The Design of a Reinforced Concrete Bridge over Eaton's Canyon on the Mount Wilson Toll Road Citation Burt, Earle Andrews (1915) The Design of a Reinforced Concrete Bridge over Eaton's Canyon on the Mount Wilson Toll Road. Bachelor's thesis, California Institute of Technology. doi:10.7907/19gf-w732. https://resolver.caltech.edu/CaltechTHESIS:06042024-173146791 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: None, None Defense Date: 1 January 1915 Record Number: CaltechTHESIS:06042024-173146791 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:06042024-173146791 DOI: 10.7907/19gf-w732 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16505 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 17 Jun 2024 21:05 Last Modified: 17 Jun 2024 21:05 Thesis Files PDF (Thesis) - Final Version See Usage Policy. 7MB PDF (Plate 1 - Rein. Conc. Arch) - Supplemental Material See Usage Policy. 1MB PDF (Plate 2 - Reinf. Conc. Arch) - Supplemental Material See Usage Policy. 1MB PDF (Plate 3 - Map of bridge site) - Supplemental Material See Usage Policy. 1MB PDF (Plate 4 - Influence lines) - Supplemental Material See Usage Policy. 1MB PDF (Plate 5 - 75 Ft. Rein. Conc. Arch) - Supplemental Material See Usage Policy. 2MB Repository Staff Only: item control page

THESIS The Ik,eign of a Reinforoed Conol!'ote Bridge over !aton' s Canon on the Mount Wilson Toll Road By Farle A. Burt Olaee of Nineteen Hundr-sd and Fifteen Departmsnt of Civil Engineering THROOP COLLEGE OF Pasadena, TECHNOLOGY Calitomia 1915 The Design of a Reinfor~ed Conerete Aroh BridgEJ, over Fat on' a Canon on the Mt ·. Wibon Toll Road The Mt. Wilson Toll Road was originally e. two-toot burro-trail. Later on the grade wae revised. and it was made into a narrow wa~on road. 'lhe a.silent began in the upper part of the Eaton' a Canon Wssh. For sever- al yea.re the approaeh to the foot of the trail wae up the bed ot the sanon, over a very rough l'Oad. About three yea.re ago, the.t ie in H)l2, it was deoided to eliminate this bad approaah by building a wood91"l trestle bridge e.orosa the @anon at the !)oint where the Toll Road starts up the sicl.e of the mountain. tlus bridge is ~onneeted to the Santa .Anita Boulevard by a short, well built approaeh. In view of the fa~ that the Solar Obssrve,tory ie hauling all of 1te materials of oonetru~tion and supplies over thie bridge, and probably will be tor many years, and that Mt. Wilson offers also a most plee.aing pleasure resort and ie beir..g ueed tor that purpose, it eeame reasonable and proper to aeslll!l8 that the traffi0 over the road will jueti:fy the replacement of the old wooden bridge by a more eubete.ntial e.nd at the sama time a more beautiful st ruGt ure. Thia theeie offere a suggestion for su@h an improve- mant. A aingle-aenter reinforeed @onorete Ar@h will be investigated. Althoue.;h other tn,ae of bridge might be built ,1hi ~h are t!lll@h oh~per, it is believed that the beauty, safety aga inst high water, and lasting qualitiee of the reintoroed ar@h e.re faotora which etror.gly recommend ite uae. -2- The site of the present bricige is at a ~oint in the oonon whare the stsep walls suddenly widen out into a rather wide we.eh. to b,1 the beet lo~tion for an aroh 'bridge. This point seems By going ferther up the oonon, a shorter span 0ould be ueed bat the approaehee would have to be bleated from thf9 solid roek <11iff on either aide ot the 0e.non, e.t the present site. On the east sid.e of the canon, the solid roek is visible at the eurfa<Je, •• and on the west sid.ft of the ae.non a water tunnel shows solid rook about ten f~at from the eur.f'e.ae. It would ther,af'ore be poeeible to loi'3ate the abutments on solid rook, at the present h.riage site. Plate III shows the main fee.turee and topography of the site seleoted. The method used in designing the 6r@h, is that outlined in "Prinaiplas of Reinforoed Conarete Construotion° by 'l'auneaure and Maurer, pages 333 339. The net.nod in brief ie as follows. A preliminary design ie esle3t• &d by the aid of approximate or empirioal formulas or by re~er~no& to ex- The selected arch is th9n exaatly analyzed and u• neoase• ary the rt1tsults are used to oorreet the preliminary desit,,-n. The anal7sis oor.sista of severel steps. P'irat,the half arch is divided into ten division& along its axis, suoh the.t the length (de) of ea.oh division divided by the moment ot inertia (I) of eaah division is a eonatant. Beeond, the points e.t wh.h h the loads trom the floor system ar9• e.pi,lied, are then determined and the values of the thrust at @rown ( Ho )' ~ the shear at erown ( Vo ) , and the b.,nding mom ant at 9!'0'1n ( Mo ), are found tor unit loads at the load points. i'hi rd, the intluenee linee for atresee~ at several ditferenteeotions are oonstrueted• Fourth, the stresses at the several eeetiorie are oornputed from the innuenee lines -aand the graphiool layout of the aroh. A Fifth step is made in this oose, e.nd. consists of a gre:phiool solution to show that the line of thru.st ate.ye within the middle third of the ar3h. Seleot ions 2!, lli !!2!!,: Howe 1 e nsymmet rioo.l Masonry Arohee II oon- te. ins a table whioh givt,e the name, loading and prinoipal dimaneions o:f five hundred e.roh bridges. rise is eelaot.ed. From this t able an arah ot 15 ft. e~.n 11 ft. ( With working stresses of 16000 lbs. pe?' square inch, for etsel ( in tension) and 660 (lbs. per aqua.re inoh) :for oomlrete in oompreseion) the nmount of tension et eel to b~ used sho\lld be about ;.66% of the e.ree. of the seotion. Th& seotion eelaoted requires, from this, about 2 aquaN_inohee per foot width in ut rados and int re.dos. Rein- toroement to be ple.oed 3 inehee tl-om eurtaae. - --- - - 08laulat ion of Values of I and. de. ---------..., ...... The half length of a:roh is found by sooling, to, oo 43.3 ft. Depth at crown 2.3 ft. and at s1"}ring ing line 3.0 tt • • tia =1 =10 + 151 , 6 T}ie moment of iner- where I 0 and I 8 are the mom-mt o,t ine•r tia of the oon- oret e and the et i,el eeot ione reapeat i vely. first neoeswry to divi~ the half aroh into a num~-~r- equal divisions. In this oe.ae the half o.r\Jh is divided into ten ~ ::'di(v,isions, ( see ·•! •• :1 " 'fte.te I) and the value of I detern.ined at the oentet: '-ot '\,aoh division • ' ' \ Tfte reoiproool of I is found v.nd is called ( 1 ). ooloule.t ions e.re given in 'l'abl .e , I. 4.33 ft. lor.g. The preliminary!! diyis~one are ea.oh As shown in Table I the vala~ Gt dsi'. ~ \a . ♦6\ -r- .. / .. :, • By rafer- 1.: enoe to Plate I a new value for the momffllt of inertiar, t91rJ,,t lj•, first new divieion 1!18.l' be e.asumed and by substitution i11, the eq~tidn~ =2.4-6, a valu& o.f d8 may be found. the arch a.xis. •oh va.lue of de as found 1s laid off on The first trial doecs not generally oome out even at the end of the half aroh but by :paying olose attention to the value of I it is quite possible to find ten valuee of ds whose sU!!l 1a exe.otly sque.l to These results are aleo shown in Table 1. the length of the halt aroh. TABLE I Division& No. of Div. Depth( d) -2.! ~ .fil!ltt· Io 151 I=L¢ +-15! • B 1~1 de ~ I l 2.aoo 1 1.012 . 835 l.34? .143 3 .30 ·'·· ' l.340 2 a .a26 1 1.0.u .844 l.1J85 • 122 a.a0' l .378 3 2 .3'15' 1.110 .363 1.4?3 .618 3.60' l.423 4 2.400' 1.150 .313 1.623 .65? a.Ga' 1.496 fj 2.475' l.258 .402 l.655 . 606 a.ea' 1.558 a 2.550 1 1.815 . 435 l.810 .558 4.0~• 1.aa. 7 2.&at>' l.500 .468 l.966 .508 4.48'' 1.a20 8 2.12e' l.670 .512 a .1a2 .458 4.89' l.990 9 2.so0' 1.920 .572 2.492 .402 5.61 1 jh240 10 2. 950' .2 .130 . 622 2.758 .864 6.56 1 2.6?0 31.l."!l 1avg.= 5.69 -ro- == .569 5.690 48.28 1 48 . 3 X .569 = !.46 = "i 10 point. Before ,,a1u~ of Ho, Vot and. Mo can '.be found, it is :n.,~esary to k&.w the points at whioh the load.a a:r-e to b"l e,x,plied to the arch. For the present we may Oonaider that the sttperstruoture has been designed and that th-e load points are A, B, C & n, as shown in Plate I. Val- ues of Ho, Vo a.nd Mo are found with a load of unity at eaoh o~ the • loe,d. points. Reterril'lt~ to Table tl', X end y are the coordlne.tes of the central Values of points of the wrioue divisions in whioh~ is constant. I ~ , MiJC and 'MrY are det emin"d when the tLl'li t load is at A, B, C and D Me:pectively. x1 as shown in plate I ia the diste.noe ot the re- spaotive load.a from the orown. From Taunee.ure e.nd Maurer we have the following formµle.s for valuas of Ho, Vo and Mo, detarninetl from a oonsideration of the aroh as a curved beam. Vo = = - ..%M + I Ho !r la N Values b-or11 i'abli, iI are substituted in thes.a :formulas. sul ts follow. The re- - 6TABLE II Caloulet ions for Ho, Vo & !Jo 2 Load at A• X1 =0 y Mp X y2 Mp u 11 2 . &a . 0004 l. 6 . 04 a .6 . 200 20 . . 400 5. 00 1 . 00 8 . 45 . G75 71 , 5 . 456 8 . 45 6. 70 :.;! th§ · ! \\ "' '"· ·;- J ;,5 4 12. 00 l e400 144.0 l. 90 12. 00 16 . 80 144 .O 5 15 , 75 2 . 400 2-48 . 0 5 . 77 16,'15 3? . 80 248~0 6 19. 5 3. 650 380 . 0 13. 30 19 . 10 11.ao 38O . O ? 23 . 35 5, 400 545 . 0 • 29 . ! 83 , 35 1 2? .00 5415 . 0 8 a1 . 50 1 . 65 75?. 0 68 . 6 27 . 60 210 . 00 '151 . 0 9 31 .'16 10. 55 1 004 . 0 117 . 0 31 .?5 ~36. 00 1OO4 . O LO 86 . 35 14 . 35 1 a20. o 2O7 . 0 438 . 09 86 . 35 5t¾4 . 00 1320 . 0 Pt. X y X 1 1.6 .02 2 6.00 3 ~ 46 . 29 4 Load at 4497 . 0 B. Xl = ll Load at 0 pt . Mr 4 1 .00 1.4 12 i 4. 7& ll . 4 ?& e 8 . 25 ao .1 168 1 12 . 35 66 . 7 8 16 . 60 9 10 M... z; y - - lfil.00 - 1a2s . M Xi 449? . 1 = 21 Hr Mr y Mr X 269 2. a5 12. 1 55 126 . 2 455 6 . 50 49 . 6 1 79 20 .?6 819 .0 660 l0 . 76 l.13 . 5 84-2 25 . 35 3-64: . 0 920 t - 88 . 95 10. :u; - 818 . 8 - 2579 - 34 . 9 ,s 220 . 0 - 395 . 8 - 11 34 Mr X 558 -6 a Load at D x1 ::t 31 pt . Mr u'l' r Ur X 9 . '75 1 . 92 23 . 8 10 - 6 . 10 5 . 35 7'5 . 80 - 84 . ?I '<.' 4 - 194. 0 211.s - 4391 . 8 8994 10( - 1 32s . 5 ) - f1s1 . rm • 46 . ail) '"' 43.91.S Load at Vo= ! OU ) = - 449~ . l 89~4 A _ - 0. 50 8994 -1s1.5 + a · 1 . 11 • 4629 20 Ho = 10( - 818 . 8 - ( - 88 . 96 • ~ - 29 ) = + . 924: - 4391 .8 Loa d a.t C = + . 18? B Mo ~ • - e8 . 95 + ( 2 · 924 • 46 . ~ ) = + • 113 ao L Ho = l0(-396 . 8) - (- 34 . 95 • 48 . 29) _ + • 682 08.d - 4391 . 8 at C ,o = H - 1134 , 0 = - .1 265 8Q94 C = Mo Ho = - 1.07 = + 1.11 - Mo = 10( ...a4. ?a) - ( -e .1 • '4¼l.t 9) .129 -4391.8 toad at Vo = -217.8 e - .0242 61194 D Mo ::: - -.293 20 _.,,_ Influence tines tor Fi bsr St res.s at e.nz 8eot ion I nfla-ence Lines are diagre.ms whioh show th,a c.,ha?"a.oter and amount of streesi at a partioulnr seotion ot the arch,. caused by a unit load pass·• i ng aeross the aroh . From a oonsidtH•ation of Z...tndar.ant a l :pri-nciples we know that Mo + P , in whioh Fo in the stress on the eeotion, o th.e T I distanoe f':r-om the ~xtreme fi ber to the neutral axis, I the moment of Fo= ± inertia of the eeotion, P the normal thrust , M tha prod.uot of P and the exoentriaity of the resultant thruat . If 1" ~quals the r'adius of gyration w~ have A r 2 = I, then: F =± Pe o I + r2 p 'i, • C I + 2 1" ] =M t 0 then F - M' C I In a :r13atungular sa,1t ion u• is equal to p b, d, X lfo and "6 2 d2 X Ho for up- per and lower fiber stress res:pootively . b, d, is vertioe.l distance from - 8- lower third point to thrust line. point to thruet line. bq d ,:;; 2 ie dieti-"1.noe from upper third Ho i s tflken fl"o~ .w,lculations following Table II . Values of M' are shown in fable III e.nd e.ra plott ed i n Plate lV . rhe~e Influenoe Lint9s show olearly ths action of the aroh under vari ous loads . There is aome diffiaulty in determinint;; whether m' shottl.d ba plotted ae tension or oompresaion • In gen~r.al this can be determined by l"6fe1~r!ng to Plata I and noting ths position of t he thrust line . Whan this line is well above t he aemt:ral axis w0 will hci.ve cornp1•eseion in the U1)per half of' t he section and tensipn in the lowar half. When the thrust line ie 'bt1 low the oentrel e.xiG th<3re will be tension i n tha upper half and cornpr'3seion i n the lower half ot the c&otion. When the p + Ye lina is doubtful, it is ne~ssary to ua-e t he formula Fa = - - - - + _ . I A p Mo When we havo o-ompression over the entire section. I A -9Tl,Bl,E III Solution 'by use of Influ.anoe tinee. Unit Load at ➔ A B M Hob2~ b2d.a Hobldl HbC0 2 4 . G? a . 52 0.4 o.5a 0. 37 0 . 49 0. 4 0. 44 0. 44 6. 0 4 . 15 4. 68 a.ea 0. 90 l . 80 1. 00 2 . 00 o.oo 0. 50 0. 46 0. 4G n 0.35 0.'10 0 . 89 0.'t? l . 35 2. 5 1. 25 2. 81 E 3. 6 2. 65 4 . 00 2.ea 0 . 46 1. ?0 . 48 l . 5? b 2d 2 Hobl dl Se'O . AA- 4 . 2' a . 20 B 0. 4 " C 11 ff it M bldl bldl D C M H It A 0. 10 1 . 85 .a?s 0. 88 l . 95 a.so. 0. 25 . 49 • . B a. 01 2 . 25 l . 6~ 1 . 19 1 . 25 0. 66 . 16 . os IJ C 6. 5 'V . 5 4 . 52 4. 0 ...:, G. 4 ·;_ 5 . 7. '. • 8$ '.. . 1f 1 . ? 3.aa . 92 1 . 18 14 . 0 11.0 1.81 1 . 42 '1 . M 9.1 a.se ,.a3 33,2-5 39 . 25 4. 28 J . 06 " E ,. Unit Loe.tl at A M H Sea . n• 0. 4 0. 4 . 44 . 44 1 .s a . 05 l.66 2 . 46 1i c• 0. 9 1 .8 1 . 00 a.oo l ."1 6 il.66 1 . 62 2 . 45 • D' 0.1 . 39 . 11 0. 8 0. 2 . 14 ,18 u E' o.ao a.a a . 65 4 .00 a.es 5. 0 4.0 4 . 62 a. 10 - 10TABLE III Continued. Unit Load at ,D 0 M M bl dl b d 2 2 Hobl dl Hob2d2 'bldl b d 2 2 Hb d o l l lt b d Sec . 3• 2 . 00 2. 90 1 . 09 l .M 2 . 90 3. 10 • il? . 48 .2 . 1 . 136 1 .11 1 . <;0 2 . 40- . al . a1 0 u a t ll D' 2 . 1_5 l . 25 1 .14 . 66 o. i 0. 2 . 10 .os If E' s.e 5. 9 s.se 3 . 13 7 . 35 G. 'b . 98 .sa J; . 25 2 The p:r-seant trafria cn~ '3 r th@ Mt . \Vils-on Toll Road consists of a few d ----:J Unirorm- 1-C::od over eotire area <JO#/ft 2 2H# - - It? '-~I~- '.) 8Mn 12·-'- - = a , ~ , . . _ _ _ , ~ - - ll - 11.a th.6 wi c~th of the road i .s. at pr('sent eif~t feet and. £1.8 tha1'e ls no probability 0£ its b >eing mr,da wide1•, it is r":lasonable to astnune the rotidway on th~ bri dge to be nine f~et , The s]?s.ndrel columns are e.ssumed to spree,d the lo(l:.d equ.a.lly over the entire width of aroh" By comparing the dia.grar.i wit h p late I it will 'be 8138n that the lrh(lel conoent:r.atiorw 1:iay be :r..a.d" to come 0.lr.tost exactly on the top of the sp11.ndrel co lur,,.ns , The t'loor sla t is dasi 1_;nsd eocording to the meth;,i given 'by ?urn~ura .. . and Maurer in •,rincipl.es -of Reinforced Cono:rste Constr11.Gtion", r,ages llS- 65 . Por a bear;1 with :f'i.:;ed onda and a concantreted. load = load L:::: length in inchae 'M = Benciing moment • P Theref ore r4 _ 8000 X 48 8 =.: 48,000 in lbs. For o hoom witfi fixad e:nda e.nd uniform load 2 '11 1' ii L =12 W!!:; · weight of load :pm• .foot • Therefore : M' _ 80 X 4.8 UJ Tote.l moment 2 = 15, 300 l n lbs . = 4B, ooo + 15, aoo = 63, 300 1 05 bd.2 D = dopth to steQJ, . With the working atresaes in concrete and. et~el a lready not ad and a resulting peroentege of steel of o.bou.t • 78, the value Solving wa h21ve d of R ahould bs about 105. = 7 inohes . kn eleht inch el.ab will be used. - . 15 equara inohes for eaoh foot width • • 75 . 25 t.he ehae.1" on the floor slab will be: Uniform live l .oad ~ . aio lbs . " :::: 400 lba . Total 8720 lbs . It 8720 2 4000 4380 == r:iaxir.rum = 6500 lbs • per eqtuare f'o\Jt , = 45 lbs • per .67 square in~h. 45 l.bs . per square i:n.}h is just a fsw pou.ncl.e too high for plain aonoreta . inchee apart • a colu.r.m . Tho method of designing the striuger ie tho same e.e that used. Uniform load weight of slab " =4 X 1 0 X . 6'1 X 150 = u live load ::: BOX 40 4000 lbs . 3200 It 7200 ti -la7;?00 lO = Maximum oo-neentrated .load M M' - 120,000 in l ba . = _ 60Q BQ X :: ?20 X 1ao 12 Total 2 sGa, ooo in lbs. = 983,000 i n lbs . 105 for 78% at ael T-' ~, = 60 12 X 25 R = 130 14 I 26 R == 104.. O.K. assume bear.1 18 ....V" 80 u tt 8000 lbs. ff Q ., • 39 = area of 5/8 inch s quare Ear;. uae ?-5/S inch, At each load. point the l oad is to be oarried to t he aroh ring , by four spandrel aolumns, er. ch to take the load from ,me stringer . The -rexi:num weight to ba oe. rrfod r.:y eny four columns will 00: 12,000 l.bs . Weight of sla"b 140,000 loo . Maximum concentret-,d load 16,.00-0 lbs. Uniform live load 9, 600 lbs. wt. of roe.c.l surfaoe 12,000 lbs. u 10,800 l bs . '' railing Total 200 1 400 l bs . 200,400 = 400 squa1•s inches aroo raquired fom.. 14" 1l.'. U, 3 ~olunme have 600 iil.nd area of 800 square inoh-,a. 14 in0hee i .s a minimum dime-nsion sinos a. dim•msion less than 14 inohos will look weak in conneotion vith tha It has b(~0n !'ou.nd. in :,;,raot ioe that it ie deelrebl6 to ~lyze a."! a1.4c,h with the <-m tire ler1..i;th ; two-third.a the length; one- third the lor>.gth ~r refarring to the diagram of a tan ton truck and to Plats I,. it will b~ seen that th@ nearest &.pproaah to ihis loads the midilo two- thirds . Secor.d: F'ront wheels at A,; r ~e.r wheels two feet t o right of' B. It is not l)OS$ible to have two truoks on the a r oh at the eame time if go- inG in opposite direetions . I:f two trucks w~re to follow ea.oh other as The load-s whiah th~ two assum'3d loaiinge bring t1J:i-:on the aroh, will now be given . Load eond.it iOl"lS Nur..1'be-r I • Front wheels s.t B' rea r wheels a t point two feet to right of A. Liva Dead Lo@.d. at D' = 0 19, 000 + = 19, 500 lbs . = 19,800 lbs . -151oad at E-' - 18,600 + 930 = 1~,nao lbe. ti IJ A == lB,250 + 1,soo :i:: 20,150 tf. It B - 1s,aoo + :: 18,900 lbs. It ti C - 19,000 +0 = 10,000 lbee If ·11' D = 19,500 + ~ 19,500 lbs. 3-00 0 lbs. Lon d Conditi.o n Number 2: Front wheel~ at A, ff.2.r wheelo two :feet t::> rieht of B. Dead Liva ?o-tal L.oa.d at n• = 18,500 + 0 = 19,500 Ii IJ O' - 19,-000 + 0 = 19,000 II It B' = 18,BOO + 300 = 1·0, 900 " If A = 18,250 + 980 - l~,l80 " 9 B = 18,600 + 1,930 = u~,6ao If If 0 = 19,000 + 300 = 19,300 ff tt D = lS1,500 + 0 = 19,500 Th$ s.otual J1Jt~esse3 at any eeot ion At B, C or n, r~y . now be ooey..it e.d f"rom the formula M' is taken from Table III. -16- Relation bat wean 'm'bl& III end Influeno~ tine& . Values of M' tak"n t'?-on Table III ere used as ord.inatas in the ·:JOnetruot ion of the Int1.uenoe Linoa (Plate IV), as mentioned before . be taken from ( Plate IV) or Tabla III . fora ueed. . U' can The results taken fl-om t-he Table Tho Innuence Lin"3s serve chtefly in ( g iving a quick m&thod of) determining the character of etrase. TADLE rv. Properti~e of Sections A, B,. c, D, E. A Saotiori D~pth C ::: -1..-fl ---,2 I AC + l.O A$ 2 . 21 + . 4:.2::: 2. 69 A 2. 80 1.15 1.a4 B a.a1 l.l\1 l . 5i C 8 . 63 l . 2.tl l.75 = 2.16 2 . 00 + . 42 = 8 . 92 D 2 .• 80 1.40 2. 24 a . 11 + . 42 == 3. 19 E a.oo 1 . 00 2.15 2 . 97 + . 4-2 2 . 34 + .4 2 = 3. 39 . 55 One exal!!Ple of the cal<)t\l.e.tio:n of st:reas et a e~otion (of o,ne foot width) will now be giv9n . Up~er half eeotion A Load Condition No . I M' :::: ( 19,600 X . 26} + (19,300 X . 378) - (l9,v30 X . a?) - (2.0,150 X 4 . ff?) - (18,900 X .3'?) + (19,000 X .372 ) F = M'o -r= -84-,3-20 X. .86 144 = 500 l 'bs • per aque.re inoh <>offl!)res a- 144 ion• There follows. the complete qalculr tions :for upper o.nd lower fiber The higb.eet aow..,ref3eivs streee :four.d out is 500 lb&• per equare inch, which is nllowable. The only oo.ees of tens ion are in the lower half sect ion A under Loa dill€ m&.ximum ten,sion t's0und is SO lbs. per square inch\;: ·;_f,_On. account of this low value and ~f the e.mount of h~vy reinforoement it ie "belii,ved sate to allow these values. This oomplatee the t:tnalyt toal solution ot th& arch. A brief atatmnent of tho methl')ct usecl in the gra-ph!oe.l aolution will ·now be given. Upper Fib"r Ssotion A Tension lB ,500 X . 25 Loadir1t; No. I • Compression = 4,880 20,1~0 ;{4.61 :::: 94,000 19,000 x .an _=1_ . ,_1_a_o___ + 24,120 18,900 X .a? = ?,100 - l.08, 820 24 2l2C 84,~00 54,200 X .86 144 Seothn A 1'eneJ.on 2o,l60 X 8 . 52 :z:: + 1lt6◊0 19,300 x .as= 11,soo - '71,400 + 1 00 19,BBO x . 49 = 2 - --ll--,-4-0~ . 8 lbe . per square· inoh tension 100 X . 86 -----== 144 Sect fon 13 e soo 2 as,voo Loading No . I • Compress ion 19,500 X . ~7 = 7,230 2-0,-l~ X ~44 = 8, S',.f.O 1s, aoo x 1.og = m, ooo lS,900 X 4.62:::; 8"1,200 l.9;530 19,000 X l.t;2 i:: 30.,800 X l.65 ::= 22,400 60,630 19,500 l .1e =. 8,120 - 130,060 . eo 2 3ao 89,430 X . ?8 14:~ Seoticn B Tension l &, 900 X 8 . 83 = 72,800 l ~tOOO X l . lB ::,: 22,600 .oa = 1 2 :'.itiO 96,350 19,500 X 19,530 X 2. 46 80,150 X .•44 = 43,100 = e,050 98,460 100 X . 78 144 = .55 lbe . per square· inch oompreseion os,auo 100 <JO!!il'• 20,1:5 0 n.oo !!'.! 20, .1 50 :rt,.iao 9:-? 1l 00 :iC •·'?.. 144 =4il5 l bth 11er eque,,re) i n,Jh o~leyrae.ai-on. ----------------·----·----------------· Con:prees ion 19,3-00 X 1.11 l.~,5:tO X 2-.4J} -.... lU,i0-0 = 48,000 20,150 X :a~oo - 48,600 1.H.,900 X ::i ~4 6 8 2 ?00 lZ0,800 ~~1,,200 ~3, uOO X • ~ 14:-4 Sootion n C 1s,ooo x . gr. = r,1100 ~,100 _,42.t 750 X . 63 144 = 181 lbs. in = l,O&O n' 19,500 X .10 o' 19, 5'30 X l . J.4 :: B' 19,530 X . '14 = 14,~00 A 20,150 X . 39 = a,aoo D 19,500 X l . 8l ::: aquare inoh eoi!qYt•sssion • 22, 000 a;300 82,050 402100 42, 750 to.V i~ F'i,l1er 2ffl".sion n' 191 500 X . 08 c• l9, ~0Q X .aa B' l9-, 630 X .18 ~ ,:l,5Q X JJ = . ., 3,t;~O .17 lS, 908 X 2. 31 ttt l.fl,800 = 4.8,100 C .-'ri, !33v ·------~------ C "l u,,a.oo ·~ ~os = 1.a,100 n l.f}, 3;)0 1t 3. G2 = 10,201J 19,.5-30 X 4 .,Q3 :ZS· B' L:,war Pi!}\')!" i'e-r~fli;;.n =· D' l9"UOO X . a:2 ci l ~, :WO l 3!'13 - B-' lQ, 53-0 X ~. 19 -· 1e,ooo 00-, ~~ = 51 l'bn . ~ eq~N inch ce~prrma-ion. ~o,ooo --mUpper Fiber Teneion n• c• 0 Compression = u,.ooo X .a,~= 19,800 . 3"12 = 19,600 X . 25 B A B' X 191 700 X . 83 144 := 18 1 900 x = 6,9SO lGa, ?2-0 ::2.t 1 oao 79,700 477 lbs . per square inoh compraasien • Lowar Fiber Seotien A Loadir~ llo . a. Oc,mpraasioh Tension __ 4,._B_s_o_,_x......_._s_a__ = 23 lbs . per equara = ~, 5"50 n• 19,500 X . 49 o' 19,0.00 X .se = 16.788 B' 18,900 X . 49 = 9,250 B 19,630 X . 49 ,,:,: C u,,3-00 X .es - 11,000 D 19,500 X . 49 = i noh oompre.e eion . 144 . 3? :'. 9,580 9,510 1a,110 67,500 4,65-0 Seotion B Up-per Fiber l'eneio:n Oompr-eesien D' 19,500 o• 19,000 .xl . 09 B' X . 8'7 = ?,.200 = 20,'ftO· 18,90Q xl . 66 = 311400 59,800 73,500 x. . 18 144 044 = S,.400 x 4 . a2 - e0,000 A 19,188 X B 19,nso C D 10, aoo x 1 .si 19, 500 X ol3 =: =380 l bs . per square inch aomp?"ession = a1, .380 8 1 +00 1a2,eoo 59,500 Seotion B .es l) =; c• 19,@C'O lt 1.54 = 29,~00 s• 18, ~f)O X 2 . 45 = 46,309 A l9-,l89 lt • 44 = s,,neo . 1,eoo 9@,100 0.a,aoe 98.,,9·1 1 5,800 = &, SOQ x • 'l·S 144 30 lbs. pe11" t1H1ua.re ine.h oompressi,.m Seotion C 'fensian Oompreesion . e6 = 12,500 c• 1,,000 x :a• 18,900 . x l efim\ = :~.-600 A D C . 82 = l3 2 &0G 116,$@3 _~1,4oe x . ?~ 144 191200 = 480 lbs . per -square 1noh oonrpreasietl , 97;4:08 Loading NQ . 2 001i11'rees ion c' 19,00:0 1 .11 = 21.,.100 X e . u,,soo x 4 .0 = ·n,000 B' 18,900 lt 2 . 45 = 46,48$ D lJ~,,600 . 114 = 14 460 1 A 19,,180 Jt 2. 00 - ' B' u~,53® ...¼6,SO;O Jt 144 X se .st-0 .n~ = aa lbth per square inch oompressio:n x .,e 88,40:Q = 9,oeo ll4 . t00 981 ~00 1e,aao Campre:u,isn . 9~ 38 2 258 X . 68 144 = l ?1;800 • 4a,aoo = 108 ios . per sque.re inch oompressic,n . P' 19,500 x C' l~, 000 x l .14. B' 181 900 x • '14 = 14, GOO A lG,lSi x . 30 := D u~,t}OO x 1.s1 .1 = 1,950 = ru., 700 ?,5SO = 35,300 80,45Q Seetion D !ensi08 Oampre-seion D' 19,500 X .oa = Q' 19,000 . 66 X = Ul,5f>G a• l8J\~0 ·x .1s = :0 1.42 :J.t~,580 X 590 a,•o& B 19,5:W lt lh3l = 45,2&0 C 19,803 = _8~~?!) l.'18 X = ,2?t ?.0~. 1~3,90& .441:1.98 44-,l9€J ?9,?10 -- 31i>O lbs • p9r ,a-qua~.e inoh aompreas ion. ----------------------·-------------tension . 42 = s,20& X ~}.ij6 = 74,500 B 10,530 .x C 1~ 1 800 ' J) 19,tJQ0 X 4~28 = 8.31!1>0<1> iea,1Go B' ' .• l.8,909 ~ *\G.2 = 87,500 ,,.'171; 00@ 144 251,300 l66,20G • 96, 18$ - 24Saoti.on E Comprc0sii>n Tension D' l .~.500 c' ui.000 2 B' l.8 1 90.0 u,,1a@ A X ,. 82 = l.6,.000 X = 59,~o 3 . 10. = 10,;·oo ;g = ~., ,ooo a . l3 i.s2 l9 1 .f>30 X 1 . 6? C 19,890 X ~h88 D l9 1 5i0 X B = aG,700 = 98,,500 5 . Q6 = 99 1 aoa ~28.2'8© l.99,50Q M,108 199,5&1 24 1 700 x . 55 = 96 lbs • per squa re in.'Jh oompressicn 144 ?'ne &>tted line H ia drawn from the PQ'int 8 te the load line . brium polygon . ed. H is 1,arellel t0 the clo-s-ing line of the equili- mm the ~int whare line H strikes the l,ond. line, e. hori ... Table V givae all oo.lou.lat ion&• from the axle . the middle thi!'d. With the new ray oeriter a n~w e.q uili- . Neta ~m Pl.&.te I! t:ti.at the p0lygon stays w,i.thin Ho This moo.nm that there ia no t ansion at e.ny S90ti3n of the e :::; Mo • -aroht and may seem to disagree with this analytiool soluti-on • ~& e;planatien is that the graphioal solution is not ?'efinad enough to detect euoh small ... 25 ... s.lso rn!! ru>ted that at the sections whioh show tensian in the llrlalyt.iool methed, Taking these things int.$ oensiderati0.n, we ffl8.y ae:y that thEt gnlphioal a0lutian sh.GWS the arch t@ be safe and therefore oheoks the analytiool method . This c~m:pl.etea the analyeie of the a:roh . All etreeeee have 'been fe.u nd allowable . The original aroh oo.n therefore be as~d . fillat ·has be-en J)Ut in mt the a butment t0 give the awoo.ranoe ef a three oentsr uart icular ehow theee,,,aJ>chitectural details to be the best eutied te the oQn<.Utions -o f the In ordsr t0 make t .he preblem oonwlate, an &stimata @f 00st is given below . COST DATA Railir..g (81 K . ·8 1 .X J. . 6)2 + (6'7 X .6'7 X l . 5)2 = 331 oubi o feat 397 cu:bie feet 695 oubio fe.e t 6'76 oubio fset !0 oubio feet 65 oubio feet 185 oubi a feet 2980 oubio f'eet 400Q 11314 ou'bio fe~t O~lu.-nn at aenter Colu:rm et l l te-et fr~m oente? tor base= Colur1m at 21 feet fro.m eenter (2Xl2Xl8 . 5)2 ( 88 . X 18 X l )4 CT = - > ( 2.8 X 12 X 86 . 5) - 2 Abutnents ( 17 X 12 X 11 )I = 21 ) .ll,814 CU'bl~ fe-et -' 48-0 C11b i o ya r.ds 420 X 15.0 = $0,300 ooet of Conorete ,;, ill.!:oavation == <j Oor.orete at ; 10. 0 :i: o, aoo .. oo 10·% tor engineerir.g i ::::: 1346 . 00 101 fol' oontinganoi6EI = 645. 00 F..stimt.-,(l total a.oat :::: $7,140 . 00 I l. 50 . 00 l o96 5,30 144 . 00 248 . 00 560 . 00 758 , 0QQ l .4 2. 3 3. '15 5. 0 1. e 10.6 ua.o 16. ?5 19 . 5 2a . 4 27 . 6 31 . ?5 4 5 e 1 8 9 10 . 66 7a.oo . '13 e.a 8 • .l. 2 l ~~l~OO_! . 208 . 00 86 . 85 JA, . 46 l 320 . 00 iil . 6~ 460f> . 68 . MR •i,,1 ;.,eoo • l.2 ~6-4 2000 , 948, OQO ... 14, 0•1, a,o a,Looo,Goo 1'1;500,0QO 10,100.000 5,680t000 $12,000 ,r,2,000 2,eoo, 000 1,100,aoo 3041,000 11e, ooo 21, 100 lttSOO ( Mt +l.m)Y 855,00(J 248, 088 181 , GOO '78, ?GG 46,300 14,800 ... s, aa2,e~·o a,011,s G , 431 . i'fa 699 000. ua.oe 1010 . 00 -'94, 000 389, 000 68&,00Q 30 . 20 -~!~ 11~10 284,0SO l.89,000 78,700 46,800 14,800 UL 6'1 . 90 ae2 . 00 0 . 90 25 . 00 .ao 5.0 tg O. OG 2 . 66 .05 1.eo l - y2 y X Point 2 X V. Inveetigation of line of th:rtlet within Arch Ring . ?ABLE I • ..:, N V TAB1E (10 x -14 1 941,aoo) - (-s,aaa,aoo x 46.65) 2 2 (46.65) - (10 X 431.9) Ho _ Mo = Sn + a Ho Ez 2 N _ -e,aaa,ooo +ex. M,500 x 46.65 2 X 10 - = + 28, ·6 00 C Cont i .nued. Mo =& = 2a,aoo 84,500 -  THESIS PLATE LT REIN: CONC ARCH THROOP CULEGE TECHNALOGY FASADENMA CALIF wale:/=8" May 15, (WE Drawn by E. Bort Traced oy LAB. B £=4950 2=18,500 20590 — i] /3 S00™ THESIS PLATE IT AEINE CONC ARCH THROOP CALLEGE TECHNOLOGY FASAQENA GCALIA Seale: /28'or 1000". May 18, 1915. Drawn by €. Burt Traced by EAB, 0 ser VaTory 4 or bridge THESIS ~ MAP. of BRIDGE SITE THROOP COLLEGE of TECHNALACLY PASADENA CAL/F Seale: 1220" May 15,15. Drawrly E. Burt Traced by Bort. SEA Sect B | SECr C (ersiorn 4 Avo, pression | Secor D es ee | \ | 7; Scr E ve THESIS PLATE X INFLUENCE LINES THROOP CULLEGE ¥ TECHNOLOGY PASADENA CALIF Sale: 12 6'or 8" Afay 15 WUE. Drawn by E. Bort, Tracedby EAB Nore. — “itfvence Lines shOwINg values of ff" 77 |B >| eb lEV.-4885 Roadwa WEAN SURETY TTT TT eI “GA 510..0;.055 0,0 = ey a WSO Bars Spaced 41/31! (=i! Ty S wu Cy NY ii s > = " ; _ 4x28" beam 7-£' Bars S oo K Ke a cin ita ae Earth Fill 7 @ Bars Spaced & = Ge, oe im My iH im \“ y LWElev3a77QlA a / ES —— ee iS i mye ZEN = \\ = ale Superstructore sane as atA ELEVATION L.0COKING DOWN STREAM : : eee Areraiiing Wall Fil Le 38" CS TO OO -/"n Bars per Colvrnn False Spandrel Wall > Slab Reintorcerneri # @ Bars 4'c-c.Altetnare ones bent up lf ongi tudinal Bars ZO Spaced l2'0-C. re - 8a Bars SECTION AT 'B" ‘@ stirrups 12" C-C along areh Ries aan Pio Ae es ind CAM: Ali, a THROOP COLLEGE %¢ TECHNOLOGY PASADENA CALIF Seale: /* 8 or 2' May 1S HF lrawn by E.Burt Traced by EAB.