18g) / ( 2.5 / 1.0)] (1 + 2 x 6.25 / 12.5) = 0.377g

Checking Limits on aH:

aH 1.6 SDS Ip aH 1.6 x 1.18g x 1.0 1.89g 9

aH 0.3 SDS Ip aH 0.3 x 1.18g x 1.0 0.35g 9

aV = 0.2 SDS = 0.2 x 1.18g = 0.235g


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Seismic load adjustment: The building codes are based on strength design where components (such as reinforced concrete structures) are evaluated on their load-carrying capacity rather than stress. Piping codes are based on allowable stress design and, while the calculated seismic load provides a good estimate of the internal loads and deflections of the piping system, these seismic loads over predict the resulting stress used here. Reviewing the basic load combinations used for both Strength Design (Section 1605.2.1) and Allowable Stress Design (Section 1605.3.1), it is clear that the seismic loads for use here should be reduced by 30%. (IBC mimics ASCE 7; see Sections 2.3 & 2.4 of ASCE 7-02.)

Adjusted seismic loads for allowable stress design:

aH = 0.7 x 0.377g = 0.264g

aV = 0.7 x 0.235g = 0.165g

Relative Seismic Displacements:

Section 1621.1.5 discusses the means of addressing relative displacements due to story drift -- this should be calculated via a structural analysis of the enclosing building. Assume this analysis yields the following displacements (with attachment points near building columns, no vertical drift is included):

Node Function Approx Elev. (m) X-Disp (mm) Z-Disp (mm) 10 Anchor 4.6 26 9 18 +Y 4.6 26 9 40 +Y 2.8 16 5 50 X, +Y 2.8 16 5 60 +Y 2.8 16 5 90 X, +Y 2.8 16 5 100 +Y 2.8 16 5 110 X, +Y, Z 2.8 16 5 120 +Y 2.8 16 5 150 X, +Y 2.8 16 5 160 +Y 2.8 16 5 170 X, +Y 2.8 16 5 180 +Y 2.8 16 5 190 +Y 2.8 16 5 240 +Y 2.8 16 5 270 Anchor 0 0 0 300 Anchor 7.3 42 14 330 Anchor 7.3 42 14 360 Anchor 7.3 42 14 390 Anchor 7.3 42 14 420 Anchor 7.3 42 14 450 Anchor 7.3 42 14

Note: Displacements need only be placed on +Y supports if friction loads are considered to be significant.

Seismic Input and Load Cases:

The g-factors calculated above should be entered as uniform loads (the Uniform load in Gs setting in the Special Execution Options must be set first, see below), U1 for X-direction, U2 for Y-direction and U3 for Z-direction. Vertical g-loads could also be accounted for by scaling the Weight load.


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Displacements can be modeled as vector D1 (for X-direction) and vector D3 (for Z-direction). They should be applied to CNODEs attached to the restraints (increment each restraint by 1000). To save inputting effort, all restraints at a common level could be connected to a single CNODE. In this case, displacements need only be entered at three locations. (Note: the Configuration/Setup parameter Connect Geometry through CNODEs must then be set to No in order to avoid a coordinate mismatch error.)


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Section 1621.1.4 discusses the combination method for the various loading directions. It states that the load along each horizontal axis shall be applied independently, but in conjunction with the vertical load. Since BS 7159/UKOOA only looks at a single stress type (OPE), this leads to the following seismic load cases (since boundary conditions are non-linear):

1 W+T1+P1 (OPE) 2 W+T1+P1+U1+D1+U2 (OPE) (Operating + X + Y) 3 W+T1+P1+U1+D1-U2 (OPE) (Operating + X - Y) 4 W+T1+P1-U1-D1+U2 (OPE) (Operating - X + Y) 5 W+T1+P1-U1-D1-U2 (OPE) (Operating - X - Y) 6 W+T1+P1+U3+D3+U2 (OPE) (Operating + Z + Y) 7 W+T1+P1+U3+D3-U2 (OPE) (Operating + Z - Y) 8 W+T1+P1-U3-D3+U2 (OPE) (Operating - Z + Y) 9 W+T1+P1-U3-D3-U2 (OPE) (Operating - Z - Y) 10 L1,L2,L3,L4,L5,L6,L7,L8,L9 (OPE) (Minimum restraint loads) (Signmin) 11 L1,L2,L3,L4,L5,L6,L7,L8,L9 (OPE) (Maximum restraint loads, stresses) (Signmax)

Note that even though results only need be retained from two load cases (the last two), we are electing to keep results from all load cases in order to help us debug in the event of an overstress.


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Now, review of the Stress Report for Load Case 11 shows that our Maximum Stress fails the code stress check:


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In order to solve this, it is necessary to know which of the seismic combination cases caused the failure.

A review of the Code Compliance Report for Cases 2 through 9 reveals that it is Load Case 4, which represents the X, +Y seismic loading. Further, it is necessary to know which component of the seismic load caused the failure the inertial, or the displacement (why?). Going back and running these two components separately shows that the culprit is the displacement component, by a long shot:


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This loading is a secondary load, so the solution is to add flexibility in this case, by removing the guide at node 170. The system now passes the stress check:


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Load cases 10 and 11 represent the envelope of loads (minimum to maximum) to which the restraints must be designed.

Load Cases for Linear B31.1/B31.3 Applications:

First, a system may not have a non-linear restraint condition, so we may be able to take advantage of load superposition. (In order to approach linearity, the +Y restraints at nodes 18, 40, 50, 60, 90, 100, 110, 120, 150, 160, 170, 180, 190, and 240 should first be changed to Y-restraints. Friction can either be removed from the individual restraints or the friction multiplier can be set to 0.00 in the Load Case Options tab in the Static Analysis Window.) The original support configuration is used here with the axial stop removed at 110 and the guide included at 170.

Secondly, the code in effect may be similar to B31.1 or B31.3, which requires load combinations such as:

SE < SA (Expansion, including seismic displacements)

SSUS < SH (Sustained)

SSUS + SOCC < k SH (Occasional)


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Thirdly, many seismic specifications require square root of the sum of the squares combination methods of simultaneous seismic directions.

In order to do this, it is first necessary to switch the piping code to B31.3 (although it must be noted that the B31.3 Code currently gives no guidelines on stress analysis of fiberglass piping this is just a lets pretend for now), and set the SC and the SH1 to the axial allowable of 42 MPa.

For linear, B31.3 applications, with the seismic loads combined in SRSS manner, and the displacements summed with the Expansion case (total displacement range):

1 W+T1+P1 (OPE) 2 W+P1 (SUS) 3 U1 (OCC)* (+X inertial) 4 U2 (OCC)* (+Y inertial) 5 U3 (OCC)* (+Z inertial) 6 D1 (OCC)* (+X displacement) 7 D3 (OCC)* (+Z displacement) 8 L3+L4+L5 (OCC) (SRSS combination) (Composite inertial) 9 L6+L7 (OCC) (SRSS comb.) (Composite displacement) 10 L2+L8 (OCC) (Scalar comb.) (Occasional stress code check) 11 L1-L2 (EXP) (Algebraic comb.) (Non-seismic expansion case) 12 L11+L9 (EXP) (Scalar comb.) (Approx Expansion code check)

* Note that defining a case as OCC case automatically activates any snubbers in the model as shown below.

Friction has been disabled by setting the Friction Multiplier to zero in Load Case Options:


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Additional load cases may be built to define minimum and maximum restraint loads, when the seismic event occurs during operating condition. (And what if the earthquake can hit in the cold condition as well?)

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1 - CoolH2O Metric Total A4