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CAESAR II Users Guide

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CAESAR II
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CAESAR II Version
12

CAESAR II has had the ability to model orthotropic materials such as FRP almost from 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.

FRP Properties Configuration Settings

Selecting material (20) FRP (FIBER REIN PLASTIC) activates the CAESAR II orthotropic material model and brings in the appropriate material parameters from the pre-selected materials.

When the software uses the orthotropic material model, it changes 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, as shown below.

These changes are necessary because orthotropic models require more material parameters than isotropic models. 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: nh/a (Poisson’s ratio relating strain in the axial direction due to stress-induced strain in the hoop direction) and na/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 - n), so that value must be explicitly input.

To minimize input, a few of these parameters can be combined due to their use in the software. 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 - nh/a * shoop / Eh) L

Where:

dx

=

extension of piping element due to pressure

sx

=

longitudinal pressure stress in the piping element

Ea

=

modulus of elasticity in the axial direction

nh/a

=

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 - shoop * (Ea / Eh * nh/a)) * L / Ea

In theory, the single new parameter, (Ea / Eh * nh/a), is identical to na/h, producing dx = (sx - na/h * shoop) * 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 Parameters 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.

SHARED Tip 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 software 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)

After selecting UKOOA, CAESAR II provides fields for entry of the following code parameters:

SH1 through SH9 = hoop design stress = f1 * LTHS

R1 through R9 = ratio r = (sa(0:1) / sa(2:1))

f2 = 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. <Product> 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 system under these loads, CAESAR II displays 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.

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.