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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.
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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
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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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