design of a 120 in.-diameter steel bifurcation with a small acute angle for a high-pressure penstock

1Design of a 120 in.-Diameter Steel Bifurcation with a Small Acute Angle for aHigh-Pressure Penstock

By: Henry H. Bardakjian P.E (1) and Mehdi S. Zarghamee Ph.D., P.E (2)

(1) Consulting Engineer, 1331 N. Maryland Ave, Glendale, CA 91207Email: [email protected]

(2) Senior Principal, Simpson Gumpertz & Heger Inc.41 Seyon St., Building 1, Suite 500, Waltham, MA 02453Email: [email protected]

Abstract: The design of the shell and reinforcing members of a 120 in. x 120 in.bifurcation (wye branch) for the Olivenhain-Lake Hodges Pumped Storage Project inSan Diego County, CA, was a major challenge because of the small acute angle of34.6 and the high design pressure of 472 psi.

The project design criteria for the shell of the wye and reinforcing elements limit thegeneral membrane stresses to the lesser of 2/3 of yield strength or 1/3 of tensilestrength of the steel and the surface stresses at points of geometric discontinuities to 3times the allowable membrane stress. Although AWWA Manual M11 designprocedure does not include calculation of discontinuity stresses, preliminary design ofthe wye and reinforcing elements in conformance with AWWA procedures does notlead to designs that are feasible to fabricate and transport due to the requiredthickness and depth of the crotch plates.

Finite element analyses (FEA) were performed to verify a modified-preliminaryAWWA baseline crotch plate reinforcement design and to predict the membrane anddiscontinuity stresses. Since the project allowable stresses of the baseline designwere exceeded, additional FEA analyses were conducted using different crotch platethicknesses and depths, different shell thicknesses, and additional localizedreinforcement schemes. Crotch plates with T cross-sections could not be usedbecause of the small acute angle.

The design assumptions and the FEA results are the focus of this paper. Theadvantages of the nonlinear analysis due to the high discontinuity stresses will bediscussed and the supporting data presented. The use of a steel reinforcing pin at theintersection of the crotch plates to reduce the maximum discontinuity effects is alsodiscussed.

Pipelines 2008 2008 ASCE

Copyright ASCE 2008 Pipelines Congress 2008 Pipelines 2008

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2Introduction

The Lake Hodges to Olivenhain 40-megawatt pumped storage project is a part of theSan Diego County Water Authoritys $939 million Emergency Water StorageProject. This project consists of a 5900 ft long, 120 in. diameter high pressure steelpipeline tunnel starting at the Olivenhain reservoir and ending near Lake Hodges, 180ft of 120 in. diameter above grade steel pipeline connected to the Lake Hodges tunnelportal and a 120 in. diameter bifurcation connecting the pipeline to the Power/PumpHouse and Lake Hodges. The above grade pipe and the wye will be encased inconcrete; therefore, it was desirable to limit the maximum depth of the crotch platesto avoid excessive concrete encasement.

The major challenges of the design of the shell and reinforcing members of the 120in. x 120 in. bifurcation (wye branch) are due to the small acute angle of 34.6(typically a minimum 45 angle is used) between the branches and the high designpressure of 472 psi. The project design criteria for the wye section are the provisionsof ASCE Manual 79 Steel Penstocks, which limits the maximum membrane anddiscontinuity stresses.

Design of the crotch plates by the AWWA M11 procedure, which is based on thedesign procedure developed by Swanson (1955), requires very thick and deep crotchplates due to the small acute angle and high design pressure. Even though theAWWA procedure does not account for discontinuity stresses, the resulting AWWAdesigns were not practical or even feasible to fabricate due to the required thickness(maximum thickness for continuous cast steel is about 5.5 inches and for ingot caststeel to 7.5 inches) and the depth far exceeding the shell diameter. Therefore, newadditional reinforcing schemes were explored. Alternative designs and reinforcementschemes are based on finite element analysis (FEA), using a special version of theNASTRAN FEA program.

Design Criteria for the 120 in. Diameter Bifurcation and Reinforcement

The design of the shell of the wye and reinforcing members was based on the ASMEPressure Vessel Code and ASCE Manual 79, which limit the general membranestresses (m) to the lesser of 2/3 of yield strength (y) or 1/3 of tensile strength (T), and the surface stresses (s) at points of geometric discontinuity to 3 m (s = 3 m).

The minimum yield, y, and tensile strength, T, of ASTM A516 Grade 70 steel usedfor the fabrication of the shell and the crotch plates are 38,000 psi and 70,000 psi,respectively. Therefore m and s are limited to 1/3 T = 23,333 psi, which is lessthan 2/3 y = 25,333.3 psi, and 3 m =70,000 psi, respectively. The ASCE procedurealso allows a maximum membrane stress (max) of 1.5 m = 1.5 x 23,333.3 = 35,000psi provided this stress drops to 1.1 m (1.1 x 23,333 =25,667) within a distance notto exceed tR where R is the radius of the shell and t is its thickness.



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3Baseline Design of the Wye & Initial Linear Finite Element Analysis

The baseline design consists of a 120 in. x 120 in. x 34.6 angle wye with 3-platecrotch plate design and dimensions and geometries as shown in Figure 1. The wyehas two120 in. x 84 in., 18 ft long reducing legs and 5 ft long 84 in. stubs. The designpressure is 472 psi. The initial design did not include a pin at the three crotch plateintersect region.

Initial finite element linear analysis was conducted on the baseline model shown inFigures 1, 2, and 3. The boundary conditions and applied loads, consisting of internalpressure P applied to pipe elements along with dead end longitudinal PA forces at thethree ends of the model. The discontinuity and membrane stresses in the acute region,flat region and intersect region, which are defined in Figure 3, all exceeded theallowable limits.

34-36-52

7-6 16-3 18-0 5-0

30

64

150

Pipe wall = 1.25 thickCrotch plates = 7.00 thick

121 ID

84ID

84ID

Height of crotch plates over the pipesurface is 30.0 at intersection point.

16-3

18-0

5-0

Figure 1. Dimensions and baseline model geometry of the wye



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4A half-model wasanalyzed utilizing

symmetry boundaryconditions on the XY

plane.

Y

XAcute

Region

FlatRegion

IntersectRegion

Figure 2. Boundary Conditions Figure 3. Stress Regions

The maximum discontinuity stress was 80,000 psi > 70,000 psi and the maximummembrane stress was 64,000 psi > 35,000 psi.

Since the allowable stresses were exceeded, the following parametric study wasperformed to determine the effect of change of pipe and crotch plate thickness anddepth:

The effects of increasing the pipe wall thickness from 1.25 inches to 1.50 inchesare:

Discontinuity stress reduced by 5%. Membrane stress reduced by 5%.

The effects of increasing the depth of the main crotch plate from 150 inches to160 inches are : Discontinuity stress reduced by 4%. Membrane stress reduced by 3%.

The effects of decreasing the crotch plate thickness from 7 inch to 6 inches are: Discontinuity stress increased by 15%. Membrane stress increased by 13%.

Finite Element Analysis with Additional Localized Reinforcement

Based on the preliminary finite element results, the following localized reinforcementschemes were considered to provide a better load path through the structure:

Redesign-1: Baseline model with a 7- inch thick stiffener at the crotch plateintersection, and two 2 in. stiffeners on either side of the largest crotch plate.

Redesign-2: Baseline model with a 7 in. thick stiffener at the crotch plateintersection and only one 2 in. thick stiffeners on either side of the largest crotchplate. Figure 4 depicts Redesign-2.



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5 Redesign-3: Similar to Redesign-2 except 3/4 in. thick plates are welded on eitherside of the acute angle.

Revised conceptusing a single2 thick plate on each side ofthe

7 crotch plate

7thick plate

2 thickplates (1on eachside ofcrotchplate)

Figure 4. Redesign 2 Concept

The peak stresses for the base line model, Redesign-1, Redesign-2, and Redesign-3are given in Table 1, and the results are summarized below.

Table1. Peak Stresses due to Additional Localized Reinforcement

24,000

24,318

24,292

26,060

IntersectRegion

56,511

57,140

57,234

81,612

IntersectRegion

52,00127,25951,88352,14553,89256,727Redesign-3

59,53027,41361,29159,72254,00171,175Redesign-2

60,98627,39965,29261,16352,39780,625Redesign-1

63,38328,33863,60963,63251,39079,179Baseline Model

7 CrotchPlates

FlatRegion

AcuteRegion

7 CrotchPlates

FlatRegion

AcuteRegion

Peak M em brane Stress (psi)Peak C om bined Stress (psi)

24,000

24,318

24,292

26,060

IntersectRegion

56,511

57,140

57,234

81,612

IntersectRegion

52,00127,25951,88352,14553,89256,727Redesign-3

59,53027,41361,29159,72254,00171,175Redesign-2

60,98627,39965,29261,16352,39780,625Redesign-1

63,38328,33863,60963,63251,39079,179Baseline Model

7 CrotchPlates

FlatRegion

AcuteRegion

7 CrotchPlates

FlatRegion

AcuteRegion

Peak M em brane Stress (psi)Peak C om bined Stress (psi)

Summary of Results forRedesign-1 Adding two new stiffener plates, 3 ft apart, in the acute region does not help

reduce the maximum discontinuity stresses in the acute region. Extending the 7 in. thick plate reduced the discontinuity stresses in the intersect

region below the design criteria (From 82 ksi to 57 ksi)

Summary of Results for Redesign-2 Adding only one stiffener plate at the middle of the acute region reduced the

maximum discontinuity stresses in the acute region by 12% (from 81ksi to 71 ksi)and the maximum membrane stress by 6% (from 65 ksi to 61 ksi).



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6Summary of Results for Redesign-3 Adding one new stiffener plate and strengthening the acute region reduces the

maximum discontinuity stress by 21% from 71 ksi to 56 ksi, and the maximummembrane stress by 15% from 61 ksi to 52 ksi.

None of the above alternative schemes were satisfactory to control the peak stresseswithin the design criteria except with the addition of the 7 in. stiffener at the crotchintersection the stresses at the intersect region were controlled.

The use of T-section crotch plates was not considered due to the lack of space in thesmall acute region of the bifurcation.

Nonlinear Finite Element Model

Since the allowable discontinuity stresses are beyond the yield strength of the steeland the stress-strain curve is not linear beyond the yield strength, the non linearanalysis was conducted to predict the actual strains and stresses. The nonlinearanalysis for the baseline model is similar to the linear analysis baseline model exceptthat the pipe wall elements and crotch plate elements yield at 38 ksi. Both materialsthen undergo strain hardening with a plastic modulus that is defined by ultimate stressand strain equal to 70 ksi and 20%, respectively. The nonlinear material responsegiven in Figure 5 is based on the true stress-strain diagram and not the engineeringstress-strain diagram.

Figures 6 and 7 depict the strains in the cylinder and crotch plates. The maximumplastic strain in the cylinder and crotch plates, which occurs in the acute region, is0.28% and 0.27%, respectively, compared to 0.13% strain at the onset of yielding(see Figure5) and 20% at ultimate. The corresponding stresses varied between 38,200psi and 38,800 psi. Figure 7 also shows that, besides the 0.27% localized plastic strainat the bifurcation depicted in red color, the plastic strain on top of the main plate nearthe intersect area depicted in green color also exceeded the elastic limit at 0.20%.

38ksi

1310

E = 29,000ksi

E = 254 ksi

Figure 5. Nonlinear Material Response



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7Figure 6. Major Principal Strain in Outer Surface of Cylinder. MaximumStrain in Acute Region is 0.0028

8Effect of a Tube (Pin) at Intersect Region

Based on earlier results and the advantage of the addition of a 7 in. stiffener at theintersect region, it was decided to explore the effect of adding a pin at the intersectionof the three crotch plates.

The steel tube is 16 in. OD with a wall thickness of 1.59 in. and has the sameproperties as the shell and crotch plate material. The tube is closed at the top andbottom by 1.25 in. thick disks. All other parameters of the finite element model werethe same as the model without the tube.

The results of the nonlinear FEA are shown in Figures 8, 9, and 10. Figure 8 showsthat the maximum discontinuity stress at the cylinder in the intersect region near thepin is 38,671 psi which is less than the allowable 70,000 psi. The maximum stress inthe crotch plates is less than 35,000 psi, which is the allowable membrane stress.

Figure 8. Maximum Principal Stresses in Cylinder and Crotch Plates with 16 in.Diameter Steel Tube at Intersect Region

As shown in Figure 9, the maximum plastic strain near the top of tube is 0.2%, and ishighly localized. Limited yielding may occur; however the equivalent stress will beless than 39,000 psi which is less than the allowable 70,000 psi.

The maximum localized plastic strain at the bifurcation is 0.135% (Figure 10). Basedon the assumptions made, the elastic limit is 0.131%. Plastic strain may not occursince the actual yield of the steel will usually be greater than 38,000 psi. Themaximum localized plastic strain without the tube, as shown in Figure 7, was 0.27%.After the addition of the pin the plastic strain was reduced by 50 % to 0.135%. Theplastic strain of 0.2% strain at top of the plate without the pin, as shown in Figure 7,was reduced to below the elastic limit (0.05 %) after the addition of the tube.



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9i i i iFigure 9. Plastic Strain near the Tube at Intersect Region

Plastic yielding onupper edge is eliminatedby adding the tube

Figure 10. Plastic Strain in Crotch Plate (Maximum at Bifurcation = 0.135%).Note Negligible Magnitude of Plastic Strain and its Localization

The addition of the 16 in. OD tube reduces the amount of plastic strain, and themaximum principle stresses in the system.

Conclusions and Recommendations

The AWWA M11 procedures for the design of large diameter, high pressurebifurcations with small acute angles should be supplemented with finite elementanalysis to check for membrane and discontinuity stresses. Typically, nonlinearfinite element analysis may be required to deal with the high discontinuitystresses.



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10

The parametric study, for this high pressure bifurcation with small acute angleshowed that the reduction of membrane and discontinuity stresses due tochanging the shell thickness and crotch plate thickness or depth is not significant.The addition of localized stiffeners in the intersect region did reduce the stressesin that region.

The addition of a tube or pin at the intersections of the crotch plates for large-diameter, high-pressure bifurcations reduces the amount of plastic strain and themaximum principle stress, and facilitates welding of the plates.

Fabrication of Wye

This 120 in. x 120 in. x 34.6 wye is being fabricated at Amerons Fontana Plant. SeeFigure 11. The two 120 in. x 84 in. reducing legs were welded to check the fit up.Due to weight and shipping limitations the two legs will be welded in the field; theweight of the main crotch plate alone is 44 tons.

Figure 11. Fabrication of the Wye

References

American Water Works Association (2004), Manual of Water Supply PracticesAWWA M11, Steel Pipe - A Guide for Design and Installation, Denver, CO.

Swanson, H.S Et AL. (1955) Design of Wye Branches for Steel Pipe, J. Am. WaterWorks Assoc., 47(6), 581-629.

American Society of Civil Engineers (1993), ASCE Manuals and Reports onEngineering Practice No. 79, Steel Penstocks.



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design of a 120 in.-diameter steel bifurcation with a small acute angle for a high-pressure penstock

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