Design of a Constant Angle Arch Dam at Devil's Gate in Connection with the Flood Control of Los Angeles County Citation Heywood, Gene Bryant (1918) Design of a Constant Angle Arch Dam at Devil's Gate in Connection with the Flood Control of Los Angeles County. Bachelor's thesis, California Institute of Technology. doi:10.7907/j50c-rm76. https://resolver.caltech.edu/CaltechTHESIS:08082024-215542673 Abstract No abstract. Item Type: Thesis (Bachelor's thesis) Subject Keywords: (Civil Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Civil Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1918 Record Number: CaltechTHESIS:08082024-215542673 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:08082024-215542673 DOI: 10.7907/j50c-rm76 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16623 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 09 Aug 2024 17:30 Last Modified: 09 Aug 2024 17:31 Thesis Files PDF (Thesis) - Final Version See Usage Policy. 21MB PDF (Plate 1: Devil's Gate Dam. Map of Dam Site) - Supplemental Material See Usage Policy. 2MB PDF (Plate 2: Devil's Gate Dam. Main Dam Details) - Supplemental Material See Usage Policy. 1MB PDF (Plate 3: Devil's Gate Dam. Auxiliary Structures) - Supplemental Material See Usage Policy. 2MB Repository Staff Only: item control page

THESIS. DESIGN OF A CONSTANT ANGLE ARCH DAM AT DEVIL'S GATE IN OO~NECTION WITH THE FLOOD CONTROL OF LOS ANGELES COW.TY. GENE HEYWOOD .. Class ot Nineteen Hundred Eighteen Department, of C1vil Engineering. THROOP COLLEGE OF TECHliOLOGY. Pasadena, California. l 9 l 8. '!'ABLR OF CONTENTS. Page Introd:uetio:n 1. , Selection of Type of Dam t6 •· . f be uaed Page .-. . • l(e.1n Dam Page 10. Gravity _Abut.ment, Pag1' . Sp1ll:wray cap~e.1tJ . Page 2(h Open Spillwa1 . - . P$lge _Tunnel~,fpillway Page 25. overfl,~W Dam Page ,26, C,r;IV) (JM'ISOn l (!,/) Sis • Per <z· Girder B:ridge Crossing . ·spillway ·•,· 19. 21 • Page 28. concrete Arch. Bridge Page 51. !)etermiriation of Unit Costs Page 31. Estimates ·or Cost Page 36. • Summary Page 38. BibliogrEtphy Page 40. INTRODUCTION The need ot flood control and flood prevention have long been felt in southern California and several investiga.t.ions ha.Ve been instigated, The raost noteworthy and commendable report on this t'lork is that or the Board of Engineex-s of Flood Control sub- mitted to the Board of Supenisors of Los Angeles County in 1915. As a resident of Pasadena, and as an engineering student, the writer has been particularly interested in the control of flood waters :t.n the Arroyo Seeo and espeoi:ally in the plans submitted by the members of the aforementioned Bo.a rd of Engineers and by Mr. J. w. Reagan, Engineer of the Los Angeles F1ood Control District. The principal features of M.r,Reagan*s plan are as follows: A dam, 130 ft, high, gre.vi ty type, arched up stream to a radius of 400 ft., is to be built or cyclopean masonry. The dam will serve also to carry the La Canada-·V erdugo Boulevard over its top, a 20 rt. roadway and sidewalks on either side being pr•t-•ed• The storage capacity or the reset-Voir tormed by this dam will be about 6(tJ aere feet. The spillway proper will consist of a channel excavated in the east embankment I the waters to be confined between two side walls of reinforced eonorete. The ajlillway tunnel, curved •-- i.11 plan, will be about 300 feet in length end have a eapaeity of '1000 sec. rt. The regulating works call for hJ'«ilte.uliely operated gates, large enough to take ca.re of a discharge of that magnitude. The combined spillway capacity will be equal to about 15 1 000 sec.rt., considering the lnaXl1Dflum. flood level at elevation 1065. A low ovel:>tlow da.m, of the arched type, will be constructed at the narrow outlet to Devil's Gate, to provide a water cushion for the spillway discharge and to deaden the erosive effect, at the 2 foundations of the dam, ea.used by the high velocity of the apillwa7 watere. The roadwa,- will e?'oss the spillway proper on a reWueed. eonerete bridge or the berun and girder type. The east .a pproaeh of the roadway ,and the seci:ton between the . . . the · . ma.in dam and the spillway \'fill be eat'th emba.nkme-nt. anti « we•t approach wi11 be 1n excavation. A ma.p of the reserl<>ir is ehown on plate 3, the profile, eroes eeet:ton and. plan v1ew$ of pl.a\e 4 1 and the emptf1ns and filling curves on plate 5 of Mr.Re:q;an•a r<;port. Two features of the forego:t.ng plan p@tieularly attracted~• attention or the write~: the seleeti<>n ot the. gravi.\7 type et d$.m f<>r a ei te. ,ici,e~l for .~ .arohed dam; and the 9hoiee of a v~l'Oeit7 of 50 . :rt.• pe:r aeeond, which woule be neoessaey to discharge '1000 tee. ft. through ·• the tunnel sect.ion .C ho$en. These QC>nstde:J?ati0ll$ 1 , and the .t a.et, ~ t the au111~ atruct- ~es had only 'be•n drawn in outline $lld .~d. not been ~•1gned in detail• led tl1.e ~i.te.r tto in,restigat$ an alternative ·plan;, and to undertake the dettign .ot •the auxiliary- stj,u.e.t ure, u t.lle , ,11bje¢t or the th~s:t.J 1ubmitt,ed. by h1JJl to TblW<>-P College of Technology., :,:: '!'he, repo1,.t, e_eleu.latt..ol:18 and desig:r:ui he??ein contained ~e the re·• ult .()f th~ t, inveat.ig~tiQn. The general ·p1~ ts ve-r;ay $:imilar to th~t ,ugge,tEld. 07 Ivir11Reagan, 1n fa.et, was purposel7 made so as to :t'Ol,"Itl. a better and more d:t.1'eot · eompe.riaon 1)etwe,en the .eatima:tes of cost of a .gravit.7 dam in one ease and ot an arohet\l dam 1n the other. between the two plans coneiat.i of; The me.in divergenoe the substitution of a d$lll of t)le so-ealled constant, $.llS1e aroh type in place ot one or the gr~v1tY type; 3 the construction o:f.' a gravity abuttriient to take the thr'U.$t or t.ha t portion of tlle SJ?eh dam coming above the belt of 11ound granite walls on the east bank; the use of-. spillway tunnel, straight in plan, with a muimum velocity oi' 30 f't. per see.; the provision if~r a spillway capacity equal to that of the estimated mu1mum flood that has ever occurred., na.111,ely • :ane: '10% greater than that. o,t 1914; and the carrying of the roadwa7 across the canyon proper on a reinforced e.o nerete arch bri.dge down stream fro~1 the dam. SELECTION OF THE '11'ZPE OF :DAM TO BE USED. The drainage area or the Arroyo seco above the d8.lit site is 35 sq. miles, and the outlet to this dl'ainage area is through a rocky gorge some 700 ft-. in length, known as Devil*s G~te. The site chos.en for the dam ts about 200 ft. be.l ow the present La Canada-Verdugo high- way bridge.• e.pproxim!ites an ir:regul~ v. rounded, forming a tr. But the bottom has been considerably iJ.lhe wails of the canyon are of' dense white granite, with telsps.r a.nd q'Uilrtz predominating, although, some biotite The weit wall r1$e,s high above the top or the propos~d dam and fo1?ms a pe,:af'eet ~bu~tif.lf; to~ an arch d$lll, ,.. , . .. The' east wall of the canyon is compo.sed Qf sound rock to about elevation 1053. Ab.ove thi~ contour the granite showt1 signs of weathering. Since the creat of the dam adopted not only conies several :t'eet above this belt of' rock between the sound and the weathered. granite, but a.otually is above the natural surraee of the ground, it is apparent that some form of masonry- ibutment must be used to take the thru~rt : of that portion of the arch dam which comes above solid rock. 'fuere are four types of ma.soney damswhioh oould be selected for this site: gravity, single center arch, multiple arohi and constant 4 angle aroh. The gravity t-ype of dam will be disoussed later in com- paring it with t.he a.J?ch dam finally chosen, and needs no mention at this point. A single centet" arch dam could be eeono:mieall-y used where the walls o:t the ca.:n:yon are nero."'lY vertid~, . but as be:Bi¥e stated, the walls at this ~:Lte a.re by no means vertical or nearly so. An economical design of a. dam of thil type would be much too light to carry a 20 ft. roadway and sidewalk$ on either side, and would contain 5O~ more masonry than the da.ni selected• The coat of the sepa.ra.te bridge wou.ld, of qourse, be identical 1n both project•. The total coat of tJ:ie bridge and dam wquld be greater in this ease tb.a.n if th.e dani wer<i1 designed with a section heavy If deaigned with this enough to carry the ro.adwa:y and aidewalkih heavier section, the volume of ma$onry would be slightly more than double that of the dam finally chosen, the eost would still be greater than the combined cost of the dam and bridge selectecl• and no advantages c.a n be cilaimed for the Edngle center arc.h dam Which are not likewise applicable to the constant angle arch, while on the other hand many disadvantages of the former are done away with in the latter type • .An estimate of cost on materials, exca.va.tio.n , form vwrk, labor, plant, o'lferhead and. 10% for engineering, show these figures: Single ee:nter arch dam with lightest possible section; abutment and separate bridge •• • . • . • • • . • • ••• $190,000 Si11gle center arch dam with section heavy enotigh • to support road:we:y; abutment • • • . • • • ~ 0 • • • • • Constant ang.le e.roh-dq1 abutment and separate bri A,..;.e ~ • • • ♦ ♦ ♦ • • t O • 0 ♦ o • ♦ ♦ • ♦ • • • • ♦ ♦ • fl~.· T 152··"•.. 000 . 5 The third type, the multiple ar.oh, is adapted to sites where a a wide valley must be closed hy "relatively low masonry dam. 'the writer beli~ves that a height or 137 feet is too great fo1~ the economical design or e. multiple arch dam, and that, in a narrow ca...tJ.yon like Defd.lt s Ga.t e, some other type of areh is better adapted to meet the req11irements , The ad"tta.nt~es and disadvantages of each type of arch dam have been fully wEd.ghed, and the writer believes that the so-.called con«1ta.nt angle a.reh otfe1,,,s the greater number of advantages without n'l.$11Y of the di$advantages of the other t'Yl)eS. The advantages claimed f"or the type ot clam chosen over other areh de.ms are: 1. Greater economy-- or material. The thickness required of any section is directly proportional to the ~adiua, an.d by changing the oenteX> at intervals, the thickness is reduced proportionately th the deeretlse in radius. 2. Due to t.he larger central angle near the fotmda.tions the a;rch action is mo:t?e complete. The deflection of an arch is proportional to the square of tb.e upstream. :radius. By ma.king the :M diutl half a.s large at the fo'Ulldations as at t.,he ere$t, the deflection would be bll.t one•i'ourth as mu.ch ai befot'e and the loaa. which cov.ld be carried by the e.reh, using the Sa.rile unit $tresses, would be fou.:r times as great as in the constant vadius type. 3. The a:verage cr¢wn def'leetion due to a decrease or inc:rease in length caused by temperature changes is a.bout half as mueh iAtf :f~,·t!i€ constant radius type•• and therefore tempera.t'Ul?e cracl,cs ai'e much less likely to occur than in the latter type. It ia believed that the only disadvantages that can be claimed against this type !U1'e the greater dif:t'iculties of design., and the 6 g;r-eater cost of the field work of sett,ing fot'm points. '!he design 1s more compliea ted, and is a proces.s of cut s.nd. tr1 until the final section is fitted to the site. However, the saving in material more than compensates for·the extra lfl.bor in design. The form carpenter gets 'his points every 10 ft. and the difficulties o:f.' building forms are not any greater than :tn the ordinar.y arch da;n1, but the computations and the field work of setting those points ~re much more eomplicated. The totacl eost of engine.e ring, however, would not be any greater because less time would be required to eonstr1..tct a dam of this type and a eon.sequent sa.ving wou.J.d be made in the necessary expense of me.:Lntait1ing an engineering fore$ during the period. of construetion" The advantagea claimed tor the type of dam 1elected over a gravity sect.ion are; 1. Eeor101'.ll'y of mat~:,:-, _, , Actually in the dam chosen the:re is but 30% as much material as :L11. the gravity section proposed. a. Gre$cter .factor of eatet,.y. A facto?> of safety twice as great a.a -1n the gravity $act.i on is attained. 5,, More fa1orable dist:r;a.ib-Ution of $tress.e s. In a gravity dam the st:re$ses are a. 1n.aximwn at the toe and zero at the heel, while in an areh they are practically uniform th.rough.out the section. 4. In an_arch dan. 1 uplift at the foundations does not affect the s.t .a bility of the strue,-ire, while in a gravity dam it is of eon.. sidera.ble important~ and must be carefully designed for .• 5. Vertie.al tetnpei:•ature cracks 8re not serious in an arch ~-d$,'l1,; for the pressure of the water tends to close them when the resei:voir i,s full, while in a. gravity dam ve:rtical cracks cause serious leakage Md terrq)erature changes must usually be t$.ken. ca.re o:f by pro'11ding expansaion joints. 6, Hori.z ontal shear p.l anes in s.n ai~c11 dam, altl1ough objection- 7 able as regards leakage II only tend to produce in.ore complete arch action, whil0 in a gravity dam the percolation of water tb.rou.gh the seai"'llS and cra;clts increases uplift anc1 seriously endangers the stability of the dam. 7. Jm overflow of an arch dam would not seriously reduce its stability, for i t .•· depends oz:-. the so1..mdness of the abutments rather than on t11e founap.tio:n.s for support, while in the gravity da'Tl. any ': erosion at the tqe is disastrous, and any overflow must be carefully guarded agai11.st. unless an adequate ap1•on on the downstream side is built. Wh.ile it 1s true that a.n arch dam is not, capable of exact analysis, because of the combined action of a.rch, cantilever, and. cu;r,ved. beam near the foundations, the fact remains that there is not on record a. failure of an arch dam, although many have been built with vwrls:ing stresses greatly exceeding those used by the writer ir1 his design. It is also true tl-i...at in the gr·a.vity dam'" the section is of sufficient size to carry a roadway across its top, while with the arch de.xi'! selected, a separate highway bridge must be built H.nd 001 abutment must be provided to tue the .·/t.l'U'iust of that part of the darn. co:m...i.ng above the natural surface of sound i-•ook. However, as it ha.a before been stated., and as will be clearly shown i:n the detailed esi.imates of' cost v-1hich follow, the cmn.bined cost of the arch dam, ahv.tment, and. bridge is but 6O1t of the cost of the gravity dru,i alone. In ma.king these estimates of cost, the v,iriter has endeaored to be as fair as possible, and it is believed that any errors made 01" approximations used have been favorable to Mr.Re@.ga:n' s plans rather thW'.l to his wwn. Unit prices have been determi ned according to present costs of' material which are higlier than when the Flood Control Board's plans were fi?)st made public, emd :!.t, is believed t.11.at all • "·/' • 8 estimates are well 011 the safe side, and that the pl?oject could actually be built at a ar11aller figure i n normal t:t:mes. The cost of each structure includes excavation., material.a,, labor., plant, overhead sn.d a'.11 other charges exclusive of engineering. estimated at 10% ot the aum of the prices of the individual structurea and put down in a lump sum.. Detailed_ estimates and the determination of unit priees are given later 111 the accompanying com.puta.tions, and only the final figu:res arrived at are given here for purposes of c:tomparison. Coat of constant, angle arch dam. , • • . . • • • $74,900 Cost of gravity abutment. . • . . . . . . . • .. 31 200 Cost or concrete s.rch bridge. • • • • • • . . • 60tOOO Total • . • • • • .. . • • . . • .. • $138 1 !dt, Cost ot overflow dart1. • • .. .. . ,. • • . . . . .. Cost of $pillway . . . . . . • . • . • ,. . . . Cpst of' regulating works, including tunnel, 1 • gate house, valves, etc. • . .. • • • • Cost of girder bridge croasing spillvray . • • • Cost of approaehe$ ,· road me.te1~1a.1, drainage and 2,100 20.,100 15., 000 8,000 Engineering at 10% • • • •• • .. • • • • • • , • • ineident$.l$ • • • • • • • ,. • . . • • • 10,000 191000 Total cost of project • ., • • • . . ~ • • $212,300 Cost of Gravity r>;a.m 34 1 000 ·eu.. yd$. of rda.SOnl:'1/ @ $6.10 . • • • .. • 12,000 eu.. yds. of rook excav~tion@ 1.50 ... ,. 6,000 eu. yda. of gravel e:x:cavation @ 60¢ • . Total , • 0 ' . • • 207,400 18,000 3t60<;> $229,000 'l1he above quanti t-y figv.res were ar:r-ived at b-y calculatJng volumes from ~he drawings $U.b:mitted by t,he office bf the Flood Control District of Los Angeles Cotmty. Figuring the a:uxiliary structu.res at t,he sarne price$ as above, this would g:tve a tota.1 of $ 302,200 for l1his is sl.ight.l y higher than hi$ estimat~ of 1 ~p290,000 submitted over a year ago, but this increas\e can be accounted for, partly by the increase in cost of :mater:ta.ls, anf partly by the 9 fact that a leJ."ger spil.lW$.Y capa.ci ty was provided fop:l than i..-ri his -;-;· plan .. This 11.attu>ally calls for a larger amount of ex.ca.vation, more concrete, and a longer bridge over t,he s.p illway, It might b~ se.id in pass:l.ng that the $(:H:~rn:tngly high figure for t.b.e spillway is caused mainly by the large amount of excavation, and the figure quoted 1n• cJ:ud.es the placing of earth and rock in the east approach• i'o;r, the material exeavated cai.1 be placed in thi$ enibanlpnent nearly as eheapl,r as it oo'Uld be wast,ed. Alao, it, will be noted that the 1tern of engineering we.a figured on a baaia of 10% of· t..rie cost of:C-.~it,he plan as suggested by ~>-· • the writer, and that this san1e fi.gu.t>e was used in the estimate of' eost of mr.Re'asan • s plan. It :ta believed that the tigu.i"e tor this latter plan would. ;:no.r e near•ly be 10;16 of the total price of' that plan., but the tvm tigures .fol." engineering expense have been madf) identical so that no question co1.1l.d be raised as to the fairness of a compel:"ison between the. two estimates. r.lllle -i,vriter has. fel.t justified in using the same unit cost$ for mASOl'lJ,'7' in · both d.a:ms . and while the eost of erection of.' f 01<>n1s m.a:y (l be slightly gr>e$¾.ter in. his plan, the overhead cb:a.rges in Mr.R:e;;gn::H1;\ plan would be much gr-e~,t11e:ri,tn. items such as· interest on inve~tment, etco because of the greater length of' time required to build a gravity dam. The r igures show ~+:n~t,r(sav-ing of ~791~ ooo, which; figuring on a basis ot the ar•ch d.axn, gravity abutment and at>ch bridge, ag.a inst the gravity dam, would amount to a saving of 4010; figured on a b~ie of the total cost of 011.e :project against the other, a saving of SO% would result. The :main features of the design of each of' tbe structtwes as well as the typical ealoitla.tion vfill now be given. 10 MAIN DAM Mr. Lara R. J(i)~gel18en., Aaaoe. Mem,. 11.s.c.E- • 1n his e.x cel.lent pta.per printed in the 'transa¢,.t ions. of the A.tnerioe:n So,c iety of (,tvil Engineers, vol .. ~III,, i11 ,Wh.ieh he firs·t . advocates the ' . ~ u:ae o:i' ~ cons.tant angle e.reh d$.:n1;, tµa;tt mathtm$.tie1l1lJ;y ~~d. ~ t •the m9.;st ecQno1d.cal the,oret1ea:1 eent~al angle ths.t ean be ado,tel in ar,eh 11;!.gure 2,.. in the ~ame paper,, s.l•o shows tn.at for danis is . 133'° 34t. . . axry angle betyteen 150° .and 11s0 th~e 'is not mo-rt t1l$n 1% ve:11i~tion in the a.mount of mateJ?ialti· and M:r. Jorgensen point,, ~ut that an angle of i20° WO\lld:. be EA'bout the economioa.l 11:mtt in pre.ettoe~ • 1' . ' • • Actually_, howev'er;; 'bhie. .a ngle will be limited by the · peetil.ia ' ,, thrusts t .oo ne~l¥ t,ang~ntial tneie~d. •of nor-.mal to t-he ~ock WG.l th in 'fi.h:l(ih eas~ only the a.n ea:rtng $.Weng'bh ¢f the ~an1t.e. instead of it.a ·J ' •• • ••• tu.11 9:omp~~ss:;t.,;e .1 tr.ength eoul.d be developed; and then, too. 'bf ~ing the lal."get- ~l~, the ~ WQUld not follow the :n.atvsl high •ri.~ e.s and t~ ·volume of ms.eonn would th~reby be 1IlQre.a,u~4, The eentral :cpest finall,- $.,d.opted was 114°. . . angle. . • ·t th~. ' .' . . tt 1.$ ea,ily 4tpparent;., ed M~. Jorgen$:en haS'. ~blt dls·e,.iffil~d \ . ·• it in the aforenientiQJled paper, th$.\ ;i.f :lh1e, angle sou:L.d. 'be ke,:pt: ·cfon:e-t ant. • ' - • a.t_the· succea·s1V$ elev~tiona between er.est and b3'Qe by allorten:tng the :r-ad1u.'3, a gt-ea:t ec·o~omy of mat~rial would x-esult and F~+r .@ ch action qould be devele~~d n,e~ the foundations than if the r(S.ditts were kept q.on~ t,an t. It th<? slopes Of' the can:yon walls ai tUiY point, a.re s11eh. the.t the ratiQ ot decr~t1.se in lengtth ot the upatt'~a.n.t re.diu.e is gi."eiter than the rati:o of increas,e in we.ter p:re·s sure, a deere/ase. in thickn.e ea 0.r the 11 dam at tJ.1.is elevation will resul.t, a:..'1.d the upper port.ions will be and e:i.thez• tJ:1s overhanging • . This, of cotwse. is irn:pratltica.1, ;,,: thickness r.10.st b0 increased or the ra.d.:tus length.ened. In ,~Ir. Jorgensen's paper t he advocates t;he use of a di.f ferent, center for the upstream and . . . downetrealt!. rad.i i, making the arch thicker at the crown tht.111 at the abutments. that this overhang wou.lt1 always occur 011 the dOVi,'11Stream face, and that a greate1,.. econo1,ry of ma..t erial would result by making the downstream tac e verticel. • ( tbrowing all of the increase in thickness on tb.e upstrean s.i .d e) and by gradually clecreasing the central angle fr1om crest to base, ~ keeping the thickness o! each sliee the same f rom c~cwn to abutment. This wsi.s made neoesaary beeaus-e of the very ir1•egtuai~ surface of the l."'Ockt which in pla◊ea was nearly h◊:t."'itonta.l, while :ln others neal."ly ver,tica.1. As ca:"! reac1il'1 be seen f:rom the topogr-apllical :map, the west canyon, wall he.e- a poJ:-tion 56 :rt. long vrhich is near:Ly flat. kept the central ru1gle constant v1ould have :resulted in a lru."'ge amount of e:-.ctra excavation !trid mason.ry nt this point, and t he adoption of different . centers i)r downstream and. upstream ~~di1 ViOuld nialte a thicker section at the crown than at the abutments. i1b,e Wl":i.ter d.oee not believe that this is justifiable i:n this oase, a11d a comparison sho,1s that- decreasing the central angle, using the sam.e ce:nte;ra for u:patrea.i-n. and downstream radii, will give a raore eco11omical dan than ,,ould resu.J. t in the other case. It is s. well Im.own .fact "i.:,ha.t there is a restra.inment of' the arch near the foundat1.o ns, due to the :relet:tvely unp.elding rock, and because Of this, full arch action can not develop, anc1 there 1vill be a combination of ro..eh, ca:nt.ilever, and curved bearn a.ct.ion. i:foar the crest the deflection of an areh of the dimensions used wouJ.d be much 12 less than the deflection Of a ctd:"ved beam of similar p:roportions or of a vertical o,:,.ntilever. .At this point the action ·would be almost the deflection of a vert:ical cantilever would be less tha,n that of the a;rch Ol" eurvell. bes.m. In this case~ cantilever action will develop befm?e fv.ll aroh action can do so~ near the sol:td reek, it may be that ·~he <nn:•ved bearo. wou1d ha;tle a small$!' deflection than t,he cs.1.ntilever, and in this case this type of action wou.J.d develop and there would "oe but partial c.a ntilever and partial a:oeh aetion. The weight of the masonry of the mass above any point will pu.t in•to compre.s a ion the m.aaonry beneath it. ;?.o.e int~a1ty will., of course; V8:X"Y e.ecord.lng to the distribution of the n1a.Ss a.bove. ltt-oh act:ton will put all of' the mason:.ry in coYtpression ru-:i.d theoretiee.11-y, 1£ the section is $r,ia.11~ the intenaity will be ·un;tforra a.t an:y one section. Curved bean1 action will develop crnmpression on the upstreai.'=1 Sidi:; ond tonaio:n. on the downstre,$;;, sj.de• Cantilevera.ction will dev¢llop tens ion on the upstream side and co1np;i?es~ ion on the down'l'emperature ehanges will d~velop co-mpre~sive or tensile streahl side. in temperature. It can readily be seen that, the actual a.t resses de·vet9'"'ped in an arch dau1 ar•e ver~r complex~ and that the stresses dentelope<i by ·t.he diffe1°ent types of action are sometimes compensating e:r1 d smriet:bnea cu.mu:.l.ative. T.h.e le.ts Mr•. R. Shirreffs, Mera • .Am .. Soc~ C.E:., ,:tn . ha.El . c:1&:EJ"Mi\. ' . _,,; _.;,-· ; ·to~~~in., '4)n the paper ent,it,led., "Lake Cheea.n1a.71 Dam lk71d Reaervoir,u develops eJ:\\ i~ntpiriea.l fo1"nt1;.tla f:' or the deflection o:f' an arch da.'1t, Ii'· ~-; taki:ng il1to e;ccou.nt all of th&se i'acto:t.,$. r.w. Jorgensen use~ tJa.lf forin:ula in the invest,igation of we stresses developed in a o<;,nst.a:1:1t 15 lfillgle arch dam imd by an ingenious method, distributes the proportion ot the water press.ure ta.ken by arch, eantilev-e1'.' and bea."lt, a.c !cording to the rat.i os of the deflection given by this formula to the deflect.ion which 11ould oce'U?'t if ea.ch of these types of act:j.on actted: alone and 'Ul:'.lrestrained. A glance, howeve·r , at the deflection c:t.iilz'ves of the Ba:rren Jack Creek Dani ir.• A;ustralia will show that the m4,ny indeterm111ate faet9r$, such a$ temperature c:hange$ a.:.'1.d changes in moisture content; may practically nullify the asau.rnptions on which • tllle investigation i.s made. In fact, the deflection curves of dams bu:ilt; as fat> as th~ witer ha$ bee11 able to aacertain, do not e,ren e~osel7 approximate the e~es vth1eh wouJ.d result fro:m an application{ oif the aforement1Pned . formula ., and the writer is convin.oed of the Uitter futility or developing an empirical f'orrn.ula for deflections oif an arch dent which would be applicable in all cases. Mr, Jorgen,ien., in his investigELtions, has eJ.so ta.1.-en into ~eoount the effect of Poiason•a ratio on. the stresses in ·a."tl arch dsin. The weight of masonry above any &ection will t..end to decrease the 'V!ertieal thickness of ·t urr horizontal laye:ra, and tbts ·will ca.use an ie ~ansion in a horizontal direction, This len.gthenu:i.g will. be partly l"esisted by tJle unyielding abutments and by t,n.~ ;1:water pressure on the upstream side when the :r~se:ttvoir is tu.:11 .. an initial uie.l com.preseion in the conc1~ete and a cert,a.in propor-tion of the head woti.l.d be held in equilibrium by this f'~oe before ~Y ahortening of the lengt,h of the ~rch would result Md only the re~inder 1'0uld havo to be t~en care of by arch, ct.U.1.t.ilever and beam action. lt is also tru.e, end capable of proof, that this effect will be m.uch greater in a dam of the e.onstruit angle ti)rpe than in the ordin~ upstream radi.11.$ arch dam. 14 seems to have ove:t:'looked the fa.ct, in his ma.in pupe1.,, that the upstrea.111 and dmmstream swel:ling of the masom,y is only restrained on the upstream side B.nd that the me.sonry is left t'ree to exp~1.:nd in the ctownstreron direct.ion. The writer can not see how the px o;portion 1 of head wriich',;will be neutralized lry the initial anal compression is capf:i.'ble of au.ch an exact solutio.n as r!Ir. Jorgensen has used, a.s pecially when t.he solution is based on a seemingly erroneous aaaumption. J A theoretical d1un d.e sie;ned purely as an arch, 11eglecting the effect of' cantil-e ver ancl. curved beam action, if investign.ted by the many intricate a.11.d complex formulae evolved try some desig..~er-s, will usually show a d.eqrease in .arch stresses near the fort.'"'.l.dations m1d ~ increase near the cr~st, Th;te value netttr the crest would never e~eeed twice the 11t.SS'lt111:ed value, t\nd. indeed, the c,ar1tilevet1 a:nd heant action being small near the crest,. it is not b$lieve-d. that t,he ~spumed values at the cr~st,, if the streh is thin• \"fill 'be g!'eatly af'fEicted.. P,:ny practical da,'111 more.o ver, has ru:1 appreciable thickness at tr.te erest, s.nc:l the atresses wo1..ud oe considerably less th....<\U the allonia ble can.tilever and beani action a.re of considerable imp.orta:nce. The net result would be to h.avo t.11.e max:tntu111 compressive stresses a.t the t.oe and the minimum at the heel. The ~Titer, in making his design, has felt that the int:ricat e and complex f'ozr111ulae which have been proposed by v~trious designe1'.s and whieh are b;ased on very app:i:\o,;.imate e.nd quett~~,nable asGtl.t"'llptions, do not, justify the expenditure o:f t;L71e and labor mad~ neeessa.r:,,r b~eir U.Ete. Sections desig11e<1 by these intricate theories do not v~ mate:rlalJ;y from those designed on the simplex- theor¥ ,! , treating ea.oh se.ction as 15 a 1"ig-:td. cylinder subjected to ext,ernal w€1.ter pressure, the thic:to.1ess being deterntlned. :l.ndependentl-y- of an:y :r>est:r•aint at the ba$e. As has before been sta.teid, there is not on :i:~~rnord a failure of an arch dam, although the majc,rit·y have been designed on this s:ibn:ple:r theory and have u:eed workirig stresses geatly exceeding tho$e proposed by the- write:r. The fOl"Jl'l.Ula U$ed is 4•62. 5 h l'\1., where q.avera.ge compression i :t11 pou11ds - . per sq. ft., h: the head of water in feet on the section in justif.1ed in uaing thie formula a$ the basis of his design, but the sections ao found he.ve been altered according to his judgm.ent to trLeet the pecuJ.1.a:r cond.it:to-as Qt' the site. T:he melUl :r•e;diiui ~ ; Wm t : i· of the cent~al angle. _ _ l'f~, t,, Vlm. : wio;th Oi' ca:eyon and ~ am 9 ,,2-~~(:· ~-- -,· - '11b.e process of design was -one or selection o.f a sectia:r,. 4IUcord:tng to the above formulae fitting it to the s1te end al'tering it to meet tho part.icular requirements at that. section. It was s_ cut, and try proce~s and the central angle theoJ:7 could not be car:ried out to its tilll extent, but it is believed that the .t'1.n&l design is economical of' mate:ria.1 a11d well on the safe si.de. The a.am as finally bu..il t called for a 137 ft. dam, oontai.."'l• T'J.1.e mean ereat length 1: ;3: 6 concrete, after 6 :n1onths I c1.wmg, has a...'l Ultimate stre:ng tb. of 380,000 lbs. per s .q . i"t. A factor or safety of 9 11.as btH:cm l).rovided, using a Inaximum allowable working stress ot " .-., elevation 106'7 an.d tho stresses given in ·the -tn.ble a.-re caleu.lated on a basis of' the reset>voir level a.t t.J.te crest of the dar11. It will be noticed that the arch st,resses have been ln4!.ter:tally 16 ~xt:ra th:i~kness wa$ &1.dded., and the, &).')Oh stress,e s con;g-e quently reduced, in 01--ciei"' ·l:..o 'bet.t,e;ri diatribute to the founc1atio:ns ·i:,b.e -v,e:tght (jf the masonry- aoov-e th~ 'm\$e ~d to. provide, s: .ls:rger section for c~ntile'Ver ~n.d ov~ved oeru-11 ~ct1Q:n nea1~ ihe bottor.1 wh~re t _ h e d.Ei:.f.'lecticn is JSrrt.411 t;nd ar.oh t\ct,ion i11complete. Tu.e ple.n -_gt the dari1 4S shown ~el)l?-esents tb.~ .a ctual b a..&El ·~'to'e:r .~xoavati~n -a nd not the ir.1.te-r'aEH)tiort gf. -~'le natttNtl ~n:wf.a¢e of the • . > .• • • • - •. • ' • ' • • • ' • g~ound -vrtth the dru11 f:e;ce$. ' into soii« <:POC-k f;o'.f? Ji, dtata.11¢~ of 12 .ft. at all ;pqt~ta. In the d~,t1gn, sierrt,.ione _v,ere ta~t~ at i:t1t$'1?~r~la <>f l-0 ft~, tlw fb~ \ '7 :rt.. 'bei..l'l$ :s:tru.ck 1'7 Sec. Height Below . Crest.. Cont.our Upsti•eam R~.dius ~--- 00:nt:eal A11gle i1lt)SX1. Width of Canyon . ■. "t ·- , ,. Thickness ~.-...- Arch Str ess Pounds per s~. Ft . 1 0 1067 174 . 0 114: 288 4.0 0 2 ~7 1060 174 03 114 288 4 . 33 17600 5 1'7 1050 1.72 . 5 109 277.f.5 5. 0 :36600 4 2f'/ 1040 167. 5 8$ 227 7.0 40400 5 57 1030 162. 5 86 215 9. 0 41700 6 4? 1020 156.5 84 201 11.0 41800 'I 57 1010 1 1:1os . 5 83 188 13.0 40700 8 67 1000 141.5 82 176 15.0 39500 9 77 9'90 l.36 . 5 75 156 16.5 39800 10 87 980 131.5 ""7 136 17.5 40800 ll 97 970 12,1.5 67 126 19 .. 0 39800 12 107 960 122.0 58 109 20 . 5 39800 13 117 950 118.0 49 89 22.5 38300 14 127 940 114 . 5 42 73 25-. 0 36300 15 13'7 930 106.0 37 59 2s.o 32400 18 eectt()n Mean Rao.iu.s ~ - i - ' '', ,. JJ.et:tn Wicl.th Sin g ... . . .- -. ]. Cen-t,ral iw:1310 Cc::-:.t r&l ;\· .n,~1,~ l4;:t:J V rJ ri1 :~a~r~ ::_,-3 n.gt,11. of J\J.'<Ch 1 1?2.0 2$8 .s~sr, 5Eh8 113.6 341 2 1?2;r,2 28B.S .83'7 56.8 113.6 3 1!2 3 r,o .o 2?7.5 .,816 5,1 .7 109.,4 325 4 16·1.0 112'7 • 1 392 43 . 8 87 . 6 251 5 158 .. 0 215 .680 42.8 65.6 236 6 151 •.() 201 . G66 41.8 83.6 220 7 142.0 , ;~ ·( ·i -'-~- __, .662 41.5 8('>.0 206 8 134.0 170 .65 17 -11.1 82 .• 2 ' 192 9 128.25 156 .608 ;37. 5 75.0 168 lO 122.7µ 1:36 .~:.55 33 .7 f/7 .. 4 -, LL II .l.. -~ 1l 11-4 . 75 120 . 550 33 .4 66.8 133.7 12 111.?fi 100 .4f;tJ !~~9 .8 !5B.4 113.7 13 106«175 (;;-;~· r -. ""' .,41"7 2,t.6 Cj:~. f.~ ~ 91.6 14 10.2 •.o r/~ ',) .358 il1.• 0 42.O 74.8 15 02~0 5 9 .O . ;)21 18.7 3'7 . !1 f1 0 II" l.9 GH.J.1JTI?"i 11.J3lY-BffiNT 'I'he griiv·i t·:;,r a.but,ment has. two functions to per•.fOl"m: to ::t'0siet the thrr1.at of tho ar•ch da:m and to form e, wa.ter..it.,izht co:ri...r1ecticn between the spillrm·y· and the. :m.a.L"'l darn. The crest of the gr•avi ty dan1. is at ele·vatior.i. 1069. A vring wall vrn.e pu.t bet.w-ae:n the main dan1 and. the gravity abutment, s.r.i.d the c1. . est of the gr,av•i ty da1n was :m.s.de ti.rm feet h.5.gher s so t.hat, in ertse tJ:J.e Illa.in dron was ove.,:o ov.ort,opped; an ove1"'flon of' two .feet could be tal~en ca;i."0 of ·1vitb.011.-t;, washing out the foundations at the t,oe of the gx..aV':1.ty abutment. 11h.e dart1 base v1as car•ried to .som1d rock and a cut.- off' wall in t~e solid rock p1"'ovided t.o prevent excessive seepage. '1:b.e_ details of design need no mention excep·t that the inte,,s:i,t-y of the ,, uplift rrn.s ass1:.rr..1ed to va:ry ,~n.ifO:t'I11ly f rom t\10-thii."'ds of the head at the heel to ze1,.o a·t "the t.oe. Inveat,igations were made at two sect.ions, one wt1e1... e the downstream hat,t,er 'bega.11 and the o.t,her at the base. The rstabili tyCl.ockwiae mo:rrwnt, ~· w ~ (8) (J..333) + (5.53) (1.383)} Counter clocl:wise moment, :: w :: 18.32w f {~;, a) ( •.6117) + (1.36) {2,.67)~ :: 26.Sw Section at the Base. Clockwiae n1on0nt ~6) (18) 2 -· + ~18) (l;.33) (4.44) 2 Counter OlookNise moment,: 2.3w f l w : 1328W (4) (18) (6.22) ; J.,8 .. 67) \~1=) + l!.66~) {-~J__(B!AA.l~:: 13;12w 'I1re total area of the section equals 13!h7 $(1. ft. ,, ·the td:,o. t,ica.i moraent about the toe equals 1201.3 Location of ·res1,,1lt,nnt wit,h :t>ese1,.voi1") empty equals .1201 •= 8.6 :ft.from toe. J:3:g.7 Limit of middle third •~ (.13.'3§) (~~), • 8.9 ft .. fr-o:m toe. These calculations show that the res11.ltant falls 1.nsid.e the mid.dle third 20 .• P. per ..f~.o t of length · • • , . • . ~. . .. i 16.2w '4 • • • • • • • f ) -.tan ~ :: l? :: 162w ·=·· · •·.0 n. n ·-w .. ?at!w' . . ,~ A coefricient of fr:i.c-t.ien equal to o.'75 p1-tovid.e s f .o r a factor of se.fetf 0f two e.galnS!t i!lid.ing, if the shear·i ng strength · of tho ee:r-iore:te is negl-ersted, •This is eonsid~red good practio~ a..Yld the Tl,e i&.lght of the <-~j ~/ .~}~/~ • • is so small that ~~tioal and inelfned stresse:g :ln the eo11ci•ete at'e negligable andn~ed no frtv-estigatiQ'n. 1'1-te thrust of the · arch d~t 1br:rve eie'lt~t..!on. 1053 rrt.v~st be t.,itk:en 1'1' the gi"av'ity nbutnient. and. the 11:el gnt o·P th$.t structure lfe.s d,efJigned heavy enough to re$ist tb.at "th:rm$t due to its w·t?,;ight. alone . •,r~eA .BJ." 4 o·• ,!. ,p <it~-~.S. ·l•o.,.,. ~..,._,. V • ,i:.i. 1'.· ·o·•..f 0 ·~ """". h ,,:s..,.,..;, • 9n . 'at . • · ,p+ v~ i;.t..,., .., -. ~ ✓1 .• V $.(q_. .L .:, l' A:r.>ea of Y/10 of s~<Jt:ton 2 o.f' arch d'Ml : 32.0 $q. ft . Ave,r age tnru.at on seet:to.nl ~ i r 8800 lbs. per sq. rt,. ·r:·. Average thru.$t on aectio11. 2 ::-· 198◊0 lbs. per nq_. ft .• Total ~1'$ust, on gtl':atrity d.f;Un. z (8800) (29.3} -. (l,9800) (5£) •:; 892,000 lbeh Tcttd weight of gravity d~u1 .~· (241) (62 •.5) (cl2} ·= 1 1 235·1 000 ·1bs. o .f>/'2◊ 1,235, ()~<Y = ·• · Tan ~. eq;uais 892,000 . . ;J The weight is then auf.ftcie.n t t.,o 1--.esist, the tJ:trust. S?ILLW'AY CAPACITY Th.e maxi.inum, flood d:i..sehl).l?ge of Feh~Y•'19l4 was l4:,l4t $eeond fe.$ t at th~ Co.19.:rado S.tPee-t B1"'idge about. s miles below DeYil 1·s Gate, ~d indieatione show that in 1884 and 1889 £looda of' about 70"/o greater 21 This will ~lve s. flisoharge nf. 24:,000 scc-:::nd. feet • .P.lt.hongh the ch.an.nel beloTI has a stJ..f'e cn.pncity of. 1n1t 1000 second feet, it was thought advisable to provide adeq,110.te ~pillvray capae>.1.ty to take It was ,lecid.cd to have the ce.1"e of' ftn'Y flood which m.igh.t occur. regu1 a ting tunnel ca.rry -4000 se·c ond f oet, and t~e ope'.".'J, spiJ.lwEt.y 20000 !t would have been p1"0ferable to ha:ve a tu..':ln.el capacity qf rtooo second feet, but, the enorrnot1.s size cf t he t 1I t1.nol capable of carr:ring that eapnc1.ty o.t ve.l ocitie.e 1ritht:n reasonable limitsJ selected. woul.d. be capa.ble of. :reducing & :f:1.o·od s.s gr.e at ~-s that of 1914 to a flow of 4000 seeond. feet. eome into.-~s~ ex.eept in caae of a flood of greatar m~nitud$ .. The level of the r~s~rvoi-r at times of' a. p!'olo.n ged flood, / f.ilqual to 24,000 second feet flow, would. be at elevation 1067. Th.:i.s would eo:rrespond to an elevation of 1064 at t:i.mes of' a flood. eq11aJ. to that or 1914. Thia is figured on a baa1s of s. res{$r,to:tr being full at the beginning of a flood• ; OPE!I SPILLWAY The open spillw.a.y is partly in excavation and the flow of' the water will be eonf'ined between t,v,; o r-e:i.n force c1; co:nc:r•ete wall$. The floor of the ~pillway no:.." th of the br•i.dge is noi.; 1:tned., but south of that :po:Lnt is lined w:tth a 0... 1.n. floor of concrete. A cut-off wall, sunk well :Lnto i:inpervious r,ook, run.s f r•o-rr; the t1,r ch dam under the upstream face of' tile gra.vi t,y abutment, ncl:Oss t,he upstream edge of the spillway floor, t10 the core-wall ctn the east Weep holes shou.ld be provided. 1-m dcr th.e concrete floor to drain any seepage which :rne.y take place and. to corn~eqt-:.eritly reduce uplift on the f'loor. The spillway was caloule.ted as suppressed weir with a velocity oi' ap:rroach. Q ;; 3.33 b [ (lI .+ hf • hf] h::; u8 where u equals velocity of approach 2g b: length ()f spillway o:rest equals 145 ft .. Cons ide1.,ing the 6.epth in the oha:nnel to be eqti.al t.o 9. 9 ft. 1 u : 2.2.!000 :: 14.43 f't. per second. (!t.wT-nr. s > h •(14.42.ll .. 3.2 f't. --· t:4. ·;•'· .. Q : Th.r1 (3.33} •· (145) [ (9,9 + 3.2)¾ ... (3.2) 1] = 20100 sec. ft,. Vfalla of' the spillw$y were designed HS a retaining wall subjected to water pressure both lritera.J.ly ar.id vertically. or the water acting on the floor, is sv.:ff"ic:t0nt·,Q give stabi lity to the vrall suhjectect to water pressure. to elevation 106~r~. a.,."'1.d in the design tho na:i;,er was assl1.:med at t11is level. - 'I ~. { l • total le:ng·t h of base h : r'..ead c,f water k : some cons ta.nt, here taken as O. :? The wid'th wan ms.de 13 f't. 4 in. x • ·width of short c~..ntilever : k l :: 2.• 65 ft. and was 111..ade equal to 2 ft. 8 L~. Upr·ight cantil.zvo1i.....- -- Mai.:ir:tvJr1 moment ~. (62.5) (15) 3 (12) : 422,000 in. lbs. 6 Steel v.sed was 0/4 in. the fa.cc' of' the slab. ':r'W. rods spr:wea. 4 in, ~. c. pJ.a.c~d. l·rt tn. f1... om 23 :E:;re~ other 1.>od v:o.s stopped at this 1:'.>oint, so ff! :· fr.~ ~~(?t·_•t~) 7 7} • tH;2°j j $} \ 6 • v) = 11,000 lbs .. per sq. in. It :1.s oonnnon pra,.ati.ce to put in a steel percent.age o.f '.004 for th:l.n walls and , 002 for ·U1.ick walls i:n Ol?dor- t,o taJrn Cm?e ot tempera.tt1.re cracks Wtth p =· 0003., the a.x•ea of steel required in which would develop. th:ts case vmv.J.d be .378 sq. i:n. per f't. €, 1n. c . c . w e r e u s e d f o r t . h e horizo:o.tal $ t e e l , ~ g i v i n g a - e e a o f .383 sq. :t.n. per :foot. Weight of concrete p~r foot of J:€:it~\ini.ng wall equals 2970 lba. Vie:tght of WEt tar acting on floor of retaining wall equals {62,5) (15) (10.t?l) ·; 10,000 lbs, : _(121,970) (_~J ... 1945 lbe. ·~1,sx, ft~ --1':':f.3~ • ~ Intens:i.ty at the joiI?,t or the short ce.ntilevor ~ • Intensity ut the joint of t.he long cantilever• ..,.... 1560 lba. per rt • 24 Inttnsity at the end of long oa.ntiJ.ever· • o Haximum. momen·:~ in sl-;.01--t cantilever : tc • (1870) (12.25)2 11rr1u,- - - (11'700) (2) (64) --· 294 1b~. ·p er·, sq_. 11."1" , -rn1T-·nrrrrr.1fr2 i.. • A '.: (111700) (8~, ..,...,..~, r.n r.•n \ 11 \ . .•o..,, _; _ • f .··..~I .186 sq. in . x "'"I:.:" , •1t ·' :.:•v1 :".:· Th is -zias figured on a bt:tsis of a th1c1':rless of 6 in. ?:hich is sufficient. Howeve1\, it was d,{iiemed advisable to be.tt0r thi s t h ickness fro:m. 6 i n . e.t the end to ; ,~ -th:icknBBS equal to that of t he lon.g ca."'.1.tilever. rerte area of the steel rertuir-Qd is so mnall, that t.he sJ~O~l neceosary ,· l•• .. to pJ:-aevent temperature c1'la.cks would be ls.-rger and will govern in this oa.se. 1lJ:11D steel would bo the same as tha.t, reqttil"'ed in the 5n spillway floor. Asa.1.mti:ng a value of p • .004 7 /16 in. 'i'-w . :r•ods ~paced 8 in. o. o • hoth wa7 e f~lfi11s the requix•emett1t$, gi·v•ing an 'iµ?ff!~ equal to .287 sq. in., pe.r ft. Long ca:ntileveri!~ax:L11um iiiei~i t ~quala ..__~,.....,_ (12) (10.67)22 (62.5) •' .'\-fl·~~:•' .' .} ...__ {15) - ,{12)(1560) 6 . (l0.67j . ... II . --...... Using a thickt1e.ss of .1.6.,5 in., a. :; lfi in.• Ustng '7/8 in. •:~w . rocls spaced 6 tn. c. c. givo.s ffil ~rea. equal to 1.53 sq.in,. r.I.,.he thJ. cltner1$ us eo. is suffic.:i.e:ntl:,r 181..rge so that the shee..i•ing a tre~u~ in W::i.ng w~lls and 0011 0 w~.11.s - one side and earth. p1,,essure on the ctho1,,. T'.a.e net rea,v.J.t would be to 25 have ,:,J lFiial lrydrQStati~ pressure on the upstream si.d e. 'J.1he seetion ha$ been made large enough. and tuffieient steel has been provided to take ea~e of this lll'.l.ba:taneed preseure by U$illg 3/4 1n. Tw .. rod.a spaced 6 ui. c.-c. gi:ving. $ . tlt<:1el p&reentage of .004 -figured on the ~ aee.t.:ion.,. The bend.t:ng m$ntel1t -o f the e.ant11ever at the .half~·w;a7 JOint will be l .e es tll:$.tl otu,l~h.al.f of t.he ?IUUt1mu.rn and every oth$r ro4 has been used f '<>r the .hol!': tzon\$.3.. attel., , <me'"!ihalf ineh TW., ;rQd$ Bpaeed 6 1.n. e.e. being ·p~flVlde-i . The 1r1:ng wall will be 1 · ubjeet.e·d to t,.f Ui'ttal. -e $rth pre$~ttre o.n the downattNQJ11 tace with the· v~S:ervo1r empty and fQ:,, this reaso.n ·the re-into~eement 'h11t been pJ.ae:e a •3.¼ :Ln, f:rom tho batter.~d tac~ .1~1'f( tht -ve3'tie-al tao~ -:u tn the ptt?evious eaae ,.; ,.,,.•r<, • ;_, d of Wm.en the r-eservo1:tt iS full there ,d.ll 'b e ftill h'Jdre,tatl:e i:ress:ttPe on both. taees, no ~einf'oreem.~nt The iame amount of reinforcement and section have been f.tJNNEL $PILLWA'l ' 1.t'he tumr~l ·t 'eoti<>n ad slope hr:tve been t~le<fbed: 10 that a dt&obrge.· of 4000 •et-. tt-. oan be 'taken care of at .a V'e.loo:Lt.7 not e.x~eedtng 50 tt. p$r ~e,,e()nd. Thu V$loo1,t.y :Ls Slightly high, but the tunnel ts bttilt. ,s tre.ipt in flan :and it :ls not thought that, thl'ough solid r .o.~k and 'Will probe.bl,- not n-aed retnltSreement axeept a.t the intake and outlet. . However; it is de~med. advtaable to adequately ... reintoree i .t at the point where. it paef.ses -u.nder the gravity abutment .• No attempt has beEm made to design the reinforcement, for the $J'!lettnt needed _w ould dep!;lnd on the character o·f the rock found Qn excavation. T.he tu:n..Y1el sho'Uld be linect, howev-er, and a 6 in. eement lining 3,:s 26 thought to be sufficient unless it is found that reinforcement is needed; the thiclmess would then depend, of' course, on the amount or pressttl'.'e that would have to be resisted. A. gate-house will be provided just north of the gravity al abutment, and hydraulic)-7 operated valves will be used. No att~~ has been made to select the gate equipment, but in the estimate of cost; quotations on gat.eJ of the as.me oapacity and apparatus used under approximately similar conditions have beenuS;Jed, and it is thought that the estimate is liberal., The tun..'1'1e1 has been designed with the ma.ximum discharge taking place when flowirlg freeJ9/lo full. When the level of the reservoir is above elevation 1036, the flow will take plaee under However, it is pressure, and larger discharges could be obtained. recommended that the gates be so regulated as to keep down the discharge to 4000 sec. feet. The sect1C>n of the tunnel at entrance has a.a.'"'l. area of 190 sq . .tt. and a hydraulic radius of s. 7 ft. 'l'his area has been made sufficiently large so as to out down the entrance velocity and consequently reduce eddies, etc. The ·section chari..ges gradually in 45 ft. to an area of 140 sq. ft. and a hydraulic radius of 3.1 f't. 'I'he tunnel is 220 ft. long with a drop of' 3.4 ft,. in that distance, givtng a slope of .0154. The v1ell known formula v+.tt .. , e ~ rs was used in the design; :._'• n was taken as .013 and the corresponding value of c calculated to be 138. This gives a value of' v : 138 ~ (3.1) ( .0154} : 30 ft. per sec. The aetual discharge then equals (3¢,) (140} : 4200 sec. ft. OVERFLOW DAM The overflow dam has been provided to form f ji;J;ttnd of comparative-:\'.-:-\· ..,. \: ly still water between it and the main darn. T:b.e eff'ect will be to deaden the erosive action caused by the high velocities of the water 27 from the spillway and tunnel di.s cnargefi which flow ov~t> the bQX'~ rock walls. The main reaion for ueing this da."11 waa to protect the piers of the proposed bridge whieh crosses the A:r-ro1ro ·below the nua.in dam. : I •. The a1 te eh0se11 te>~ the dBJ11 is at the lower end ef Df>vil'* a • Gate just before the atream leave,s the lllllrrow <Hm7on and w;tdens. out into the wider fl.ats of the lower Arroyo. The granite walls are nearly -perpendieular at this point; for a. height, of 30 ft. and t.he tite is ideal for ~ .a rch dam of the constant up.s tream ra.di:Wf type. The dam' wae made 30 tt.. high,. the ma.aonry being ea:rwied 5 ft. below the po:Ln\ where solid rock foundations supposedl7 Jd.e. If solid rock sho:uld 11$- deeper t ~ eatime.ted, the 'batter ot the do-wnst,ream f:a.ee AhOuld be <,o.:ntinued,: giving an inerease 1n thickness at the bottom 'l'he width ot the eany<:>n at proportional to the tnerease Son height~ the e:raes·t is 51 te·e:\.. 'l!lt41- upstream :radi'lll tiuio.p ted :ta eq~l to 30.5 ft, giving a central angle ef' l:221:ij• 'lb.e mean length of the eres-ti if! 62 tt, At the ba.se the ·. een:tr.al $.DSl;e is lG2· degrte., atlld the, raean length 49<•.8 ft, .•. It ·a .f loed Qf 24,0eo se.eond. teet sn;ould eve~ oeetw $.gain d~ing the 11.f e of th$: prOJlQs.e d w()r-ks, ,:and all of this should AAVe to pass the npper dam. at one time, this dam wo:uld ·be fn.t'b jeeted to an overflow ,0f 24 ft. The ordinary llUilX!.mum of 7000 second ft,, woitld give an overflow o.f 10 ft. Air vents should be provided so .$ $. to ,uow full a.t :mospheric pre..s.sure. on the under e1d.~ of the overflowing sheet of water•. bAve not been ahown in the dr·s,wings. These ~ / additional safety, however, ~~ the dam wa$ designed for the above mentioned overflow ·O f 24 ft. plus tull atmo.&pheri.e pressure,. Air vents must ·be provided 1 hQwever. to pr-event vibration ·which might b.e set up by the · .a lternate. making and 28 bre~king of the vacuum rorm~d on the downat.res.m aide •Q f the dam.• :t,\ wa8.., of .c ourst, ir.npos:s:ible to de$1gn the downttrean fa.ee to f i t the •01.tt''V'G of the ta11.1ng sheet ot wa tar, because of' .the s,J,.ender s-e.e t,ion uaed~ butr- the tij;>$t:re.am crest was deaigned to fit the curve over.flow of 7000 second feet. 0£ the $he.e t of wate~ with -~ The upstream f-aee was nm,de v:~rtteal fo~ a height o.t so rt. $nd then asatnned 4 back• w~d 'batter efj.ual to that dt th'G downatve$.tU tace, g1:vtng: the same · tbi.ek• ness .a t the ere.st as 6 rt~ belo• that point, . The downst~e~ race hat a· straight batter. Atmo3phe:ric prea•we -tt: (14.7) ,(14;4) •:. 2.i.12& lbs, per a.q . rt. i:L1he ~eh st~e-ss tben equals p :: (62.5 h -1- 2.l~Ol Rn~, . t; . , . ,_!:~%:~.\. it the et-ee:t t,h1$, st,:te$t 1JJ 40700 lbs. pei' aq. rt. a.'l'.l.d at the base is 55 1 .800 lbs• per 14• tt.-. GXRDD BRIME CROssnm- SPILLWAY ' The widg:$ i$ of the tJrdin~ e.onti..Y1uoua gird.er tn,e .end is 144. .t t. long nonaii-td,ng of n;tne spans <,f 16 ft.. e.a(}h. It will ~e.:rry ·a 2-0 ft. ?>$$;att,a:y ·and 4½.ft. sidewalk$ ·on eithe~ ·s id.e.. Ji l'.Oad1ng ~,quivQle.nt •to; that ot a 20:-ton t:ruek was ued in the design.. Although the. dl'avd.ng$ do not ~ow tt, the bridge t!'.b.Ould be built on a s:1:1.gllt,, gradie::fl.\; •and :the top ot the floor alab .pl~:e~d o;.t elevation. 1070 at the east end~ . ..1 . 069 at the west . . . end and ' . ' . . . . . . pr.ovide fer d:rainageJ ·~ . .. . . . Thie. is to vents,, covered with grillage, ,nould be plaeed at treq_uent intervalt near the ell?ib throughout the length ·of the bridge. A 20..t .<Jn 'W'UCk has a distance of 5 ft. between 'Wheels and lO ft. between axles; , the load:tng on each rear r,heel is 14;000 J.bs. ·To assume this heavier eoneentrated 29 load acting on a l•ft. st::rip of sl,a.b would give a slJa.b thioknes.$ 9es,tl1 in excess of that. .Usf.)d on an.,r modern highway bridge .. •'11he 'ftl:'i ter eons.1 ders tba.t the •slab on ea.ch aide aids 1n the Sut)POX't '" of this eon.een\x-ate:a. laad,. and ror his purpos.e s of design has eon..e.idered the 40•000 lb. lead as unttormJ;y dist-ributed over the area enclosed by the "truck t,hee~s. 'l.111$. giV'e S a ' lea.ding of 800 lbat pe:r • • ~~ sq • •• tt~ ,· •Thi~ will give . a Slab sect'ion COrt'espond.ing to that . lidopied by d.&.signe:rt :. of ~Ult ·~ l.us :mQ:dejtn high~ay b:r:t(lgea and is bel;te-red. to greater ·bending mom.ent t ~ the concentrated load of l4'"ooo l'bs. •• Slab design~ a .6~£t, $.pan wa.s chosen betJteen beams. De.,d weight of a- 6=,,d.n, al.a b •=- 75 lb;. per $tl• t't-,• . , ' Total load on siab •: 87$ lb$~ per sq;,, tt. Moment * (875J ·t6;~~ (12) 1 31;500 1n. lbs. • 11 · · .. to ~- ,~ fitJOtt·, ff4,~?~)&el t 640 lbs·. per sq. in. 1 hsmn:tng a value •Of '7/S for j .ahd, 3/8 fo:r k. wliieh correspond& ' with ,"W' eomihon pract:tce. .' ½" 'l'w. Reds spaced 6 in. c .o. we~e used tor the t:ransverie st.e el. t, ;f ~1,,500) l~l •-·_:1,,-.400 Lba. pe~ •• }'u ;,r • · • . ,, 11.l! b!:.. <·I\ ff ·r iI . . $4_, . in_. _ , ' 'l1w,- rods apaoed 12" o.() •. were used. tor :,t.ongitud.inal steel• Over supptrte s\e.e l 4' -~~~. of same size as ~bove, wa.s · u.sed to tak~ ear~ or the ne.gat.i ve moment. Beama.- The b8.Jll11S wer'.e deE&igned as 1! bemts with ~ width of flange not greater than 4 t. namely~ 52 in • .in this case. 30. slab and live load per root of beam= (875}(6) • 5,250 lbs. dead weight or the beam per foot= (18)(8)(150) • 150 lbs. 140 5,400 lbs. Total load per ft. Moment= (5,400)(12)(16) 2 = 1,380,000 in~ lbs. 12 An investigation of values of j and k show these quantities not to vary ·,1 ~:, materially from the ordina~y assumed values of 7/8 and 3/8 respectively. fc = =(1,380,000){8) • 632 lbs. per sq. in. ~ 1-k~btJd ti-~ ~;1, ~ ( 32)( 6) ( 7 )( 21) Mc gn g~ Using 4- l•l/8 in. tw. rods f 8 = (1,380,000)(8) • 14,850 lbs. per sq. in. (5.06)('){21) Reaction equals (5,400)(8.) = 43,200 lbs. : maximum shear. Intensity v = V o'Ja • (43,200)(8) = 294 lbs. per square in. (8 )( '1 ){ 21) Concrete takes 40 lbs. per sq. in., steel takes 254 of shear = 37,300 lbs. '294 p = vs =(37,300)(4) = 7,100 lbs. considering stirrups $.paced 4 in. apart. 21 0:-- A= 7,100 = . 111 sq. in. (4)(1~~:000) 3/8 in. round rods were· used for stirrups and were bent as shown in the drawing. The other details of design are clearly a hown in the drawings and need no explanation. Two of the 1-1/8 in. rods were bent up 4 ft. from the center-to take care of negative moment over the columns. Column Walls. ---- The walls were made 14 in. thick. 'rhe 12 in. by 24 in. per - tions coming directly under the beams, and enclosed by the reinforcing steel, were ~esigned as columns with sufficient strength· to carry the applied loads. The walls were made homegenious throughout their length and only the reinforcement was changed at the point before mentioned. Total load on a column• (43.200)(2) = 86,400 lbs. Axial compression • 86,400 (12)(24) • 300 lbs. per sq. in. 31. This is much less than the allowable 460 lbs. per sq. in. and the walls would stand without reinforcement :lf it were not for ,aec~lentrm, loading. Reinforcement as designed calls for 1/2 in. rods, spa.eed 6 in. c.c. W1der the beams and 12 in. apart in between. Va:?"tical rods shpuld be tied together by a band of 1/4 in. round steel, spaced every 12 in. 12 in. e.c. Horizontal steel was made 1/2 in. tw. rods spaced In the bottom of the spillway floor under the columns, rods 4 ft. long, with the spacing .and size used in the floor slab, were put in. As the floor is excavated in rock, no other footings are required to support the column loads. CONCRETE ARCH BRIDGE. The design of the concrete arch bridge was undertaken by ur. Kenneth Harrison of Throop College as the subject of his thesis. The drawings are here included, and for the details of design, the reader is referred to Mr. Harrison's report. It will suffice here to say that the central arch has a s "p;an of 155 ft. with a rise of 4:0 ft .. The east approach is about 9U feet in length and the west approach about 100 ft. The total cost, ready for traffic, is con- servatively estimated at $60,000.00. Notice is called to the very favorable topography for a. structure of this type and the economical as well as light and graceful bridge attained by Mr. Harrison in his design. UNIT COSTS. In determining unit cos~, the following items have been taken into consideration: finishing. Concrete, falsework and forms, steel and Each of the above may be further subdivided into materials, labor, plant, overhead and engineer!n.g. No attempt has been made to design a construction plant 32. layout and te> figure the exaet cost of each 1 tern that goes into the making up of the plant. The damsite is but a few hundred yards ·"'f'.rom the tracks o.f the s. P.L.A. & S.L.R.R. and good paved roads eonneet ', , the railroad with the damsite •. Th.ere are then no transportation difficulties and materials not available at the site eould be cheaply delivered. This. appliee especially . to the ma~h.inery, etc., 9f t he . con$truotton plant. . It is planned to place all concrete by derrick or from r a central to"el', p:r-eferably the latter. .. . l,i'our years a.go,. masonry ·eoul~ be placed 1ri large mass~s such as ~n a dam, by m,echanical methods and un~er less favorable conditions for 80 cents per cu. yd. An i:r1crease of 2~ bas been previded for, in the writer rs es- timate, to take care of' the increase in cost of power, freight, mater- ials, etc., ani it is estimated that the net cost of the plant for this job would be about $13,000.00 or $1.00 a <H1bic yd. or masonry. Othe~ unit prices have been figured on a basis of the cost of Materials in Pasadena at the present time. Cement --- Cement ... ........... ..... . $ ~ Cost of testing •..•.•.•.• ~ .• C.e$t of llnloading ••..••.•... Cost of teaming •..••.•••••.• Oest of' handling, bundling, sacks, eto.,.iag!d•~tala ... 2.10 net including er~dit for sacks; fr$1ght, ete. .05 .03 .05 .04 $ S.25 i barrel. The ordina~y cost of sand is $1.00 per cu. yd. washed, screened, delivered on the job. .S uitable sand, however, is available at the damsite and it is estimated that it coald be dug for $ .30 per ou. yd. S~reening and washing, delivering into the hoppel"s ready f'o r use :a t the mi,c.er,., would bring this up to about $.50 a cu. yd. for sand. Grrushed st.one ea.n be bought at $1.00 a cu. yd. in cargo at the present time in thie vicinity. It is tht?u.ggt since the:re is suit- I able roek at the damsite~ that the rook couldbe crushed, screened, 33. graded, handled and stored ready for use for $.80 a cu. yd. Concrete - With a mechanical plant it is thought the following labor prices will apply: Floor slabs and beams ........•.•. $1.00 a yd. eolumns, walls of spillway... . . . . 1. 50 " t, Arch overft0w' dam.... . . • • • • .. • • . .. • Main dam and grs.vi ty abu'tmen-t t ... • 70 " .60 " 0 " n Main dam a.nd gravity abutment a:a~ overflow da.m. --Cement 1.2 'bbls"@ $2.25 ............. $2.'70 Sand 1/2 y~ .. . • . 50 •. • • .. • • • • .. • • • • .. • 25 Stone 1 yg. ff $.80.............. .80 Labor.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Plant ................... .,. .... • . . . 1. 00 $5.35 a cu. yd. ·spillway walls, core wall, wing walls, column walls of bridge Cement 1•2/3 bbls. @ $2. 25 ••.•... $:3.76 Sand 1/2 yd.@ f.50 ................ 25 Stone l yd. at w.80 ................... BO .Labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. 50 Plant . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 1. 00 • ,7.30 e. cu. yd. • Floor of spillway,&: bridge, and beams of bridge --Cement lt2/3 bbls.@ $2.25 ......... $3.76 Sand 1/2 yd. @ $. 50 • . • • . • . • . . . . .. . • 25 Stone 1 yd. at $.80 ................... 80 Labor... • . • • . • • • • • .. • • . . • . . . . • .. .. . . • 1.00 Plant ••••. ·. ··•••·••·•• ·•·••·•·•···· 1.00 ,6.80 a cu .. yd. Steel --Costa of steel are very unfavorable at the present time, but are here considered at present stock mill rates plus freight .. If it were possible to obtain steel in a large mill order the base price could probably be cut in two. Labor costs on steel work --Cost of unloading and piling steel on job ---------------------·----$.02 per 100 lbs. Cost of teaming ........... . • .........•...... o. . .01 Cost of cutting and placing steel in floors ...... 26 Cost or cutting, bending, placing steel e.nd stirrups in beams ............• 50 cutting and placing steel in walls Cost of including t!sdsng, eto ••..• o . . . . . . ., .. .. • .65 34. Steel costs --3/4 in. or larger .. Mill price .............•...•...... $ 2.90 Freight · and · traneportat.ion tax . • •. 1.02 --$3.t>SZ per 100 lbs. 6/8 in. Mill price. , •..•..••....•...•...••. $ 2. 95 Freight., etc •...•.. -~.•.•••.••..•.• •1 .• 02 $3. 9'7 per 100 lbs. l/2 in. Mill price ................•....... $5.00 Freight, etc ......••............•. 1.02 $~.62 per 100 lbs. 5/8 in. Mill price ...•.......... ~-... .•.. ~ .. $ 3~15 Fretght, ete •........... ~ ......•.. 1.02 ,4.17 per 100 lbs. 1/4 in. Mill price ......................... $ 3.-60 Freight , etc . . . . . . . . . . . ..• . . . . . . . . . 1 • O2 · $4.62 per 100 lbs. Forms --Lumber prices a.t the present time are high a nd variable, ranging from $36.00 to $42.00. These are list prices and can be reduced by $5.00 to $7.00 when bought in large quantities. The cost of form lumber, brae 1.pg, • studs; etc., would perhaps .c o11e to ab out $ 60.00 per 100 sq. ft. or form s urface. It is bel ievei t hat all lum- ber could be used twice, bringing the lumber tost down to $30.00 per 100 sq. rt. The cost of nails, wire, oil, etc., wou1d. cane to perhaps $10.00, making a total of $40.00 per 100 sq. ft., or 4 cents per sq. rt. of form.,· surface . ?l ain Dam, Gravi t:y; Abutment end overflow Dam forms -- - Lumber, nails, wire, etc ......••.• $ .04 Labor making, erecting, plumbing, wiring, etc ......•.•.. . . •Labor stripping •• ·• ••, ••.•••••.•••.•.. .10 • 01 $ .16 a sq. ft.. 36. Spillway walls, core walls, wing walls; column walls or bridge --Lumber, etc •.....•.........• $ .04 Labor ma.king and erecting . . . • oa Labor stripping •.......•....• 01 $-.13 per sq. ft. F'loor of bridge --- Lwnber, etc .....••.......... $ .04 Labor making •.....•......•... • 03 Labor erecting .....•••....... • 04 Labor stripping •••......••..• • 01 • $ .12 per sq. rt. Beams of bridge, ~--' Lumber, etco••••••••••••••••$ .04 Labor making ••......••......• 04 Labor erecting •.•...........• 04 Labor stripping .•.••......•.• 01 r-:-I~per sq. ft. Finishing For surfaces which are to be finished a cost of 4 cents per sq. ft. can be added for materials; labor, etc. Form work in main dam --Number of Sq. Ft. of Form Work per Cu. Yd, of Masonry: = 4.68 or 70 cet1t~5a cu. yd. Main dam --- 52,500 11,22~- Gravity dam --- 3,160 460 Overflow dam --- 3,000 270 • 11 or $1,66 a cu. yd. (.70)(11,220) = .668 (1.03)(460)( • .040 : .037 11950 11,950 { 1.66 )( 270} 11,956 $.736 per• eu. yd. of masonry. A cost of 76 cer1ts a cu. yd. of masonry was given for form work in the main dam, gravity abutment and over.flow dam. This gives a total unit cost of $6.10 for masonry for these three structures. 36. It is n.ot thought that there is any need of showing the calculations by which the masonry volumes, exc.ava.tion, area. of form work, amounts of steel, etc., were determined, a.s their solution presents nothing new and their method or ealeu.la.tion is self evident. It might be pointed out, ~owever, that the method employed in obtaining the masonry volume in the main dam was the following: The area of each 10 ft. section was calculated and multiplied by the average of the ihean lengths of the dam at the top and bottom of that section. The sums, of course, gave the total volume. The final estimates of cost follow and include everything except engineering, this being added at the end in a lump sum. ESTIMATES OF COST. Main Dam 11,220 cu. yds. of masonry@ $6.10 ..... $68,500.00 • 60. . . . . 1,860. oo 3 1 100 cu. yds. of ·~gravel @ 3,000 cu. yds. of , J!08kf3 l @ 1. 50 •• •••• 4, 5QO.OO $'74,860.00 Gravity Dam --460 cu. ya.s. of masonry 290 cu. yds. of rock @ $6.10 .... ~, @ 1.50..... 2,810.00 435.00 @ $6.10 ...••• 1,?10.00 165.00 130.00 $ 3, 245.'5c5 Overtl~w Dam --- 270 cu. yds. of masonry 110 cu. yds. of roek 220 cu. yds. of gravel 2,040 lbs. of :3rt 1n. steel @ @ @ 1.50..... .60..... .0392... ao.oo ·;-2-,o,..,s....5--.....0~0- Open Spillway --Concrete --- 517 cu. yds. •or concrete 304 .cu. yds. of concrete Forms ,• ..... 13,590 sq. ft. Steel --- @ $7.30 ....•• @ 6.ao ..... 3,780.00 2,070.00 @ $ .13 ..... $ 1,740.00 7/8 in. rode .. - 16,750 lbs.@$ .0392 •.• Labor @ • 0028 ••• 660.00 48.00 3'7. 3/4 in. rods 25,550 lbs. @i .0392 ••• $ 1,000.00 - Labor .0068 ... 174.00 '/, @ @ @ 7/16 in. l:>Ods- 40,400 lbs. Labor rods 2,310 lbs. @ in. 3/8 @ Labor .0417. •. .0028 •.• .0417 ... .0028 .... 1,680.00 112.00 100.00 6.00 Finishing --50,000 sq. ft. .03 ..... 900.00 - Excavation --'7, 850 cu. yds. @ 1.00 •.... 7,860.00 ,~0,120.00 Girder Bridge•~Concrete 155 yds. a.t $?.30 ......................... $ 1,133.00 140 y-ds. @ 6 • 80 . ...... • ........ ,. .... • • 952.00 R.ailing . ....... ~ ........... e 4!I • • • • • • • • • • • 350.00 Forms --- 7,440 sq. ft.@ $.13 ...............•... 3,200 sq. ft.@ .13 .........•..•...... 4,360 sq. ft.@ .12 .................. 416.00 522.00 Steel --1-1/8 in. rods 812.00 0 .. 20,900 lbs. 1/2 in. rods 3/8 in. rods 1/4 1n. rods .0053 •• .0402 •• -@ .0068 •• 12,?50 lbs. @ @ Labor 1,480 lbs. @ @ Labor 7.120 lbs. @ @ Labor .0402 •• .0028 •. .0402 •. .0028 •• .0417 •. .0053 •. .0462 •• .0068 •• .0462 •. Labor - @ $.0392 •• @ Labor 19,060 lbs. @ "/50 lbs. - Labor l,310 Labor lbs. @ @ @ @ .oo~a .. Finishing --- 9, 000 sq. .f t. @ $. 03 .•..•...••..•...•.. 966.00 111.00 766.00 130.00 512.00 36.00 60.00 4.00 296.00 38.00 35.00 5.00 60.00 4.oo 270.00 Road. :material, surf'acing; · sidewalk fill, drains and incidentals •..•.•.••.... 600.00 ,7,985.00 Tu.n nel Spillway -· Excavation @ $5.00 per cu. yd ••.••.•••• $ 26.80 per ft. Lining and reinforcement, forms, etc... 13.20 $ 40.06 per ft. Total coat of tunnel ......•.••...•..... $8,800.00 Cost of gate, house, valves, regulating apparatus, etc. e.200.00 $15,000.00 Total cost of regulating works .... 38. The total costs have been given before 1n comparison with the figures of Mr. Reagan's plan and will not here be repeated. The drawings enclosed are complete and need no explanation, and details of the design not included in this report are clearly shown on these drawings. SU· MM AR y. In conclusion the writer wishes to state that he believes 0.&Sllmp all the ~tions and approximations made hav·e bee.'1 on the safe side and that an economical design otI the various structures has been obtained. The estim~tes of cost are liberal and while they may not repr·esent the exact expenditures tba.t would be ma.de if the plan as advocated were to be actually constructed, still the figures form a fair and equal basis on which the two plans as outli1"1ed can be can.pared. The writer claims the following points of superiority in his design over that submitted by the office of the Engineer of Los Angeles County Flood Control District: 1. A saving of 30% on the cost of the total project and 40% on the dam alone. 2. A factor of safety twice as large in the main dam as well as the other advantages previously described of an arch dam over a gravity dam. 3. Elimination of the erosive action in the spillway tun- nel by the reduction of grade and velocities to a: reasonable value. 4. A spillway capacity large enough to take care of the maximum florid recorded, even if the regulating works of the tunnel spillway fail to work. The provision of a separate highway bridge, ma.king the means of comm:unication between the two sides of the Arroyo independent of the dam structure. 6. Better aesthetic treatment. The light, graceful arch bridge a.nd dam are more pleasing to the eye and capable or better treatment than the rather heavy and cumbersome looking gravity dam. rhe writer rea.1izes the following limitations to his plan: 1 That the capacity of the spillway tunnel is smaller than that planned on by :Mr. Reagan, and that the full capacity of the open spillway may so seldom be used as not to warrant the expenditure necessary to prov:tde for such a large discharge. However the large discharge calculated f'or ·the tmmel spillway of Mr. Reagan's plan was only obtained by the use of excessive velocities, the use of which cannot be justified. If it is thought, on further study, that the likelihood of the full ca.pa.cl t-y cf the open spillway\} ever being used were too small to wa.:rrant the extra expense necessary to provide for it, and that the tunnel spillway must be able to take care of a flow of 7,000 sec. ft., the writer would suggest the .c onstrue tion of a pair of tunnels, each with a section of 120 sq. f't., and the re- duction of the open spillway section, by narrowing the width, so that its capacity would be equal to a flow of 14,000 sec. ft. The expenditure would not be greatly in excess of the present estimat~ and a better regulation of the reservoir storage would be obtained. The writer does not in any way wish to deprecia. te the value of Mr. Reagan's plan and doea not say that the design of each atru.cture submitted by himself is the most economical or the best that is capable of design, but t.1.e f' irmly believes that the study made · by him . and here submitted conclusively shows th.at a material saving and a better dam can be obtained by the use of' a constant angle arch dam. BIBLIOGRAPHY. Constant Angle Arch. ?lam l1esign, By Mr. Lars Jorgensen, Engineering Newa, Volume 68, Page 155. Influence of Poisson's ratio on atre$ses in Arch Dams, :By Mr •. Lars Jorgensen, Engineering News, Volume 68, Page 208. ••lleglected First Principles of Masonry Drun Design, By Mr. George H. Moore, Engtneerlng News, Volume '70, Page 442, 623, 832. Uplift Pressure, . By Mr. Edward Godfrey, Engineering News, Volume 70, Page 371 . Stresses in Masonry Dams with Discussions, By Mr. William Cain, Transactions Am. Soc. C.E., Volume LXIV, Page 208. The Action of water under Dams and Discussions, By Mr. J.B. T. Colma.n, Tremsaet1ons Am. Soc. C.E., Volume LXXX, Page 421. Provisions for Uplift and Ice Pressure in the Design O:f Masonry Dams, By Mr. c. L. Harrison, Transactions Am. Soc. c.E., Volume LXXV, Page 142. The Ultimate Dam, By Mr. J. s. Eastwood, Weste:t•n Engineering, September, 1913 .. Hua.cal Dam, Sonora, Mexico, By Mr .• H. Ha.wgood, 'l'ransactiona Am. Soc. C.E.; Volume LXXVIII, Page 564. Constant Angle Arch. Dam, By M.r. Lars Jorgensen, Transactions Am. Soc. C .?. . , Volu.l'fi.e LXXVIIl, Page 685., Concrete Arch Dam near Cheyenne, Wyoming, By Mr. M. "J. Moulton, Engineering Record, February 8th, 1913, Volume 67. Construction of a Pathfinder Dam, By Mr. E. H. Baldwin, Engineering Record, "November 7th, 1908, Volu..ile 58. A remarkable Concrete Arch Dam at Crowley Creek, Oregon, Engineer.lng News, August 24th, 1911, Volume 68. Salmon Creek Dam - First Constant Angle Arch, Engineering News, March 11th, 1915, Volume 73.  Elev 984. Fresent bridge elev. 1046. Slaing~valve -— Foor of excavation Wing wall ~~ —— K \ Hh il I! | I |! i! ae ~ i! f i it Core wall tt O 0 20 30 40 50 ~\ a Scale in freer Tunnel capacity = 4000 sec. fr Wath of spillway =/40 fr. Elevation of spillway floor = 1054. Length of wing walis=40 ft Length of core wall =30 ft Length of west spillway wall =73 Tr. Length of éast spillway wall =/4/ fT. Length of tunne! =Z2Z/ fr. Slope of tunnél= ft in 65 fr. Llevation at entrance = 10Z0. + water cushion. ee GENERAL NOTES, eK aa = Maximum flood level at elevation 1067, \. Opillway capacity = 20000 sec. FT _-<-areh aam ror | ji DEVIL'S GATE DAN FLATET MAP OF DAM SITE THROOP COLLEGE OF TECHNOLOGY PASADENA, CALIFORNIA Scale-1"=30' April 1,718 Drawn by Ame : Liev. 1067. Tle. 968 — Backfill Llev 742 Llev. 950 Developed elevation of main arch dam and gravity abutment. Length of main dam= 341. Length of gravity dam=82! Scale - 1"= 15. Crest of dam elev. 10o7 ~ Wing wall, 1' thick. Crest of dam elev. 1064. y Height be-\ Upstream Elev. |low crest) radivs | stress |g ba in feer | in feer | */fr* 455" | /060 7 174.9 17600 jo 1050 /7 ITZ. 36600 5 reciting cnet ana 1/040 27 1675 40400 7: = \ 10350 a7 162.5 4/700 b}— q. = 10Z0 47 6.5 4/800 inn doe Cole < rn 1010 57 148.5 40700 13 1000 67 INS 39500 790 77 136.5 29800 980 67 V9.5 40800 970 77 IZ45 39800 9760 107 122.0 37800 950 H7 H8.0 98500 740 /27 HAS 36500 7350 137 106.0 | 32400 -75—= | | Cross-section and stréss table +—— 26.0'—>4 \ of main arch adam. Seale- /"=15' Elev. 106% -{- ” +}. _______ 80 eae Liev. 1057. —- Elev. 1051. . i \ is} | 7 . | { ig \ + - 4 , . AP 7 Liev. 1047. el | [7 be ———— 13'4"——_ ares 50’ a ag (ores sete of gravity abutment and wing wall Heavy dashed line indicates outline of arch dam Scale- #'=1' f \ Elev. 1010.6~-———" Original rock surtace~ (XSi, Excavation for bottom of dam~_ a7 UT RIRUSTSIN TS TNT ~ \, 3 \ } 4 H 4 ! Fe ! g Section at exit = 10'~ 4 uA Jame as at valve. Section ar valve. ——— Llev 10177 = 12" Flan of main arch dam Jeale-/"=20' Excavation for cut-off ~ { — 14 Cy a | Wd ( lye \ +8 | eI Section at entrance. i ! Ly <t “~~ 1 Elev. 1020 DEVILS CATE Dam. PLATE I. MAIN DAN DETAILS THROOP COLLEGE OF TECHNOLOGY PASADENA, CALIFORNIA Jcale-as shown. Designed and drawn by Btu Keyrok April 1, "18. Elev. 1009. Elev. 1054 Liev. 1047 _ Liev. 1000 == 24! L£lev. 976 Elev. 995. | | Liev. 945 I L£lev. 740 — ZR ‘al]~—Horizontal rods ~%" Tw. rods 6.6. Lvery other vertical rod should be stopped 1" from top. Core wall and wing walls have same cross-section but reinforce— |. A —verrical reinforcement-3'"Tw. rods ooh \ \ L I ppeti petit | iy ment should be placed if" from { battered face in the wing walls. \ Length of core wall =30° Length of ‘wing walls = 40° —_ 1S > be id 14 the () Eiaaeons AA A TSA | 24"— i Cross-section of coré walt. Scale-F =/' Max. tlood level. ' Cross-section of spillway Wall and floor. Fart elevation and reinforcement layout Of spillway wall and floor Scale — 3° =1' se 3 Pb et Fart elevation and reinforcement layouT of core wall and wing walls. Seale - 3 "=/' [ vt 4 Tw rods 4 long every 12" 6 from bend to end of rod i t ite 2' overhang over suppor?.-\t if ‘ iN \ | Liev. 106 ' } ] | \ | it \ ] | | The walls and floor of spillway designed as a | | retaining wall with water lebel at elev. 1069. H rH Every other vertical rod to be stopped 7'6" from top. + | _— Vertical ana transverse steel Yy end in 6" hook 4 | _-— Vertical steel=3' Tw. rods spaced 4°t.6 mae r i - Horizontal steel- %'Tw. rods spaced 6"C.6. | dtl, . : mee Transverse steel-#'Tw. rods spaced 6° 6.6.~ ‘ int i { my ” , i i ka? 7 Tw rods spaced BC | } itt ] . S <f Clow 1054 =F aeeee a A ARAERELAA EARNER cian AA Macadam wearing surface with 4 "crown. Space ro be filled with cinders. ,£ "Tw rods 6'C.c iar Se ~ 40 60 — 4 +; Ss a vas ” | # TW rods 12° 6.65 LO [a or ad LS tn T Epa el Le 3’9" 14 (8° go" —— NIST P= Cross-section of overtlow warer cushion arch adam. Dam aesigned for max. flood Flow of 24000 sec. fr plus full atmospheric pressure. crest designed to fit curve of overflow of 7000 sec. ft which 18 ordinary maximum Upstream radius = 30.5" Max. arch stress =40700 Yin* Upstream face vertical to elev. 970 then same batter as downstream fact = 1:19 \srirrups-#" round rods. 4-15 Tw. rods. L-Vertical rods— # "Tw. rods wpaced 6 “¢.6.under beams Nand 12" ce. in between \~ Vertical roas under beams should be wrapped with “round rods 12" apart. | Horizontal steel- Z" Tw rods spaced IZ" cc. 3 boats 4° # Tw. rods spaced 8'c.c~ Litt spaway rior LI y ~L9, ot, 2 pz 21. 3] SL SL Soe DEN Sed Scale-1"=6' BoB Sat ee A SS art Longitudinal section thru reinforced concreré girder bridge crossing spillway. oral length of 9 spans @ 1b’ = 144) Designed for RO ton truck loading. Ucale— Z"=/" Tro: CRS se fae! CES (0 as Transverse section thru reinforced concrete girder bridge crossing spillway. Scale-#'=1' 4 S| $ mE @ ‘S INGNTININ TIN] NN EN Tad GR POS EN NTN ENS CN ERENT AEN LOD NT I DEVIL'S GATE Dam FLATE AUXILIARY STRUCTURES THROOP COLLEGE OF TECHNOLOGY| PASADENA, CALIFORNIA Scale -a5 Shown. Apr 1, 18. Designed and drawn by Anu aut