Evaluation For Vessel [PDF]

Zitiervorschau

Proceedings of the ASME 2014 Pressure Vessels & Piping Conference PVP2014 July 20-24, 2014, Anaheim, California, USA

PVP2014-28439

EXTERNAL NOZZLE LOAD EVALUATION FOR FILAMENT WOUND FRP CYLINDRICAL VESSELS Jeffrey D. Eisenman, P.E. Maverick Applied Science, Inc. 1915 24th Ave. E. Palmetto, Florida 34221 USA [email protected]

Dale W. DeCola, P.E. Maverick Applied Science, Inc. 1915 24th Ave. E. Palmetto, Florida 34221 USA [email protected]

ABSTRACT The evaluation of external nozzle loading on filament wound Fiber Reinforced Plastic (FRP) storage tanks and pressure vessels can be a challenging task. While established methods for metallic vessels exist, limited guidance is available to account for the unique characteristics of FRP composite materials and standard FRP fabrication practices. Anisotropic material properties can have a significant effect on the stress/strain distribution due to external nozzle loading. Typical FRP nozzle installation practices introduce additional concerns, including the potential for peeling or overstraining the nozzle attachment overlays. In this paper, the effects of various orthotropic material properties of cylindrical vessels with external nozzle loading are explored using finite element analysis and compared with existing methods established for isotropic materials. Modifications to account for the effects of filament wound FRP material properties are proposed. A simplified FRP nozzle load evaluation procedure, along with additional commentary, is presented to address some of the special considerations regarding nozzle load evaluation for FRP storage tanks and pressure vessels. INTRODUCTION Fiber Reinforced Plastic (FRP) storage tanks and pressure vessels are becoming more common and trusted for corrosive service in the power, chemical processing, and mining industries. As FRP composites replace metallic materials of construction for critical components of systems, the importance of properly defining and evaluating FRP nozzle connections to attached piping is growing. Currently, both ASME RTP-1 and ASME Boiler and Pressure Vessel Code Section X [1,2] require considerations of external loading on FRP nozzles, but neither provides much guidance. As such, many FRP tank designers

proceed with the assumption of zero external loads on nozzles, which can be an unrealistic assumption in most cases where piping is attached. To address these assumptions or when no allowable nozzle loads are available, expansion joints are often implemented at some or all nozzle connections to attached piping systems to minimize potential loading on the nozzles. In many scenarios, expansion joints may not be a preferred or possible solution considering associated costs, maintenance requirements, spatial constraints, or necessary revisions to the attached piping system support configuration. Regardless, external loading on FRP tank nozzles is a realistic design loading that deserves proper evaluation. Otherwise, expansion joints can be an expensive assumption or afterthought if FRP nozzles were not evaluated. There are a number of existing methods for external nozzle load evaluation; however, since many of these methods were developed for metallic materials and construction practices, including assumptions for isotropic material properties, many FRP engineers are appropriately reluctant to apply these to FRP tanks and vessels, which are typically anisotropic in nature. Cylindrical filament wound FRP tanks and vessels typically have increased strength and stiffness in the hoop (circumferential) direction for pressure containment. This increased directional stiffness affects stress/strain distribution and magnitude when external nozzle loading is applied. With typical FRP nozzle installation, new concerns arise for peeling of the external nozzle installation laminate and strain in the internal corrosion barrier laminate at the nozzle opening, which are not concerns with metallic nozzles. Considering the time and effort required for existing methods, along with the uncertainty if these approaches are even suitable for FRP typical construction and materials, it is understandable why many FRP tank and vessel designers are reluctant to use these resources to provide allowable nozzle loads.

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To address some of these concerns unique to FRP tanks and vessels, numerous geometries have been simulated with finite element analysis (FEA) to show the effects of orthotropic material properties on the stress magnitude and distribution due to external nozzle loads. FEA results are compared with existing methods, and a simplified, conservative approach for nozzle load evaluation on FRP tanks is proposed based on the theoretical simulations performed. Additional commentary is also provided to help FRP tank and pressure vessel designers evaluate external nozzle loads for safe and reliable performance in corrosive environments. NOMENCLATURE CP CMC CML D Ea Eh MC ML P Rm T d fpeel ro t λ σP σMC σML

Stress Factor for Radial Loading Stress Factor for Circumferential Moment Stress Factor for Longitudinal Moment Shell Diameter Shell Axial (Longitudinal) Modulus of Elasticity Shell Hoop (Circumferential) Modulus of Elasticity Circumferential Moment Longitudinal Moment Radial Load Shell Mean Radius Shell Thickness at Nozzle Location Nozzle Diameter Peel Force per Unit Length Around Nozzle Nozzle Outer Radius Nozzle Thickness Geometry Parameter per WRC 297 [3], (d/D)(D/T)1/2 Stress in Shell due to Radial Load Stress in Shell due to Circumferential Moment Stress in Shell due to Longitudinal Moment

In general, each of these approaches presents curves for dimensionless factors that are dependent on the geometric configuration, including diameter and thickness of the shell and nozzle. The engineer can then calculate stress due to a defined applied loading or solve for maximum allowable nozzle loads. The engineer must consider the combined effects of multiple components of external nozzle loading in addition to stresses in the vessel due to pressure before any external loading. For many engineers, FEA is a preferred analysis method to more accurately evaluate nozzle loads for particular applications. A simple shell model may be sufficient to evaluate nozzle stiffness, calculate stresses or strains, or include the effects of distance to discontinuities. In many cases, a basic FEA may be a quicker solution in the design process as compared with looking up numerous curve factors and interpolating for each iteration of thickness, for each nozzle on a tank or vessel, and for each component of loading. COMPONENTS OF NOZZLE LOADING External nozzle loading from attached piping systems can be resolved into three force components and three moment components at the nozzle to shell junction. Of these components, the radial load, P, and circumferential and longitudinal bending moments, MC and ML, typically generate the most significant effects [3,4]. These loading directions and exaggerated deformations are illustrated in Fig 1.

METHODS FOR NOZZLE LOAD EVALUATION The topic of nozzle loading has been widely discussed and explored for isotropic metallic materials. Existing guidelines for the evaluation of external nozzle loading on metallic vessels have gained acceptance, including Welding Research Council (WRC) Bulletins 107 and 297 [3,4] and a simplified approach presented in Bednar’s Pressure Vessel Handbook [5], which is based on older WRC publications. In fact, some pipe stress analysis software packages now have built-in modules to conduct nozzle load analysis according to WRC 107 and 297. There are also commercial software packages available to simplify FEA for tee and nozzle intersection analysis. However, since each of these methods were originally developed for metallic materials and construction practices, they contain inherent assumptions for isotropic material properties. The European Standard EN 13121-3 for FRP vessels [6] provides an approach for nozzle load evaluation based on WRC publications; however, the anisotropy of filament wound FRP materials is not directly addressed. Further, many engineers accustomed to the ASME design standards are not familiar with these references or may not be comfortable incorporating parts from various references without better guidance.

FIG. 1 NOZZLE LOADING DIRECTIONS

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Maximum values of stress due to each loading component independently may occur in either the axial or hoop direction, but stresses in both directions are generated from each of the components shown in Fig. 1. Significant hoop direction stresses can be developed from longitudinal bending moments, especially in the case of filament wound FRP vessels. Combined stresses due to multiple components of external nozzle loading in combination with pressure typically govern.

approach per Bednar [5] suggests that stresses due to external loading can be reasonably estimated with one factor for each loading component and direction being considered. For the simplified procedure presented later in this paper, Eq. (2) - Eq. (4) were initially assumed for the simplified relationships between stresses, applied loading, and geometry. For applied radial load (P), a directionally specific geometry factor (CP) is used to predict stress due to loading (σP) as a function of vessel thickness (T) according to the general relationship:

CHECK FOR PEELING Along with an evaluation of stresses or strains in the shell due to external nozzle loading, peel loading requires consideration for FRP nozzles. Maximum allowable external nozzle loads for FRP construction may be governed by peeling of the attachment laminate rather than stresses or strains in the shell. Typical nozzle installation includes an exterior structural FRP overlay along with a thinner corrosion barrier replacement laminate on the interior [1,2]. When subjected to external nozzle loading, the exterior structural laminate could fail first by peel, applying significant loading on the interior corrosion barrier overlay and potentially leading to leaks or reduced service life. Some nozzle installation methods are not subject to peel, such as penetrating type nozzles and nozzles with internal structural overlays designed to safely handle the required loading. If the nozzle structural installation configuration could peel, basic calculations can be used to check that the nozzle loads are actually transferred to the shell. Similar to nozzles with blind flanges subjected to internal pressure loading, peel force per unit length around the nozzle circumference can be checked for external loads. Equation (1) below presents a simple formula to determine peel force per unit length due to external nozzle loading for cylindrical nozzles without gussets, which is based on developing an equivalent force per unit length for the resultant externally applied bending moment. Depending on the configuration of the attached piping, forces developed due to pressure acting on the inside area of the pipe may or may not need to be reacted at the nozzle. In cases where the pressure force adds to external nozzle loading, the pressure force can be added to the external radial load (P) in Eq. (1):

2





1

If peel loading exceeds the allowable criteria, it is recommended that alternate nozzle attachment laminate configurations be explored. Otherwise, the resulting strain in the internal corrosion barrier overlay due to nozzle loading should be evaluated as the next step before checking the shell. CALCULATION OF STRESSES IN THE SHELL Following considerations for the nozzle attachment laminates, stresses/strains in the shell due to external nozzle loading should be evaluated. While the WRC 107 and 297 approaches [3,4] present separate figures for a more detailed division of membrane and bending stresses, the simplified



2

The factor (Cp) is established as a function of size and thickness of the nozzle and shell. Equation (2) can be extended to both hoop direction and axial direction stresses by different factors, although hoop direction stresses are typically most important for combined stress considerations. For moment loading, the nozzle radius (ro) is included in the initial assumed relationship for applied circumferential moment in Eq. (3) and for longitudinal moment in Eq. (4):

3



4

The simplified approach presented later in this paper was developed by starting with the above assumed relationships and adding different terms for geometry and material properties to capture observed trends from the FEA. Equations for the simplified stress evaluation method are presented following a discussion of the material property comparison results. SIMULATION OF FILAMENT WOUND SHELLS In the FEA investigation, numerous vessel and nozzle configurations were modeled with 2D shell elements using Femap with NX Nastran. Geometries were first evaluated using an isotropic assumption for hand lay-up (HLU) properties, with an elastic modulus of 1.5 x 106 psi (10 GPa) and a Poisson’s ratio of 0.25. While hand layup FRP is not truly isotropic and typically has a lower shear modulus, this approach was selected as a baseline comparison with existing nozzle load evaluation methods. It should be noted that with the isotropic assumption and a constant Poisson’s ratio, stress due to external loading is theoretically independent of elastic modulus. Next, filament wound (FW) construction was simulated as a 2D orthotropic material with axial modulus of 1.5x106 psi (10 GPa), hoop modulus of 3.0x106 psi (21 GPa), shear moduli of 0.4x106 psi (2.8 GPa), and a Poisson’s ratio of 0.15 to represent a filament wound laminate optimized for pressure containment, with a hoop modulus twice the axial modulus (Eh/Ea=2). As a final comparison, hoop properties were increased to 4.5x106 psi (31 GPa) while maintaining other properties previously defined to simulate an FRP laminate heavily biased in the hoop direction (Eh/Ea=3) as an upper boundary for shell anisotropy with most FRP tank and vessel applications.

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The selected FEA geometries included shell diameters ranging from 6 ft to 16 ft (1.8 m - 4.9 m), nozzle diameters ranging from 6 in to 48 in (150 mm - 1200 mm), and thicknesses ranging from 0.25 in to 1 in (6.4 mm - 25 mm). A summary of geometry is included in Annex A. The minimum ratio of shell diameter to nozzle diameter was four (4), since larger openings on smaller shells are significant structural discontinuities that deserve proper attention with the specific system configuration. The nozzle thickness was set equal to the shell thickness (T/t=1) for the initial analyses. No local reinforcement was modeled for the initial comparison in order to preserve WRC assumptions and the defined Eh/Ea ratios, since reinforcement is typically hand layup for filament wound shells. Hand layup FRP properties were used for the nozzle. For all geometries, the shell height was assumed to be the same as the shell diameter, with the nozzle located at the center of the height. An example of a typical FEA model is shown in Fig 2.

FEA RESULTS FOR MAXIMUM SHELL STRESS FEA results for maximum hoop and axial stresses due to the independent external loading components are illustrated in Fig. 3 - Fig. 8. These graphs show a comparison between isotropic (Eh/Ea=1) and orthotropic (Eh/Ea=2 and Eh/Ea=3) material assumptions due to the same applied loading. Stresses from the FEA are normalized to WRC 107 stresses [4], with the FEA stress divided by the WRC 107 stress. Results are displayed as percentages of WRC 107 results for comparison, with 100% being equal to the maximum stress estimated using the WRC 107 methods. This presentation allows for a comparison between isotropic and orthotropic FEA results and a comparison between FEA and WRC 107. Normalized stresses are plotted with respect to WRC 297 [3] geometry parameter λ on the abscissa. The nozzle thickness was set equal to the shell thickness for all included geometries, for T/t=1.

σML.h (FEA)  / σML.h (WRC 107)

250% Isotropic, Eh/Ea=1 Orthotropic, Eh/Ea=2 Orthotropic, Eh/Ea=3

200%

150%

100%

50%

0% 0

2

6

8

λ

FIG. 2 FEA MODEL EXAMPLE

As illustrated in Fig. 2, translational constraints were defined at the boundary curves on the shell. Loads were applied to the central node of a rigid body (spider) element defined at the end of the nozzle at centerline elevation. It should be noted that the load application at the end of the nozzle for the FEA model is intended to represent resolved external loading at the nozzle to shell junction with the assumed FEA nozzle boundary conditions. The nozzle projection length was held constant for all geometries at 6 in (150 mm). Loads were preliminarily estimated using an average of WRC 107 and Bednar predictions [4,5] based on a 1500 psi (10.3 MPa) allowable stress for each component, although the magnitude of applied load is not significant since linear static analyses were performed and since results are presented as comparisons. The magnitude of applied loading and all geometry were held constant for each of the material property iterations for a direct comparison of the effects. Loading components were independently evaluated in the FEA to determine stresses due to each loading shown in Fig. 1.

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FIG. 3 COMPARISON OF MAXIMUM HOOP STRESS DUE TO LONGITUDINAL MOMENT (ML), NORMALIZED TO WRC 107

Figure 3 shows the most significant effects of typical filament wound properties on stress due to external longitudinal moment loading. The FEA results for isotropic material assumptions are reasonably consistent with WRC 107 results, around 100%. However, hoop stresses due to longitudinal moment loading with orthotropic properties are increased significantly, in some cases by a factor of two or more. With increased hoop stiffness, the hoop direction carries a larger share of the external longitudinal moment bending as compared with an isotropic assumption, resulting in significantly higher hoop direction stresses. Maximum stress for longitudinal moment loading with the existing methods is assumed to be axial direction stress, which is not necessarily the case with filament wound FRP vessels. Orthotropic effects are most significant for lower values of λ and indicate a clear relation to the ratio of hoop to axial modulus (Eh/Ea).

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Effects on the maximum magnitude of stress are less significant for the other stress directions and loading components. As illustrated in Fig. 4 - Fig. 5, there is a small increase associated with the effect of orthotropic properties for maximum magnitude of hoop stress due to circumferential moment loading and radial loading. The increase is negligible for lower λ values, with a maximum increase around 10-15% for higher λ values. Even though hoop stiffness has increased, the hoop direction already carries a larger share of loading than the axial direction due to circumferential moment and radial load, partly due to the curvature of the vessel. These results indicate that existing methods developed for isotropic materials still have potential application to filament wound FRP tanks and vessels with orthotropic shell properties, although most FEA for circumferential moment loading indicated hoop stresses higher than predicted using the WRC 107 methods, as shown in Fig. 4.

120% 100% 80% Isotropic, Eh/Ea=1 Orthotropic, Eh/Ea=2 Orthotropic, Eh/Ea=3

60% 40%

140%

20%

σML.a (FEA)  / σML.a (WRC 107)

σMC.h (FEA)  / σMC.h (WRC 107)

140%

Hoop direction stresses will likely govern, since hoop direction stresses due to external nozzle loading add to hoop pressure stresses. For storage tanks and low-pressure vessels with relatively low axial direction stresses, adequate axial direction strength may be available for reasonable external nozzle loading. However, in certain cases with filament wound vessels optimized for pressure containment, axial direction combined stresses, even if lower in magnitude, may govern because of the lower directional allowable limit. Fig. 6 - Fig. 8 illustrate the effects of orthotropic material properties on the maximum magnitude of axial direction stress due to external nozzle loading. There is a small decrease in axial direction stress due to each component of external loading associated with higher hoop stiffness. The difference between isotropic and orthotropic material assumptions is small for longitudinal moment loading and radial loading, but more noticeable for circumferential loading. Part of this difference has to do with the stress distribution around the nozzle circumference as discussed in the next section, so the maximum magnitude of stress is not the only aspect for a proper comparison. However, in cases where axial direction stresses govern because of a significantly lower axial direction allowable limit, the results suggest that it may be justified to account for the reduced axial direction stresses associated with increased hoop stiffness of filament wound FRP shells, as best illustrated in Fig. 7.

0% 0

2

4

6

8

λ FIG. 4 COMPARISON OF MAXIMUM HOOP STRESS DUE TO CIRCUMFERENTIAL MOMENT (MC), NORMALIZED TO WRC 107

σP.h (FEA)  / σP.h (WRC 107)

120% Isotropic, Eh/Ea=1 Orthotropic, Eh/Ea=2 Orthotropic, Eh/Ea=3

100%

120% 100% 80% 60% Isotropic, Eh/Ea=1 Orthotropic, Eh/Ea=2 Orthotropic, Eh/Ea=3

40% 20% 0% 0

2

80%

4

6

8

λ

60%

FIG. 6 COMPARISON OF MAXIMUM AXIAL STRESS DUE TO LONGITUDINAL MOMENT (ML), NORMALIZED TO WRC 107

40% 20% 0% 0

2

4

6

8

λ FIG. 5 COMPARISON OF MAXIMUM HOOP STRESS DUE TO RADIAL LOAD (P), NORMALIZED TO WRC 107

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(σML.h (FEA)  / σML.h (WRC 107))*(Eh/Ea)‐0.5 

σMC.a (FEA)  / σMC.a (WRC 107)

120% 100% 80% 60% 40% Isotropic, Eh/Ea=1 Orthotropic, Eh/Ea=2

20%

Orthotropic, Eh/Ea=3 0%

250% Isotropic, Eh/Ea=1 Orthotropic, Eh/Ea=2

200%

Orthotropic, Eh/Ea=3 150%

100%

50%

0% 0

2

4

6

8

0

2

λ

8

FIG. 9 COMPARISON OF MAXIMUM HOOP STRESS DUE TO LONGITUDINAL MOMENT (ML), NORMALIZED TO WRC 107, WITH PROPOSED MATERIAL PROPERTY CORRECTION

Using the effective modulus to account for the differences in isotropic and orthotropic material properties provides a simple way to account for the effects when methods developed for isotropic materials are used for nozzle load evaluation. The results indicate that including the effective modulus is conservative for λ > 3, although it may not completely capture all differences for smaller λ values. However, if hoop stress due to external longitudinal moment can be calculated based on isotropic assumptions, multiplying by (Eh/Ea)1/2 provides a much better estimation as compared with ignoring these effects.

60%

σP.a (FEA)  / σP.a (WRC 107)

6

λ

FIG. 7 COMPARISON OF MAXIMUM AXIAL STRESS DUE TO CIRCUMFERENTIAL MOMENT (MC), NORMALIZED TO WRC 107

Isotropic, Eh/Ea=1 Orthotropic, Eh/Ea=2 Orthotropic, Eh/Ea=3

50%

4

40% 30% 20% 10%

STRESS DISTRIBUTION AROUND THE NOZZLE

0% 0

2

4

6

8

λ FIG. 8 COMPARISON OF MAXIMUM AXIAL STRESS DUE TO RADIAL LOAD (P), NORMALIZED TO WRC 107

To quantitatively utilize the results presented in the previous figures, correction factors to account for the effects of increased hoop stiffness with orthotropic materials were explored. The results indicate it is most important to account for the significant increase in hoop stress due to longitudinal moment loading. Fig. 9 shows normalized hoop stress due to longitudinal moment, similar to Fig. 3, but with FEA stresses divided by (Eh/Ea)1/2. With significantly less difference between isotropic and orthotropic results, Fig. 9 as compared with Fig. 3 suggests that the increase in maximum hoop stress due to longitudinal moment with filament wound FRP construction as compared with isotropic materials can be reasonably simplified by multiplying isotropic stress by (Eh/Ea)1/2 in the nozzle load evaluation. For a direct comparison, the ordinate in Fig. 9 is set identical to Fig. 3 to show the advantage of this correction.

The previous results show a significant increase in magnitudes of peak stress in the hoop direction due to longitudinal moment loading, and a method to account for this increase was proposed. At first glance, the results for other directional stresses and directional loading appear to have no significant effect when comparing magnitudes of peak stress. However, it is important to note that the stress distribution around the nozzle circumference is also affected with orthotropic material properties. Figure 10 shows a comparison of hoop stress distribution due to an applied circumferential moment with isotropic (Eh/Ea=1) and orthotropic (Eh/Ea=3) material assumptions. The geometry shown is a 6 in (150 mm) nozzle on a 168 in (4300 mm) cylindrical vessel with all 0.5 in (13 mm) component thicknesses. The applied load and legend stress scale is identical for both FEA stress contours. Although the maximum stress value for the orthotropic material assumption is slightly lower in magnitude, a larger region of the shell around the nozzle circumference is exposed to hoop direction stresses worthy of consideration, which is an important difference to consider before using the approaches presented in existing methods for combining stresses due to external loading.

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0°

0°

90°

90°

FIG. 10 CIRCUMFERENTIAL MOMENT (MC) HOOP STRESS DISTRIBUTION FOR Eh/Ea=1 (LEFT) AND Eh/Ea=3 (RIGHT)

The effect on load distribution is further illustrated in Fig. 11 with a comparison of stresses in the 0° to 90° region of the nozzle circumference for the geometry and loading previously described. Calculated hoop stresses from the FEA are divided by the maximum stress value from the isotropic assumption so that the curves for orthotropic materials show how much larger stresses are around the nozzle circumference. For example, at a location of about 22.5°, stresses with an isotropic assumption are only around 30% of the maximum value at 90°. In comparison, stresses for the orthotropic assumption with Eh/Ea=3 is over 70% of the maximum value.

3000

80%

σMC.h + σML.h [psi]

σMC.h  / max(Eh/Ea=1)

100%

For combined stresses in cylindrical vessels, a reasonable assumption included in the WRC approaches [3,4] is to assume that the maximum stress value due to P occurs uniformly around the nozzle circumference. The WRC methods combine stresses due to P plus MC, and P plus ML, to account for stresses at the 0° and 90° points. For spherical vessels, it is appropriate to use a resultant bending moment, since geometry is axisymmetric about the nozzle centerline axis. As discussed by Peng [7], this simplification is not completely applicable for cylindrical vessels, since the shell curvature shifts the location of peak combined stress due to equal magnitudes of MC and ML towards the 90° point. Regardless, Peng [7] explains that a resultant stress combination can be justified since the stress distribution is narrower than the cosine/sine distribution, which the FEA confirms for isotropic material assumptions as shown with the sine curve in Fig. 11. However, the FEA results on the opposite side of the sine curve in Fig. 11 suggest that this justification does not necessarily apply to vessels constructed from orthotropic materials like filament wound FRP. Figure 12 shows the distribution of hoop stresses around the nozzle circumference due to a combined moment loading from the FEA of the cylindrical vessel geometry previously discussed. The maximum combined stress occurs at different points around the nozzle for the orthotropic materials as compared with the isotropic materials. The maximum magnitude of combined stress can also be around 50% greater for Eh/Ea=3 as compared with isotropic materials (Eh/Ea=1).

60% Eh/Ea=1 Eh/Ea=2 Eh/Ea=3 sin(x)

40% 20%

2500 2000 1500 Eh/Ea=1 Eh/Ea=2 Eh/Ea=3

1000 500

0% 0

22.5

45

67.5

90 0

Location on Nozzle [deg]

0

45

67.5

90

Location on Nozzle [deg]

FIG. 11 NORMALIZED HOOP STRESS DISTRIBUTIONS AROUND NOZZLE DUE TO CIRCUMFERENTIAL MOMENT (MC)

This effect on stress distribution is most important when combined loads are considered, since most actual nozzle connections will experience multiple components of loading. In general, the maximum value of stress due to circumferential moment (MC) component alone occurs at the 90° point, while maximum stress due to longitudinal moment (ML) alone occurs at the 0° point. As mentioned in WRC 297 and further discussed by Peng [7], the maximum stress due to combined moment loading will not necessarily occur at the orthogonal directions aligned with the vessel axis; maximum combined stress is likely to occur at a location somewhere in between.

22.5

FIG. 12 COMBINED HOOP STRESS DUE TO LONGITUDINAL (ML) AND CIRCUMFERENTIAL (MC) MOMENT LOADING

These results suggest that the WRC combined stress approach is not always appropriate for filament wound FRP. The resultant stress equation discussed by Peng [7] may also not be appropriate. One possible solution is to independently calculate stresses due to each component and combine as if they occurred at the same point. An alternative would be to calculate maximum allowable nozzle loads for each component of loading and then combine with a unity check summation of actual load divided by the allowable load in that direction.

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SIMPLIFIED APPROACH FOR NOZZLE EVALUATION

Hoop stress due to MC: σMC.h = CMC.hMCro‐1T‐2 = (‐0.13(roRm‐0.5T‐0.5) + 0.95) MCro‐1T‐2 = MC T‐2 (0.95 ro‐1 ‐ 0.13 Rm‐0.5 T‐0.5)

0.9 0.8 0.7 0.6

y = ‐0.13x + 0.95

0.5 0.4 0.3 0.2 0

1

1.6

0.8 0.6

y = 0.8x‐0.95

0.2 0.0 3

4

5

CML.h = σML.hML‐1roT2(Eh/Ea)‐0.5

1.0

2

5

0.13 .

.



6

1.4

1.2

1

0.95



Hoop stress due to  ML: σML.h = CML.hMLro‐1T‐2 (Eh/Ea)0.5 = 0.5(roRm‐0.5T‐1t0.5)‐0.8MLro‐1T‐2 (Eh/Ea)0.5 = 0.5 ML ro‐1.8 Rm0.4 T‐1.2 t‐0.4(Eh/Ea)0.5

1.2

0

4

A simplified approach to determine hoop stress in the shell due to an applied circumferential moment is:

1.4

0.4

3

FIG. 14 SIMPLIFIED APPROACH STRESS FACTOR (CMC) FOR HOOP STRESS DUE TO CIRCUMFERENTIAL MOMENT (MC)

Hoop stress due to P: σP.h = CP.hPT‐2 = (0.8(roRm‐0.5T‐0.5)‐0.95)PT‐2 = 0.8 P ro‐0.95 Rm0.475 T‐1.525

1.8

2

roRm‐0.5T‐0.5



2.0

CP.h = σP.hP‐1T2

1.0

CMC.h = σMC.hMC‐1roT2

In addition to the geometric combinations previously analyzed for comparison of isotropic and orthotropic properties with T/t=1, a large number of other thickness combinations were simulated as part of this investigation. A variety of additional geometries were analyzed, including thicker regions around the nozzle opening to simulate local FRP reinforcement, and different ratios of local shell thickness to nozzle thickness (0.66 ≤ T/t ≤ 4). In all, around 300 combinations were analyzed. In an attempt to simplify a complex problem, all data points for calculated stress factors were plotted and curves were fit for conservative results based on all geometries and properties considered. Fig. 13 - Fig. 15 illustrate stress factors and relationships used to develop a simplified approach for FRP nozzle load evaluation. These are admittedly oversimplified solutions to a complex problem, based solely on the numerical simulations conducted using FEA, but are an important first step for the FRP industry. The reduced equations presented as Eq. (5) - Eq. (7) are intended to allow FRP tank designers to easily estimate stress due to applied external nozzle loading or to determine safe maximum allowable load limits. Equation (7) includes the material property correction (Eh/Ea)1/2 previously discussed.

1.0 0.8 0.6 0.4

y = 0.5x‐0.8

0.2

roRm‐0.5T‐0.5 0.0 0

FIG. 13 SIMPLIFIED APPROACH STRESS FACTOR (CP) FOR HOOP STRESS DUE TO RADIAL LOAD (P)

A simplified approach to determine hoop stress in the shell due to an applied radial load is:

.

0.8 .



.

5

Alternatively, Eq. (5) can be rearranged to solve for maximum allowable nozzle radial load based on a defined allowable or available stress limit.

1

2

3

4

5

roRm‐0.5T‐0.5(T/t)‐0.5 = roRm‐0.5T‐1t0.5 FIG. 15 SIMPLIFIED APPROACH STRESS FACTOR (CML) FOR HOOP STRESS DUE TO LONGITUDINAL MOMENT (ML)

A simplified approach to determine hoop stress in the shell due to an applied longitudinal moment is:

.

0.5 .



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.



.

.

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ADDITIONAL COMMENTARY The results of this investigation are intended to supplement an RTP-1 Subpart 3A or BPVC Section X Method A design. In these approaches, stresses/strains in the axial and hoop vessel directions are independently checked for the defined allowable stress or strain limits in each vessel direction. In certain cases, detailed stress analysis based on Subpart 3B or Method B may be warranted to provide a more accurate evaluation. It is important to note that the accuracy of nozzle load evaluation depends not only on estimation of stresses due to an applied loading, but also on calculation of the design nozzle loads. FRP tank nozzle connections can be an order of magnitude more flexible than metallic vessels, which helps to reduce the magnitude of applied loading. As discussed in WRC 297 [3], including reasonable tank stiffness values in the pipe stress analysis of the attachment piping system can be crucial in determining realistic nozzle loads. It is encouraged to consider the effects of a range of stiffness values from minimum to maximum possible scenarios so that external loads are not underestimated. For example, local reinforcement and overlays that increase stiffness should be considered in determining appropriate stiffness values for realistic nozzle loads. It is also necessary to consider combined loading effects. Typically, pressure stresses/strains will govern shell thickness, and for an optimized design, there may be little available strength for external nozzle loading. It may be necessary to add additional local reinforcement or increase the reinforcement diameter to handle the required or estimated loading. It should be noted that the FEA conducted does not include pressure stiffening or fatigue considerations. For critical applications, exploring these effects may be warranted. It should also be noted that the existing methods [3,6] suggest that stresses due to internal pressure and external loading can be added for a combined loading verification, but a similar combination may not apply when buckling due to vacuum / external pressure is a concern since the external loading has the tendency to increase the out-of-roundness of the shell. All FEA conducted assumes a nozzle located at the center of the tank height, sufficiently far away for discontinuities. Proximity to discontinuities can have a significant effect on both stress and stiffness for nozzle load evaluation. Investigation into the effects of nozzle location is planned for future research and development. CONCLUSIONS The FEA results from the investigation of filament wound material FRP properties indicate that the existing WRC approaches to nozzle load evaluation are good resources that can be applied to FRP vessels, with certain additional considerations. The increased hoop direction stiffness for typical filament wound shells have the most influence on hoop stress due to longitudinal moment loading. A possible correction for this effect is to multiply isotropic hoop stress due to longitudinal moment by (Eh/Ea)1/2 for hoop stress in orthotropic filament wound FRP shells.

Orthotropic properties also influence the extent of stress distribution. The location of maximum combined stress due to multiple loading components can occur at a different location around the nozzle circumference for anisotropic materials as compared with isotropic assumptions, potentially invalidating combined stress approach assumptions used for isotropic materials. This effect can be considered by assuming that the maximum stress due to each component of loading occurs uniformly around the nozzle circumference, or alternatively, by applying a unity check summation of each component of actual loading divided by its allowable limit for combined loads. A simplified approach has been presented based on FEA simulations of various FRP vessel geometries. These simplified equations are intended to be conservative and to capture typical vessel and nozzle configurations. The distance from the nozzle to discontinuities and peeling of the nozzle installation overlays should also be considered when using these simplified equations. The authors of this paper hope that this investigation will encourage more FRP tank and vessel designers to include external nozzle loading in their calculations or to provide reasonable allowable loads at external connection points. ACKNOWLEDGMENTS A special thanks is extended to Darryl Mikulec and the engineering division at Maverick Applied Science, Inc. for their continual support and encouragement to discuss and investigate challenging issues related to FRP design. The authors of this paper are grateful to work with other engineers in the FRP industry who contribute to the advancement of FRP codes, standards, and engineering methods. Lastly, the authors would like to thank end-users who choose FRP piping and equipment and insist on proper engineering and analysis. REFERENCES [1] ASME, 2011, Reinforced Thermoset Plastic CorrosionResistant Equipment (RTP-1), American Society of Mechanical Engineers, New York. [2] ASME, 2011, Boiler & Pressure Vessel Code Section X, American Society of Mechanical Engineers, New York. [3] Mershon, J. L., Mokhtarian, K., Ranjan, G. V., and Rodabaugh, E. C., 1987, “Local Stresses in Cylindrical Shells due to External Loadings on Nozzles,” Bulletin 297, Welding Research Council, New York. [4] Wichman, K. R., Hopper, A. G., and Mershon, J. L., 2002, “Local Stresses in Spherical and Cylindrical Shells due to External Loadings,” Bulletin 107, Welding Research Council, New York. [5] Bednar, H., 1991, Pressure Vessel Design Handbook, Krieger Publishing Company, Malabar. [6] CEN, 2008, GRP Tanks and Vessels for Use Above Ground Part 3: Design, EN 13121-3, European Committee for Standardization, Brussels. [7] Peng, L. C., 1988, “Local Stresses in Vessels – Notes on the Application of WRC-107 and WRC-297,” Journal of Pressure Vessel Technology, Vol. 110, pp. 106-109.

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ANNEX A GEOMETRY USED IN FEA FOR EFFECTS OF ORTHOTROPIC MATERIAL PROPERTIES Tank Dia D [in] 168 168 120 120 168 72 120 168 72 168 120 72 120 168 72 120 120 72 168 120 72 168 120 72 72 72 120 120 72 168 120 72 120 120 168 72 72 192 168 120 192 72 120 168 192 168 120 192 168 192

Noz Dia d [in] 6 6 6 6 6 6 6 10 6 10 10 6 10 10 10 10 14 10 18 14 18 18 18 10 14 18 14 18 14 18 30 18 30 18 42 14 18 48 42 30 48 18 30 42 48 42 30 48 42 48

Tank Thk T [in] 0.5 0.38 0.5 0.38 0.25 0.5 0.25 0.5 0.38 0.38 0.5 0.25 0.38 0.25 0.5 0.25 0.5 0.38 0.5 0.38 1 0.38 0.5 0.25 0.5 0.75 0.25 0.38 0.38 0.25 1 0.5 0.75 0.25 1 0.25 0.38 1 0.75 0.5 0.75 0.25 0.38 0.5 0.5 0.38 0.25 0.38 0.25 0.25

Noz Thk t [in] 0.5 0.38 0.5 0.38 0.25 0.5 0.25 0.5 0.38 0.38 0.5 0.25 0.38 0.25 0.5 0.25 0.5 0.38 0.5 0.38 1 0.38 0.5 0.25 0.5 0.75 0.25 0.38 0.38 0.25 1 0.5 0.75 0.25 1 0.25 0.38 1 0.75 0.5 0.75 0.25 0.38 0.5 0.5 0.38 0.25 0.38 0.25 0.25

λ

D/d

T/t

0.76 0.85 0.90 1.00 1.00 1.16 1.19 1.20 1.29 1.35 1.42 1.53 1.59 1.62 1.83 1.92 1.93 2.05 2.07 2.18 2.34 2.35 2.45 2.47 2.49 2.64 2.64 2.77 2.81 2.85 2.91 3.16 3.31 3.37 3.38 3.41 3.58 3.60 3.87 3.99 4.12 4.35 4.55 4.68 4.99 5.35 5.56 5.70 6.55 7.00

28 28 20 20 28 12 20 16.8 12 16.8 12 12 12 16.8 7.2 12 8.57 7.2 9.33 8.57 4 9.33 6.67 7.2 5.14 4 8.57 6.67 5.14 9.33 4 4 4 6.67 4 5.14 4 4 4 4 4 4 4 4 4 4 4 4 4 4

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

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Tank Ht [in] 168 168 120 120 168 72 120 168 72 168 120 72 120 168 72 120 120 72 168 120 72 168 120 72 72 72 120 120 72 168 120 72 120 120 168 72 72 192 168 120 192 72 120 168 192 168 120 192 168 192

Noz Ht [in] 84 84 60 60 84 36 60 84 36 84 60 36 60 84 36 60 60 36 84 60 36 84 60 36 36 36 60 60 36 84 60 36 60 60 84 36 36 96 84 60 96 36 60 84 96 84 60 96 84 96

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