Design criteria for exposed hydro penstocks

Mot~rrerrl El~gilleeril~g C O I ~ P [ I I I ~ , Limited, P.O. Box 6088, Srariotl ' ' A ' ' . Motzrreal, P.Q., Crrt~rrda H3C 328 Received October 20, 1977 Accepted March 17, 1978

At present there are no national codes for the design of exposed hydro-electric penstocks. Thus an engineer must either make reference to other national codes for- similar work, such a s the American Society of Mechanical Engineers boiler and pressure vessel code or the American Water Works Association Standard for steel water piping, or he must write his own code and is then faced with the decision of having to select design criteria that must cover a wide range of steels; different operating and waterhammer conditions; a wide range of quality control proce- dures used in manufacture and erection of the penstock; and different types of penstocks, isostatic where the stresses can be calculated with precision, and hyperstatic where the stress calculation is more imprecise. This paper discusses design criteria, factors of safety, and corre- sponding quality control procedures that can be used for either isostatic or hyperstatic penstocks using mild, intermediate. or high strength steel for penstocks supplying reaction of impulse turbines.

Presentement, il n'existe pas de reglements nationaux pour le calcui de conduites fol-cees exposees qui sont utilisees dans les projets hydroelectriques. C'est pourquoi I'ingenieur doit se refkrer a des normes pour ouvrages similaires, comme Boiler and pressure vessel code par I'ASME et le Sta~~drirclfvrsteel waterpipe de I'AWWA, ou encore ecrire ses propres normes. I1 doit par I;I suite choisir les crittres de calcul qui doivent s'appliquer i une large gamme d'aciers, i diffirentes conditions d'exploitation et divers types de coups de belier, h une multitude de procedes de contr6le de la qualite i la fabrication et i la mise en place de la conduite forcee. e t a differents types de conduites, isostatiques lorsque les contraintes peuvent etre determinees avec precision, ou hyperstatiques lorsque la determination des contraintes est plus imprecise. Cet article porte sur les criteres de calcul, les coefficients de securite et les procedes de contrble de la qualite correspondants qui peuvent 611-e utilises pour les conduites forcies isostatiques ou hyperstatiquesenacier dedifferentes nuanceset destineeshalimenter des turbinesi reaction ou i impulsion. Can. 1. Civ. Eng., 5.340-351 (1978)

Introduction Quality Control Only 30 years ago liiost structural and plate steels Within a steel mill quality control standards are

in common use on hydro power penstocks had a established by national codes and need no further yield point in the region of 193-248 MPa (1 MPa = discussion. However, quality control standards fo r 145.04 psi). Now we have a multiplicity of steels with fabrication and erection of penstocks are not cover- yield points ranging fro111 206 to 690 MPa, with the ed except in part by such standards as the American design engineer having the problem of deciding which Society of Mechanical Engineers (ASME) boiler steel should be used in a particular application. and pressure vessel code. The 'weak link' in any Furthermore, since tliere are often advantages in penstock lies in the welding of the lo~igitudi~ial seams. using a high strength steel, or even a range of steels It is obvious that in order to make full use of the in one penstock, a consultant can no longer design a steel strength, the weld must be equal to or stronger penstock without having an intimate knowledge of than the parent metal. For this reason any quality steel purchase and fabricating costs. Since steel control procedure must be aimed a t obtaining a costs change for each grade of steel, and since 1 0 0 z weld joint efficiency. fabrication costs vary depending on plate thickness, Welding of mild steels is a relatively simple pro- coliiplexity of welding, and shop and site erection cedure. However, welding difficulties increase in conditions, it is no longer possible for a consultant proportion to the yield strength of the steel, so that to undertake the detailed design of a penstock and for high strength quenched and tempered steels, pre- expect to arrive at the most economic solution. heating of the steel, use of low hydrogen electrodes, Instead a consultant must write a performance type and storage of these electrodes in ovens are all specification that covers quality control, design con- necessary measures required t o achieve a full ditions, allowable stresses, and type of penstock, so strength weld. that contractors can bid on the work, and the bids There are several approaches to quality control of call be assessed on the basis of cost. welding on a penstock. In addition to testing of

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GORDON 34 1

welds, these are: (i) pressure test and no radi- ography; (ii) radiography of all welds and no pressure test; (iii) partial pressure test and radiography.

Pressure testing of a penstock at the site is time consuming and expensive, often requiring larger anchor blocks to resist the test forces. Since the test pressure varies throughout the length of the pen- stock, the penstock must be divided into short lengths, each of which must be capped and pumped full of water. Accordingly, it is preferable to rely on full radiography and only pressure test penstock bifurcations, the design of which is more complicated.

However, there is one exception. Where the pen- stock can be delivered to the site in full cans, the penstock ~nanufacturer may have a factory test facility where every can is pressure tested. In such a case, field welding is only required on the circum- ferential welds that are not stressed in the same manner as the longitudinal welds. Some penstocks have been built where these welds were not radio- graphed; however, the steel was of intermediate strength. Where a h ~ g h strength steel is used, radi- ography of at least four points on the circum- ferential weld, including every T-weld junction, should be mandatory. If a deficiency shows up, then the entire circumferential weld should be radio- graphed. Furthermore, in order to verify the welder's qualifications, it is preferable to fully radiograph the first three circumferential joints made by each welder. Procedures for radiography and interpreta- tion of radiographic negatives have been well estab- lished by the ASME boiler code.

Where automatic welding machines are used on the longitudinal welds, runon and runoff tabs are required at each end of the can. The length of these tabs should be increased by about 20 cm to serve as samples for testing by the engineer. Each of these samples should be marked with the penstock call number and sent to a laboratory for tensile testing. At the start of fabrication, tensile tests should be undertaken for every welding machine, until it is proved that consistent results meeting the strength criteria are attained. The tests should be repeated for each change in plate thickness. However, for the higher strength steels, where welding is more diffi- cult, all runon and runoff tabs should be tested, since the weld strength is more susceptible to changes in amperage, voltage, and even the ambient temperature.

Recently, due to the cost, and due to the interrup- tion of the work schedule required by radiography, particularly where a high strength source must be used for thick plates, contractors have been re- questing the substitution of ultrasonic testing for radiography. There are two problems associated

with ultrasonic testing. One is that it requires intense continuous concentration on the task by the opera- tor, with only a few secoilds distraction required to miss a flaw. The other is that there is no perinanent record available of the testing operation. For these reasons it cannot be regarded as providing the same degree of quality control as radiographic inspection. Ultrasonic testing rnay be used on the transverse seams of a penstock, but for the highly stressed longitudinal seams, radiography or pressure testing is mandatory in order to prove the weld quality.

Design Conditions The most important design condition for a pen-

stock is the hydrostatic water pressure within the penstock, and the associated hydrodynamic o r waterhammer pressure. The waterhammer pressure within a penstock varies a s the flow changes, with higher waterhammer pressures being caused by more abrupt changes in flow. There are two conditioils that must be considered in the design, namely, waterhaminer pressures due to normal changes in flow and waterhammer pressures during an emer- gency. Furthermore, since controls o n a turbine are different in reaction turbines and impulse turbines, the type of turbine must also be considered in establishing the design criteria (Smith 1961).

In a reaction turbine, it is current practice t o design for a nornlal waterhammer in the region of 25-5017, above static pressure, except where a syn- chronous bypass valve or pressure relief valve has been provided, in which case the waterha~n~ller pressure is limited to around 15-25x above normal. However, as will be established later, a normal waterhammer pressure of 25% above static pressure should be considered a minimum, since no saving in penstock steel will be achieved by adopting a lower figure. The limiting value of the waterhammer, between 25 and 5017, above static pressure, to be used in design will depend on an economic study. Design for a normal waterhammer in excess of 50%, above static pressure is not advisable since it is usually associated ki th speed regulation difficulties.

For an irnpulse turbine, where the needle valves have different opening and closing times, the unit can achieve adequate governing characteristics by means of rapid opening and slow closing of the needles, while the speed rise on load rejection is limited by the deflectors. I n this case, it is customary to design for a normal waterhamn~er in the region of 15-25%, with 25% being the recommended minimuln figure, since as will be shown later, the lower 1517, waterhammer will not reduce the weight of penstock steel. Furthermore, in order to limit the water- hammer t o 15% above static water pressure, very

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342 C A N . J . CIV. ENG. VOL. 5 . 1978

slow needle-valve closing tiines are required, which proxiinately proportional to gate opening, velocity are not always coinpatible with the fast needle open- and time can be related as follows: ing times necessary for unit startup and load acceptance.

Establishing a design value for the einergency waterhammer condition presents a greater problem. There is no current practice that can be used as a guideline, and opinion differs as to the minimuill value that should be used.

Arthur and Walker (1970) recoinillend a con- dition that postulates an inoperative governor cushioning stroke and part gate closure in 2Llo seconds at the maximum rate of gate movement (L = conduit length, rr = pressure wave velocity). Under such conditions, the maximum waterhammer will occur when the wicket gates in a reaction turbine move at their most rapid rate, and the wave return period is the longest. A preliininary design value (which must be checked for the actual pen- stock velocity and governor time selected) for the emergency waterhaminer can therefore be obtained from the limiting values of these two conditions.

The maximum allowable rate of wicket gate movement is obtained when the penstock is design- ed for a large waterhanlmer under normal wicket gate closure conditions. Since, based on the fore- going, most penstocks are designed for a water- hammer of between 25 and 50% above maximum static water level, the higher waterhamiller of 50% will give the faster closure rate, for which a close approximation of the wicket gate closure time can be obtained from the followiilg formula quoted by Brown (1 958).

where: t, = effective governor time; g = accelera- tion due to gravity; /I = head; V = water velocity; L = penstock length.

In a hydro development with a reaction turbine, the maximurn length of penstock is about four tiines the head, assuming, for this discussion, that long penstocks where relief valves and vernier stabilizers are used to control waterhamnler are not considered. Thus, for the longest pressure wave return time,

Substituting in [I], [31 t, = 1 0 ~ / g

The pressure wave return time interval t can also be rewritten as

With no cushioning, the rate of gate movement is constant and, since velocity in the penstock is ap-

[51 A V/ v = ~ ~ j ~ , The change in velocity in the pressure wave return

time is thus

[61 A V = VAtlt, The waterhaminer caused by gate closure in the

wave return time is given by

[71 All = aA l//g Substituting, with At = t,

C8l VAt al/ 811 g All = n ---- - = 0.811 gte g a 1 0 V

Thus, waterhainmer upon loss of cushioning from a part gate closure in time 2L/n will be limited to a maximum of about 80% above static water pressure.

Unfortunately, there have been several occur- rences when malfunctions of equipinent have caused water pressures in penstocks to fluctuate in a har- monic pattern, with the surge pressure varying from zero head to 100% above static, as reported by Jaeger (1963). Such resonant pulsations have oc- curred with sufficient frequency to make it advisable that allowances be made for them in design of the penstock. Harmonic pulsation can be caused by such minor colnponents as a vibrating penstock valve seal, as at Bersimis, Canada, reported by Abbott et rrl. (1963), or a governor pilot valve with incorrect porting, as a t Chururaqui, Bolivia, de- scribed bv Gordon (1 970).

Accordingly, it is proposed that the minimuin emergency waterhammer condition should be a surge equivalent to 100% of the static pressure on the unit.

There are other emergency conditions that should be examined, such as slain closure of a single needle valve in an impulse unit, which could produce water- hammer pressures in excess of twice static. On large multi-jet pelton units this is not often a problem. The instantaneous valve-closure waterhaininer can be obtained from [7] and, allowing for a sound wave velocity of 1000 m/s, the instantaneocs waterhanlmer pressure becomes 100V, where V is the velocity in the penstock prior to slam closure of the needles. The minimum head cn an impulse unit is in the region of 300 in; hence, substituting these values into [7], an emergency waterhainmer equal to static head would be caused by a 3 m/s change in velocity. Impulse unit penstock velocities are usually in the region of 9 m/s; hence reduction of velocity by one third or 3 m/s would cause a 100% waterhamrner surge. Only one needle can slam closed at any one time. Hence pelton units with 3 or more needles will have a 113 o r

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GORDON 343

less instantaneous reduction in flow upon a needle failure, producing a waterhammer equal to or less than static head. On the other hand, small pelton units with only one or two needles will have a corres- pondingly higher waterhammer surge, perhaps in excess of 100% static head. If so, then this higher emergency waterhammer head should be considered in design of the penstock.

The design levels for normal and emergency waterhammer in an exposed penstock are illustrated schematically in Fig. 1.

In addition to the stresses caused by water- hammer, there are other stresses due to temperature, supports, and rim bending that must be added to the hoop tension stresses to produce the maximum combined stress. The calculation and combination of these other stresses have been well established for conventional isostatic penstocks (where the penstock is supported on saddles or ring girders, and contains an expansion joint between anchors) and is not discussed further.

Allowable Stresses for Isostatic Penstocks Prior to discussing stress levels in penstock steels,

it should be pointed out that, due to modern quality control of welding, it is customary to assume a 1007, weld joint efficiency (Hornberger 1965).

One of the aims in establishing allowable stress levels is to have all the different strength steels stressed to the same degree under the same normal design conditions, and to have the same percentage increase in stress under emergency waterhammer conditions. If this can be attained, there should be no change in the governing design condition, resulting in the minimum weight of steel and hence lowest cost.

As a guide in establishing stress levels, reference should be made to codes developed by national societies and other agencies. European codes, as reported by Eberhardt (1965), relate the allowable design stress to the yield point of the steel. For steels having a yield point below about 300 MPa this method of establishing design stress is adequate. However, for high strength steels the design stress should be related to both the yield and the ultimate stress of the steel, due to the smaller relative differ- ence between these figures, as will be established in the following discussion.

The yield point of steel is currently the most common measure of steel strength. The range of steels now available with yield points from 200 to 690 MPa can be divided into three groups: (i) mild steels comprising steels having yield strengths to -275 MPa; (ii) intermediate strength steels comprising steels having yield strengths from -275 t o -520

- -

ABOVE 2 OH D E S I O W P R E S S U R E F O R EYLRBENCY W A l E R H A ' d Y E R I U P U L S E U N I T S W I T H I o r 2 J E T S

- - 4 2 OH (.IN 1 0 E S I . N P R E S S U R E / 1 FOR EMERQENCY WATERHAMMER I U P U L S E AND R E A C T I O N U N I T S --(

FIG. 1. Sche~iiatic of penstock design conditions.

MPa; (iii) high strength steels comprising steels having yield strengths from - 520 to > 690 MPa.

The intermediate strength steels have been de- veloped over the past 15 years and offer the advan- tages of good resistance t o brittle fracture and easy weldability. The high strength steels are quenched and tempered in the manufacturing process, hence require very careful quality control o n welding.

In addition to the yield point, a~lother measure of strength is the tensile stress level at rupture. Table 1 lists the yield and tensile stress for 40 steels common- ly used in penstocks from I I countries. Figure 2 shows the relationship between yield and tensile stress for these steels. Examination of these data will indicate that the remaining strength beyond yield is far greater in mild steels than in high strength steels, being about 170 MPa above yield point for the mild steels, reducing t o about 110 MPa above yield point for the high strength steels. As a per- centage, these figures represent a 707, increase over yield a t tensile stress for the mild steels, reducing t o only 17% for the high strength steels. This lower 'reserve strength' beyond yield for high strength steels must be taken into account when selecting design stress levels.

The United States Bureau of Reclanlation (USBR) has established criteria for isostatic pen- stock stresses related t o both yield and tensile stress, as described by Arthur and Walker (1970). These are shown in Table 2.

Based on the previously established 2 5 x minimum normal waterhammer and 1007, minimum emer- gency waterhainmer criteria, the foregoing stress criteria are such that for a normal condition the

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344 CAN. J . CIV. ENG. VOL. 5 . 1978

TABLE 1. Penstock steels, elastic limits, and breaking strengths

Country Specification No.

Minimum Minimum yield tensile

Steel grade (MPa) (MPa) Australia

Austria

Canada

France

Germany, Federal Republic of

Italy

Japan

Switzerland

USA

Yugoslavia

A-135-1965 A-135-1965 A-151-1966 ALDUR ALDUR ALDUR CSA G40.21, 1976 CSA G40.21, 1976 CSA G40.21, 1976 CSA G40.21, 1976 CSA G40.21, 1976 CSA G40.21, 1976 C F 24 C F 36 DIN 17100 DIN 17100 DIN 17100 DIN 50-04913 2-210 2-210 2-210 2-210 Idrotub Idrotub Idrotub JISG 3106-SM JISG 3106-SM

-

BH 24 K HOAG 29 BH 36 K ASTM A662-74a ASTM A662-74a ASTM A633-75 ASTM A633-75 ASTM A533-76 ASTM A533-76 ASTM A533-76 A ST 52 ST 52 cbv

. A B -

50165 58/72 58 38 T 44 T 50 T 60 T 70 T

loo Q -

-

RST 34-2 RST 37-2 RST 42-2

B 55 60 65 70 48 58

56/40 50 B 41 B

WEL-TEN-60 -

-

-

A B

C, D E 1 2 3 -

-

allowable stress will always be controlled by the 33.3% tensile stress value, and for the einergency condition the controlling stress will be 100% of yield for the mild steels, gradually shifting to 66.6% of tensile stress for the high strength steels, as illus- trated in Fig. 3.

In a high head penstock for a reaction turbine, where the design head may vary from a few metres at the intake to over 800 m at the powerhouse, several steels would be used, from a mild steel in the upper reaches, where minimuin thickness is set by erection requirements rather than structural strength, to an intermediate strength steel in the middle reaches, and finally to a high strength steel in the lower levels; use of the USBR criteria would result in some sections of the en stock having a greater capacity for emergency stresses than others. Table 3

illustrates this point. It will be seen that the mild steel can withstand a 64% increase in stress during an emergency, whereas the high strength steel can with- stand a 100% increase.

In order to have all steels stressed to the same degree under the same design conditions, a slight modification of the USBR standards outlined in Table 2 will be required as shown in Table 4.

Using these criteria, the penstock illustrated in Table 3 would now have the stress levels indicated in Table 5. As shown, the emergency stress level is a constant 60% over the normal stress level.

The relationship between normal and einergency stress levels based on yield and ultimate stresses is illustrated in Fig. 4, -which can be compared with Fig. 3.

The design conditions and stress levels proposed

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0 0 100 200 300 400 500 600 700

M I N I M U M Y I E L D - MPa-

FIG. 2. Yield and tensile strength relationship in penstock steels.

TABLE 2. USBR penstock design criterla 700

Allowable stress not to exceed

Deslgn condition % yield % tensile 600

Normal 66 6 33.3 Intermittent 80.0

m

44.4 T Emergency 100.0 6 6 . 6 z 500

"3 "3 u x r

herein will result in a penstock that, when used for a multi-jet impulse turbine, will be stressed close to the 400 maximum permissible level under both normal and emergency conditions. This is illustrated in Table 6. : If a lower normal waterhammer is selected for the 5 300 design, the emergency waterhammer will become the governing condition and there will be no saving in the weight of steel. ZOO

Penstocks supplying reaction turbines will be able to accept more than twice the static emergency pressure, owing to the higher normal waterhammer

loo pressure. In penstocks designed for a normal water- ZOO 300 400 500 600 700 hammer pressure equal to 1.5H, the emergency Y I E L D STRESS I N MPa stress level at 60% above normal will permit an FIG. 3. USBR allowable design stress criteria.

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346 CAN. J . CIV. ENG. VOL. 5 . 1978

TABLE 3. Comparison of design stresses - allowable stress (USBR criteria)

Normal condition Emergency condition Increase

0.333 0.66 0.666 1 .O emergency Steel tensile yield tensile yield above normal

designation (MPa) (M Pa) (M Pa) (MPa) (%I ASTM-285C 126" 136 252 207" 64 CSA G40.8B 149' 173 298 262" 7 6 ASTM A517 263" 455 528" 690 100

'Governing stress.

TADLE 4. Proposed penstock design criteria

Allowable stress not to exceed

Design condition % yield % tensile Normal waterhammer 60 3 8

96 6 1 Emergency waterhammer

emergency waterhanlmer of 2.4H, which is more than adequate. In this case, normal waterhammer will usually be the governing design condition.

Intermittent Loads and Stress Levels To avoid complicating the issue, the discussion so 5 3 0 0

far has been confined to loads on penstocks caused " by waterhammer. There are other loads that can cause local stresses in excess of those due to normal waterhammer. Such are, for instance, the loads due to earthquake, and to filling the penstock when the full water pressurc is not available to hold the pipe rigid between supports. The USBR has published loo 200 3 0 0 400 5 0 0 6 0 0 7 0 0 criteria for the latter condition, as reported by Y I ELD STRESS I N MPa Arthur and Walker (1970), which are iaken into FIG. 4. Proposed allowable design stress criteria. account in Table 7 as allowable stress increases of between 20 and 33.3% above normal.

This lllagnitude of stress increase is of the right Allowable Stresses for Hyperstatic Pellstocks order. ow ever, it is suggested that, in order to-be A hyperstatic penstock is one wherein a bend is consistent, the allowable stress be 2 5 z above norinal introduced between two anchor blocks, and there is stress, whether based on yield or ultimate stress. The no expansion joint between the end anchors. A t the suggested stress levels would then be as outlined in intermediate saddle supports the penstock is allowed Table 8. to move both longitudinally and transversely to

TABLE 5. Allowable stresses based on new criteria

Normal condition Emergency condition Increase

0.38 0.60 0.61 0.96 emergency Steel tensile yield tensile yield above normal

designation (M Pa) (M Pa) (MPa) (M Pa) (%I ASTM 285C 114 124* 23 1 199" 60 CSA G40.8B 170 157* 273 252* 60 ASTM A517 301" 414 483* 662 60

'Governing stress.

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GORDON

FIG. 5. Hyperstatic bend. Note absence of anchor block. horizontal angle at this location.

The penstock curves through a 20" vertical angle and a 42"

TABLE 6 . Percentage increase In waterhammer pressure and allowable stress, emergency condition above nornlal condition

Normal Emergency condition cond~tion % increase

Waterhammer 1.25H 2.OH 6 0 Stress, % yield 60 96 6 0 Stress, tensile 38 6 1 61

TABLE 7. USBR allowable stresses for nornlal and intermittent loads

Allowable stress the lower of

% yield % tensile Normal condition 66 .6 33 .3 Intermittent condition v '

80 .0 44.4 /, intermittent above nornlal 2 0 . 0 33 .3

TABLE 8. Des~gn conditions and allowable stresses

Allowable stress the lower of Design % yield % tensile

Normal waterhammer 60 38 Intermittent loads 75 47.5 Emergency waterhammer 96 6 1

allow for thermal expansion and contraction, which is mainly taken care of by deflection of the bend between the anchors. At the bend there is no support as shown in Fig. 5, thus allowing the pipe to move in any direction to accommodate thermal movements.

The advantage of this type of design over the Inore conventional isostatic design is that about half the anchor blocks are eliminated at bends, and the other half are considerably reduced in size due to the elimination of the unbalanced hydrostatic force caused by the adjacent expansion joint. It is a type of design that is particularly useful where soft founda- tion conditions would require the use of large con- crete anchor blocks. The disadvantage is that the determination of the stresses within a hyperstatic penstock is difficult, and can only be accomplished by use of a computer. Even so, the stress determina-

0 200 300 400 500 600 700

YIELD STRESS I H MPa

FIG. 6 . Allowable design stress for type 2 and 3 stresses.

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C A N . J . CIV. ENG. VOL. 5. 1978

TABLE 9. Penstock design safety factors, type 1 stresses

Allowable stress Safety factor to

Design criterion % yield % tensile Yield Tensile Normal waterhammer 60 38 1.67 2.63 Emergency waterhammer 96 61 1.04 1.64

TABLE 10. Penstock design safety factors, type 2 stresses

Allowable stress Safety factor to

Design criterion 2 yield 2 tensile Yield Tensile Normal waterhaninier 40 25 2.5 4 . 0 Emergency waterhammer 64 40 1.56 2.5

tion is not as precise as can be achieved with a con- ventional isostatic penstock. For this reason, a different set of stress levels or factors of safety must be used with a hyperstatic penstock.

for type 1 stresses in an isostatic penstock. In view of this, the allowable yield stress should be reduced by about 50%, to 40% of yield. Even with this change, the design stress will be governed by the tensile stress

The forces causing stresses in a hyperstatic pen- stock can be divided into two classes based on the degree of precision in the stress calculation, as follows:

The stress caused by internal hydrostatic and hydrodynamic water pressure can be calculated with exactitude; on the other hand, stresses caused by thermal expansioil and contraction, by weight of the penstock, especially at the unsupported bend, and by other forces such as those due to earthquake cannot be calculated with exactitude, and are usually calcu- lated with a computer using the ADLPIPE program developed for use on high pressure steam pipes de- signed to the requirements of the American Boiler. ntld yiess~ire vessel cock (ASME 1975).

Thus the stresses can be divided into: type 1, pre- cise stresses, due to water pressure forces; and type 2, imprecise stresses, due to all other forces.

For type 1 stresses, the same allowable stress, or factor of safety, as used for an isostatic penstock can be used. However, for type 2 stresses a higher factor of safety must be used, resulting in a lower allowable stress. Since type 2 stresses are determined by a com- puter program developed for use in coi~junction with the ASME boiler code (1975), the allowable stresses as stipulated by this code should be used. This code liinits the allowable design stress, for the type of steel usually used in penstocks, to the lower of 518 yield or 114 tensile stress. For the steels listed in Table 1, the allowable design stress would be governed by the 114 tensile stress as shown in Fig. 6, with the only exception being a mild steel with an unusually high tensile stress. However, due to the design problems involved, the 518 yield stress is considered too high, being higher than the corresponding allowable stress

except for mild steels as shown in Fig. 6. Since both type 1 and type 2 stresses must be

combined to obtain the effective stress acting on any portion of the penstock, and since each type of stress has a different ~naximuin value, the stresses cannot be simply added together, neglecting for the moment that they may be acting in different directions. T o solve this problem, the concept of a stress safety factor must be used.

The stress safety factor can be defined as the inverse of the allowable stress expressed as a ratio of the yield or tensile stress, whichever applies. Thus for a type 1 stress, the factors of safety can be obtained as shown in Table 9, which call be compared with Table 4.

Using this concept for type 2 stresses, with t h e allowable stresses as defined previously, and allowing a 6 0 z increase in stress for the emergency water- hamnier condition, safety factors for type 2 stresses can be obtained as shown in Table 10. All type 1 stresses act circumferentially, tending to 'burst' t he penstock. On the other hand, most of type 2 stresses act longitudinally, tending to 'stretch' or 'compress' the penstock. Tlle one exceptioil is the stress due t o torque from an unsupported horizontal bend, which will act in the same plane as type 1 stresses. Thus type 2 stresses should be subdivided into two other stress types; type 2, which acts a t right angles t o type 1 stresses; and type 3 stresses, which act in t h e same plane as type I stresses. Type 3 stresses would still have the same allowable design stress levels a n d factors of safety as type 2 stresses.

Since type 1 stresses and type 2 o r 3 stresses d o no t act in the same direction, they have to be combined. By multiplying the design stress level by the safety

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GORDON 349

TABLE 11. Penstock weld tensile tests

Yield strength Ultimate Extensometer Elongation (%) 0.29, offset strength gauge length

Sample No. (MPa) (MPa) (cm) 5 c m 15cm 2-A 656 803 15 24.0 8.25 2-B 603 798 5 23.5 8 . 0 2-C 671 798 15 24.0 8 .0 3-A 712 826 15 - - 3 -B 5 69 719 5 20.0 5.0 3-C 712 8 24 15 19.0 6 .8

factor, the yield point is approached. According to the distortion energy theory (Roark and Young 1975) failure by yielding will occur when the stresses are combined as indicated in [9], and as developed in [lo] and [12]. However, when attempting to carry out the same exercise for the ultimate stress level, the distortion energy theory has to be replaced by the maximum stress, maximum shear, or internal friction theories. Since it is only necessary to obtain a design stress level, which is well below the yield point, it was decided to retain the distortion energy theory concept in order to provide a uniform basis for comparison, and combine stresses as shown in

I [ I l l and [13]. To combine stresses acting at right I angles to each other, the distortion energy theory

gives the following formula:

stress due to ail other stresses acting in a transverse direction; F,, = combined stress, which must be below the yield stress; FCL = combined stress, which must be below the tensile stress.

From the foregoing it would appear that four design conditions would have to be checked, an expensive and time consu~ning task. However, an experienced penstock designer can tell from an in- spection of the penstock profile which hydrodynamic condition will govern the design of each penstock section. Furthermore, a quick calculation of the allowable stress level will determine whether the yield stress or the tensile stress will govern; hence the governing design conditions can be quickly determined, and the work reduced to the calculation of the combined stress for only one condition.

1 [gl F , ~ = F~~ + FB2 - FAFD Practical Problems where: F, = combined stress; FA and F, = stresses in planes at right angles to each other, positive for tension, negative for compression.

Using the safety factors given in Tables 4 and 9, the combined stress a t any point in the penstock with normal waterhammer can then be obtained for the various types of stresses fro111 the following formulae :

and with emergency waterhammer, the combined stresses can be obtained from the following fortnu- lae :

where: F, = stress due to water pressure, acting in a transverse direction; F2 = stress due to all other stresses acting in a longitudinal direction; F3 =

Where a penstock is surrounded by concrete such as at an anchor block, the higher stresses associated with high strength steel are accompanied by higher strains that cannot be resisted by the concrete. Con- sequently, cracks often appear at the point of mini- mum concrete cover, usually above the penstock centre line. Since an anchor block depends on the weight of the mass concrete for stability, such cracks can be disregarded and merely sealed with a caulking compound.

The area where most problelns are encountered with high strength steel is in quality control. On a project completed several years ago, routine testing of weld tabs indicated a yield strength in the region of 586-621 MPa with the break occurring in the weld metal, whereas the yield point of the parent metal was 690 MPa. It was decided to cut samples from two penstock cans, machine test lengths, and undertake new tests at the Mechanical Testing Sec- tion of the Physical Metallurgy Division of the Department of Mines and Technical Surveys in Ottawa. The results of these tests are shown in Table 11. The tests were undertaken o n an Amsler 200 000 Ib (0.89 MN) capacity universal testing machine. The yield strengths for samples 2-B and 3-B were obtained from load elongation diagrams

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CAN. J . CIV. ENG. VOL. 5, 1978

0 0.1% 0 . 2 % 0 .3% 0 . 4 % 0 . 5 % 0 . 6 %

STRAIN -

FIG. 7. Tensile test of weld.

plotted by means of a Baldwin autographic recorder when the outdoor temperature was in the vicinity of and a Templin type 5 cm gauge length clamp-on - 15 to -20C. Hence the cold draught must have extensometer. The other samples were tested with a affected the weld quality. 15 cm Te~nplin extensometer. It is interesting to note Another area where strict quality control pro- the difference in yield point with the two extenso- cedures are mandatory is during site welding, where meters. A plot of the load and strain is shown in inspectors must conti~ually be on the look-out for Fig. 7 for samples 2-B and 2-C. procedures that contravene the specifications, as

These tests indicate that where the weld strength illustrated by Fig. 8, which shows the welding of a is suspect, the yield is likely to occur entirely in the stiffener onto a high strength steel penstock. 111 the weld metal or the heat affected zone, hence use of a lower left corner of the photograph there is an open short extensometer just covering the weld length will can of weld rods, which, according to the pro- give a more accurate determination of the yield cedures, should have been kept in an oven. point than a longer extensometer that would have to When using radiography for quality control, it is include some length of the parent metal. important that all radiography be undertaken by the

These tests also raise an interesting point: if the consulting engineer or by an inspecting agency under test on sample 3-B is disregarded, the yield strength contract to the engineer, and not by the penstock would be a minimum of 603 MPa, with an ultimate contractor. This is because there are many 'tricks minimum of 798 MPa, just above the guaranteed of the trade' that can be used by the radiographer t o ultimate of the parent inetal of 793 MPa. The design mask poor quality welds that would otherwise show stress, referring to Table 5, would then be the lower up on the radiographic negative. For site welding of 3 8 z of 793 MPa = 301 MPa (governing stress) this principle is easy to apply. However, at the or 60% of 603 MPa = 362 MPa; thus there would be factory quality control of production welding is no reduction in the allowable design stress even with usually undertaken by the contractor's own quality a poor weld. In fact the yield strength would have to contrdl group, hence the best solution is for the be reduced to below 503 MPa before it governs the engineer to have an inspector attached to this group. allowable design stress.

An investigation of the probable causes of the Conclusions defective welds indicated that they were all under- Quality control standards based on tested and taken on an automatic welding machine, located approved procedures must be established for pen- next to a window that was kept open for ventilation, stock welds. These standards should be more

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GORDON 35 1

I FIG. 8. Welder. Note open can of weld rods in bottom left corner.

rigorous for high strength steel. Weld strength must be verified by tensile testing, and quality by radi- ography or pressure testing.

Exposed steel penstocks should be designed for two waterhammer condit~ons:

(a) Normal waterhammer - equivalent to a pres- sure of 25% over static water level at the unit centre line on a penstock feeding an impulse turbine; equivalent t o a minimum of 25% but not exceeding a maximum of 5041, over static water level a t the unit centre line on a penstock feeding a reaction turbine.

(b) Emergency waterhammer - equivalent to a pressure of 100% over static water level at the unit centre line for both reaction and multi-jet impulse turbines. Where the penstock is supplying an im- pulse turbine with only one or two jets, the emer- gency waterhammer should be equal to that caused by instantaneous closure of one jet.

The maximum combined design stress levels in steel penstocks should be the lower of that de-

TABLE 12. Penstock design stress safety factors

Safety factor to Design condition and stress type Yield Tensile

Nortttnl waterlm~~ti~rer Isostatic penstock 1.67 2.63 Hyperstatic, type 1 force 1.67 2.63 Hyperstatic, type 2 force 2.50 4.00

E117ergency iu(~ter l~nr~~t~ter Isostatic penstock 1.04 1.64 Hyperstatic, type 1 force 1.04 1.64 Hyperstatic, type 2 force 1.56 2.50

termined by using a safety factor defined as yield or tensile stress divided by design stress as shown in Table 12. In hyperstatic penstocks, the forces pro- ducing stresses within the pipe should be divided into two classes, type 1 due t o water pressure and type 2 due to all other forces. The stresses produced by these forces have to be calculated with a com- puter. In all penstocks, stresses must be combined in accordance with the strain energy theory in order to obtain the maximum combined stress level.

ABBO~T, H. F., GIBSON, W. L. , and MCCAIG, I. W . 1963. Measurements of auto-oscillation in a hydro-electric supply tunnel and penstock system. Trans;~ctions, ASME Journal of Basic Engineering. Series D, 85, p. 625.

AMERICANSOCIE~I.;OF M E C H ~ N I C A L ENGINEERS. 1975. Boiler and pressure vessel code, Section VIII, Division I , summer 1975. Addenda UA500, p. 18.

ARTHUR, H. G., and WALKER, J . J . 1970. New design criteriafor USBR penstocks. ASCE Journal of the Power Division, 96(P01), pp. 129-143.

BROWN, J . G., editor. 1958. Hydro-electric engineering prac- tice. Vol. 2. Blackie & Sons Ltd., London, England. p. 200.

EBERHARD-I , A. 1965. Penstock codes-United States and foreign practice. Electric power today and tomo~.row. ASCE Conference Papers. Power Division Specialty Conference, Denver, CO, pp. 725-770.

GORDON, J . L. 1970. The Harca Hydro Development. Canadian Electrical Association, Hydraulic Power Section, Spring Meeting. Transactions. Canadian Electrical Association, Engineeringand Operating Division, 9, Part 2:70-H-105.

HORNBERGER, R. G. 1965. Use of high-strength steels in penstocks. Electric power today and tomorrow. ASCE Con- ference Papers, Power Division Specialty Conference, Den- ver, CO, pp. 807-828.

JAEGER, C. 1963. The theory of resonance in hydropower sys- tems. Discussion of incidents and accidents occurring in pres- sure systems. Transactions. ASME Journal of Basic En- gineering, Series D, 85. p. 63 1.

ROARK, R. J., and YOUNG, W. C. 1975. Formulas for stress and strrlin. 5th edition. McGraw-Hill, New York, NY. p. 24.

SMITH, W. J . 1961. Design of high head penstocks. Transactions of Engineering Institute of Canada, 5(2), Paper 61-EIC- 10.

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