# Stress Analysis of FRP Pipe by Using Caesar II Software (A Guideline)

**1. Introduction**

Fiber reinforced polymers are made of two primary constituents; fibers and a polymer matrix. In FRP, the fiber is embedded in a polymer matrix. This structure gives completely different chemical and physical properties than the properties of the individual materials.

Fiberglass or GRP is a composite material made out of glass fibers and uses polyester, vinyl, or epoxy as the polymer.

If the fiber of composite is glass, it is known as GRP (Glass reinforced plastic). Fiberglass (GRP) is one type of FRP.

**2. STRESS ANALYSIS OF FRP PIPE**

Von Mises stress or maximum shear stress such as those determined by Mohr’s circle, have no correlation for an isentropic

material like a composite and only apply to an isotropic material like steel. These material’s calculated stresses compares in the

hoop axial direction to a “trapezoidal design envelope”. This envelope defines the allowable combinations of axial and hoop stress.

**3. Generation of design envelopes**

**3.1. Partial factors**

**3.1.1 Design life**

A0 shall be used to scale the long term envelopes to the design envelopes at design lives other than 20 years.

A0 shall be defined by the following equation.

where

t time expressed in hours;

Gxx gradient of regression line at xx °C.

A0 shall not be greater than 1.0.

**3.1.2 Chemical degradation**

A2 shall be used to scale the long term envelopes to the design envelopes to account for the effect of chemical degradation.

**3.1.3 Fatigue and cyclic loading**

A3 shall be used to scale the long term envelopes to the design envelopes. Refer to Annex B (ISO/WD 14692-3.10).

Figure 1 — *A*3 as a function of the number of cycles and the loading ratio

Key

1 Fully Static Loading

2 Fully Cyclic Loading

*f*c Cyclic long term strength factor (default value of 4,0), =

X Number of Cycles

**3.1.4 Part factor, f2**

The part factor for sustained loading, *f*2, to be used in the assessment of sustained loads, shall be determined taking into account operating conditions and risk associated with the pipe system. The value to be applied for specific piping systems shall be specified by the user. The recommended value for *f*2 is:

a) 0,67 for sustained loading conditions;

b) 0,83 for sustained loading plus self-limiting displacement conditions; and

c) 0,89 for occasional loading conditions.

**3.1.5 Combinations of part factor and partial factors**

The designer shall determine the applicable combination(s) of loading cases.

For the field hydrotest loading case, *A*0, *A*2 and *A*3 shall be 1.0 and *f*2 shall be 0,89.

where

*f*2 part factor for loading;

*A*0 partial factor for design life;

*A*2 partial factor for chemical resistance;

*A*3 partial factor for cyclic service;

σa,LT,2:1,xx long term envelope axial stress for an unrestrained, hydraulic (2:1) condition at xx °C, expressed in MPa;

σh,LT,2:1,xx long term envelope hoop stress for an unrestrained, hydraulic (2:1) condition at xx °C, expressed in MPa;

σa,LT,0:1,xx long term envelope axial stress for a pure axial loading condition at xx °C, expressed in MPa.

Figure 2 — Relationship between the long term envelope(s) and design envelope(s)

**4. Analysis at Caesar Software**

**4.1 Input data**

Pipe input will be similar to that of steel pipe. Except few input

**4.2 Pipe diameter & Wt/Sch: **These values will be as per vendor catalogue.

**4.3 Mill tolerance:** This value will depend on vendor information if nothing is available then any value between 0 to 12.5 % can be used.It Will be conservative approach if value will be greater than zero.

**4.4 Corrosion:** Default value will be ‘0’.

**4.5 Poisson’s Ratio changes to “E _{a}/E_{h}*V_{h/a : }**0.1527, if value id not available then one can start calculation with this value.

**4.6 Elastic Modulus/axial from Elastic Modulus: **2.2063E+004, this values will be given by vendor, if not available on can start the calculation with this value.

**4.7 Under allowable stresses section **

**4.7.1** At Code drop down menu select ISO 14692

Note:

(2:1) means: 2 times axial stress = Hoop stress

(1:1) means: axial stress = hoop stress

(0:1) means: only axial stress

(1:0) means: only hoop stress

**4.7.2** Values of Failure Envelope for Plain Pipe and Joints/Fittings will be required from manufacturer.

**4.7.3** If the operating temperature is less than or equal to 65°C, then vlA_{1} is generally equal to 1.0. Otherwise you need to get these values from manufacturer

**4.7.4** Default value of Chemical Resistance (A2) is 1 (normal service water) until unless values is not given by manufacturer.

**4.7.5** Default value of A3 is 1.0. If calculated number of pressure or other loading cycles exceeds 7000 over the design life then severity, R_{c}, of the piping system. R_{c} is defined as:

where F_{min} and F_{max} are the minimum and maximum loads (or stresses) of the load (or stress) cycle.

The partial factor, A_{3}, for cyclic service is given by:

where N is the total number of cycles during service life.

This equation is intended for cyclic internal pressure loading only, but may be applied with caution to axial loads provided they remain tensile, that is, it is not applicable for reversible loading.

**4.7.6** Default value of System Design Factor is 0.67. If this value is multiplied by occasional load factor then it will generate the value of Part factor (f_{2})

**4.7.7** Default value of Thermal Factor (k) is 1.0. In the absence of information value for liquids is 0.85 and 0.8 for gases.

**4.8 Modeling of fittings**

**4.8.1 Bends and Tees**

Chopped strand mat (CSM) and multi-filament roving construction with internal and external surface tissue reinforced layer

The value of EpTp/(EbTb) will be provided by vendor and in the case of unavailability need to be calculate.

For fittings that have an MPR equal to the pipe, the fitting should be modeled in the stress analysis with the dimensional properties (ID, *t*r,min) of the pipe, not the fitting.

For fittings that have an MPR different than the pipe, the fitting should be modeled in the stress analysis with the dimensional properties (ID, *t*r,min) of the equivalent-rated pipe, not the fitting.** **

**EXAMPLE** A 200NB piping system is constructed with 10 bar rated pipe and 20 bar rated fittings. The minimum

reinforced wall thickness of the 10 bar components is 3,0 mm for the pipe and 5,0 mm for the bends. The minimum reinforced wall thickness of the 20 bar components is 6,0 mm for the pipe and 10,0 mm for the bends. The fitting should be modeled in the stress analysis with a 6,00 mm wall thickness, which is the wall thickness for the equivalent-rated (20 bar) pipe.

**NOTE** Some software programs for stress analysis model tees and other branches as a single node (the intersection). This does not allow for modeling the tee different than the pipe. If the tee has an MPR different than the pipe and the designer wishes to properly model the tee, it will require the designer to model 3 nodes for the tee. For simplicity, it may be acceptable to use a default laying length of 1.0 × D for each leg of the tee, where D is the nominal pipe size. The same practice would be required for saddles (also called olets), except that only one additional node would be required.

**4.8.2 Stress intensification factors**

Axial stress intensification factors (both in-plane and out-of-plane) for GRP bends and tees shall be

1) 1,5 or

2) Shall be qualified in accordance with A.5 of Annex A (ISO/WD 14692-3.10).

Since all components are subject to the qualification programme in ISO 14692-2, which includes the generation of hoop stresses from an R=2 test, hoop SIFs are not required for any components.

There are no SIFs for flanges nor reducers nor pipe joints. Since all components are subject to the qualification programme in ISO 14692-2, pressure stress multipliers are not required.

**4.9 Special Execution Parameters**

- Coefficient of thermal expansion will be provided by vendor.
- Ratio of Shear Modulus to Axial Modulus need to be calculated.
- If FRP lamination data is not available then keep the default value.

**4.10 Default Load cases**

Default Load cases for analysis of FRP are similar to that of steel pipe

- WW+H……………………Hydro
- W+T1+P1………………..OPE – Design Temperature
- W+T2+P1………………..OPE- Operating Temperature
- W+P1……………………..Sustained

**5. Supports**

FRP/GRP pipe and metallic pipe have similar principal as of metallic piping system for supporting. However need to be careful while selecting standard size support as it is not necessary that pipe outside diameter will match. The use of saddles and elastomeric (neoprene) pads may allow the use of standard-size supports.

For GRP pipes following guidelines can be useful

- In all cases, support design should be in accordance with the manufacturer’s guidelines.
- Supports shall be spaced to avoid sag (excessive displacement over time) and/or excessive vibration for the design life of the piping system.
- Point support should be avoided and sufficient support should be lined with an elastomer or other suitable soft material. Also this can be accomplished by using supports with at least 60 degrees of contact. And where ever required it should be locally reinforced.
- Where there are long runs, it is possible to use the low modulus of the material to accommodate axial expansion and eliminate the need for expansion joints, provided the system is well anchored and guided. In this case, the designer should recognize that the axial expansion due to internal pressure is now restrained and the corresponding thrust loads are partly transferred to the anchors.
- Valves or other heavy attached equipment shall be adequately and, if necessary, independently supported.
- GRP pipe shall not be used to support other piping, unless agreed with the principal.
- GRP piping should be adequately supported to ensure that the attachment of hoses at locations such as utility or loading stations does not result in the pipe being pulled in a manner that could overstress the material.

Reference

- https://www.linkedin.com/pulse/composites-grp-vs-frp-whats-difference-between-them-emre-g%C3%BCnd%C3%BCz/
- https://www.differencebetween.com/difference-between-frp-and-vs-grp/
- Petroleum and natural gas industries — Glass-reinforced plastics (GRP) piping — Part 3: System design (ISO/WD 14692-3.10 Date: 2013-09-24)
- Intergraph Caesar II software.

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