usbr engineering monograph 03

7/22/2019 USBR Engineering Monograph 03

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A WATER RESOURCES TECHNICAL PUBLICATION

ENGINEERING MONOGRAPH No. 3

Steel ,Pensthcksy- ;rUNITED STATES DEPARTMENT 6F Tt-tE INTERIORBUREAU, OF RECL-AMATI-ON .,-


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- . I

The lower ends of the penstocks at Shasta Dam emerge from conerefa nnckors and pbcnge into the pozus~ho~csc


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A WATER RESOURCES TKZHNICAL PUBLICATION

hrginooring Monograph No. 3

United States Department of the Interiorl

BUREAU OF RECLAMATION


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As the Nations principa l conservation agency, the Department of theinterior has responsibility for most of our nationally owned publ ic

lands and natural resources. This includes fostering the wisest use ofour land and water resources, protecting our fish and wildlife, preserv-ing the environmental and cultural values of our national parks andhistorical places, and providing for the enjoyment of life through out-door recreation. The Department essessei our energy and mineral

~ resources and works to assure that iheir development is in the best~ interests of all our people. The Departmerit also has a major respon-1 sibil ity for American Indian reservation communities and for people

who live in tsland Territories under U.S. Administration.

ENGINEERING MONOGRAPHS are prepared and used by the technicalstaff of the Bureau of Reclamation. In the interest of dissemination of re-search experience and knowledge, they are made available to other inter-ested technical circles in Government and private agencies and to thegeneral public by sale through the Superintendent of Documents, Govern-ment Printing Office, Washington, D.C.

First Printing: 1949Revised: 1959Revised: 1966Reprinted: 1977Reprinted: 1986

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON : 1977


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Preface

THIS MONOCRAPHwill assist designers in thesolution of problems in design and construc-tion of safe penstocks which may be fabricatedin accordance with modern manufacturingprocedures. Certain rules relative to materials,stresses, and tests might be considered un-necessarily conservative. Safety is of para-mount importance, however, and penstocksdesigned and constructed according to theserules have given satisfactory service throughyears of operation.

Welded Steel Penstocks presents informationconcerning modern design and constructionmethods for pressure vessels applied to pen-stocks for hydroelectric powerplants. The dataare based on some 40 years experience in pen-stock construction by the Bureau of Reclama-tion. During this period many of the largestpenstocks in service today were designed andconstructed.

Welded Steel Pmstocks was first issued in1949 under the authorship of P. J. Bier. Be-cause of the continuing interest in penstockdesign, the monograph has been revised andupdated to incorporate present day practice.

This edition now represents the contributionsof many individuals in the Penstocks and SteelPipe Section, Mechanical Branch, Division ofDesign, on the staff of the Chief Engineer,Denver, Colo.

This monograph is issued to assist designersin the solution of problems involved in the de-sign and construction of safe and economicalwelded steel penstocks.

Because of the many requests for informa-tion concerning Bureau of Reclamation de-signed and built penstocks, a comprehensivebibliography has been added in the back.

Included in this publication is an informa-tive abstract and list of descriptors, or key-words, and identifiers. The abstract wasprepared as part of the Bureau of Reclamationsprogram of indexing and retrieving the litera-ture of water resources development. Thedescriptors were selected from the Thesauwof Descriptors, which is the Bureaus standardfor listings of keywords.

Other recently published Water ResourcesTechnical Publications are listed on the insideback cover of this monograph.

iii


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Contents

Report on Welded Steel PenstocksIntroduction ______________- _________---------------_-__________Location and Arrangement ____ _____ -___--- ____ ____ --__-_- ____Economic Studies ___________________________.___ __-__-- ____ -___Head Losses in Penstocks ________________________________________-Effect of Water Hammer _______ _____ _____ - ____ _-_-- ____ - ____

Pressure Rise in Simple Conduits ___________________________Pipe Shell __--_______-____-_______________________------- - _______

Temperature Stresses ________________________________________Longitudinal Stresses Caused by Radial Strain __________-----_Beam Stresses _______________-________________________-------

supports -- ----------_--------_-----------------------------------Expansion Joints ___________________ ____ _____________- ______Bends, Branch Outlets, and Wyes _________________________________

Pipe Bends ____________-_____-_____________________----------Branch Outlets and Wyes _____________________ _____________

Penstock Accessories _____-__________________________________-----For Installation and Testing __________________________________For Operation and Maintenance ______________________________

Design of Piers and Anchors ______________________________________General ___ -_ ___________ ------------------------------------Support Piers __ -_----- ------------------------------------Anchors ---------------------------^------------------------~-.

PWC

. . .111

1155

111214171717192326

262733333334343435


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vi CONTENTS

Materials --____---__-_-_-_--_____________________~~~~-~-~~~~~~~~~ 35Steel Plates ___---_-_-____--_-_--~-~-~~-~~---~--~~~~~~~~~~~~~~ 35Flanges, Fittings, Valves, and Other Appurtenances _- ________ 37

Fabrication ____----__________-_____________________-------------- 37Structure and Arrangement _- ____ ____ _____ ---------__-__-_ 37Nondestructive Inspection of Welds ___---_-_-_--_-__--_______ 39Preheating and Postweld Heat Treatment ________- __________ 42

Installation -_-__-__---_--__________________________-~~~-~--~~~~~~ 42Handling __-_----_-__--___-______________________~~~-----~~-~ 42Placing and Welding --__--__--_--_--___--------- _____________ 43Hydrostatic Test -_-_-_-_--_--_----______________________---- 44

Specifications and Welding Control _____ __-_-_-__-__-_---_-______ 45Specifications -___-___--_-____________________________-------- 45Welding Control _- ______ ___________________________-_______ 45Weld Tests ____-__---_-__----______________________-~~~~~~-~~ 45

Corrosion Control for Penstocks ____ -___- ______ ____ ___-_-_---_-_ 45

A Selected Bibliographyrnd References _____-________-_________________________--------

Coder and Standards _________________ -- ____ -- ______ -__-_----_

Appendix -_----_---_-_------- _______ __----__-_-___- _______ -_--

Absract _---___-------_- __________________ _______________ -- ____

47

47

48

51

LIST OF FIGURESNumber PSLW

1. The 30-foot-diameter lower Arizona and Nevada penstock andoutlet headers were installed in two of the diversion tun-nels at Hoover Dam. The upper headers were installed inspecial penstock tunnels. The tunnels were not backfilledwith the exception of the inclined portions leading from theintake towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2. At Anderson Ranch Dam, the 15-foot-diameter penstock and

outlet header were installed in the diversion tunnel, whichwas not backf illed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33. General plan and typical profile of 15-O-diameter penstocks at

Glen Canyon Dam . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 34. Mass concrete of Kortes Dam encased the g-foot-diameter pen-

stocks, which were installed as the concrete was placed . . . 45. The 15-foot-diameter penstocks at Shasta Dam were embedded

in the concrete of the dam at the upstream ends and wereexposed above ground between dam and powerplant . . . . . 4


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CONTENTS vii

Numbo

6. The full length of the %foot-diameter penstock at Marys LakePowerplant lies above ground . . . . . . . . . . . . . . . . . . . . . . . . ,

7. Economic diameter of steel penstocks when plate thickness is afunction of the head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8. Economic diameter of steel penstocks when plate thickness is afunction of the head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,

9. Friction losses in welded steel pipe based on Scobeys formulafor 6-year-old pipe and nonaggressive waters . . . . . . . . . . .

10. Losses for various values of 5 ratios and deflection angles up

to900 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11. Head losses in 90 pipe bends as determined for various

R5

ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12. Loss coefficients for divided flow through small tees and branch

outlets as determined for various flow ratios &a. . . . . . . . .Q13. Water-hammer values for uniform gate motion and complete

closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14. Equivalent stress diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15. A graphica l illustration of heads and stresses determined for

the hydrostatic testing of the Shasta penstocks . . . . . . . . .16. The Shoshone River siphon crosses the river on a 150-foot span17. Moments and deflections developed in a pipe precisely full, using

various types of supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18. Formulae and coefficients for the computation of stresses in ring

girders as developed for stiffener ring analyses . . . . . . . . .19. Formulae and coefficients for the computation of stresses in ring

girders due to earthquake loads . . . . . . . . . . . . . . . . . . . . . . .20. Typical ring girder and column support . . . . . . . . . . . . . . . . . . . .21. Typical rocker support. The angle yoke is used only for aline-

ment during grouting . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22. Typical sleeve-type expansion join t . . . . . . . . . . . . . . . . . . . . . . . .23. Flexib le sleeve-type expansion joint with two stuffing boxes used

to permit longitudinal temperature movement and trans-verse deflection . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24. Constant diameter bend with the radius of the bend five timesthe diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25. Bend reducing in diameter from 9 feet to 8 feet, the radius equalto four times the smaller diameter . . . . . . . . . . . . . . . . . . . .

26. Computation method for determining true pipe angle in a com-poundpipebend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27. Loading diagrams for the development of reinforcement ofbranch outlets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28. Loading diagrams for the development of reinforcement of wyebranchesinpenstocks................................

29. Typica l internal and external reinforcement for a branch outlet30. Installation of a piezometer connection in shell of penstock for

turbine performance tests . . . . . . . . . . . . . . . . . . . . . . . . . . .

Pans

10

11

11

1516

1820

21

22

2324

2525

25

26

27

28

29

3032

33


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Vsii CONTENTS

Nwllbw

31. Typical manhole designed for inspection and maintenance . . . . .32. Typical monolithic pier construction for rocker supports . . , . .33. Resolution of forces on pipe anchors . . . . . . . . . . . . . . . . . . . . . . .34. Typical concrete anchor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36. Shop fabrication of large diameter penstock . . . . . . . . . . . . . , . .36. Shop joints are welded with automatic equipment . . . . . . . . . . .37. Radiographic inspection of welds is performed using portable

X-ray equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38. Postweld heat treatment is accomplished by heating in an en-

closed furnace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39. Transporting large wye-branch into place . . . . . . . . . . . . . . . . . .4G. Penstocks being placed, showing temporary support . . . . . . . . .41. Penstocks installed in Flaming Gorge Dam are encased in mass

concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

LIST OF TABLESNumber

1. Basic conditions for including the effects of water hammer inthe des ign of turbine penstocks . . . . . . . . . . . . . . . . . . . , . .

2. Testing methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3436373839

40

424343

44

1341


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Report on Welded Steel Penstocks

Introduction

A penstock is the pressure conduit betweenthe turbine scrollcase and the first open waterupstream from the turbine. The open watercan be a surge tank, river, canal, free-flowtunnel, or a reservoir. Penstocks should be ashydraulically efficient as practical to conserveavailable head, and structurally safe to preventfailure which would result in loss of life andproperty. Penstocks can be fabricated ofmany materials, but the strength and flexibil-ity of steel make it best suited for the range ofpressure fluctuations met in turbine operation.

The design and construction of pressurevessels, such as penstocks, are governed by ap-propriate codes which prescribe safe rules andpractices to be followed. Until a special pen-

stock code is formulated, steel penstocks shouldbe constructed in accordance with the ASMEBoiler and Pressure Vessel Code, Section VIII,Unfired Pressure Vessels, issued by the Ameri-can Society of Mechanical Engineers, herein-after referred to as the ASME code. This codeis subject to periodic revision to keep it abreastof new developments in the design, materials,

construction, and inspection of pressure vessels.Present design standards and construction

practices were developed gradually, followingthe advent of welded construction, and are theresult of improvements in the manufacture ofwelding-quality steels, in welding processes

and procedures, and in inspection and testingof welds.

LOCATION AND ARRANGEMENT

The location and arrangement of penstockswill be determined by the type of dam, locationof intake and outlet works, relative location ofdam and powerplant, and method of riverdiversion used during construction. At damsrequiring tunnels for diversion of the river flow

during construction, the penstocks may beplaced in the tunnels after diversion has beendiscontinued and the intake of the tunnel hasbeen plugged. This arrangement was used forthe 30-foot lower Arizona and Nevada penstockand outlet headers at Hoover Dam as shownin figure 1, and for the l&foot penstock headerat Anderson Ranch Dam as shown in figure 2.

1


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POWER PLANT

FXGUXE l.-The SO-fooGdia?neter &now Arieona and Nevada penstock and outlet keadem were in&u&d in two of the diversion tunnels at HooverDam. The upper headere were installed in special penstock tunnels. The tunnels were not backfilled with the exception of the inclined portionleading from the intuke tower.


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WELDED STEELPENSTOCKS 3Outlet pipe

No S----.

SECTION

P. . Horimtol bend---Sta 1sto6.03 - El. 3810

PLAN

FIWRE2.-At Anderson Ranch Dam, the l&foot-d&am-eter penstock and outlet header were installed in thediversion tunnel, which wae not backwed.

For low-head concrete dams, penstocks may beformed in the concrete of the dam. However,a steel lining is desirable to assure watertight-ness. In large concrete dams which have bothtransverse and longitudinal contraction joints,such as Glen Canyon Dam, steel penstocks are

-% Penstocks

PLAN

Fxeuav s.-Gener~Jplan and typical pro@ of I s-

used to provide the required watertightness inthe concrete and at the contraction joints.Figure 4 shows the g-foot penstocks which areembedded in Kortes Dam.

Penstocks embedded in concrete dams, en-cased in concrete, or installed in tunnels back-filled with concrete may be designed to transmitsome of the radial thrust due to internal waterpressure to the surrounding concrete. Moregenerally, such penstocks are designed to with-stand the full internal pressure. In either case,the shell should be of sufficient thickness toprovide the rigidity required during fabrica-tion and handling, and to serve as a form forthe concrete. Embedded or buried penstockshells also should be provided with adequatestiffeners or otherwise designed to withstand

any anticipated external hydrostatic or grout-ing pressures. At Shasta Dam the upstreamportions of the 15-foot penstocks are embeddedin the dam, while the downstream portions are

3. Outlet popes


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4 ENGINEERING MONOGRAPH NO. 3

-18 Dia. air vent

,-Main unit trashrack

--Penstock oir inlet

,-15-o Dia. mainI unit pensfocks

:Concrete anchor

-Line of excavation --I

FIGURE 4.-Mass concrete of Kortes Damencased the g-foot-diameter penstocks,which were installed as the concretewas placed.

FIGURE S.-The 15-foot-diameter pen-stocks at Shasta Dam were embeddedin the concrete of the dam at the up-

stream end8 and were exposed aboveground between dam and powerplant.

exposed above ground, between the dam andthe powerplant, as shown in figure 5. At other

plants, the entire length of the penstock maybe situated above ground, as in figure 6, whichshows the %foot-diameter penstock at MarysLake Powerplant.

When a powerplant has two or more turbinesthe question arises whether to use an individ-ual penstock for each turbine or a single pen-stock with a header system to serve all units.

Considering only the economics of the penstock,the single penstock with a header system will

usually be preferable; however, the cost of thisitem alone should not dictate the design.Flexibility of operation should be given con-sideration because with a single penstock sys-tem the inspection or repair of the penstockwill require shutting down the entire plant. Asingle penstock with a header system requirescomplicated branch connections and a valve


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WELDED STEELPENSTOCKS 5

TYPICAL SECTION AT SUPPORT

FIGURH B.-The full length of the d-foot-diameterpen-stock at Marys Lake Poweqdant lies above ground.

to isolate each turbine. Also, the trashracksand bulkhead gates will be larger, resulting inheavier handling equipment. In concretedams it is desirable to have all openings assmall as possible. The decision as to the pen-stock arrangement must be made consideringall factors of operation, design, and overall costof the entire installation.

Proper location of the penstock intake is im-portant. In most cases the intake is locatedat the upstream face of the dam, whichprovides short penstocks and facilitates opera-tion of the intake gates. In some casesthe penstock intake may be situated in an in-dependent structure located in the reservoir, asat Hoover and Green Mountain Dams, wherediversion tunnels or topographic conditionsinfluenced the arrangement. Regardless ofarrangement, the intake should be placed at anelevation sufficiently below low reservoir leveland above the anticipated silt level to allow anuninterrupted flow of water under all condi-tions. Each intake opening is protectedagainst floating matter by means of a trash-rack structure and is controlled by suitablegates.

To prevent the development of a partialvacuum during certain operating conditions,penstock profiles from intake to turbine should,whenever possible, be laid on a continuousslope.

ECONOMIC STUDIES

A penstock is designed to carry water to aturbine with the least possible loss of headconsistent with the overall economy of installa-tion. An economic study will size a penstockfrom a monetary standpoint, but the final di-ameter should be determined from combinedengineering and monetary considerations. Anexample would be an installation where theeconomic diameter would require the use of asurge tank for regulation, but a more economi-cal overall installation might be obtained byusing a penstock considerably larger than theeconomic diameter, resulting in the eliminationof the surge tank.

Voetsch and Fresen (1) l present a method of

determining the economic diameter of a pen-stock. Figure 7 was derived from theirmethod, and figure 8 is an example of its use.Doolittle (2) presents a method for determiningthe economic diameters of long penstockswhere it is economical to construct a penstockof varying diameters. This step by stepmethod requires considerable time but shouldbe considered for final design for long pen-stocks.

All the variables used in an economic studymust be obtained from the most reliable sourceavailable, keeping in mind that an attempt isbeing made to predict the average values of allvariables for the life of the project. Specialattention must be given to the plant factor,figure 7, as this item materially affects the cal-culations.

HEAD LOSSES IN PENSTOCKS

Hydraulic losses in a penstock reduce theeffective head in proportion to the length ofthe penstock and approximately as the squareof the water velocity. Accurate determinationof these losses is not possible, but estimates canbe made on the basis of data obtained frompipe flow tests in laboratories and full-scaleinstallations.

Numbers in parentheses refer to literature cited in mxtlon, ASelected Bibliography and References. at the end of thla mono-mwh.


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t=

a : Cost of pipe per lb., instolled, dollars.8 = Diometer m ultiplier from Groph 6.b = Volue of lost power in dollorr per k wh.D = Economic diometer in feet.e = Overall plant efficiency .eJ = Joint efficiency.f = Loss factor from Groph A.

NOTATIONIi = Weighted overage heod including woter

hommer. (based an design head )KS = Friction coefficient in Scobeys formula (0.34).n = Ratio of overweight to weight of pope shell.Cl = Flow in cubic feet per second. (ot design head of turbine)r z Ratio of onnuol cos t taa( see explanotion)sg = Allowable tension, p.s.it = Weighted overage plate thickness(ot design head) for total length,t, 2 Averoge plote thickness for length L,.

EXPLANATIO N AND EXAMPLE

L,t,+L*t2+LJts...+LntnL,+ Let Ls+...+ Ln t4

% o a M, ~ 0. 8 M. per footCast per foot of pipe

0.8 M = Cost of mointainmg interior ond exterior surfaceOreo of pipe( inside surface oreo for embedded pipe,inside ond outside surface areo for exposed pipe )per year.

Depreciation = See Reclamation Monual, Vo l. PI Fewer, page 2,4,llD.r : Interest t Depreciation l % 0. 8 M.

ASSUME

Example for penstock Q = I28 CFS

Dia.: 5-0 Avg. plate =Value of power per kwh:0.005- bCost of steel pipe mstolled=sO.27/Ib =aPlont factor (see GraphA):0.75(f~0.510)Interest =3% n= 0.15Depreciation = 0.0051350.8 M.=0.02 per sq.ft. Weight/ foot=l57lx lO.2= 160.24 Ibs.

Gast/foot=l6a24x0.27=*43.26

r

L,:22$ L,= 150; L,=(50, L,ZlOOH,=fJO; H,=l20, Hs=l7 0, H,= 2301i H,=240

I ~~lL,t(~~Lz+ ~~)L,tlH~~L , _L, t Lx + L, + L,

0,8M,~u225x15.71)~~4wx 15.71x2)10.02 z)o,5,625

= 0.03 t0.005135+0.0119=0.0470 % 0.8 M.= sz o.ollg

Kz %efsgejb-Ior( I+n)

0.34x095x 0.510x15.000x0.90x0.00~~ 6900.27x 0.0470 x I.15

156.4

5

9: 1.285 (from GmphB);D=3.7(from GmphG); Economic dia.: I.285 x3.7= 4.75 ( use 4-10dia.)

NOTE: Calculated economic diameter should be very clo se to ossumed diameter as itis in this exomple. The problem should be reworked until this condition ex ists

Depreciation is bosed on the accumulation of on onnual smkrng fund eorning 3%interest required to replace 50% of the pipe in 45 years, The annuolpoyment required is equal to 0.005135 times the first cost.

FIGUREI 8.-Economic diameter of steel penstocks when plate thicknes s is a function of the head.


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The various head losses which occur betweenreservoir and turbine are as follows:

1. Trashrack losses2. Entrance losses

3. Losses due to pipe friction4. Bend losses5. Losses in valve and fittings.Losses through trashracks at the intake vary

according to the velocity of flow and may betaken as 0.1, 0.3, and 0.5 foot, respectively, forvelocities of 1.0, 1.5, and 2.0 feet per second.

The magnitude of entrance losses dependsupon the shape of the intake opening. A cir-cular bellmouth entrance is considered to bethe most efficient form of intake if its shape isproperly proportioned. It may be formed in

the concrete with or without a metal lining atthe entrance. The most desirable entrancecurve was determined experimentally fromthe shape formed by the contraction of a jet(vena contracta) flowing through a sharp-edged orifice. For a circular orifice, maximumcontraction occurs at a distance of approxi-mately one-half the diameter of the orifice.Losses in circular bellmouth entrances areestimated to be 0.05 to 0.1 of the velocity head.For square bellmouth entrances, the losses areestimated to be 0.2 of the velocity head.

Head losses in pipes because of frictionvary considerably, depending upon velocity offlow, viscosity of the fluid, and condition of theinside surface of the pipe. Among the con-ventional pipe flow formulae used for thecomputation of head losses, the Scobey, Man-ning, and Hazen-Williams formulae are themost popular. For large steel pipe the Scobeyformula is favored ; for concrete pipe, theManning formula ; and for cast-iron pipe inwaterworks, the Hazen-Williams formula.

The Scobey formula(3), derived from ex-periments on numerous steel pipe installations,is expressed as follows:

H*=K+. . . . ..,.............. (1)

in whichHP= head loss due to friction in feet per

1,000 feet of pipeKs = loss coefficient, determined experimen-

tally

V =velocity of flow in feet per secondD =diameter of pipe in feet.

Values for I& vary for different types of pipe.For new continuous interior pipe unmarred by

projections on the inside (as for butt-weldedpipe) a value of 0.32 may be used. Scobeygives values of Ks for old pipe allowing fordeterioration of the interior surface. To allowfor deterioration a value of Ks=0.34 is usuallyassumed in design for pipes whose interior isaccessible for inspection and maintenance.Friction losses for this value of KS, for pipesup to 10 feet in diameter, can be read from thechart, figure 9. For pipes too small to permitaccess for maintaining the interior coating avalue of Ks=0.40 is usually assumed.

Bend losses vary according to the shape ofthe bend and the condition of the inside sur-face. Mitered bends constructed from platesteel no doubt cause greater losses than smoothcurvature bends formed in castings or concrete ;however, there is no way to evaluate sucheffects since data on actual installations arevery meager. Laboratory experiments on verysmall size bends with low Reynolds numbersare not applicable to large size bends with highReynolds numbers. When water flows arounda bend, eddies and secondary vortices result,and the effects continue for a considerable

distance downstream from the bend. In sharpangle bends the secondary vortex motion maybe reduced by guide vanes built into the bend.

Thomas (4) formula is based on experimentsmade at the Munich Hydraulic Institute with1.7-inch-diameter smooth brass bends havingReynolds numbers up to 225,000, as shown onthe chart in figure 10, and is expressed as:

Ha=CL......................2g (2)

whereH,, = bend loss in feet

C =experimental loss coefficient, for bendlossV =velocity of flow in feet per second.

The losses shown in figure 10 vary accordingto the R/D ratio and the deflection angle ofthe bend. An R/D ratio of six results in thelowest head loss, although only a slight de-crease is indicated for R/D ratios greater than


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WELDED STEEL PENSTOCKS

FRICTI ON LOSS - FEET PER 1000 FEET

,URE 9-Fmktion losses in welded steel pipe based on Scobeys formula for &year-old pipe and nonaggressivewat em.


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IO ENGINEERING MONOGRAPH NO. 3

.26

.24

; .I6Wi?E .I4

go .I2

:

2 .I0

.06

.02

0 5 IO 15 20 25* 30 35O 40= 45. 50 55 60 65 70 75= 80 65

DEFLECTION ANGLE A0Fxoum lo.-LO88e8 for vari5248 value8 of g ratios and d43flection andes UP to 90'.

four. This relationship is also indicated bythe curves of figure 11, which were plottedfrom experiments with 90 bends, As thefabrication cost of a bend increases with in-creasing radius and length, there appears to beno economic advantage in using R/D ratiosgreater than five.

Head losses in gates and valves vary accord-ing to their design, being expressed as:

H,=K-& . . . . . . . . . . . . . . . . . . . . . . (3)

in which K is an experimental loss coefficientwhose magnitude depends upon the type andsize of gate or valve and upon the percentageof opening. As gates or valves placed in pen-stocks are not throttled (this being accom-

plished by the wicket gates of the turbines),only the loss which occurs at the full opencondition needs to be considered. Accordingto experiments made at the University ofWisconsin (5) on gate valves of l- to Z-inchdiameter, the coefficient K in Equation (3)varies from 0.22 for the l-inch valve to 0.065for the 12-inch valve for full openings. For

large gate valves an average value of 0.10 isrecommended ; for needle valves, 0.20 ; andfor medium size butterfly valves with a ratio ofleaf thickness to diameter of 0.2, a value of 0.26may be used. For sphere valves having thesame opening as the pipe there is no reductionin area, and the head loss is negligible.


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WELDED STEEL PENSTOCKS II

-Rough pipe

-Smooth pipe

0012345670 9 IO

FRIES ll.-Head bsoea n so0 pipe benda as &to+minsd fm uariuu.9E ratios.

Fxoua~m-LO88 CO&i8Td8 for dbidd &HO hmwhamall tees and breach tnd8t8 a.8 da- fW d0488 jtOl8 Vf3tiO80".

Q

Fittings should be designed with smoothand streamlined interiors since these result inthe least loss in head. Data available on lossesin large fittings are meager. For smaller fit-tings, as used in municipal water systems, theAmerican Water Works Association recom-mends the following values for loss coefficients,K; for reducers, 0.25 (using velocity at smallerend) ; for increasers, 0.25 of the change invelocity head ; for right angle tees, 1.25; andfor wyes, 1.00. These coefficients are averagevalues and are subject to wide variation fordifferent ratios between flow in main line andbranch outlet. They also vary with differenttapers, deflection angles, and streamlining.Model tests made on small tees and branch out-lets at the Munich Hydraulic Institute showthat, for fittings with tapered outlets and de-flection angles smaller than 90 with roundedcorners, losses are less than in fittings havingcylindrical outlets, 90 deflections, and sharpcorners. (See figure 12.) These tests servedas a basis for the design of the branch connec-tions for the Hoover Dam penstocks.

EFFECT OF WATER HAMMERRapid opening or closing of the turbine

gates produce a pressure wave in the penstockcalled water hammer, the intensity of which isproportional to the speed of propagation of thepressure wave produced and the velocity offlow destroyed. Joukovskys fundamentalequation gives the maximum increase in headfor closures in time less than 2L/a seconds:

AH=- %8

. . . . . . ..F* . . . . . . . . . . . . . . . (4)

in whichAH =maximum increase in heada =velocity of pressure waveL=length of penstock from forebay to

turbine gatev =velocity of flow destroyedg =acceleration due to gravity.

From this formula, which is based on theelastic water-hammer theory, Allievi, Gibson,Durand, Quick, and others developed inde-pendent equations for the solution of water-hammer problems (6).


22/63

ENGINEERING MONOGRAPH NO. 3

In his notes published in 1903 and 1913,Alhevi introduced the mathematical analysisof water hammer, while M. L. Bergeron, R. S.Quick, and R. W. Angus developed graphical

solutions of water-hammer problems which aremore convenient to use than the analyticalmethods. A comprehensive account of methodsfor the solution of water-hammer phenomenaoccurring in water conduits, including graphi-cal methods, was published by Parmakian (7).

For individual penstocks of varyingdiameter, the pressure reflections at points ofchange in diameter complicate the problem.However, if the varying diameter is reducedto a penstock of equivalent uniform diameter,a close estimate can be made of the maximumpressure rise. For penstocks with branchpipes, it is necessary to consider the reflectionof pressure waves from the branch pipes anddead ends in order to determine the true pres-sure rise due to velocity changes.

As the investment in penstocks is often con-siderable, they must be safeguarded againstsurges, accidental or otherwise. Surges of theinstantaneous type may develop throughresonance caused by rhythmic gate movements,or when the governor relief or stop valve isimproperly adjusted. A parting and rejoiningof the water column in the draft tube or a

hasty priming at the headgate may also causesurge waves of the instantaneous or rapid type.Adjustments iw the profile of a penstock maybe necessary to prevent the development of avacuum and water column separation duringnegative pressure surges. As water-hammersurges occurring under emergency conditionscould jeopardize the safety of a penstock if theyare not considered in the design, their magni-tude should be determined and the shell thick-ness designed for the resultant total head.Stresses approaching yield-point values may beallowed. By using ductile materials in thepenstock, excessive surge stresses may be ab-sorbed by yielding without rupture of platesor welds. Design criteria for including theeffects of water hammer in penstock and pumpdischarge line installations, as used by theBureau of Reclamation, is shown in table 1.

Surge tanks are used for reduction of waterhammer, regulation of flow, and improvement

in turbine speed regulatipn. A surge tank maybe considered as a branch pipe designed to ab-sorb a portion of the pressure .wave while theremainder travels upstream toward the fore-

bay. When located near the powerhouse, itprovides a reserve volume of water to meetsudden load demands until the water column inthe upper portion of the penstock has time toaccelerate.

When the length, diameter, and profile ofthe penstock have all been determined, con-sidering local conditions and economic factors,the selection of a minimum closure time for theturbine gates will require a compromise be-tween the allowable pressure variation in thepenstock, the flywheel effect, and the permis-sible speed variation for given load changes onthe unit.

With reaction turbines, synchronous reliefvalves, which open as the turbine gates close,may be used to reduce the pressure rise in thepenstock. Reduction of pressure rise isproportional to the quantity of water released.As relief valves are usually designed to dis-charge only a portion of the flow, this portionis deducted from the total flow in computingthe reduced velocity and the correspondingpressure rise.

Pressure Rise in Simple Conduits

With instantaneous gate closure, maximumpressure rise in penstocks of uniform diameterand plate thickness occurs at the gate ; fromthere, it travels undiminished up the conduitto the intake or point of relief. For slowerclosures which take less than 2L/a seconds(L = length of penstock ; a = velocity of pressurewave), the maximum pressure rise is trans-mitted undiminished along the conduit to apoint where the remainder of the distance tothe intake is equal to Ta/2 (T=time for fullgate stroke), from which point to the intakethe pressure rise diminishes uniformly to zero.With uniform gate closure equal to or greaterthan the critical time, ZL/a, the maximumpressure rise occurs at the gate, from whichpoint it diminishes uniformly along the lengthof the penstock to zero at the intake. An anal-


23/63

TABLE l.-Basic conditions for including the effects of loater hummer in the design of turbine penstocks.The basic conditions for ineludIng the &acts of water hammer in the design of turbine Denstock instaIlat.ions are

divided into normal and emergency conditions with s&able factors of safety assigned to each type of oDeratIon.

Nomad conditions of omwation

1. The turbine Denstock installation maybe werated at any head between the maxi-mum and minimum values of the forebaywater surface elevation.

2. The turbine eaten may be moved atany rate of steed by the action of the BOV-emor head UD to a Dredatermined rate. orat a slower rate by maneal control throughthe aorili relay vaIve.

2. The turbine may be operating at anywte Dosition and be required to add ordrop any or ail of its load.

4. If tbe turbine penstock installation iseanipDed with any of the following Dres-sure control devices it will be assumed thatthese devices are properly adjusted andfunction in tbe manner for which theequipment is designed:

(a) Surge tenks(b) Relief valves(e) Governor control SDPa ratus

(d) Cushioning stroke device(e) Any other pressure control device.

6. Unless the actual turbine character-istics are known. the efieetive areathrough the turbine gates during t hemruimum rate of gate. movement will beUpk as * linear relation wxth resDect to

6. The water hammer &ecta will be

computed on the basis of governor headaction for the governor rate which is BE-anally set on the turbine for speed regal&tion. If the r&w valve stoos are adinstedto Bive a slower governor setting thanthat for which the governor is designed,this rate shall be determined DriOr toDroceeding with the design of turbinepenstock installation and later adhered toat the Dower plant so that an economicalbasis for designing the penstoek. sclDuWE=% etc.. Under ma-maI ODersting wndi-tions can be established.

I. In those instances where. due to ahigher reservoir elevation. it is necessaryto set the st.,DS on tbe main relay valvefor a slower rate of gate movement. thewater hammer elTen3.a will be computedfoe this slower rata of gate movement

8. The reduction in head at variouspoints along the penstock will be corn-puted for the rate of gate opening whichis adually set in the governor in thosecases where it aDDears that the u,mfiIe oftbe Denstock is unfavorable. This mjni-mum Dressure will then be used as a bqsisfor normaI design of the pentik to in-sure that subatmospheric Dressures willnot cause a penstock failure due to col-IaDse.

9. If a surge tank is Drasent in thepenstock system the upsurge in the surgetank will be computed for the maximumreservoir level condition for the rejectionof the turbine flow which correspondb tothe rated output of the generator duringthe gate transversing time which is ac-tually set on the governor. Unless anoverflow sDiIlway is provided the top d-evation of the surge tank will be deter-mined by adding a freeboard of 20 Darcent of the com~utd upsurge to the max-imum height of water at the highestIlDSnrge.

10. The downsurge in the surge tankwill be e0m~ut.d for the minImum reser-voir level condition for a load additionfrom sDeed-no-load to the full Bate Do&tion during the sate traversing iimewhich is actually set on the governor. The

bottom of the surge tank will be Iocatsdat a distance of 20 per cent of the com-DUti downsurge b&w the lowest down-surm in the tank to safeguard against airwtering the Denstock.

11. The turbine, pens&k. surge tank.and other DRaWre control devices will bedesigned to withstand the conditions ofnormaI operation which are given abovewith a minImum factor of safety of 4 to5 based on the ultimata bursting or col-laDsing strenpth.

-

Emergsncu conditiona of operation

The bssic conditions to be considered asWlergeneJT ODeration are as foIIows:

1. The turbine gates may be closed atany time by the action of the governorhead. manual control knob with the mainrelay valve. or the emergency solenoiddevice.

2. The cushioning stroke will be as-sumed t.0 be inoperative.

a. If a relief valve is Dresent it, will beassumed to be inoperative.

4. The Bate traversing time will betaken as the minimum time for which t hegovernor is designed.

6. The maximum head including waterhammer at the turbine and along thelength of the panstock will be computedfor the maximum reservoir head condi-tion for 5naI DWt gate closure to thezero-gate position at the -imum gover-nor rate in 2& seconds.

a

6. If a surge tank is present in theDenstock system the upsurge in the surgetank wiII be eOmDUted for the maximumreservoir head condition for the rejectionof fnil gate turbine flow at the maximumrate for which the governor Is designed.The downsurge in the surge tank will becomputed for the minimum r-air headcondition for a fuI1 gate oDening fromthe speed-n*Ioad position at tbe maxi-mum rate for which the governor is de-sign+. In determining the tom and bottomelevatmns of the surge tank, nothing willbe added to the UPsurgea and downsurgesfor this -3EZX,CY eO&it&X, Of OD--tion.

7. The turbine. Denstuck. surge tank.relief valve. or other control devices willbe designed to withstand the above emer-BemY wndltions of operation with a min-imumfa+rofsafetqof2288anthgeh~mIbte bmxtmg or C0Sapaing

Emarmncu wnditious +wt to be comideedas a basis for design

1. Other Doesible emereency conditions ofoperation are those during which certainpieces of control equipment are assumed tomalfunction in the most unfavorable man-ner. The most severe emergency conditionof o~aration which wiII yield the maximumhead rise in a turbine Denstock installationwill oeeur from either of the two following

conditions of operation:(a) Rapid & sure of the turbine

gatesinIessthan2&seconds, (Lbthe

length of the Denatik and a is thewave velocity). when t& flow of waterin the Denstock is a maximum. (Themaximum head rise in feet due to thiswndition of oDeration is 100 to 126times the water velocity in feet per sac-and. )

(b) Rhythmic opening and closing ofthe turbine gates when a complete cy-cle of gate owration is performed in4L seconds. (Under extreme condIt,icm s

tie m aximum head rise due to this con-ft$) of OD-tiOn is twice the static

Since these conditions of operation re-mire a complete malfunctioning of thegowrnor control apDaratus at the most un-favorable moment . the DrobabiIIty of obtain-ing this t4pe of. oDeration is exceedingIyremote. Hence. these wnditioM will not. beused as a basis for design. However. afterSe design has been eatabIiied from otherconsiderations. it is desimbIe that thestresses in the turbine scrdl case. ~enstock.

Bnd Dressme contrd devices be not in ax-:ess of the ultimate bursting strength of;he structures for these emergene~ con%-tiOns Of ODeratiOn.

w


24/63


Ysis of pressure time curves shows that themaximum pressure rise is determined by therate of change of velocity with respect to time.Maximum pressure rise will develop in a pen-stock when closure starts from some relativelysmall percentage of full stroke so that somefinite velocity is cut off in a time equal to 2L/aseconds.

The governor traversing time is consideredto be the time required for the governor tomove the turbine gates from the rated capacityposition to the speed-no-load position. As therate of governor time is adjustable, it is im-portant that a minimum permissible rate bespecified if maximum pressure rise in the pen-stock is to be kept within design limits.

Water-hammer conditions should be deter-

mined for the unit operating at rated head andunder maximum static head. The highest totalhead, consisting of static and water-hammerheads, should be used for computing platethickness of the penstock.

R. S. Quick (6) simplified water-hammercomputations by using a pipeline constant, K,and a time constant, N, in the equations(similar to Allievis) which determine pressurerise, or water hammer, resulting from instan-taneous closure. The chart in figure 13 showsthe relative values of K and P (equal to

h) for various values of N. Also in-h ..I

eluded is a chart which shows the velocity, a,of the pressure wave in an elastic water columnfor various ratios of penstock diameter tothickness. Figure 14 gives only the maximumvalues of P for uniform gate motion and com-plete closure. It covers a range of closuresfrom instantaneous to 50 intervals, and a rangeof values of K from 0.07 to 40, which includesthe majority of practical cases. The nearlyvertical curve shows the limiting value formaximum pressure rise at the end of the firsttime interval, 2L/a. Values of pressure rises

to the left of this line attain their maximumvalues at the end of the first interval.

PIPE SHELLAs has been stated, penstocks should be

c designed to resist the total head consisting of

static and water-hammer heads. Workingstresses which will assure safety under all ex-pected operating conditions should be used.However, stresses approaching the yield pointmay be used in designing for emergency con-ditions. For penstocks supported on piers inopen tunnels or above the ground, allowanceshould be made for temperature and beamstresses in addition to the stresses due to in-ternal pressure. The diagram shown in figure14 permits a quick determination of equivalentstresses if principal stresses are known. Thediagram is based on the Hen&y-Mises theoryof failure, sometimes called the shear-distor-tion or shear-energy theory. The plate thick-ness should be proportioned on the basis of anallowable equivalent stress, which varies with

the type of steel used. The ASME code givesmaximum allowable tensile stresses for varioustypes of steels.

The hoop tension, S, in a thin shell pipe, dueto internal pressure is expressed as:

s=* . . . . . . . . . . . . . . . . . . (5)in which

D=inside diameter of pipe in inchesp=internal pressure in psit =plate thickness in inchese =efficiency of joint.

Regardless of pressure, a minimum plate

thickness is recommended for all large steelpipes to provide the rigidity required duringfabrication and handling. For penstocks thedesired minimum thickness for diameter, D,may be computed from the formula:

&in= D+zo.. . . . . . . . . . . . . . . . . . . . .400

(6)

A thinner shell may in some cases be used ifthe penstock is provided with adequate stiff-eners to prevent deformation during fabrica-tion, handling, and installation.

Joint efficiencies for arc-welded pipe dependon the type of joint and the degree of examina-tion of the longitudinal and circumferentialjoints. The ASME code stipulates a maximumallowable joint efficiency of 100 percent fordouble-welded butt joints completely radie-graphed, and of 70 percent if radiographicexamination is omitted. Corresponding jointefficiencies for single-welded butt joints with


25/63

EXPLANATION

0.60.5Ok

0.3

0.2

0.100.09

E0.06

0.050.04

0.03

0.02

O.OlW - 7\L- -NJ l-+-J- 007 0.1 0.2 0.5 IO 2 3 45Values of Pipe - Line Constant K- $$

0

CHART SHOWING MAXIMUM PRESSURE RISE WITH UNIFORM GATE MOTIONAND COMPLETE CLOSURE : BASED ON ELASTIC-WATER-COLUMN THEORY

NOTE:Ratio of Pressure Riseh to Initial Steady HeadrH~determined from relation 2 Kp~b~,

Cu. Ft. per sec.

CHART SHOWING VELOCITY OF TRAVEL OFPRESSURE WAVE IN ELASTIC WATER COLUMN

Formula : a - -*=vyfTgb

Where o - Velocity of Tmvel of. Pressure Wave. Ft. per Sec.k- Bulk Modulus of Elast icity of Water- 294.000

Lbs. per Sq. In.E = Younqs Modulus for Pi pe Walls = 29.400.000

Lbs. per Sq. In. approx. for Steel.b = Thickness of Pips Walls, Inches.d = Inside Diameter of Pipe, Inches.

FIGURE 13.-Water-hamm.er values for uniform gate motion and complete closure.

VI


26/63

I6 ENGINEERING MONO GRAPH NO. 3

NENCKY-YISES THEORY

FIGURE 14.-Equivalent stress diagram


27/63

WELDED STEEL PENSTOCKS 17

backing strips are 90 and 65 percent, respec-tively. If radiographic spot examination isused, allowable joint efficiencies are 15 percenthigher than for nonradiographed joints.

Postweld heat treatment of welds is requiredif the wall thickness exceeds a specified mini-mum thickness. Joint efficiencies and radio-graphic inspection procedures used by theBureau of Reclamation conform to the require-ments of the ASME code.

Specifications issued by the Bureau ofReclamation for construction of penstocksusually require that they be welded by arigidly controlled procedure using automaticwelding machines, that the longitudinal andcircumferential joints be radiographed, andthat either the individual pipe sections or theentire installation be tested hydrostatically.

Since the head varies along the profile of apenstock in accordance with its elevation andpressure wave diagram, it is customary to plotthe heads and stresses as shown in figure 15.The total head at each point along the profilecan then be scaled off and the plate thicknesscomputed accordingly.

Other stresses which must be considered inaddition to hoop stresses are as follows:

Temperature stressesLongitudinal stresses which accompany

radial strain (related to Poissons ratio)Beam stresses.

Temperature Stresses

For a steel pipe fully restrained againstmovement, the unit stress per degree of tem-perature change is equal to the coefficient ofexpansion of the steel multiplied by itsmodulus of elasticity, or 0.0000065 X 30 X lo6 =195 psi per degree of temperature change. Fora pipe having expansion joints and being freeto move on supports, the longitudinal tempera-ture stress is equal to the frictional resistancebetween supports and pipe plus the frictionalresistance in the expansion joint. The resist-ance at supports varies according to the typeof support and its condition. The followingaverage values of coefficients of friction havebeen determined by tests:

Steel on concrete (cradle supports) .0.60Stee l on steel-rusty plates . . . . . . . . .0.50Steel on steel-greased plates . . . . . . .0.25Steel on steel-with two layers

of graphited asbestos sheetsbetween . . . . . . . . . . . . . . . . . . . . . . . .0.25Rocker supports-deteriorated. . . . . .0.15For expansion joints a frictional resistance

of 500 pounds per linear foot of circumferencewas determined by test and may be used forthe computation of longitudinal forces in apipeline.

Longitudinal Stresses Caused byRadial Strain

Radial expansion of a steel pipe caused byinternal pressure tends to cause longitudinalcontraction (Poissons ratio), with a corre-sponding longitudinal tensile stress equal to0.303 of the hoop tension. This is true, pro-vided the pipe is restrained longitudinally. Thisstress should be combined algebraically withother longitudinal stresses in order to deter-mine the total longitudinal stress.

Beam Stresses

When a pipe rests on supports it acts as abeam. The beam load consists of the weightof the pipe itself plus the contained water.Beam stresses at points of support, particu-larly for longer spans, require special consider-ation. This matter is discussed in the sectionon design of supports.

Based on a preliminary design, variouscombinations of beam, temperature, and otherstresses should be studied so as to determinethe critical combination which will governthe final design. It may be necessary ordesirable to reduce the distance between an-chors for pipes without expansion joints toreduce the temperature stresses or to shortenthe span between supports ti reduce beamstresses. For penstocks buried in the ground,and for all other installations where the


28/63

m

32-k i&t----...s19Byposicowi.: -

1; f

IntOk-El. bl j-:

5-

)-

i-

)-

I-

)-

t---Test pressure ine - El. 1460

I I

\+---uownsrreom mce bI uWn

2n.1

I Efficiency of joints : 99 X-.-.

Plate thickness es ary from ito 2b

FIG- 16.-A graphical illustrati on of heada and stresses de temnined for thehydrostatic testing of the Shasta pen&o&.


29/63


temperature variation in the steel correspondsto the small temperature range of the water,expansion joints may be eliminated and alltemperature stresses carried by the pipe shell.

For a pipe without expansion joints and an-chored at both ends in which the beam stressesare negligible, the longitudinal stresses maybe kept within allowable limits by welding thelast girth joint in the pipe at the mean temper-ature of the steel. A procedure similar to thiswas used for the penstock and outlet headersat Hoover Dam where expansion joints for the30-foot pipe were not considered to be feasible.In this case it was desired to eliminate alllongitudinal tension in the penstock becausethe pinned girth joints had an efficiency ofonly 60 percent in tension but 100 percent in

compression. The lowest anticipated servicetemperature was.46 F. In order to reduce thelength of a penstock section between anchorsto that corresponding to a temperature of 45F, mechanical prestressing by means of jacksapplied at the periphery of the pipe was re-sorted to. A compressive force correspondingto the difference between the erection tempera-ture and the lowest service temperature wasapplied. After welding the final closing jointthe jacks were removed, leaving the penstock incompression. At 46O F. the longitudinal stressis then zero, and at higher temperatures thepenstock is in compression.

SUPPORTS

Modern trend in design requires that steelpipes located in tunnels, above ground, oracross gullies or streams be self-supporting.This is possible in most cases without an in-crease in plate thickness except adjacent tothe supports of the longer spans. If the pipeis to function satisfactorily as a beam, defor-mation of the shell at the supports must belimited by use of properly designed stiffenerrings or ring girders. A long pipeline with anumber of supports forms a continuous beamexcept at the expansion joints, where its con-tinuity is lost. Ring girders prevent large de-formation of the pipe shell at the supports.Stresses may therefore be analyzed by the

elastic theory of thin cylindrica l shells (9).The shell will be mainly subjected to directbeam and hoop stresses, with loads beingtransmitted to support rings by shear. Be-

cause of the restraint imposed by a rigid ringgirder or concrete anchor, secondary bendingstresses occur in the pipe shell adjacent to thering girder or anchor. Although this is only alocal stress in the shell, which decreasesrapidly with increasing distance from thestiffener, it should be added to the other longi-tudinal stresses. For a pipe fully restrained,the maximum secondary bending stress is:

%=1.82+. . . . . . . . . . . . . . . . . . . . . (7)

in whichp =pressure in psi

r= radius of pipe in inchest=plate thickness in inches.This secondary bending stress decreases withany decrease in restraint.

If use of Equation (7) results in excessivelongitudinal stresses, it may be necessary toincrease the p ipe shell thickness on each sideof the stiffener ring for a minimum length of3/q, in which q=1.236/\lx At this distancefrom the stiffener ring, the magnitude of thesecondary stresses becomes negligible. Sec-ondary bending stresses at edges or cornersof concrete anchors may be reduced by cover-ing the pipe at these points with a plasticmaterial, such as asbestos -or cork sheeting,prior to concrete placement. This will alsoprotect the edges or corners of the concreteagainst cracking or spalling.

Pipes designed in accordance with the pre-ceding principles may be supported on longspans without intermediate stiffener rings.Figure 16 shows the lo-foot S-inch ShoshoneRiver siphon, which has a 150-foot span. Thelength of the span to be used on any particularjob is usually a matter of economy. Very long

spans, such as shown in figure 16, are econom-ical only under certain conditions, as in thecrossing of rivers or canyons where the con-struction of addit ional piers, which shorterspans would require, is not feasible.

If continuous pipelines with or without ex-pansion joints are supported at a number ofpoints, the bending moments at any point


30/63

20 ENGINEERING MONOGRAPH NO.3

FIGURE 16.-Tke Shoshone River siphon cro8ses the river on a 150-foot span.

4. By stiffener rings which carry the loadto concrete piers by means of supportcolumns.

As the static pressure within a pipe variesfrom top to bottom, it tends to distort thecircular shape of the shell. This is especiallypronounced for thin-shelled large-diameterpipes under low head or partially filled. Theweight of the pipe itself and the weight ofbackfill, if the pipe is covered, also cause dis-tortion of the shell.

Depending on the method of support,stresses and deformations around the circum-ference of a filled pipe will assume variouspatterns as shown in figure 17. These dia-grams indicate the best location for longitudinal

along the pipe may be computed as in anordinary continuous beam by using applicablebeam formulae. Spans containing expansionjoints should be made short enough that theirbending moments will correspond to those ofthe other spans. Expansion joints should beplaced at midspan where deflections of the twocantilevered portions of pipe are equal, thuspreventing a twisting action in the joint.

A pipe can be designed to resist safely thebending and shear forces acting in a cross-sectional plane by several methods, as follows:

1. By sufficient stiffness in the shell itself2. By continuous embedment of part of the

periphery of the pipe3. By individual support cradles or saddles


31/63


Moments Deflrct,onr

saddle wpport Moments

Rmg Girder and Poor Support Moments Deflectwns

FIGURE 17.-Momenta and deflections developed in a

pipe precise ly full, using various types of supports.

joints in pipe shell and joints in stiffeners toavoid points of highest stress or largest defor-mation. The saddle and the ring girder withcolumn supports are widely used. The one-pointsupport should not be used for a permanent in-stallation. It is included merely to illustrate itsflattening effect on an unstiffened pipe.

For the ring girder and column-type support,the support columns are attached to the ringgirders eccentrically with respect to the cen-

troidal axis of the ring section so as to reducethe maximum bending moment in the ring sec-tion. In computing the section modulus of thering girder, a portion of the adjacent shell maybe considered as acting with the girder. Thetotal length of the shell thus acting is:

l=b+1.56ds . . . . . . . . . . . . . . . . . . . . (8)in which b is the width of the ring girder (seefigure 18) and r and t are as defined in Equa-tion (7). Essential formulae and coefficientsfor the computation of stresses in ring girdersare given in figure 18. These formulae and

coefficients were developed from the stiffenerring analysis for the Hoover Dam penstocks.The table gives stress coefficients, Kl to K6,inclusive, for various points around the cir-cumference of the ring. These coefWentsare to be inserted in the appropriate equationsshown for the determination of direct stress,T, bending moment, M, and radial shear stress,

S, in the ring section. By adding the direct,bending, and tensile stresses in the ring dueto internal pressure in the pipe, the total unitstress in the inner and outer fibers of the ringmay be determined.

In installations subject to seismic disturb-ances, the severity of the earthquake shocksshould be ascertained from local records andconsidered in the design of the supports. Un-less the project is located close to a fault zone,a horizontal seismic coefficient of 0.1 to 0.2 ofthe gravity load is adequate for most areas inthe United States. Stresses due to earthquakeloads for various points along the peripheryof the ring girder may be computed from theequations and stress coefficients given in figure19. In determining the required section for a

ring girder, stresses so computed should beadded to the stresses caused by static loads.A typical ring girder and column support

designed for an S-foot penstock with a spanof 60 feet is shown in figure 20. The girderconsists of two stiffener rings continuouslywelded to the pipe on both sides and tiedtogether with diaphragm plates welded be-tween the two rings. Two short columnsconsisting of wide-flange l-beams are weldedbetween the rings to carry the load to therockers by means of cast-steel bearing shoes.A typical rocker assembly is shown in figure21. It consists of an Winch cast-steel rocker, a3-l/2-inch steel pin with bronze bushings, and acast-steel pin bearing. The rockers are kept inalinement by means of a steel tooth bolted to theside of each rocker and guided between twostuds threaded into the bearing shoe of the sup-port. The two pin bearings transmit the load tothe concrete pier. After being positioned inaccordance with a temperature chart so as toprovide effective support for the range oftemperature anticipated, they are grouted intothe top of the pier as shown in figure 21. Theadjustable steel angle yoke shown in figure 21is used only during erection and grouting,after which time it is removed.

Thin-shelled pipes, when restrained longi-tudinally, are subjected to buckling stressesbecause of axial compression. The permis-sible span between supports is limited by thestress at which buckling or wrinkling will


32/63


STIFFENER RING

N-Pr p +,w]

p= Area combined rinq

Al= Poissons ratio = 0.3

cs~-)pJ-+

I = Moment of inertiasection in square inches

of Section Y-Y.=t(b+ls6m)+2lt,

L= Lenqth of one spon in inches.MaBendinq moment in the rinq, inch pounds.

N - Tension due fo, inferno1 pressure, on section of rinq, in pounds.P: Pressure head WI paynds per square inch.qs=Weiqht of pipe sh+U in one span in pounds.Q ZCompined welqht pope, shell and water in one span, in pounds.S = Rodlot shear stress III. stiffener rinq in pounds.T = Direct stress In the rmq e%lusive ot N, inpounds.Total stress in outer fiber of rinq =r-Mftf.To)ol stress in inner fiber of rinq t Et MT +*.

COEFFICIENTS

t

t = Tension, - = Compression

+ f &7sion, - = Compression

RtFERLNC~ - WULDER CANYON PRoJtXT - FINAL RLPoRTS, PART S,- bULLLlIN 5, 1ASLU NO% 3.4 i 6.

FIGURE 18.-Fomnulae and coeficienta for the computation ofSt+%8888n ring girders aa developed for stiffener tinganalyses.


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4 e .w. 1,--Centroid of combined

c.rt;nn;;nn

23

1 - KI 1 K2 KS KI KS KS / , , A

_Li , .2.zbIIV8, I ,u,*

Fl* 1 M=nO(RKI +WK2) 1 T=nP(Ks+BK4) 1 S=nQ(Ks+ CKe)

0 0 0 0 0 +.079571 +.31631015 -.019651 -.064705 -.019651 -.082365 +.066082 +.30746430 -.032380 -.I25000 -.0323BO -.I59155 +.027249 +.275664

1 45 I-.032119 l-.176776 I-.032119 1-.2X079 I-.p32119 +.225079Y..

60 -.014411 -.216506 j-.014417 j-.275664 I-.10 4549 +.I59155 ,75 +,022g46 -,241482+,022g4c I- 3n-fl.C~ I- tmx'm

.U , ..J I-J.37 -.,Yd~IL nrr3lnc 5

. ... aI I ;\ -

go- l .079577 ^-_a^^ -e-F--.LWUUU ,+.u,rs/l -.318310 -.250000 0 SECTION F-F^m^^^^ . ^-^r-- '

L...."-"0 +.250000 0 -.__-__ Hinqed

B

032380L

064705-.125ooo

.250000

241482h [+-.367464

13601 01 01 0 )+.0?9577 I+.31831

LJ Poisson's

K=f[/& +(I -u?(l-$)

A = Area of combined sectio n rinq in square inchL = Lenath of one soon in inchesM =Bendinq mome nt in the rinq, inch poundsPs= Weiqht of pipe shell in one span, pounds(I = Combined weie ht of pipe shell and w ater in onen = Seismic coefficientS * Radial sheor stress in stiffener ring. poundsT = Direct stress in stiffener rinq. poundsTotal stress in outer fiber of rinq . i-M p

Totol stress in inner fiber of rina - r + M &

es=t(b+l56

span, pounds

ratio= 0.3

'+w]

LIT)+ 2l.Q

FIWRE lg.-Formulae and coeficimate for the ompututkm of strsssee in ring #i&8 dus to eadhqu& &a&.

occur. The theoretical buckling stresses in acylindrical shell of perfect form is given byTimoshenko (12) and others as:

For buckling failure by the formation of asingle wrinkle

s= E td3(1-W) -7 )

. . . . . . . . . . . . . . . (9)

EXPANSION JOINTS

For penstocks above ground, the tempera-ture of the steel is influenced principally bythe temperature of the water when filled, andby the temperature of the air when empty.If the pipe is exposed, its temperature will beaffected by heat from the sun. In undergroundinstallations, the pipe temperature is af%ctedby the temperature of the contained water andsurrounding soil.

The main purpose of expansion joints is topermit longitudinal expansion of the pipe

which results from temperature change. Ex-pansion joints also serve as construction jointsto adjust discrepancies in pipe lengths. Dis-regarding frictional resistance, the change inlength of a pipe of length L per degree temper-ature change, is 0.0000066 L.

Among the several types of expansion jointsin use, the sleeve type is the most popular forlarge steel pipes. Longitudinal movement ispermitted by two closely fitting sleeves , onesliding in the other, with a stuffing box andpacking to prevent leakage. A bolted packinggland is used to compress the packing which

consists of long-fibre braided flax impregnatedwith a suitable lubricant.A typical expansion joint of this type de-

signed for an &foot penstock under 210-footstatic head is shown in figure 22. The ex-terior surface of the inner sleeve is clad withchromium to prevent corrosion and insure ,free sliding in the joint. This type of joint


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-

+--G Rocker support

TYPICAL ELEVATION HALF SECTION

Support ring-,.

FPipe shell

SECTION B-B

SECTION C-C SECTION A-A

TYPICAL SECTIONSFmuae 20.-Typical kg girder and column support.


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Fx~mm21.-Typical rocker support. The angle yoke is used only for alinement during grouting.

Packing gland---..,\\ ,,---Retainer ring

k- _ _ _ _ - . -A %\

JI----Inner sleeve

.----Inside of pipe shell

:---Packing rings

FIGUREI2.-Typica l sleeve-type expansion joint.

,/,.-.Stlffener r,ng /ymmetrlcal about E

,/-Ladder rung

I

.---lnslde of pipe shellL .__ _ b ._._. i

----Packmg r,nqs

FIGURE 23.-Flemble sleeve-type expansion joint with two stuflng boxes used to pemnit longitudinal temperaturemovement and transverse dejIection.


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may also be designed with two stuffing boxes,as shown in figure 23, to permit longitudinaltemperature movement and transverse deflec-tion in the line. Such a flexible joint is desirablewhere a penstock passes through a constructionjoint separating the concrete masses of a damand a powerhouse. As the dam is built on afoundation considered to be elastic, its down-stream toe will deflect vertically with respect tothe powerhouse when subjected to reservoirpressure.

Sleeve-type expansion joints have been usedsuccessfully for penstocks up to 22-foot-dia-meter, as at Davis Dam, and for heads up to700 feet. This type of expansion joint can beused only on pipes which are accessible fortightening and replacing the packing. Also,the lubricated flax packing may lose its plas-ticity and water-sealing effect after a periodof service. This is particularly true where the

, pipeline is frequently empty and exposed tothe direct rays of the sun.

The sleeve-type expansion joint must bewell-fitted with reasonably close tolerances to

insure watertightness under high heads. Ifit is deemed necessary to machine portions ofthe expansion joint in order to obtain water-tightness, postweld heat treatment will assistin maintaining dimensional tolerances.

BENDS, BRANCH OUTLETS,AND WYES

Pipe Bends

Changes in direction of flow are accom-plished by curved sections commonly calledbends. Plate steel bends are made up of short

FIGOIUC 24.-Con&ant diamdw bend with the radiw of the bend five tima the dimnetm.


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FIGURE 26.-Bend reducing in diameter from 9 feet to 8 feet, theradius equal to four times the smaller diameter.

segments of pipe with mitered ends. To con-serve as much of the available head as pos-sible, bends for penstocks should be made withlarge radii and small deflections between suc-cessive segments. Bend radii of three to fivetimes the pipe diameter and deflection anglesof 5 to 10 between segments are recommended.Bends may be designed with a constant diam-eter or with a different diameter at each end.Figure 24 shows a typical constant diameterbend with a total line deflection angle of about38O designed for a g-foot penstock. The bendradius is 45 feet, while the seven mitered seg-ments have deflection angles of about 5-1/2Oeach. Figure 25 shows a reducing bend with areduction in diameter from 9 feet to 8 feet.

Compound or combined bends, in which theplane of the bend is neither vertical nor hori-zontal, require certain trigonometric computa-tions. Usually the plan angle and profileangles are known and it is required to deter-mine the true angle in the plane of the bendand the bend rotations. These computationsand applicable formulae are shown in figure 26.

Branch Outlets and Wyes

On some large penstocks, specially fabri-cated branch outlets and wyes are used fordiverting water from the headers. The mainconsiderations in the design of branch outletsand wyes are structural strength to withstandthe internal pressure, and proper streamliningto reduce hydraulic losses.

Since outlet openings reduce the strengthof the pipe at the opening, reinforcement mustbe provided to compensate for the removedmaterial. As a general rule the reinforcementshould be adequate to make the connectionequal in strength to that of the pipe without

the opening. Several branch outlets and wyesare illustrated in figures 27 and 28, respec-tively. These two figures show some of the fit-tings commonly used and the different methodsof providing necessary reinforcement. The un-supported pressure areas in the pipe shells areshown by shading, and the distribution of loadin the reinforcing members is indicated graphi-cally. The right angle tees shown in figures 27a


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FIGURE 26.-Computation method fmdetermining true pipe angle in a compound pipe bend.


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(a)

W SECTION A-A

SECTION 8-B

SECTION C-C

NOTATIONC = Corrosion allowonce

SECTION D-D pz Internal pessure,pounds per sq in.Y = Reaction force pfoduced by

restraining members.

FIGURE ST.-Loading diagram for the development of reinforcement of branch outlets.


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SECTION G-G

(b) SECTION F-FSECTION E-E

-SECTION H-HI ..-

Id)

(e)

SECTION K-K

Notationp=lnternol pressure,pounds

per sq. in.FIGURE .%.-Loading d&grams for the development of reinforcement of zvye branches in penstocks.


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and 27d are hydraulically ineffi&nt and shouldbe avoided whenever possible. The use of afrustum of a cone with convergence of 6O to P,as shown in figure 27b, reduces the branch loss

to approximately one-third that of a cylindricalbranch or outlet. Branch losses may also be re-duced by joining the branch pipe to the mainpipe at an angle less than 900 as shown in figure27~. Ordinarily deflection angles, 0, of branchoutlets, vary from 30 to 750. However, diffi-culties are encountered in reinforcing branchoutlets and wyes with deflection angles lessthan 45. The hydraulic efficiency increasesas the deflection angle decreases. Branch out-lets of the type shown in figures 27f and 27gare not desirable when the diameter of thebranch pipe is in excess of, say, three-fourths

of the diameter of the header, since the curva-ture of the reinforcement becomes very sharp.In such cases the type of reinforcement shownin figure 27e is preferable. Branch outletsand wyes are usually designed so that theheader and the branches are in the same plane.

Branch outlets as shown in figures 27a, 27b,and 27~ may be reinforced with a simplecurved plate designed to meet the require-ments of the ASME code referred to previously.Branch outlets and wyes as shown in figures27d to 27g inclusive, and in figures 28b to28f inclusive, may be reinforced with one ormore girders or by a combination of girdersand tie rods. The type and size of reinforce-ment required depends on the pressure, theextent of the unsupported areas, and clearancerestrictions. For branch outlets which inter-sect in a manner as shown in figures 27d and27e, and for wyes asshown in figure 28f, threeor four exterior horseshoe girders may be used,the ends of which are joined by welding. Thewelding of the ends of the horseshoes will befacilitated by use of a round bar at the junc-tion. For wyes used in penstocks designed

for low velocity flow, an internal horseshoegirder, sometimes called a splitter, as shownin figure 28a, may be used. Although thesplitter is structurally efficient, it will causedisturbances if the flow is not equally dividedbetween the branches.

Stress analysis of branch outlets and wyesis approximate only. Exact mathematical anal-

.ysis based onthe theory of elasticity becomestoo involved to be of much practical value. Inthe approximate method, simplifying assump-tions are made which give results considered

sufficiently accurate for practical purposes.The reinforcement of a fitting should be pro-portioned to carry the unsupported loads, theareas of which are bhown shaded in figures 27and 28. The total1load ,to be carried by thereinforcement is equa l $0 the product of theinternal pressure and the unsupported areaprojected to the plane of the fitting. A por-tion of the pipe shell is considered as actingmonolithically with the girders as in the caseof stiffener rings.

In the analysis of ring girder reinforcementof the type shown in figures 27f and 27g it isassumed that the curved girder acts as if it layin one plane, that the loads in both directionsare uniformly distributed, ,and that the ring iscircular. The first of these assumptions i sbelieved to be reasonably accurate because thering girder is supported along its entire perim-eter by the pipe she ll and cannot be appre-ciably twisted or deflected laterally. Theassumption of uniform load distribution is onthe side of safety. In regard to the circularityof the ring, however, it should be noted thatthe ring girder is egg-shaped for branch out-lets with small deflection angles, while forlarger deflection angles the shape is morenearly circular and the assumption of circu-larity is more proper. The ring girder isstatically indeterminate when used as thistype of reinforcement and, for the stress anal-ysis, the ring dimensions must first be assumed.Computations will be simplified by using aring of constant cross section. Where tie rodsare used, the deflections of the girder at thejunctions with the tie rods must be calculated.These deflections, which are due to the loadsin both directions, and the redundant tie-rodforces are then equated to the elongation ofthe tie rods and the forces in these obtained bysolving the resulting equations. A symmetricalarrangement of the tie rods with respect to thecenterline of the ring will simplify calculations.To provide additional strength at a branch out-let, the plate thickness of a portion of the header


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ENGINEERING MONOGRAPH NO. 3

I 1SIDE ELEVATION

EN 0 ELEVATION

SECTION A-A

SEC. C-C

DETAIL x SEC D-D SEC. E-E SEC. F-F

FIGURE 29.-Typica l internal and external reinforcement for a branch outlet.


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around the outlet openings and of the joiningbranch pipes is sometimes increased as shownin figure 29.

The reinforcement for the wyes shown in

figures 28a and 28b are statically determinate.The bending and direct stresses for any sectiondue to the loadings shown can be calculatedwithout difficulty. The increase in the bendingstress caused by the small radius of curvatureat the throat of the member can be evaluatedby using a correction factor in the bendingformula for straight beams.

The method of analysis briefly discussedabove has been used extensively in the designof special fittings. Branch connections arehydrostatically tested at pressures equal to 1%times the design pressure. In some casesstrain gage readings have been taken duringthe hydrostatic test and results of these testslead to the conclusion that the approximatemethods of analysis of the reinforcing mem-bers are satisfactory.

The design of branch outlets and wyes isdiscussed in a number of publications (13, 14,15).

PENSTOCK ACCESSORIES

For Installation and Testing

Among the penstock accessories whichshould be given consideration in design are thefollowing :

a. Temporary supports are generally re-quired for penstocks embedded in dams ortunnels. They should be designed to carryonly the empty pipe and to anchor the pipeto prevent flotation during placement of con-crete. These supports remain in place and areconcreted in with the pipe.

b. Standard dished test heads are used inhydrostatic pressure tests of the installed pen-stocks.

c. Piezometer connections for turbine per-formance tests, one type of which is shownin figure 30, should be placed in straight sec-tions of pipe away from bends and branchoutlets.

Grmd end flushwith pipe ---___

-. -. *-It Dio CA

Inside of penstock-.,I Std. thread i

\.\I -.-t--fDrill, round edge

I.* tPipe tap

FIGURE 30.-Znstallation of a piezometer connection inshell of penstock for turbine perfovmunce tests.

For Operation and Maintenance

Proper maintenance of penstocks requiresthe following accessories :

a. Fill ing lines, which are used to fill thepenstocks from the reservoir and place themunder balanced pressure to facilitate openingof intake gates. They should be provided withsuitable control valves.

b. Air inlets located below the intake gateadmit air into the penstocks and prevent nega-tive pressures during draining and admit airduring emergency gate closure. In addition,air pipes or air valves should be installed at

summits in the penstocks to release air duringfilling and admit air during draining.

c. Drains at the upstream and downstreamany water leakingnds of penstock to handle

past the intake gate.

\ TYPICAL ASSEMBLY I

FIGURE 31.-Typica l manhole designed for inspectionand maintenance.


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d. Manholes for inspection and maintenancework shall be located to facilitate ventilationand the entry of men and materials duringinspection and maintenance work. One type

is shown in figure 31.e. Walkways and stairs are required for in-spection and maintenance of large penstocksin open tunnels or above the ground.

f. Service connections are usually requiredto provide a source of water for the power-plant, dam, or municipal use.

g. The reinforcement of all openings in apenstock such as manholes, connections fordrains, waterlines, filling lines, and air ventsshall be designed in accordance with theASME code.

DESIGN OF PIERS AND ANCHORS

GeneralPenstocks installed above ground or in open

tunnels are usually supported on piers spacedfrom 20 to 60 feet apart. At bends, anchorsare used to resist the forces which tend tocause displacement of the pipe. Sometimesanchors are also placed at intermediate pointsbetween bends. Piers and anchors are usuallyof reinforced concrete. As the sizes of piersand anchors are influenced by the type of soilon which they rest, information regarding thesoil is required before a design can be prepared.It is preferable to construct piers and anchorson rock foundations wherever possible. Bases

should be placed at elevations sufficiently belowthe frostline to protect the structures againstfrost damage.

Support PiersPiers are designed to support the deadload

of pipe and contained water and resist thelongitudinal forces resulting from temperaturechange. Earthquake forces may be consideredin the design in areas subject to seismic dis-turbances. For large thinshell pipes and pipessupported on high piers or bends, lateral wind-loads on the empty pipe may affect the designof the supports. The magnitude of longitud-inal forces in a penstock provided with ex-pansion joints is dependent on the methodsof support between pipe and pier. Piers whichcarry the pipe directly on the concrete or onsteel bearing plates are subjected to largelongitudinal forces when axial movement ofthe pipe occurs. These longitudinal forcesmay be reduced by placing lubricated plates orother low friction factor material between pipeand pier or by use of rocker and roller supports.The friction coefficients recommended in eachcase have been mentioned in the section ondesign of pipe shell. After all the forces actingon the supports have been ascertained, theproportions of the pier may be determinedfrom the moments and shear forces. Piersshould be designed. so that the resultant of thevertical load (including the weight of the pierand the prism of earth over the base) and the

FICXJIU 32.-Typical monolithic piesStrUCtiOn for rocker SuppWtS.


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longitudinal and lateral forces will intersectthe base within its middle third. Figure 32shows a typical concrete pier designed for an 8-foot penstock supported on rockers. This pier isof monolithic construction with two grout re-cesses on top for the rocker bearings, whichare fixed in place with anchor bolts.

Anchors

Freely supported penstocks must be an-chored at bends, and sometimes at intermedi-ate points, to prevent shifts in the pipelineduring installation and to resist the forceswhich tend to cause displacement in a bentpipe under pressure. Displacement at bendsmay be caused by a combination of forces.They may result from temperature changes, orfrom gravitational, dynamic, or hydrostaticforces. The spacing of anchors in long tangentsections between bends depends primarily onthe magnitude of the longitudinal forces inthe line. For buried pipes the usual practiceis to provide anchors only at horizontal bendswith large deflections, using a sliding coeffi-cient of l:OO, and at vertical bends whereconsiderable uplift is expected. If, during in-stallation, a long pipe section is exposed to the

atmosphere for some time before backfilling, itshould be anchored in place and should haveone field girth joint between each pair of an-chors left unwelded to permit free movementwith changes in temperature. After the pipehas been backfilled and its temperaturebrought to normal, the open joints may bewelded, coated, and backfilled.

Figure 33 shows a resolution of forces actingon an anchor under conditions of expansion andcontraction. As has been stated in the case ofpiers, the resultant of these forces should inter-sect the base of the anchor within its middle

third. The weight of the pipe and containedwater and the weight of the concrete in theanchor itself are included in the combination offorces. The size of the anchor is also influencedby the sliding coefficient of friction between theconcrete and the underlying soil. This slidingcoefficient varies from 0.30 for clay to 0.76 for agood rock base.

_ Anchors may be of the type which encasesthe entire circumference of the penstock orthey may be of the type which is in contactwith only a lower segment of the circumfer-ence as shown in figure 34. This latter typeof anchor may be constructed before the pen-stock is installed, in which case recesses areprovided in the concrete for grouting the pipeand stiffener rings in place after installation.The stiffeners will assist in transferring thelongitudinal forces from the pipe to the anchor.

MATERIALS

Steel Plates

The types of steels used by the Bureau ofReclamation for penstocks conform to theStandard Specifications of the American Soci-ety for Testing and Materials (ASTM) listed inthe bibliography. Low carbon steels are con-sidered to be the most satisfactory because oftheir favorable fabrication and welding char-acteristics and their high ductility. Thesteels most often used conform to ASTMSpecifications A-286, Grade B or C or A-201,Grade B. Firebox quality grades are alwaysused because of the more restricted limits on

chemical ingredients and the more extensivetesting required to assure a greater degree ofuniformity of composition and homogeneity.The A-236 steel, which is 8 semikil led steel,is often specified where plate thicknesses arenot greater than about 1 inch. For thicknessesexceeding 1 inch the A-201 steel, which isfully killed, is preferred as it has greaternotch toughness than the A-286 steel whichminimizes the danger of brittle failures.A-201 steel made to fine grain melting prac-tice in accordance with ASTM SpecificationsA-300 has been used for special fittings such

as branch outlets and