,; ,’ ‘r_i -,L. ,--, Y..~. ;r.. : _ A WATER RESOURCES TECHNICAL PUBLICATION ENGINEERING MONOGRAPH No. 3 Steel ,Pensthcksy- ,’ r ; UNITED STATES DEPARTMENT ’ 6F Tt-tE INTERIOR BUREAU, OF RECL-AMATI-ON ’ . ,-
-. IThe lower ends of the penstocks at Shasta Dam emerge from conerefa nnckors and pbcnge into the pozus~ho~csc
A WATER RESOURCES TKZHNICAL PUBLICATIONhrginooring Monograph No. 3 United States Department of the Interior l BUREAU OF RECLAMATION
As the Nation’s principal conservation agency, the Department of the interior has responsibility for most of our nationally owned public ’ lands and natural resources. This includes fostering the wisest use of our land and water resources, protecting our fish and wildlife, preserv- ing the environmental and cultural values of our national parks and historical 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 sibility 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: 1949 Revised: 1959 Revised: 1966 Reprinted: 1977 Reprinted: 1986 U.S. GOVERNMENT PRINTING OF’FICE WASHINGTON : 197’7
Preface THIS MONOCRAPH will assist designers in the This edition now represents the contributionssolution of problems in design and construc- of many individuals in the Penstocks and Steeltion of safe penstocks which may be fabricated Pipe Section, Mechanical Branch, Division ofin accordance with modern manufacturing Design, on the staff of the Chief Engineer, procedures. Certain rules relative to materials, Denver, Colo.stresses, and tests might be considered un- This monograph is issued to assist designersnecessarily conservative. Safety is of para- in the solution of problems involved in the de-mount importance, however, and penstocks sign and construction of safe and economical designed and constructed according to these welded steel penstocks.rules have given satisfactory service through Because of the many requests for informa-years of operation. tion concerning Bureau of Reclamation de- Welded Steel Penstocks presents information signed and built penstocks, a comprehensiveconcerning modern design and construction bibliography has been added in the back.methods for pressure vessels applied to pen- Included in this publication is an informa-stocks for hydroelectric powerplants. The data tive abstract and list of descriptors, or key-are based on some 40 years experience in pen- words, and “identifiers.” The abstract wasstock construction by the Bureau of Reclama- prepared as part of the Bureau of Reclamation’stion. During this period many of the largest program of indexing and retrieving the litera-penstocks in service today were designed and ture of water resources development. Theconstructed. descriptors were selected from the Thesauw Welded Steel Pmstocks was first issued in of Descriptors, which is the Bureau’s standard1949 under the authorship of P. J. Bier. Be- for listings of keywords.cause of the continuing interest in penstock Other recently published Water Resourcesdesign, the monograph has been revised and Technical Publications are listed on the insideupdated to incorporate present day practice. back cover of this monograph. iii
Contents PWC ... 111Report on Welded Steel PenstocksIntroduction ______________ _______ -- -__---------------_-__________ 1Location and Arrangement ____- _____--___--- ____- ____ --__-_- ____ 1Economic Studies ___________________________ -__-__-- ____--___ - .___ 5Head Losses in Penstocks ________________________________________- 5Effect of Water Hammer _______ _____ _____-- ____-_-_-- ____-- ____ - - 11 Pressure Rise in Simple Conduits _____________________ - ______ 12Pipe Shell __--_______-____-_______________________------- - _______ 14 Temperature Stresses ________________________________________ 17 Longitudinal Stresses Caused by Radial Strain __________-----_ 17 Beam Stresses _______________-________________________------- 17supports -- ----------_--------_----------------------------------- 19Expansion Joints ___________________ ____- _____________ ______ - - -- - 23Bends, Branch Outlets, and Wyes _________________________________ 26 Pipe Bends ____________-_____-_____________________---------- 26 Branch Outlets and Wyes _____________________ _____________ 27 - -Penstock Accessories _____-__________________________________----- 33 For Installation and Testing __________________________________ 33 For Operation and Maintenance ______________________________ 33Design of Piers and Anchors ______________________________________ 34 z General ___--_ ___________------------------------------------- 34 Support Piers __--_-----^------------------------------------ 34 Anchors ---------------------------^------------------------~-. 35
vi CONTENTSMaterials --____---__-_-_-_--_____________________~~~~-~-~~~~~~~~~ 35 Steel Plates ___---_-_-____--_-_--~-~-~~-~~---~--~~~~~~~~~~~~~~ 35 Flanges, Fittings, Valves, and Other Appurtenances _- ________ 37Fabrication ____----__________-_____________________-------------- 37 Structure and Arrangement _- ____- ____- _____ ----------__-__-_ 37 Nondestructive Inspection of Welds ___---_-_-_--_-__--_______ 39 Preheating and Postweld Heat Treatment _______ __________-_- 42Installation -_-__-__---_--__________________________-~~~-~--~~~~~~ 42 Handling __-_----_-__--___-______________________~~~-----~~-~ 42 Placing and Welding --__--__--_--_--___--------- _____________ 43 Hydrostatic Test -_-_-_-_--_--_----______________________---- 44Specifications and Welding Control _____ -__-_-_-__-__-_---_-______ 45 Specifications -___-___--_-____________________________-------- 45 Welding Control _- ______ ___________________________-_______ - - 45 Weld Tests ____-__---_-__----______________________-~~~~~~-~~ 45Corrosion Control for Penstocks ____--___- ______ ____-___-_-_---_-_ - 45A Selected Bibliographyrnd References _____-________-_________________________-------- 47Coder and Standards _________________ -- ____ -- ______ -__-_----_ 47Appendix -_----_---_-_------- _______-__----__-_-___- _______ -_-- 48Absract _---___-------_- _________________________________ -- ____ 51 LIST OF FIGURESNumber PSLW 1. The 30-foot-diameter lower Arizona and Nevada penstock and outlet headers were installed in two of the diversion tun- nels at Hoover Dam. The upper headers were installed in special penstock tunnels. The tunnels were not backfilled with the exception of the inclined portions leading from the intake towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2. At Anderson Ranch Dam, the 15-foot-diameter penstock and outlet header were installed in the diversion tunnel, which was not backfilled . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3. General plan and typical profile of 15’-O’-diameter penstocks at Glen Canyon Dam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4. Mass concrete of Kortes Dam encased the g-foot-diameter pen- stocks, which were installed as the concrete was placed . . . 4 5. The 15-foot-diameter penstocks at Shasta Dam were embedded in the concrete of the dam at the upstream ends and were exposed above ground between dam and powerplant . . . . . 4
CONTENTS viiNumbo Pans 6. The full length of the %foot-diameter penstock at Marys Lake Powerplant lies above ground . . . . . . . . . . . . . . . . . . . . . . . . , 7. Economic diameter of steel penstocks when plate thickness is a function of the head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Economic diameter of steel penstocks when plate thickness is a function of the head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , 9. Friction losses in welded steel pipe based on Scobey’s formula for 6-year-old pipe and nonaggressive waters . . . . . . . . . . .10. Losses for various values of 5 ratios and deflection angles up to900 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1011. Head losses in 90° pipe bends as determined for various R ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 512. Loss coefficients for divided flow through small tees and branch outlets as determined for various flow ratios &a. . . . . . . . . 11 Q13. Water-hammer values for uniform gate motion and complete closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1514. Equivalent stress diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1615. A graphical illustration of heads and stresses determined for the hydrostatic testing of the Shasta penstocks . . . . . . . . . 1816. The Shoshone River siphon crosses the river on a 150-foot span 2017. Moments and deflections developed in a pipe precisely full, using various types of supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2118. Formulae and coefficients for the computation of stresses in ring girders as developed for stiffener ring analyses . . . . . . . . . 2219. Formulae and coefficients for the computation of stresses in ring girders due to earthquake loads . . . . . . . . . . . . . . . . . . . . . . . 2320. Typical ring girder and column support . . . . . . . . . . . . . . . . . . . . 2421. Typical rocker support. The angle yoke is used only for aline- ment during grouting . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2522. Typical sleeve-type expansion joint . . . . . . . . . . . . . . . . . . . . . . . . 2523. Flexible sleeve-type expansion joint with two stuffing boxes used to permit longitudinal temperature movement and trans- verse deflection . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2524. Constant diameter bend with the radius of the bend five times the diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2625. Bend reducing in diameter from 9 feet to 8 feet, the radius equal to four times the smaller diameter . . . . . . . . . . . . . . . . . . . . 2726. Computation method for determining true pipe angle in a com- poundpipebend ... ....... ...... ...... .. .... ...... .. 2827. Loading diagrams for the development of reinforcement of branch outlets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2928. Loading diagrams for the development of reinforcement of wye branchesinpenstocks................................ 3029. Typical internal and external reinforcement for a branch outlet 3230. Installation of a piezometer connection in shell of penstock for turbine performance tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Report on Welded Steel Penstocks construction, and inspection of pressure vessels.Introduction Present design standards and construction A penstock is the pressure conduit between practices were developed gradually, followingthe turbine scrollcase and the first open water the advent of welded construction, and are theupstream from the turbine. The open water result of improvements in the manufacture ofcan be a surge tank, river, canal, free-flow welding-quality steels, in welding processestunnel, or a reservoir. Penstocks should be as and procedures, and in inspection and testinghydraulically efficient as practical to conserve of welds.available head, and structurally safe to preventfailure which would result in loss of life andproperty. Penstocks can be fabricated of LOCATION AND ARRANGEMENTmany materials, but the strength and flexibil-ity of steel make it best suited for the range of The location and arrangement of penstockspressure fluctuations met in turbine operation. will be determined by the type of dam, location The design and construction of pressure of intake and outlet works, relative location ofvessels, such as penstocks, are governed by ap- dam and powerplant, and method of riverpropriate codes which prescribe safe rules and diversion used during construction. At damspractices to be followed. Until a special pen- requiring tunnels for diversion of the river flowstock code is formulated, steel penstocks should during construction, the penstocks may bebe constructed in accordance with the ASME placed in the tunnels after diversion has beenBoiler and Pressure Vessel Code, Section VIII, discontinued and the intake of the tunnel hasUnfired Pressure Vessels, issued by the Ameri- been plugged. This arrangement was used forcan Society of Mechanical Engineers, herein- the 30-foot lower Arizona and Nevada penstockafter referred to as the ASME code. This code and outlet headers at Hoover Dam as shownis subject to periodic revision to keep it abreast in figure 1, and for the l&foot penstock headerof new developments in the design, materials, at Anderson Ranch Dam as shown in figure 2. 1
POWER PLANTFXGUXE l.-The SO-fooGdia?neter &now Arieona and Nevada penstock and outlet keadem were in&u&d in two of the diversion tunnels at Hoover Dam. The upper headere were installed in special penstock tunnels. The tunnels were not backfilled with the exception of the inclined portion leading from the intuke tower.
WELDED STEELPENSTOCKS 3 Outlet pipe No S----. used to provide the required watertightness in the concrete and at the contraction joints. Figure 4 shows the g-foot penstocks which are embedded in Kortes Dam. Penstocks embedded in concrete dams, en- cased in concrete, or installed in tunnels back- SECTION filled with concrete may be designed to transmit some of the radial thrust due to internal water pressure to the surrounding concrete. More P. I. Horimtol bend---’ Sta 1sto6.03 - El. 3810 generally, such penstocks are designed to with- stand the full internal pressure. In either case, PLAN the shell should be of sufficient thickness toFIWRE 2.-At Anderson Ranch Dam, the l&foot-d&am- provide the rigidity required during fabrica- eter penstock and outlet header were installed in the tion and handling, and to serve as a form for diversion tunnel, which wae not backwed. the concrete. Embedded or buried penstockFor low-head concrete dams, penstocks may be shells also should be provided with adequateformed in the concrete of the dam. However, stiffeners or otherwise designed to withstanda steel lining is desirable to assure watertight- any anticipated external hydrostatic or grout-ness. In large concrete dams which have both ing pressures. At Shasta Dam the upstreamtransverse and longitudinal contraction joints, portions of the 15-foot penstocks are embeddedsuch as Glen Canyon Dam, steel penstocks are in the dam, while the downstream portions are 3. Outlet popes “-% Penstocks PLAN Fxeuav s.-G’ener~Jplan and typical pro@ of I s’-
4 ENGINEERING MONOGRAPH NO. 3 -18’ Dia. air vent FIGURE 4.-Mass concrete of Kortes Dam encased the g-foot-diameter penstocks, which were installed as the concrete was placed.,-Main unit trashrack ‘--Penstock oir inlet ,-15-o” Dia. main FIGURE S.-The 15-foot-diameter pen- I unit pensfocks stocks at Shasta Dam were embedded in the concrete of the dam at the up- :Concrete anchor stream end8 and were exposed above ground between dam and powerplant. ‘-Line of excavation --I’exposed above ground, between the dam and Considering only the economics of the penstock,the powerplant, as shown in figure 5. At other the single penstock with a header system willplants, the entire length of the penstock may usually be preferable; however, the cost of thisbe situated above ground, as in figure 6, which item alone should not dictate the design.shows the %foot-diameter penstock at Marys Flexibility of operation should be given con-Lake Powerplant. sideration because with a single penstock sys- When a powerplant has two or more turbines tem the inspection or repair of the penstockthe question arises whether to use an individ- will require shutting down the entire plant. Aual penstock for each turbine or a single pen- single penstock with a header system requiresstock with a header system to serve all units. complicated branch connections and a valve
WELDED STEELPENSTOCKS 5 ECONOMIC STUDIES A penstock is designed to carry water to a turbine with the least possible loss of head consistent with the overall economy of installa- tion. An economic study will size a penstock from a monetary standpoint, but the final di- ameter should be determined from combined engineering and monetary considerations. An example would be an installation where the economic diameter would require the use of a surge tank for regulation, but a more economi- cal overall installation might be obtained by using a penstock considerably larger than the TYPICAL SECTION AT SUPPORT economic diameter, resulting in the eliminationFIGURH B.-The full length of the d-foot-diameter pen- of the surge tank. stock at Marys Lake Poweqdant lies above ground. Voetsch and Fresen (1) l present a method of determining the economic diameter of a pen- stock. Figure 7 was derived from theirto isolate each turbine. Also, the trashracks method, and figure 8 is an example of its use.and bulkhead gates will be larger, resulting in Doolittle (2) presents a method for determiningheavier handling equipment. In concrete the economic diameters of long penstocksdams it is desirable to have all openings as where it is economical to construct a penstocksmall as possible. The decision as to the pen- of varying diameters. This “step by step”stock arrangement must be made considering method requires considerable time but shouldall factors of operation, design, and overall cost be considered for final design for long pen-of the entire installation. stocks. Proper location of the penstock intake is im- All the variables used in an economic studyportant. In most cases the intake is located must be obtained from the most reliable sourceat the upstream face of the dam, which available, keeping in mind that an attempt isprovides short penstocks and facilitates opera- being made to predict the average values of alltion of the intake gates. In some cases variables for the life of the project. Specialthe penstock intake may be situated in an in- attention must be given to the “plant factor”,dependent structure located in the reservoir, as figure 7, as this item materially affects the cal-at Hoover and Green Mountain Dams, where culations.diversion tunnels or topographic conditionsinfluenced the arrangement. Regardless ofarrangement, the intake should be placed at anelevation sufficiently below low reservoir level HEAD LOSSES IN PENSTOCKSand above the anticipated silt level to allow anuninterrupted flow of water under all condi- Hydraulic losses in a penstock reduce thetions. Each intake opening is protected effective head in proportion to the length ofagainst floating matter by means of a trash- the penstock and approximately as the squarerack structure and is controlled by suitable of the water velocity. Accurate determinationgates. of these losses is not possible, but estimates can be made on the basis of data obtained from To prevent the development of a partial pipe flow tests in laboratories and full-scalevacuum during certain operating conditions, installations.penstock profiles from intake to turbine should, ‘Numbers in parentheses refer to literature cited in mxtlon, “Awhenever possible, be laid on a continuous Selected Bibliography and References”. at the end of thla mono-slope. mwh.
NOTATION a : Cost of pipe per lb., instolled, dollars. Ii = Weighted overage heod including woter 8 = Diometer multiplier from Groph 6. hommer. (based an design head ) b = Volue of lost power in dollorr per k wh. KS = Friction coefficient in Scobey’s formula (0.34). D = Economic diometer in feet. n = Ratio of overweight to weight of pope shell. e = Overall plant efficiency. Cl = Flow in cubic feet per second. (ot design head of turbine) eJ = Joint efficiency. r z Ratio of onnuol cost ta”a”( see explanotion) f = Loss factor from Groph A. sg = Allowable tension, p.s.i t = Weighted overage plate thickness(ot design head) for total length, t, 2 Averoge plote thickness for length L,. EXPLANATION AND EXAMPLE Example for penstock Q = I28 CFS ASSUME L,:22$ L,= 150; L,=(50’, L,ZlOO’ Dia.: 5’-0” Avg. plate =f H,=fJO’; H,=l20’, Hs=l70, H,= 2301i H,=240’ Value of power per kwh:‘0.005- b ” I ~~lL,t(~~Lz+~~)L,tlH~~L, _ Cost of steel pipe mstolled=sO.27/Ib =a 156.4’ L, t Lx + L, + L, Plont factor (see GraphA):0.75(f~0.510) 0,8M,~u225x15.71)~~4wx 15.71x2)10.02 z)o,5, Interest =3% n= 0.15 625 5 Depreciation = 0.005135 0.8 M.=‘0.02 per sq.ft. Weight/ foot=l57lx lO.2= 160.24 Ibs. L Gast/foot=l6a24x0.27=*43.26 r = 0.03 t0.005135+0.0119=0.0470 % 0.8 M.= sz o.ollg L,t,+L*t2+LJts’...+Lntn Kz -I %efsgejb 0.34x095x 0.510x15.000x0.90x0.00~~ 690t= or( I+n) 0.27x 0.0470 x I.15 L,+ Let Ls+...+ Ln t4 9: 1.285 (from GmphB);D’=3.7(from GmphG); Economic dia.: I.285 x3.7= 4.75 ( use 4’-10”dia.) NOTE: Calculated economic diameter should be very close to ossumed diameter as it is in this exomple. The problem should be reworked until this condition exists % o a M, ~ 0. 8 M. per foot Depreciation is bosed on the accumulation of on onnual smkrng fund eorning 3% Cast per foot of pipe interest required to replace 50% of the pipe in 45 years, The annuol 0.8 M = Cost of mointainmg interior ond exterior surface poyment required is equal to 0.005135 times the first cost. Oreo of pipe( inside surface oreo for embedded pipe, inside ond outside surface areo for exposed pipe ) per year. Depreciation = See Reclamation Monual, Vol. PI Fewer, page 2,4,llD. r : Interest t Depreciation l % 0. 8 M. FIGUREI 8.-Economic diameter of steel penstocks when plate thickness is a function of the head.
8 ENGINEERING MONOGRAPH NO. 3 The various head losses which occur between V =velocity of flow in feet per secondreservoir and turbine are as follows: D =diameter of pipe in feet. 1. Trashrack losses Values for I& vary for different types of pipe. 2. Entrance losses For new continuous interior pipe unmarred by 3. Losses due to pipe friction projections on the inside (as for butt-welded 4. Bend losses pipe) a value of 0.32 may be used. Scobey 5. Losses in valve and fittings. gives values of Ks for old pipe allowing for Losses through trashracks at the intake vary deterioration of the interior surface. To allowaccording to the velocity of flow and may be for deterioration a value of Ks=0.34 is usuallytaken as 0.1, 0.3, and 0.5 foot, respectively, for assumed in design for pipes whose interior isvelocities of 1.0, 1.5, and 2.0 feet per second. accessible for inspection and maintenance. The magnitude of entrance losses depends Friction losses for this value of KS, for pipesupon the shape of the intake opening. A cir- up to 10 feet in diameter, can be read from thecular bellmouth entrance is considered to be chart, figure 9. For pipes too small to permitthe most efficient form of intake if its shape is access for maintaining the interior coating aproperly proportioned. It may be formed in value of Ks=0.40 is usually assumed.the concrete with or without a metal lining at Bend losses vary according to the shape ofthe entrance. The most desirable entrance the bend and the condition of the inside sur-curve was determined experimentally from face. Mitered bends constructed from platethe shape formed by the contraction of a jet steel no doubt cause greater losses than smooth (vena contracta) flowing through a sharp- curvature bends formed in castings or concrete ;edged orifice. For a circular orifice, maximum however, there is no way to evaluate suchcontraction occurs at a distance of approxi- effects since data on actual installations aremately one-half the diameter of the orifice. very meager. Laboratory experiments on veryLosses in circular bellmouth entrances are small size bends with low Reynolds numbersestimated to be 0.05 to 0.1 of the velocity head. are not applicable to large size bends with highFor square bellmouth entrances, the losses are Reynolds numbers. When water flows aroundestimated to be 0.2 of the velocity head. a bend, eddies and secondary vortices result, and the effects continue for a considerable Head losses in pipes because of friction distance downstream from the bend. In sharpvary considerably, depending upon velocity of angle bends the secondary vortex motion mayflow, viscosity of the fluid, and condition of the be reduced by guide vanes built into the bend.inside surface of the pipe. Among the con- Thoma’s (4) formula is based on experimentsventional pipe flow formulae used for the made at the Munich Hydraulic Institute with computation of head losses, the Scobey, Man- 1.7-inch-diameter smooth brass bends havingning, and Hazen-Williams formulae are the Reynolds numbers up to 225,000, as shown onmost popular. For large steel pipe the Scobey the chart in figure 10, and is expressed as:formula is favored ; for concrete pipe, theManning formula ; and for cast-iron pipe in Ha=CL...................... (2)waterworks, the Hazen-Williams formula. 2g The Scobey formula(3), derived from ex- whereperiments on numerous steel pipe installations, H,, = bend loss in feetis expressed as follows: C =experimental loss coefficient, for bend H*=K+. . . . ..,.............. loss (1) V =velocity of flow in feet per second.in which The losses shown in figure 10 vary according HP= head loss due to friction in feet per to the R/D ratio and the deflection angle of 1,000 feet of pipe the bend. An R/D ratio of six results in the Ks = loss coefficient, determined experimen- lowest head loss, although only a slight de- tally crease is indicated for R/D ratios greater than
WELDED STEEL PENSTOCKS FRICTION LOSS - FEET PER 1000 FEET,URE 9-Fmktion losses in welded steel pipe based on Scobey’s formula for &year-old pipe and nonaggressive wat em.
IO ENGINEERING MONOGRAPH NO. 3 .26 .24; .I6Wi?E .I4go .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 A0 Fxoum lo.-LO88e8 for vari5248 value8 of g ratios and d43flection andes UP to 90.four. This relationship is also indicated by plished by the wicket gates of the turbines),the curves of figure 11, which were plotted only the loss which occurs at the full openfrom experiments with 90” bends, As the condition needs to be considered. Accordingfabrication cost of a bend increases with in- to experiments made at the University ofcreasing radius and length, there appears to be Wisconsin (5) on gate valves of l- to Z-inchno economic advantage in using R/D ratios diameter, the coefficient K in Equation (3)greater than five. varies from 0.22 for the l-inch valve to 0.065 Head losses in gates and valves vary accord- for the 12-inch valve for full openings. Foring to their design, being expressed as: large gate valves an average value of 0.10 is H,=K-& . . . . . . . . . . . . . . . . . . . . . . (3) recommended ; for needle valves, 0.20 ; andin which K is an experimental loss coefficient for medium size butterfly valves with a ratio ofwhose magnitude depends upon the type and leaf thickness to diameter of 0.2, a value of 0.26size of gate or valve and upon the percentage may be used. For sphere valves having theof opening. As gates or valves placed in pen- same opening as the pipe there is no reductionstocks are not throttled (this being accom- in area, and the head loss is negligible.
WELDED STEEL PENSTOCKS II Fittings should be designed with smooth and streamlined interiors since these result in the least loss in head. Data available on losses in large fittings are meager. For smaller fit- tings, as used in municipal water systems, the American Water Works Association recom- mends the following values for loss coefficients, K; for reducers, 0.25 (using velocity at smaller end) ; for increasers, 0.25 of the change in -Rough pipe velocity head ; for right angle tees, 1.25; and for wyes, 1.00. These coefficients are average values and are subject to wide variation for -Smooth pipe different ratios between flow in main line and branch outlet. They also vary with different tapers, deflection angles, and streamlining. 0 012345670 9 IO Model tests made on small tees and branch out- lets at the Munich Hydraulic Institute show that, for fittings with tapered outlets and de-FRIES ll.-Head bsoea in so0 pipe benda as &to+ flection angles smaller than 90” with rounded minsd fm uariuu.9 ratios. E corners, losses are less than in fittings having cylindrical outlets, 90” deflections, and sharp corners. (See figure 12.) These tests served as a basis for the design of the branch connec- tions for the Hoover Dam penstocks. EFFECT OF WATER HAMMER Rapid opening or closing of the turbine gates produce a pressure wave in the penstock called water hammer, the intensity of which is proportional to the speed of propagation of the pressure wave produced and the velocity of flow destroyed. Joukovsky’s fundamental equation gives the maximum increase in head for closures in time less than 2L/a seconds: AH=-!% . . . . . . ..F*!. . . . . . . . . . . . . . . (4) 8 in which AH =maximum increase in head a =velocity of pressure wave L=length of penstock from forebay to turbine gate v =velocity of flow destroyed g =acceleration due to gravity. From this formula, which is based on the elastic water-hammer theory, Allievi, Gibson,Fxoua~m-LO88 CO&i8Td8 for dbidd &HO thmwh Durand, Quick, and others developed inde- amall tees and breach tnd8t8 a.8 da- fW d pendent equations for the solution of water- 0488 jtOl8 Vf3tiO80". hammer problems (6). Q
ENGINEERING MONOGRAPH NO. 3 In his notes published in 1903 and 1913, in turbine speed regulatipn. A surge tank mayAlhevi introduced the mathematical analysis be considered as a branch pipe designed to ab-of water hammer, while M. L. Bergeron, R. S. sorb a portion of the pressure .wave while theQuick, and R. W. Angus developed graphical remainder travels upstream toward the fore-solutions of water-hammer problems which are bay. When located near the powerhouse, itmore convenient to use than the analytical provides a reserve volume of water to meetmethods. A comprehensive account of methods sudden load demands until the water column infor the solution of water-hammer phenomena the upper portion of the penstock has time tooccurring in water conduits, including graphi- accelerate. cal methods, was published by Parmakian (7). When the length, diameter, and profile of For individual penstocks of varying the penstock have all been determined, con- diameter, the pressure reflections at points of sidering local conditions and economic factors,change in diameter complicate the problem. the selection of a minimum closure time for the However, if the varying diameter is reduced turbine gates will require a compromise be-to a penstock of equivalent uniform diameter, tween the allowable pressure variation in thea close estimate can be made of the maximum penstock, the flywheel effect, and the permis-pressure rise. For penstocks with branch sible speed variation for given load changes onpipes, it is necessary to consider the reflection the unit.of pressure waves from the branch pipes and With reaction turbines, synchronous relief dead ends in order to determine the true pres- valves, which open as the turbine gates close,sure rise due to velocity changes. may be used to reduce the pressure rise in the As the investment in penstocks is often con- penstock. Reduction of pressure rise issiderable, they must be safeguarded against proportional to the quantity of water released.surges, accidental or otherwise. Surges of the As relief valves are usually designed to dis-instantaneous type may develop through charge only a portion of the flow, this portionresonance caused by rhythmic gate movements, is deducted from the total flow in computingor when the governor relief or stop valve is the reduced velocity and the correspondingimproperly adjusted. A parting and rejoining pressure rise.of the water column in the draft tube or ahasty priming at the headgate may also causesurge waves of the instantaneous or rapid type. Pressure Rise in Simple ConduitsAdjustments iw the profile of a penstock maybe necessary to prevent the development of a With instantaneous gate closure, maximumvacuum and water column separation during pressure rise in penstocks of uniform diameternegative pressure surges. As water-hammer and plate thickness occurs at the gate ; fromsurges occurring under emergency conditions there, it travels undiminished up the conduitcould jeopardize the safety of a penstock if they to the intake or point of relief. For slowerare not considered in the design, their magni- closures which take less than 2L/a secondstude should be determined and the shell thick- (L = length of penstock ; a = velocity of pressureness designed for the resultant total head. wave), the maximum pressure rise is trans-Stresses approaching yield-point values may be mitted undiminished along the conduit to aallowed. By using ductile materials in the point where the remainder of the distance topenstock, excessive surge stresses may be ab- the intake is equal to Ta/2 (T=time for fullsorbed by yielding without rupture of plates gate stroke), from which point to the intakeor welds. Design criteria for including the the pressure rise diminishes uniformly to zero.effects of water hammer in penstock and pump With uniform gate closure equal to or greaterdischarge line installations, as used by the than the critical time, ZL/a, the maximumBureau of Reclamation, is shown in table 1. pressure rise occurs at the gate, from which Surge tanks are used for reduction of water point it diminishes uniformly along the lengthhammer, regulation of flow, and improvement of the penstock to zero at the intake. An anal-
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 Emergsncu conditiona of operation Emarmncu wnditious +wt to be comideed as a basis for design I. In those instances where. due to a The bssic conditions to be considered as 1. Other Doesible emereency conditions of higher reservoir elevation. it is necessary WlergeneJT ODeration are as foIIows: operation are those during which certain to set the st.,DS on tbe main relay valve pieces of control equipment are assumed to 1. The turbine Denstock installation may for a slower rate of gate movement. the 1. The turbine gates may be closed at malfunction in the most unfavorable man-be werated at any head between the maxi- water hammer elTen3.a will be computed ner. The most severe emergency conditionmum and minimum values of the forebay foe this slower rata of gate movement any time by the action of the governor head. manual control knob with the main of o~aration which wiII yield the maximumwater surface elevation. relay valve. or the emergency solenoid head rise in a turbine Denstock installation device. will oeeur from either of the two following 2. The turbine eaten may be moved at 8. The reduction in head at various conditions of operation:any rate of steed by the action of the BOV- points along the penstock will be corn-emor head UD to a Dredatermined rate. or puted for the rate of gate opening which 2. The cushioning stroke will be as- sumed t.0 be inoperative. (a) Rapid &sure of the turbineat a slower rate by maneal control through is adually set in the governor in those gatesinIessthan2&seconds, (Lbthethe aorili relay vaIve. cases where it aDDears that the u,mfiIe of tbe Denstock is unfavorable. This mjni- a. If a relief valve is Dresent it, will be length of the Denatik and a is the 2. The turbine may be operating at any mum Dressure will then be used as a bqsis assumed to be inoperative.wte Dosition and be required to add or for normaI design of the pentik to in- wave velocity). when t& flow of waterdrop any or ail of its load. sure that subatmospheric Dressures will in the Denstock is a maximum. (The 4. The Bate traversing time will be maximum head rise in feet due to this not cause a penstock failure due to col- taken as the minimum time for which the 4. If tbe turbine penstock installation is IaDse. wndition of oDeration is 100 to 126eanipDed with any of the following Dres- governor is designed. times the water velocity in feet per sac-sure control devices it will be assumed that 9. If a surge tank is Drasent in the and. )these devices are properly adjusted and penstock system the upsurge in the surge 6. The maximum head including waterfunction in tbe manner for which the tank will be computed for the maximum hammer at the turbine and along the (b) Rhythmic opening and closing ofequipment is designed: length of the panstock will be computed the turbine gates when a complete cy- reservoir level condition for the rejection cle of gate owration is performed in of the turbine flow which correspondb to for the maximum reservoir head condi- (a) Surge tenks the rated output of the generator during tion for 5naI DWt gate closure to the -4L seconds. (Under extreme condIt,icms the gate transversing time which is ac- zero-gate position at the -imum gover- (b) Relief valves tually set on the governor. Unless an nor rate in 2& seconds. tie maximum head rise due to this con- (e) Governor control SDParatus overflow sDiIlway is provided the top d- a ft$) of OD-tiOn is twice the static (d) Cushioning stroke device evation of the surge tank will be deter- mined by adding a freeboard of 20 Dar 6. If a surge tank is present in the (e) Any other pressure control device. cent of the com~utd upsurge to the max- Since these conditions of operation re- Denstock system the upsurge in the surge mire a complete malfunctioning of the imum height of water at the highest tank wiII be eOmDUted for the maximum 6. Unless the actual turbine character- IlDSnrge. reservoir head condition for the rejection gowrnor control apDaratus at the most un-istics are known. the efieetive area of fnil gate turbine flow at the maximum favorable moment. the DrobabiIIty of obtain-through the turbine gates during the 10. The downsurge in the surge tank rate for which the governor Is designed. ing this t4pe of. oDeration is exceedingIymruimum rate of gate. movement will be will be e0m~ut.d for the minImum reser- The downsurge in the surge tank will be remote. Hence. these wnditioM will not. beUpk as * linear relation wxth resDect to voir level condition for a load addition computed for the minimum r-air head used as a basis for design. However. after from sDeed-no-load to the full Bate Do& condition for a fuI1 gate oDening from Se design has been eatabIiied from other tion during the sate traversing iime the speed-n*Ioad position at tbe maxi- considerations. it is desimbIe that the 6. The water hammer &ecta will be which is actually set on the governor. The mum rate for which the governor is de- stresses in the turbine scrdl case. ~enstock. computed on the basis of governor head bottom of the surge tank will be Iocatsd sign+. In determining the tom and bottom Bnd Dressme contrd devices be not in ax- action for the governor rate which is BE- at a distance of 20 per cent of the com- elevatmns of the surge tank, nothing will :ess of the ultimate bursting strength ofanally set on the turbine for speed regal& DUti downsurge b&w the lowest down- be added to the UPsurgea and downsurges ;he structures for these emergene~ con%-tion. If the r&w valve stoos are adinsted surm in the tank to safeguard against air for this -‘3EZX,CY eO&it&X, Of OD-- tiOns Of ODeratiOn.to Bive a slower governor setting than wtering the Denstock. tion.that for which the governor is designed,this rate shall be determined DriOr to 11. The turbine, pens&k. surge tank. 7. The turbine. Denstuck. surge tank. Droceeding with the design of turbine and other DRaWre control devices will be relief valve. or other control devices will penstock installation and later adhered to designed to withstand the conditions of be designed to withstand the above emer-at the Dower plant so that an economical normaI operation which are given above BemY wndltions of operation with a min- basis for designing the penstoek. sclDu with a minImum factor of safety of 4 to imumfa+rofsafetqof2288an WE=% etc.. Under ma-maI ODersting wndi- 5 based on the ultimata bursting or col- thgeh~mIbte bmxtmg or C0Sapaingtions can be established. laDsing strenpth. - w
14 ENGINEERING MONOGRAPH NO. 3 Ysis of pressure time curves shows that the static and water-hammer heads. Working maximum pressure rise is determined by the stresses which will assure safety under all ex- rate of change of velocity with respect to time. pected operating conditions should be used. Maximum pressure rise will develop in a pen- However, stresses approaching the yield point stock when closure starts from some relatively may be used in designing for emergency con- small percentage of full stroke so that some ditions. For penstocks supported on piers in finite velocity is cut off in a time equal to 2L/a open tunnels or above the ground, allowance seconds. should be made for temperature and beam The governor traversing time is considered stresses in addition to the stresses due to in- to be the time required for the governor to ternal pressure. The diagram shown in figure move the turbine gates from the rated capacity 14 permits a quick determination of equivalent position to the speed-no-load position. As the stresses if principal stresses are known. The rate of governor time is adjustable, it is im- diagram is based on the Hen&y-Mises theory portant that a minimum permissible rate be of failure, sometimes called the shear-distor- specified if maximum pressure rise in the pen- tion or shear-energy theory. The plate thick- stock is to be kept within design limits. ness should be proportioned on the basis of an Water-hammer conditions should be deter- allowable equivalent stress, which varies with mined for the unit operating at rated head and the type of steel used. The ASME code gives under maximum static head. The highest total maximum allowable tensile stresses for various head, consisting of static and water-hammer types of steels. heads, should be used for computing plate The hoop tension, S, in a thin shell pipe, due thickness of the penstock. to internal pressure is expressed as: R. S. Quick (6) simplified water-hammer computations by using a pipeline constant, K, s=* . .... .... . . . . . . . . . . . . . . . (5) and a time constant, N, in the equations in which (similar to Allievi’s) which determine pressure D=inside diameter of pipe in inches rise, or water hammer, resulting from instan- p=internal pressure in psi taneous closure. The chart in figure 13 shows t =plate thickness in inches the relative values of K and P (equal to e =efficiency of joint. h) for various values of N. Also in- Regardless of pressure, a minimum plate h ..I thickness is recommended for all large steel eluded is a chart which shows the velocity, a, pipes to provide the rigidity required during of the pressure wave in an elastic water column fabrication and handling. For penstocks the for various ratios of penstock diameter to desired minimum thickness for diameter, D, thickness. Figure 14 gives only the maximum may be computed from the formula: values of P for uniform gate motion and com- plete closure. It covers a range of closures &in= D+zo.. . . . . . . . . . . . . . . . . . . . . (6) 400 from instantaneous to 50 intervals, and a range A thinner shell may in some cases be used if of values of K from 0.07 to 40, which includes the penstock is provided with adequate stiff- the majority of practical cases. The nearly eners to prevent deformation during fabrica- vertical curve shows the limiting value for tion, handling, and installation. maximum pressure rise at the end of the first Joint efficiencies for arc-welded pipe depend time interval, 2L/a. Values of pressure rises on the type of joint and the degree of examina- to the left of this line attain their maximum tion of the longitudinal and circumferential values at the end of the first interval. joints. The ASME code stipulates a maximum allowable joint efficiency of 100 percent for double-welded butt joints completely radie- PIPE SHELL graphed, and of 70 percent if radiographic As has been stated, penstocks should be examination is omitted. Corresponding jointc designed to resist the total head consisting of efficiencies for single-welded butt joints with
EXPLANATION Cu. Ft. per sec. 0.6 0.5 Ok 0.3 0.2 0.10 0.09 E! 0.06 0.05 0.04 0.03 CHART SHOWING VELOCITY OF TRAVEL OF PRESSURE WAVE IN ELASTIC WATER COLUMN 0.02 Formula : a - - *=vyfTgbO.OlW - 7L- -NJ l-+-J- ’ ’ 007 0.1 0.2 0.5 IO 2 3 45 Values of Pipe - Line Constant K- $$ Where o - Velocity of Tmvel of. Pressure Wave. Ft. per Sec. 0 k- Bulk Modulus of Elasticity of Water- 294.000CHART SHOWING MAXIMUM PRESSURE RISE WITH UNIFORM GATE MOTION Lbs. per Sq. In.AND COMPLETE CLOSURE : BASED ON ELASTIC-WATER-COLUMN THEORY E = Younq’s Modulus for Pipe Walls = 29.400.000 Lbs. per Sq. In. approx. for Steel. NOTE:Ratio of Pressure Rise’h” to Initial Steady HeadrH~determined from relation 2 Kp~b~, 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
WELDED STEEL PENSTOCKS 17backing strips are 90 and 65 percent, respec- Steel on concrete (cradle supports) .0.60tively. If radiographic spot examination is Steel on steel-rusty plates . . . . . . . . .0.50used, allowable joint efficiencies are 15 percent Steel on steel-greased plates . . . . . . .0.25higher than for nonradiographed joints. Steel on steel-with two layersPostweld heat treatment of welds is required of graphited asbestos sheetsif the wall thickness exceeds a specified mini- between . . . . . . . . . . . . . . . . . . . . . . . .0.25mum thickness. Joint efficiencies and radio- Rocker supports-deteriorated. . . . . .0.15graphic inspection procedures used by the For expansion joints a frictional resistanceBureau of Reclamation conform to the require- of 500 pounds per linear foot of circumferencements of the ASME code. was determined by test and may be used for Specifications issued by the Bureau of the computation of longitudinal forces in aReclamation for construction of penstocks pipeline.usually require that they be welded by arigidly controlled procedure using automaticwelding machines, that the longitudinal andcircumferential joints be radiographed, and Longitudinal Stresses Caused bythat either the individual pipe sections or the Radial Strainentire installation be tested hydrostatically. Since the head varies along the profile of apenstock in accordance with its elevation and Radial expansion of a steel pipe caused bypressure wave diagram, it is customary to plot internal pressure tends to cause longitudinalthe heads and stresses as shown in figure 15. contraction (Poisson’s ratio), with a corre-The total head at each point along the profile sponding longitudinal tensile stress equal tocan then be scaled off and the plate thickness 0.303 of the hoop tension. This is true, pro-computed accordingly. vided the pipe is restrained longitudinally. This Other stresses which must be considered in stress should be combined algebraically withaddition to hoop stresses are as follows: other longitudinal stresses in order to deter- Temperature stresses mine the total longitudinal stress. Longitudinal stresses which accompany radial strain (related to Poisson’s ratio) Beam stresses. Beam Stresses When a pipe rests on supports it acts as aTemperature Stresses beam. The beam load consists of the weight of the pipe itself plus the contained water. For a steel pipe fully restrained against Beam stresses at points of support, particu-movement, the unit stress per degree of tem- larly for longer spans, require special consider-perature change is equal to the coefficient of ation. This matter is discussed in the sectionexpansion of the steel multiplied by its on design of supports.modulus of elasticity, or 0.0000065 X 30 X lo6 = Based on a preliminary design, various195 psi per degree of temperature change. For combinations of beam, temperature, and othera pipe having expansion joints and being free stresses should be studied so as to determineto move on supports, the longitudinal tempera- the critical combination which will governture stress is equal to the frictional resistance the final design. It may be necessary orbetween supports and pipe plus the frictional desirable to reduce the distance between an-resistance in the expansion joint. The resist- chors for pipes without expansion joints toance at supports varies according to the type reduce the temperature stresses or to shortenof support and its condition. The following the span between supports ti reduce beamaverage values of coefficients of friction have stresses. For penstocks buried in the ground,been determined by tests: and for all other installations where the
m t---Test pressureline - El. 1460 5- )- i- )- I- )- I ‘I32-k i&t----...s19”Byposicowi.:- - 1; f ” +---uownsrreom mce bI uWnIntOk-El. bl!j-: 2’ n.1 Plate thicknessesvary from i’to 2b’ I Efficiency of joints : 99 X -.-. FIG- 16.-A graphical illustration of heada and stresses de temnined for the hydrostatic testing of the Shasta pen&o&.
WELDED STEELPENSTOCKS 19 temperature variation in the steel corresponds elastic theory of thin cylindrical shells (9).to the small temperature range of the water, The shell will be mainly subjected to direct expansion joints may be eliminated and all beam and hoop stresses, with loads being temperature stresses carried by the pipe shell. transmitted to support rings by shear. Be- For a pipe without expansion joints and an- cause of the restraint imposed by a rigid ring chored at both ends in which the beam stresses girder or concrete anchor, secondary bendingare negligible, the longitudinal stresses may stresses occur in the pipe shell adjacent to thebe kept within allowable limits by welding the ring girder or anchor. Although this is only alast girth joint in the pipe at the mean temper- local stress in the shell, which decreases ature of the steel. A procedure similar to this rapidly with increasing distance from thewas used for the penstock and outlet headers stiffener, it should be added to the other longi-at Hoover Dam where expansion joints for the tudinal stresses. For a pipe fully restrained,30-foot pipe were not considered to be feasible. the maximum secondary bending stress is: In this case it was desired to eliminate alllongitudinal tension in the penstock because %=1.82+. . . . . . . . . . . . . . . . . . . . . (7)the pinned girth joints had an efficiency of in whichonly 60 percent in tension but 100 percent in p =pressure in psicompression. The lowest anticipated service r= radius of pipe in inchestemperature was.46” F. In order to reduce the t=plate thickness in inches.length of a penstock section between anchors This secondary bending stress decreases withto that corresponding to a temperature of 45” any decrease in restraint.F, mechanical prestressing by means of jacks If use of Equation (7) results in excessiveapplied at the periphery of the pipe was re- longitudinal stresses, it may be necessary tosorted to. A compressive force corresponding increase the pipe shell thickness on each sideto the difference between the erection tempera- of the stiffener ring for a minimum length ofture and the lowest service temperature was 3/q, in which q=1.236/lx At this distanceapplied. After welding the final closing joint from the stiffener ring, the magnitude of thethe jacks were removed, leaving the penstock in secondary stresses becomes negligible. Sec-compression. At 46O F. the longitudinal stress ondary bending stresses at edges or cornersis then zero, and at higher temperatures the of concrete anchors may be reduced by cover-penstock is in compression. ing the pipe at these points with a plastic material, such as asbestos -or cork sheeting, prior to concrete placement. This will alsoSUPPORTS protect the edges or corners of the concrete against cracking or spalling. Modern trend in design requires that steel Pipes designed in accordance with the pre-pipes located in tunnels, above ground, or ceding principles may be supported on longacross gullies or streams be self-supporting. spans without intermediate stiffener rings.This is possible in most cases without an in- Figure 16 shows the lo-foot S-inch Shoshonecrease in plate thickness except adjacent to River siphon, which has a 150-foot span. Thethe supports of the longer spans. If the pipe length of the span to be used on any particularis to function satisfactorily as a beam, defor- job is usually a matter of economy. Very longmation of the shell at the supports must be spans, such as shown in figure 16, are econom-limited by use of properly designed stiffener ical only under certain conditions, as in therings or ring girders. A long pipeline with a crossing of rivers or canyons where the con-number of supports forms a continuous beam struction of additional piers, which shorterexcept at the expansion joints, where its con- spans would require, is not feasible.tinuity is lost. Ring girders prevent large de- If continuous pipelines with or without ex-formation of the pipe shell at the supports. pansion joints are supported at a number ofStresses may therefore be analyzed by the points, the bending moments at any point
20 ENGINEERING MONOGRAPH NO.3 FIGURE 16.-Tke Shoshone River siphon cro8ses the river on a 150-foot span.along the pipe may be computed as in an 4. By stiffener rings which carry the loadordinary continuous beam by using applicable to concrete piers by means of supportbeam formulae. Spans containing expansion columns.joints should be made short enough that their As the static pressure within a pipe variesbending moments will correspond to those of from top to bottom, it tends to distort thethe other spans. Expansion joints should be circular shape of the shell. This is especiallyplaced at midspan where deflections of the two pronounced for thin-shelled large-diametercantilevered portions of pipe are equal, thus pipes under low head or partially filled. Thepreventing a twisting action in the joint. weight of the pipe itself and the weight of A pipe can be designed to resist safely the backfill, if the pipe is covered, also cause dis-bending and shear forces acting in a cross- tortion of the shell.sectional plane by several methods, as follows: Depending on the method of support, 1. By sufficient stiffness in the shell itself stresses and deformations around the circum- 2. By continuous embedment of part of the ference of a filled pipe will assume various periphery of the pipe patterns as shown in figure 17. These dia- 3. By individual support cradles or saddles grams indicate the best location for longitudinal
WELDED STEEL PENSTOCKS 21 S, in the ring section. By adding the direct, bending, and tensile stresses in the ring due to internal pressure in the pipe, the total unit stress in the inner and outer fibers of the ring may be determined. Moments Deflrct,onr In installations subject to seismic disturb- ances, the severity of the earthquake shocks should be ascertained from local records and considered in the design of the supports. Un- saddle wpport Moments less the project is located close to a fault zone, a horizontal seismic coefficient of 0.1 to 0.2 of the gravity load is adequate for most areas in the United States. Stresses due to earthquake loads for various points along the periphery of the ring girder may be computed from the Rmg Girder and Poor Support Moments Deflectwns equations and stress coefficients given in figureFIGURE 17.-Momenta and deflections developed in a 19. In determining the required section for a pipe precisely full, using various types of supports. ring girder, stresses so computed should be added to the stresses caused by static loads. A typical ring girder and column supportjoints in pipe shell and joints in stiffeners to designed for an S-foot penstock with a spanavoid points of highest stress or largest defor- of 60 feet is shown in figure 20. The girdermation. The saddle and the ring girder with consists of two stiffener rings continuouslycolumn supports are widely used. The one-point welded to the pipe on both sides and tiedsupport should not be used for a permanent in- together with diaphragm plates welded be-stallation. It is included merely to illustrate its tween the two rings. Two short columnsflattening effect on an unstiffened pipe. consisting of wide-flange l-beams are welded For the ring girder and column-type support, between the rings to carry the load to thethe support columns are attached to the ring rockers by means of cast-steel bearing shoes.girders eccentrically with respect to the cen- A typical rocker assembly is shown in figuretroidal axis of the ring section so as to reduce 21. It consists of an Winch cast-steel rocker, athe maximum bending moment in the ring sec- 3-l/2-inch steel pin with bronze bushings, and ation. In computing the section modulus of the cast-steel pin bearing. The rockers are kept inring girder, a portion of the adjacent shell may alinement by means of a steel tooth bolted to thebe considered as acting with the girder. The side of each rocker and guided between twototal length of the shell thus acting is: studs threaded into the bearing shoe of the sup- l=b+1.56ds . . . . . . . . . . . . . . . . . . . . (8) port. The two pin bearings transmit the load to in which b is the width of the ring girder (see the concrete pier. After being positioned infigure 18) and r and t are as defined in Equa- accordance with a temperature chart so as totion (7). Essential formulae and coefficients provide effective support for the range offor the computation of stresses in ring girders temperature anticipated, they are grouted intoare given in figure 18. These formulae and the top of the pier as shown in figure 21. Thecoefficients were developed from the stiffener adjustable steel angle yoke shown in figure 21ring analysis for the Hoover Dam penstocks. is used only during erection and grouting,The table gives stress coefficients, Kl to K6, after which time it is removed.inclusive, for various points around the cir- Thin-shelled pipes, when restrained longi-cumference of the ring. These coefWents tudinally, are subjected to buckling stressesare to be inserted in the appropriate equations because of axial compression. The permis-shown for the determination of direct stress, sible span between supports is limited by theT, bending moment, M, and radial shear stress, stress at which buckling or wrinkling will