Analysis of a Concrete Arch Highway Bridge Reinforced with Structural Steel Citation Barnett, Harold Arthur (1923) Analysis of a Concrete Arch Highway Bridge Reinforced with Structural Steel. Bachelor's thesis, California Institute of Technology. doi:10.7907/G3M1-S889. https://resolver.caltech.edu/CaltechTHESIS:06162015-110042804 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 1923 Record Number: CaltechTHESIS:06162015-110042804 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:06162015-110042804 DOI: 10.7907/G3M1-S889 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 9022 Collection: CaltechTHESIS Deposited By: INVALID USER Deposited On: 17 Jun 2015 15:22 Last Modified: 16 Aug 2023 22:00 Thesis Files Preview PDF - Final Version See Usage Policy. 11MB Preview PDF (pg.38) - Final Version See Usage Policy. 1MB Preview PDF (p.39) - Final Version See Usage Policy. 891kB Preview PDF (p.40) - Final Version See Usage Policy. 749kB Preview PDF (p.41) - Final Version See Usage Policy. 552kB Preview PDF (p.42) - Final Version See Usage Policy. 649kB Preview PDF (p.43) - Final Version See Usage Policy. 758kB Preview PDF (p.44) - Final Version See Usage Policy. 638kB Repository Staff Only: item control page

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S-/re::.s Cvr¥es /t!Jr y"q~~'ovs <e,,.,¢,·/;,,,*S ~ ~ ,L. ,·ve Lo--~~ .s-"-5"/ C"'7/&L//.,./,:;,, t!Jr Rey;..re~ 4,.&.4 r,>,-,b .Se c/;o ns q / - C,,...,., vv";1 .a- ~ 4 // b;-./7~/77 e '7-;I-. ~HES IS Analysis of a Concrete Arch Highway Bridge rleinforced with Str~ctnral ~teel. By HAROLD A BARNETT Class o~ Nineteen Hundred end Twenty-~hree. Department of Civil Engineering. California Institute of ~echnology Pasadena ualif. 1923 ~esorlption of ~ridge at Springfield. Mess. An article in the Engineering News-Record for March 30. 1923, describes a new concrete arch bridge across the connectic11t .t<iver between Springfield and West Springfield. Mess. There are seven arch spans with span lengths varying between 110 end 176 ft. 19.l to 29.7 ft. ~he rise of the arches varies from The width is 80 ft. The arches are made of five ri bs, three grouped near the middle, and one et each aid e. The reinforced concrete road- way is carried on col11mns resting on pedestals on the arch ribs. The ribs ere parabolic in shape, are 4 ft. 6 in. wide, and of constant depth in each s pan, b11t va7y in d epth with the span lengths, from 4 to 5 ft. The reinforcement consists of heavy riveted str11ctural steel lattice g irders, with a small number of hoops end longi t11d ina l rods. The girders were erected es three-hinged arches and later spliced et the orown to act as two-hinged arches. •rom the steel work were then hung the forms in which the concrete of the ereh ribs was piacea. ~he edjus1,ment o.f the steel ribs was secu.red by heavy screws thro~gh the cast steel shoes. by which the distance between the face .of the grant te skewback and the base of the shoe could be varied. After adjustment, thes speoe was filled with an all oy of antimony and lead which d oes not shrink on oo~ling . The cone•ete was poured in 20 f t. s ections from each end alternately in or der to avoid distorti on. each rib being po~rea in one day's continQoas poQring. The structural steel frame of the arch ribs snpporta the concrete until it becomes set, after which the steel acts es reinforcement in supporting additional loads •• This method of construction - makes it possible to develop an initial stress in the steel in addition to its stress as reinforcement, a result which cannot be accomplished with roi reinforcement. The worging stresses established for the design for live, dead, impact end temperature stresses were 16000 lb. per square inch in steel and 600 lb. per square inch in concrete. The ratio between the moduli of elasticity was taken as 12. In one of the ribs of the longest span the maximum stresses were as follows: cteel.~Construction stresses due to weight of ribs end forms ~tresses 9820 lb. per sq. in. d11e to relll81ning dead-load, live-loads, and tempera t11re 6570 lb. per sq. Total Concrete.--.Maximnm stress 16390 593 " in. n n " " " " The etreseJd11e to the loedingJ in rod reinforcement at this pertic11lar section coul d not have exceeded 593 lb. m11lt1plied by the ratio between the mod11li ot elasticity, or l~ 593 : 7116 lb. per sq. in. Hence the economy of material due to the 11se of the above type of str11ct11rel steel rib is apparent. Lnasm11ch as the steel ribs wo11ld cost more per ponnd than rod reinforcement, it was necessary in order to determine the relative economy of the two types of reinforcement to make comparative studies of the relative cost of ribs reinforced with rods and ribs reinforced with tiveted members such es those used, due allowance being given not only to the edditlooel cost per pound of steel ribs, but to the saving in false work end the reduction in the cost of the piers due to the lesser weight of the ribs . ~hese studies showed a marked saving for the steel rib type; they also showed it to be economical to make each rib in any one span c&nstent in crosssect1on for its entire length. tience the maximum fiber stress at the different sections varies somewhat. An additional and important argument in favor of thas type of rib was the anticipated rapidity and ease with which such ribs could b& erected, end the consequent lessening of danger to the permanent structure from floods and ice 9 an important factor in the Oonnecticut niver. These anticipations were fully realized during construction. ~o direct allownece wee made for stresses caused age of the rib concrete during setting. by shrink- ouch shrinkage would tend to bring it into tension end to cause some compression in the steel ribs. The application of partial dead-load to the rib during construction caused stresses in the diagonals which disappeared when the rib concrete was completely poured , uonsequently, except for the condition existing during construction 9 the steel rib flanges act es longitudinal reinforcing bars in the ordlnary reinforced-concrete member, and the diagonals serve as shear reinforcement. ~oat of the work was done with 1:6 concrete with a f-in. 4 maximum aggregate. 'l'ests showed a compressive strength of' 2260 lb. per sq. in. af'ter 28 days. This thesis will be concerned with the analysis of stresses in the ribs of a selected arch bridge of the type ed above. describ· The span and rise have been made to fit the Linda Vista crossing of the Arroyo Seco in the City of' Pasadena. The trial cross-sectional area and amount of reinforcement have been selected by comparison with the Connecticut River bridge described on the preceding pages. In the design and construction of the bridge considered in this thesis, the following procedure will be followed: Construction: ·(1) The abutments will be constructed and fitted with adjustable cast steel shoes. ( 2) 'I'he steel ribs will be swung into place by cranes, and fastened with pins at both ends and the crown. Wind bracing will be provided by steel lattice girders between ribs which will be covered with concrete. Steel hoop and longitudinal rod reinforcement will be fastened in place around the steel ribs. (3) Forms for the rib concrete will be built around the steel rib and the concrete will be poured in 20' sections trom each end simQltaneoQsly. fhe three hin ges will be left Qncovered. l4) ~olu.mns and roadway will then be constru.cted. - - (5} The hinges will be filled with concrete and re- inforcing rods. Design: (1) The shepe of the arch axis will be determined by compnting the coordinates of points on a parabola. (2) The forces du.e to the load of the ste~l and con- crete of the arch rib will be compu.ted. A cu.rve of momenta and normal thru.ets will be constr11ct.ed. .h be designed ~o carry these loads with a max. stress of abou.t 7000:/f per sq. (3) ~he steel rib will. ~n. dead weight of the colQmns end roadwey will be estimated. (4) The forces du.e to the load of the oolwnne end roadway will be compu.ted. A ou.rve of moments and normal thru.ets will be oonstru.cted. (5) As the hicges will be closed before any live load is applied, an analysis ol the fixed arch w111 be made to find values for the moment. shes r and thrust et the crown, for l6) l ive lo.:r.c/ 0'76'. rhe maximum unit stress in the concrete at certain sections with live lead in various positions will be oomputed and plotted. (7) Thrust diagrams for the same loadings wlll be eonetrticted end the maxtma.m anit stresses compated and plotted. es a comparison with the val'O.es f 1rst o btaineo.. WE~T PflQF/Le OF NEW LINDA VI.STA AfiflOYO SECO PA.SAOENA SCALE: 1"=40' 8RID6c /;/TE SHAPE OF ARCH .AXIS To find coordinates of points on the axis: Span = 230' Rise • 44' z2 : A Y x = o. y =0 x 132~ = 11!:>,_~ y = 44 • A = 13225 : 300.6 44 x.2 y ~ 10 20 30 40 50 60 70 80 90 100 110 115 : ·~ 300.6 • X 62 100 400 900 1600 2500 3600 4900 6400 8100 10000 12100 13225 2 : x .003327.X2 (IBg l.33 3.00 5.33 8.33 12.0 0 16.30 21.30 26.95 33.27 40.30 44.00 tiHA£E OF CROo~:sECTiuN A trial section 3'x 5' will be ased. - a"X/6 COMNTA1ION OF FORCES ON RIB s : Ni A !!!..2. • N ;. Ko r I -Y ._. '°'~ · -- ST~EL DUE TO DEAD WEIGHT OF 11HE RIB = s max. anit stress in steel. N • th~st normal to any cross-section. M a1bending moment on any section • v • eccentrioi ty of N. A : area of any cross-section. C • l dist. from newtral axis to •~ter fiber. I : moment of inertia of resisting section. Length of arch rib axis from crown to abutment equals 125', by scale. (/ "= .5' .sca/e) ~ivide the axis into 5' lengths. Draw a line through each dividing point normal to the axis at that point. ~his divides the rib into sections which are a boat 5' x 6 1 , and whose centers of gravity are approx. on the axis halfway between the dividing points. If the rib is made 3' thick; the weight of each section will be 0 1 x 5' x 31 x 150'/f ll,250f = C-C is a section normal to the axis. A-B is a tangent to the axis et any section C-C. oe is the angle "' between the tangent and the - ,_ J-o.r1!>. horizontal. X - u.r1.sti c }zy are,, el;rls } r... \ ) ¥lc:c. ::Y.._.C (\\S- X ) - HL(44--:r -~~L.) N,, = L P s i n 0(,. -t He. cos o<. Z:F : sum of loads between C-C and the crown H, horizontal thrust at crown. = Each half-rib inclui ea 25 sections. 25 x 11,~50 : 281,250# s V : vert . reaction at end. See sheet 'If r for moment arms. = li e. By equating mo~ents about the crown : + H • 44 + 1495..7 x 1~25 - 115 x 28l.25 • 0 H, a + 32343 . 7 - 16826,6 .... 44 - - + 15517 • + 35~6 thousand lb . HL - 44 equating moments eboat the left end • =1384 . 8 44 x 11. 25 15579 • 354.0 thousand lb. 44 Average • 353.3 thousand lb. = 1" Z. L S11m of moment arms of dead weight loads of the areh rib abo11t: ( /r'7o'F1e'? T Qr'71 s -- Crown Left s::: 10,2 144 18'6 22'9 27)~ 31.6 36.0 4Q5 46.b 49.6 54.2 58.9 63.6 b8.4 '73,2 +> J..I s;::o 0 Q) Q) .-f Q)d !'!: <O +><n Q) cq OJ s:: B: 0 1-t 0 1'7.1 219 26.7 31;4 3Ql 3bl 7,1 11.7 163 20.8 253 29:7 34.11 39:6 44P 5ti.5 60.1 64.b 40,7 4b,3 49.8 543 58,7 63.l b~.l b7.4 b5.4 73,5 77.9 71.7 7:>9 69.5 73.6 662.8 462 6u:9 12~ 48~ b2.7 57.0 bl,2 82,2 ao:1 78.0 82.9 86.5 84.2 90.7 88.3 87.8 92,7 949 9349 976 99:0 102p 1031 lO'l.6 1253;3 112.7 1384.8 c a: Q) 2,4 2.5 7.4 '°s::l +> s::l 2!1 7,2 12.0 167 214 26°0 30:6 2.5 7,5 12,4 17,3 2B,2 27.l 31,9 36,7 41.5 Q) Q) E 2p e:: s::: s::: Q) .µ 'H CD .-f 38;4 42.7 4b.9 51,1 F G H 2~ 2.2 2,1 6,8 11,3 157 20). 24.4 28.7 32.9 371 41:2 6.6 10.9 152 19!l 236 27.'7 ~3 2,0 61. 8:1 10.5 146 18.7 52.2 31.8 137.4 45.3 265,8 b5,2 593 4410 , \ G cq s:: rd Q) Q> +>s::l +> +> Q) Q CD CD ~ H s::: aro CD CD Q +> 'H G> ,..... ~ s::l CD CD ii: Q) s:: 11:1 Q) s:: Q) • i!: +> +> 11:1 s:: 11:1 (I) s::1 <D CD CD CD QQ fxl Q) g: a:+> Cl> 'H :q CD .-f E-f +> 'H ll'.HQ CD s:: QJ ~ 'H i:xl> <D r4 ft:J . I!: +>+> <CJ s::l s::l CD CD CD a:+> +3'H 11:1 rd s::: s::i s::: B: +> +:» 'H +>'H 0 CD CD Q) CD CD CD a: +> .... CD 'H ~ <D .-f <D CD ~ .-f :::0 .-f ~ .-f '°s:: rO s:: QJ ro Id 'd <O QJ QJ cu cu cu 0 A •..!) ~ Q 1%1 c :%.j CD CD s:: ;, I~- ::,:,.;, 1Je1:een C.11 D B &l /'~ S '.cl,.er>Y/7 o ~ Hrcl, rib) c A 7.6 l-1 sc:4/e~ f,..,;on end ~5 12.6 17.6 22.5 27.4 " ' 32;3 ~ 37.2 ·~ 42.0 ~.., 468 . ""1 516 • ' 5b3 It) 6l0 ~ b5:6 ~ 70.2 74.7 7'Jj. 83.6 88.0 92.3 96.6 100.8 1050 109..l 113.2 1495,7 l'Vl',-e <D Q) s:: f-e ,,.r .. r T lf f?U S T S AND B £ NDJNQ .MOME NT..5 ... HJ... (t 4--Y) - Z (PL) ( 44 - Y) 44 . 00 43 . 67 4 1. 94 38 . 78 34 . 33 X (1 15-x) 67 . 8 4 7. 2 8 1. 3 33 .7 94 . 4 20 . 6 1 06 . 9 8.1 115 . 0 0. 0 Mc~ VL )CC 11s-x) - IX (115 - X) 11 5 . 0 105 . 0 90 .1 75 . 4 61.1 0 10. 0 24 . 9 39 . 6 53 . 9 1 " v"',.(11 ~-x) H-'-(.+4 -~) 1 P (44-Y ) I 28 .71 ~ 22 . 01 14 . 35 5 . 98 O. OOJ £.. ( L) ~ $ U ~ s. Mee. 115 - 353.3 x 44 - 1 1.25 x 1495.7 = 32343.7 - 16826.7 - 1 55 1 7 = 0 105 - 353.~ x 43,67 - 1 1~5 x 1253.3 29526 - 1 5429 141 00 3 90J. - 3 533 x 4194-11 2 5 x 9 3 49 = 253 36 -14817 10518 =i 1 7 54 _ 3 53.3 x 38.78-11:2 5 x 662:8 • 21202 -1 3 7 0 1 7456 t 45 53.9 28~2 x 6 il 3 5az x 3433- 1125x 441P 17181 -121 2 9 4961 '= t 91 6 7..8 281.2 x 4 7:2 3 53.3 x 28:71-1~25 x 265.8 13273 -10143 2990 l-40 81.:? 281.2 x 3 3.7 353,3 x 22.01-11,,2 5 x 137.4 : 9476 7776 1546 154 587 .. + 1 3 6 ~~ t~ ~ 2Q6 - 353.3 x 1~35-11,,25 x 52~ - 5793 5070 1 1 5.0 281_2 X 8.1 3 5 3.3 X 5.98-1125 X 8.1 a 2278 2113 i QO ~5~3 x QO -1~ 2 5 x QO 0g 281,2 x lQO 28 1 2 x 244 2ai2 x 39:6 2s i 2 x 0 = =+ = =• = .. = = i6t§ 9: : = SElTIO~ A B c D E F G H X2 X y z y +ctn oc s in oe c.o.s d:. Z p Q333 2.06 3 5.217 9.666 0.66 6 4.1 2 6 1 0.434 19.332 30.58 4 3.98 59.30 76.04 8 8.00 .0 6 66 .1658 .2640 .3585 .4610 . 5410 ,6280 ,7110 .765 0 .0665 . 1 62 6 . 2552 .3375 .4110 .4759 . 5 318 .5796 .6078 .9978 . 9865 . 9668 .9415 . 9116 .8796 . 8469 .815 0 . 7942 22.50 1.5 56.25 9.2 9QOO 22.9 123.80 41.8 157.4 0 64.7 l9l2 0 91~ 22ao o 11~6 258.70 150.0 28~25 171P 100.0 1 0.0 620.0 24;.9 156&2 39,6 2905.2 5 ~9 4596.8 67..8 15~9 6609.7 81;'3 2 1.99 8911~ 94.4 29.65 11428 1 0 u9 38.0 2 1 3 225 115.0 44.00 £ ~J,.,c{' f-IG (.061/C 2 8 0.6 27 7.5 272.0 264.7 2 5 6.5 24?~ 2 ? a4 2 2 9.0 22~0 76 Nc.c.. 282.1 286.7 294.9 306.5 321.2 338.5 3 58.0 379.0 394.0 FORCES O/'l llRCH OUE TO WE16HT OF RIB. 400 ---0-... ---0-- ""'"""-0--- Force 11Clrme1/ fo .5ecf/()17 in 1 .' ---0-- 0>---- -0 fl701.1~q11d-pov11cls. 300 200 /()O Moment Cff sect/011 111 rhovsnnd - root-po1.111d.s. /IS /()() 9() 80 70 60 so 40 30 2() 10 reer. O/e,tR11ce f rotn fhe cro~n. ~· ~ - ./ ~J l y .::. y e. ~ t- ~r ... 9 / ..1 I C t;. i- 7 - I iJ J< "?: .., 4 ..., '!.-) t") ~- - -' n ~- rt: .~ ...+- }/- .J //;. - + j ~st1mate of Deadweight of a uperettuctnre Dead weight per Colamn The raili~g will be assamed to weigh 3ooff per lineal foot . (Lo/v1n,-,s / .S'4f-'' c-':) 15 . 33 X 300 a 4,600 lb. The roadway will be aseamed to have a total width of 32 feet, including sidewal~e. with a thickness of 11 inches . The weight per sqqara foot will be about 140 ff . l6xl5 . 33xl40 : 34,400 Floor beams will be assumed to be placed 5 feet apart. Beams end girders will be as~nmed to weigh~ 300 per lineal foot . 52 x 300 -r~.f-q / = 15,600 54,60 0 An additional allowance of 10%° will be made 5400 60. 000 COLUMN HEIGHT ~~ IGHT TOTALWEIGHT on COWMN The columns will be assumed to be 18 inches s quare . They will therefore weigh about 31 0 lb . per :f oot of height. A B 5 D E F G 14 c 7 9 20 29 38 1700 2400 3100 4 800 6800 9900 12900 61700 62400 63100 64800 66800 69900 72900 461600 Z (t"L) (pL) OF ~UPERST~~CTJRE LOADS ABOUT CROWN . COMIUTATION OF .Fee .,t- Th1v.11ntl/Js: Column A Load Mom. Arm (PLJ 61.7 B 62~ 470 7.67 1440 23.00 2440 38.33 3480 53.67 4610 69.00 5890 84.33 7270 99.67 2- (PL) . 25000 c 63.l D 64.8 E 66.8 69.9 72.9 F G Z (PL) B c D E F G to left of section A-B 62!1 63.l. 64.8 66.8 69.9 729 . Z (PL) c D E F G 7.67 23.00 38.33 53.67 69.00 84.33 479 146!n 2484 3585 4823 6148 £{PL) ::189 7 0 to left of sec. B- C 63.l 64.8 66.8 69.9 72.9 7.67 480 23.00 1490 38.33 2560 53.67 3750 69.00 508 0 ,£(P'-) : 13310 L (.PL) to left of sec . C- D D E F G 64.8 l ) 6.8 69.9 72.9 7.6 7 23.00 38.33 53.67 500 1540 2680 3910 £{rL) = 8630 £ (PL) to left of sec . D- E E 66.8 F G 69.9 7 2.9 7.07 23.00 510 1610 3833 2800 ,,f. (rL) ::: 4 9 20 £(PL) to left of sec. E-F F G 6Q9 7 ~9 i67 540 23.00 1680 £/?J.} 2220 L(PL) to left of sec . F-G G 72.9 7.67 560 · .£.{rL) MOMENT OF INERTIA ( ~"" c,~,,; refe "'""" sl<e/ s~~1,.,-v To calc I : I in biq~adretic inches Ic + (n-i)~Ie Io : w• 36 x 60 3 12 = (n-1) : 14 16 • 3 x 216000 = 648000 I irJ 32288 (see sheet ):'Se) Ie('(n-1) : 452000 I : 452000 + 648000 - 1100000 In biqQadratic feet. 10 : (n-l)~Is bd 3 • 3 x53 • 125 • 31.25 rr 12 : 452000 : 452000 1124 I s T 10 ..,... Cn-l)~Is L - .010s4 I ------ ~ ~0736 - 21 .8 • 21.8 + 31 . 25 : 53.05 I I ., Computation of Stresses Due to Dead Weight of Superstructure V1 • 461,600# ,,-J~&et" sheet JI ) Comp. of~R eactions: E q ~ati~n of moments about the crown: +H1 x 44 +~(PL) - V1 x 115 : O 4 .6 x 115 - 25600 : HL x 4 4 53100 - 25600 : HL x 44 HL • 27500 44 -- 625 +h•'-'SOnDY/ ~ ee sheet /~ for E( PL) ., /1. He :: HL Comp. of B.M. at sections halfway between columns: Equation of moments to left of section M= VL~ (115-X) - HL ( 44-y}- E(PL) x x2 y 11&-X 44-y • 7819 99.67 43.2181 15.33 235.009 30.67 940. 649 3.1295 84.3 6 40.8705 46.00 2116. 7.0399 6QOO 3~9601 y,_ >< 01E-X) )-/'- ,, { 44 -y) i~B B-C C-D D-E E-F F-G :x.2 x y 376137 12514 5878:29 19."557 846400 28.160 61.33 76:67 f 92.00 D-~ E-F F-G 53.67 38.33 31.49 0 24.4 43 23.00 15.840 z. (['-) = = 461.6 x 99.67 - 625 x 43.2181 - 18980. 461.6 x 84.33 - 625 x 40.8705 - 13310. 461.6 x 69.00 - 625 x ·36.9601 - 8630, = 461.6 x 53.67 - 6~5 x 31.490 4920 : 461.6 x 38.33 - 625 x 24. 443 2t;,20.-: 461.6 x 23.00 - 625 x 15.84 0 560 -6'i?.5,-{-r1r .. . r 1 0 4 d r--1.-16• = * ). \ P~•H•4' .,, M A-B B-C C-D 115-X 44-y 46028. - 27011. - 38927. - 31850. - 24774. - 2554 4 23100~ 17693_ 10617. - 19681 . 15277 9900_ - 1 8970 . 13310· 8630 . 4 920. ~220 560 . = = - = = = = 1.{ + 43 i + 47 + 12Q V 163 196 -t- 157 v 65 + + ..!' ..L f ,,._ ') h• eF~ ~ ( F~m(/45) .;:;;,,.= ~G 22 39 53 64 51 21 £ _ / 'f~#aOJti?.S;cplrl'+ ~m- = 4'>4-~ /.-,. 4- , ..... Dead .Load ,.,..,,. "" ~ "'-.Y c{I.+w*.-.. .S••,-,,,-c x Sec x 2Y "'"'" oc.. A-B 15.33 1.56 .1018 B-C 30.67 6.26 .204 C- D 46.00 14.00 .306 D-E 61.33 25.00 .408 .E- F '16.o7 39.00 .510 F- G 9200 56.40 . 613 107.33 {ff - 1) = sn •• r <!::"""'~- ...,1-./J. .S/-,, o( C O&.C. ~p ~ r.s,-;,~ .101 .995 617 6.2~ .199 .980 124 't:.4.7 . 292 .956 1872 54.6 .378 .926 252 96.2 .454 .891 318 145. .522 .853 388 203. ~<"'""" 622. 613. 5 98. 579. 557. 533. N 0 211 214 819 226 236 247 765 257 I 4- + 8"/K' =- z 9 7r s7. iH. ~" 628. 638. 653. 674. 702. 736. 6 tJx 36 = z / h o sf, /H. ;2../b .. FORCES ON RRCH DUE TO W£16HT OF C()J.VMN~ HNO fl()/IOWRY. 700 600 500 . 300 I ~(r;..,p~ s'neer ~) N/Qmenr at section in fhew.so11el -rpof-pov11t:ts. IQO !J() 80 70 01.:;fqdce 6JJ Feet .5() "1'0 rrom il!e Crown 31) iUJ IO ' l ~ zoo /PO " ;. . c De t ---( T /;,.. 19, - , t7H. ~11 '//J - , ~ II· JCJ=Jl< -.-res f ,-, - .t 2: Q's £.£._-!~ /, - I//; , ds x.I( rT y d;r - yt// ~lxds JY.d! I' J', ,_ fc I?. -:tit/ ; =F d¢ - eEi;ft ilS tis (~ c -[I. c. 'f~S [;.. ( , t e_L_! /Y/- x Cl! /.., c.. I ho. . ,,. /.. r r I T l' G Bl -Y 1,J.r I/ l.v h~ p I? e f <-C I~ I~ 1n7 /-- ke 7e. / T 7&- u/v.;:. T/ t?.6/~ 'n </. J A 10' ;- " x 0 10 . !..O 30 40 50 60 70 80 90 100 11) 115 N 0 1 2 3 4 5 6 7 t3 9 10 11 ll b x 0 10 :::o 30 4U 50 60 70 80 y 0 0.3.53 1 .vu 3.00 5.33 c.... ~ 1 .:...0 0 16.30 2G.~5 ;~;..~2? I= D3.05 .01884 .0000 -.018t37 .00G3 .01900 .0~53 . 01~}20 .05'16 .01948 .1038 .Ol 9tl0 .1050 .02028 .2435 .02080 .3390 .0:2130 .4535 .0:21S5 .E920 . 02~6~ 520 .94G0 .· 430 2Y ~~.66 i ~~;~o Q00 1066 16.66 24.00 32.60 42.6 0 .2000 .2665 .333<:. .4000 .4657 .5325 .fi 990 .6654 .7330 ,7650 66.54 80.60 ll 8.JO y" -r 17 .r· 0 0 JJ r)21 .Ol do 7 .03~:6 .03UOO .1'130 .0G760 . ' [;;~b .07u00 1.3 72 /'9900 2920 .1 21 8 r.:5z.o .14 5G 9.6 70 .1704 . 1~76 15.96 , ;.:~60 r.5.04 5t.3.UO . 3560 46.00 . 27 C6 ,, .. I' ny J: 0 J .')H b7 .()0628 .07600 .050~>0 .17 30( .1720 .3 1 200 .41£ 6 .4-.1 [,Q .8250 .7310 1.4 63 l .n 1 uo ;.'.370 ]. vOv ' ·rz 3,0 30 1.778 5.3 2S ~ .<260 2.830 ~140 .fg q oC 0 0 .666 .0666 53.~0 40.30 44.0') / ' y ~rI~ . 02~7 see sheet 21.ZO 100 110 115 . O<.,~~~ I 6' T . ul884 l~ 90 __L_ I D 7. ~ [,0 10.36 1290 C,,<# o<.. ~-,ec... 1.0 000 1.000 ,99?8 1po2 .9912 1/ 09 .a i06 1.020 .Y6G4 l 034 .9489 1052 .9205 1.077 .0063 1.1 03 .f: 0 2 9 1,132 .8581 1,1 65 .8325 ~ ,.oo .8065 l ,<;,40 .7046 1.259 30 Vert'. Sc.ale : 1:/::10 ' 17 -f N . S (rnu;;r.) I'= I cos cc Fifi · I Ft':J . 5 t ~r B 7 cc DD t Ve r f . Genie / '; .5 '• l'l - - -~- EE FF Yer!. Sa~/e /';, 2 Fij. 3 F/j 7 :33 7 1 11 I Verf. 5a~/e I '_;. /~ , Dt 5he#!d-.. _ .... . .. II 10 9 INFLUENCE Ordim:tfe ColvtKm ' !Y1c Jr 1..INES -F.1.!t>• li5;zOE6 111 CJE2'UKi'. -t-o 8 He Ve ;::; 7 .6 7 7. 5 3 /. 18 ."1. 50 B 2 3 . 00 /. lb ~ /. /3 -354 c 3 EJ. 3 3 - 1. 9 1 o. 9 7 .Z.55 0 53.6 ? - 3 . ;?~ 0. 7 6 ,/ 8 0 £ ~ 9.00 - 3. 3 5 0. 53 , / 10 F S "f.. 33 -?. oo t1 27 .055 G 9 9 . '57 - o. V;? Cl. 0 8 ,CJ 18 /"'/&>I red fro,n t:la .fa o n s heef: . .... . .. ... 7 /.3 .6 LZ /./ 5 /.0 .5 .9 I I I I I I I let It I I I I k.) I 4o It It I~ I~ ![) It It I~ I~ I~ + .8 fl ,7 .3 ·'- .3 .5 ~z !I .2 c:;) .3 ~, .2. ./ \.) ./ Ia I~ II..! 20 10 Mc. lie. Vc I 2 3 BB Ctirve N BB-AA 0 • Orig R. Di:ff R2 Di!t 0 3.738 4,952 1 1.704 2.721 2 10.026 10.865 3 8.675 9.352 4 7.617 8.145 5 4.247 4.648 6 3.660 3.951 7 3.264 3463 8 3.020 3l4 1 9 2894 2.957 10 2.848 2.872 11 2.838 2.841 0 115 0 1.214 l.017 .889 .677 .528 .401 .291 .199 .121 .063 1.214 1017 '.839 .8390 .674 .530 .402 .296 .197 .123 .063 .022 .002 0 .6755 .5290 .4020 .2910 1980 .1220 .0630 .0230 .003 0 6.166 3.738 11.704 10026 8.675 5.055 4.247 3.660 3.264 a.020 2.894 2$43 0 1.782 .149 1.9 31 .149 1.633 A:!:A .024 ( D-D DD-CC 0 0 1 2 3 3-498 1.837 5.866 4;674 3.704 4 6 2,939 6 2373 7 t, 1973 8 i .7 20 9 1.5 89 10 is37 11 1.530 115 0 C!;C 5.789 .954 .831 .710 .485 .383 .282 5:406 3498 '7.291 5.866 4.674 3.706 2.939 .201 .126 .068 2373 1:'973 1.725 .199 .127 .068 1,663 .026 1.589 l.5335 0.0036 1.6307 0 0 0 .12e 6.034 .123 4.452 2667 6:581 5.271 4il89 3322 2.655 2.174 l.846 l.657 5.911 .954 .830 .715 .597 Av. Val11e ].iC140 l017 .0025 0 14.228 11,919 9.833 7917 S:200 4,711 3!111 2.321 l430 .738 .270 .0293 0 .149 2,3 1 (1.21..,.ox 11.72.: I= I~ ~2 K) '/ .5-.,.0 >< , /, 72.,)<,,,,,,,,,.-lli".d9 ) . 9540 .8305 .7120 .6960 .4850 3830 ·.2830 .2000 .1265 .0680 llJ,.8.09 97,.3,35 .026 .0260 ~.47 0.0036 0 .0035 0 1\4.102 0 .1225 14.,;3.57 .596 .485 .383 .284 8~1 .1 6 69,.8.51 5Q,.8:4 2 44._8~8 3~(l8 .._3,.4~0 l4J3.26 7,..9.70 Cu.rve FE-EEn N Orig. R Ditt R2 0 1 2 8,060 8.758 .698 7.442 .620 6284 .541 4.8225 .457 5 3983 .379 2990 .303 2.454 .234 2050 .169 1.774 .107 1.6085 _0685 l528 .021 1.504 .0030 0 0 9.460 Q313 Q393 6.822 5.743 4.3650 3.604 5 2.687 2.220 6 7 1881 8 1.667 9 15500 10 1.507 11 1_501 11.5 0 3 4 9"- EE Q232 .081 Dif f Av. .7000 .6190 .5395 52840 .4615 .4590 4.365 .382 .3805 3.ZfJ()- _30 4- .3035 2687 .2335 .233 2220 .170 ,1695 1.881 .107 .1070 l.6670 .0585 _0585 .022 -0215 ~550 1.507 .0030 .0030 0 0 0 8_0 60 6.822 .702 .618 .538 .080 Valve (l"'"oxl~7i!X .,.o ~ '3 ~i'. 1' ) .0805 328.16 29010 252_92 215.18 178.38 142.28 109.46 79:46 50.16 27.42 1008 1.406 0 37.74 (· 3 z '7 6 6.703 ~033 . 330 '(361 .328 .329 ~I of: s- >< a oo -=. I o "i?.. O) 510 1020 . (/) 0 l 2 3 4 5 6 7 e 9 10 11 115 (3) fr) (.s) (~ /':!:!..![_~ /, 1~ 1~;:x I r· / ~~x " ¥ (4}·~:) (z ) 14228 lll8Q9 328i6 ~31 119.19 973~5 2901~ 98.33 79.17 ~~iit ~i~i.~ ~~~5:~ 6200 56ti4.2 1783.8 "> 4120,6 4'rll 4488.8 142~8 " "' 3286.7 "' 34.11 3316.8 1094.6 ~- ~ 2628.5 ~ 23.21 2344.0 794.6 ,, " lt:335.5 " 1.4.30 1482.6 501.6 (91 1~ 1168.7 ~ 797.0 2742 ~,'-. 6334 '-7.38 304.7 ioo:a ~ 232.a 111 2.70 029 4io2 1406 3248 0.00 0.00 00 000 .._ = n 0 l 2 3 4 5 6 7 8 9 10 11 115 rz# (!?) rv (z.)'f?J (hj-(P) (! o) I( (//_) I,,~~~ ~.z-, " 758Qo 37.74 5369.6 221Q9 1863,8 11180.9 670~4 4498.2 2205,2 Az 2xl020.x ~31 -2 x loi74) = • 471~4 - 284&6 186~8 {I) (7) (1z) (1..:sj He.. Yc.. ~ ( ~) {u) (/6) M~ ~,c(i/) z~aj.(7) (2.)--(i~ ~€) ],186 .5000 89.5 52.8 11;42 1_183 .4353 8~3 29,9 6.5 1.144 .3732 8Q3 120 2.6 10 64 .3124 803 - 1.1 - 2:4 .'955 .2542 72.l -101 -2.2 .809 .2007 6i1 -140 - 3.0 .666 .1483 503 -16.2 - 3.51 .515 .1048 38.9 -157 - 34 .332 .0663 2~1-10:8 - ~3 -190 0356 14.3 - 6.9 - 16 .ano ~0136 5.3 -2.6 -0~6 . 011 .0018 QB - Q5 - o.l 0 00 0 0 0 ~i~~:~ i§~~.~ 2339.9 17 80.7 I 1777.9 1508.8 ~") 1287.3 12412 I')'"! 8759 959·. .b (I 539.7 6190 278.5 354'9 II, 101.9 130.9 ,, 11.06 214 'I~ ~ 0 0 ""'\II " "l ~ ~ ~ ~ ,. Loading' Dead Looct plus Live Loact over enlire bridge. Vpper ~ctge } Graphical 19ntJ(y5h Lo11Ver edge (/pper edge } lrfafhemalical //11a(yis L oi,-ver edge -- =-~ _-::_-::.acr---- -<( / , ... ... /15 100 90 80 70 6() 50 40 30 i?O 10 Feet- Di5tance t'rom crown. I_ Loading : Oead Load plt.15 Lire Load over middle third. iti' 800~ ~ Lower edge ~ } Upper edge Cirqphicol 1'9no(ysis 700 \.) .,~ \ ~ \ ' '' ~oo ·~ ~ ~ \ ' 500 ~ 8I 400] ~ 300 II) ... ... ~ .... ... ... ... ... '()-_ --- ~ , __ 4 200~ 'b-. 115 100 90 80 Feer- 70 GO 50 40 Distance fro/?7 crow,,_ 30 100 '' 20 '' § ~ / ' / 10 100 t::: ·~ ~ 200~ L o cu:T1 n!F I I Oead J.()eu::I plus Lower L /ve Lood OYer ed9e.} and leFf Me1f n1/ qq/e 1· th/rds I 1.1,Pp•r t1ut17tr 19 /II 1 ' I II / ·1 . I ~ower e~eJ trre1p ~ i I .:.900 ~ '. / Upper e«"ge ·-- l'OOO ~ I iI ~ / 800 ·~ / ~ I -~ I 700 Ir\ JI ----a.. .... C) ~ 6()0 ... ... f ~ \) / ---- / 5()() / .I I ~ / I \.) I ,i/()() ;f -~ t::),. U) '\. '' I I I I I I 3()0 ~ '' '' '' ~' I I I '' I '' ' ,Wt I I I ~ ,j -- -- ' ' I 191 ....-.d --. .... "--~~~~~~~~~~~~~~~~......;: / !_$ ..... . . ..a ~ /{)(} . !!JO 80 70 60 50 ~~~~~~~~~~~-'&J:.L-~~~~~~~~~~~~__.J"-~~~~~~~~~~----~~--~--------- 40 .:30 ,2 0 10 10 i?O .3.0 40 50 60 (0 80' 1\ !J'O 115 \ Fee~ - \ Di.stance -Fro1?1 crOvv'7. \ \ \ \ .,: \ \ \ \ .. ,. •. t -~ • ! Looclinq' Oet:Td Load plvs L/Ve Load OV6'/. ben•h e:nd rlhrel$ Lowe·/' edge} 6rqph/cal /1nt,(ysis v pper- edge /..O>-Ver edge} Mafhemafical f?m::r(ys/9 U,Pper edge ,A - ' .... ' .... !IS 100 90 BO 70 60 50 4-o 30 .i'O 10 100 1100 q ~ I I ~1000 \ I L oeu:ling : I \.) ~ I Oead 1. aod plus I I I Livr Load.-a v er J/~t'f I I \) 900 ·~ Thi rd . \ ~ \ · II) ~aoo \ s:~ ~700 ~ \) '\ '\ '' '' '' 100 I 90 115 70 so 60 30 I I I \ I I I 0 30 40 so 60 ?O 80 90 11)0 'O /15 100 I \ I 20 I \ I 10 I I I 10 Feet - Oi.s.ta n ce rron? crown. I I 20 I I ~ ~ I ' I ', : t.200 ·~ II) ~300 I ' I ' ., II \~ 401) I 0-____ ,o1' ---a 500 Re vi.s e -c/ -). ..5 . ...,_ //?t'J 7-rO / - 7 ~ I fA w L f b - ~ J I l - es II IT' tJ .5t:c-~~,, rt!? s _.. ' D' r t? ~ sl..f het:f lt.'r " _, 6- "' ..: -.; tvl'J ,a ..,L ~rD W'/, "':  ne eee aie 104 8000" MATHEMATICAL ANALYSIS Find bending moment and thrust at certain sections, and the resulting stresses on the concrete. Bending WYioment= Me t tHe y t Vex -Z (PL) Section z£(PL) oO 18.33 FIX 267 = 329.8) 30.67 43% (767 23.00) = /3/8.81 46.00 43BX (30.67438.33) = 2967.00 6/.33 43x (€69,.004+S3.67) = 274.8! 76.67 43x (122.674 69.00) = FAFILSBI 22.00 43 x (191.67 +8433)= /' 868.00 JO7.33 43 x (276.00+99,67) =/6/55.8) 1/G.00 Section > Me Hey Vex Z(FL) Maz Fe oO ra) ATzZ Oo oO (a) -/?7Q.6 "“-5S ($33 7 GIE - P3205 . 329.8 \ -774.3 SE 30.67 3/29 {323.9 “ /3/8.8 | -7669 “FS 46.00 7,OFO fe 2978.8 # 29670 -/60.2 — 5B 6/.373 12.57 : G293.2 SZ274G| —-/536 -$S0O 76,67 19256 i 6276.2 ‘ B24 | ~ 1326 -4S 9208 28/6 " i a : I! F6ELO\-1 250 -4/ /O7.383 BGoeBF . (67/86 us SEIS 2, G\ -7076 -3S5 11$.00 F400 5) : * Thrust <-ZF sinK +e cos& Section x? ay |¢tanx| sink|cose |ZP_|Z2fsink|\Wecas<| M oO $$ FF 23B5:0|\/(5676| ./02 Of 99S |43 4-3F- A Biy 425 30,67 IFO. 6 €@7580| 2oFt | 1/77 760 BG AW ae BIT #32 46.00 2B/s/@ 14060 | GOO |\,292 G56 /29% 27-7? 4-OF YF 3 6439 B76/ ZG 0 AOF WI7E | P2O f7Z 66.0 BIZ 457 76.67 | SF78 BF/Z | b/s AES | £90 215 I7¢ are ATS 92,00| #64 56,82 | G12. S22 £53 Z2GEF | (324.7 96/ \F#76 407.37\71 520 76. 66| .FItF |.58/ OF 30/ VS (i etd |S/9 171$.00 | sect/ay Fe No tM Mp + (Vk Upper Fage Lower Fage oC /$3 3 SSF —4 § 206 402 4 6,00 2O’ -/B ISS PF 64.33 PIF +? It2 276 76-67 IFS t+sGF 4 / 4 376 92.00 FID FPO F2F 4AOB 107.33 Fa — /4- FI? AAS JIG.00 Scare: /” = 100.000* Loading : entire bridge. Dead Load plus Live Loao over Scale: [28° GRAPHICAL ANALYSIS Thousand —Founds Ordinates te of Dead 4044 = 628, with no eccentricity, See sheet... ..... Dbpeqdhoad\sivehoad\Teta/l | Me te He Of hive khoad= BPA XFFZ=- ABZ. Total He= 625 F7AZI=/0F-8, G17 43 [04,7 |\+769\ 418 Total Me = -FOOx FR= -/72 62.4 4 105.4 \+ 402| 113 Eccentricity of total He -I7Z- 104& = —2./764' below the é7./ " 106. 4 —([{3/ O97 Crewn. E48 x 107.6 |-arz2| 276 66.9 (09,8 |\-335| A573 DATA: TAKEN: FROM -THRUST: LINE 9.9 * J(2.% |\-200| G27 72.9 us 113.9 \-0.67\ 0CF 7 Prast Fe Tota / 7@2.@ | ~-2.00| 492 section | Total | *K@ein. | Fecen. | Mem. | #K6a. in. 2 Ge\Lewer 2°92. -4.00| F.EF4- 2:00 1 O47 G Bs / -0.164 = (72 sé 2IS 407 7.67 1/053 3SF +0.08 tr EF 24 sre SIO Z2F.00 1070 2IF 0,00 oO Pa) Sa7 SSF FE.33 1095 267 FO-.E7 ae 25 SIZ BAL S32.E67 2 SEO +0.) 0 T/IIF 37 4l7 S43 69.00 (178 39ST t+ O./6 +16 E 6é/ 4-6 334 GRAFF (Zax 1 + + 0./F +222 7F FET SF /. FF.67 1297 FBS Tet & +150 49 4 G4 3&6 WsNWG: OL 1297 4-35 +. 200 Q Oo 4aS 43S THESIS H. BARNETT ~ 1923. CALIF. INSTITUTE OF TECH. ah ere hh B865000~ ° MATHEMATICAL ANALYSIS ‘B.M1 = Met Hey re A- £ CL) Section Zz) 0 1$.33 42 * 767 = 32249 30.67 43 10767 +220) = J3189 Scale: /'-!00,000 46.00 43 xX (2300730.67) ¥ BISK767 = B4A7B7 G/.3F 49 x (28233746.00) t+ 21.5% 23.00= G12 3 76.67 43 x (£3,677 64323) ¥ 215 %36.33 = 57649 92.00 43 ~ (69.00 7-76.62) + 2L5 x 53.67 = FAILS 107239 43 x (99.33 7+ 92.00) + BIS * 6400 = 7067.1 143.02 i Q Section | + Me He ¥ Ye X Z(PL) WD 2. Fe 8 Oo iN 4$.3F |.7 818 +704.9| /F7.9 2 324.8 +5629 HPF ‘I 30.67 3129 " | toe 1, 1316.8 +/BE.25 4+ 4A 46.00 | 7040| » 752-2 ‘i 24727 | - 758 -25 | 6/. 33 12.97| * pea « 4121.3 ~FOF.1 ~ aH 76.67 19.56\ *% ~ wees # 5764.9 -362.9| -7/9 92.00 O2F./G) " <p 782-2 4 . 7418.5 | +F6.0\| +-I1F |. . ee /E7.23 Fb.FF| » ree 78% ZL ps GOO) | + 522) +279 /14&S,00 F 9 2Z2/4,5 7 i 7 Thrust= 2 PsinK t+ Hecos cK Section ZF ZF sine fe Cos Nz Fe oO ; 76.393 | FF | AF 239.2\| 2eez5| F2 20.07 FO |, LHL 235.6| 2527| FS 46.00 i 37. + 2E6 7| 2é2/%- 21 FF 6/.339 “ FOG 222.6 263.2 FS 7b.67 ¢ AEG ZIG4=.O 262.G SF G 2-00 = 56.) es Nf 261.2 5S SOF FF “ 625 ES? | BEEZ ¥7 445,00 i | sectsen Fe No + A Mo +MY. \ Upper £dge\ Aower Fage Pe ‘ 1 $39 293 tH) G2 AGS 76/ Loading : 30.67 299 +87 2@e eae Dead Load plus Live Load over 46-00 307 a 32/ 297 HAD Ee thie. @/,33 FIT — £f 2337 BIS 76.67 22F — SS” 26F 377 F2?.00 335 + GF 4 OF 266 GRAPHICAL ANALYSIS 127 F3 att + FOO OFF 44 118s C0 LLoaded |__Tbeuwsand - Pounds Ora nares Ordinate xCoumn Load He oF weed Lood=-628, wil no wetendrictey. Columns bead Lead | Live load| Teta! \ Me te Me He He ef Live LegaqGd= 2FO.F. Votal KHe=~ ORPE+?+2FO> 06G A G17 as LOF47 253 4/8 +S2BS F227 Jota! Muz= + 70k 6 rood 62,4 Fz LOS, + 262 4/2 + 69.7 4b - Fecertric/7y aF Sotal He= FOWG w FOF = wie” phage Phe eve. c 23,1 21.5 £46 |-79/ | (97 on i 20.9 v2) O48 — 64¢@\| — = ~ _ | E 66.8 ae 65.9 — ue . oF DATA TAKEN FROM THRUST LINE. F 64.9 = G44 aa = - se TAarust fe o 72.9 —_ 72.9 _ ‘aia — _ section | Tetal\ Vsg.in| Eccen,| Mom. \|*fsg.in Upper Lage Lower Edge. | Tames FEE + 3S. F {20.2 0-00\ 665 | 2F/ \ HO8/S \ +705 230 eR@y Gl A - +704, G ZF O.F 7:67 ¥7oO 292 t J /O |\+ 9°56 3/2 CDF ~ 20 22.00 E70 ZGY | tFa70 |\t 623 203 So2 Sé BF. 33 W/2 BOG | tO/S5S |t 137 FS ea 26/ : $3.67 F/2 306 \|-0.35 |- 3/9 (OF 202 F/0 GF. 00 93S GIF} -O4S + F20 (38 17S SP GF, 77 G62 S23 | -B2e |- 242 Ee 2s Zo} 99,.¢67| s033| FF7 | tro,25|t 2SF &F F3/ 263 J1$,00\| /E323 S471 3.95| +4780 320 667 27 THES!IS mH, BARNET Ti Se 3S. CALIF. INSTITUTE OF TECH. MATHEMATICAL ANALYSIS g BM. = Me t+ Hey tex ~2 (PL) section Z(PL) Qo : oO 16,23 Ox 267 = a) Scale: /°-/00 0007 320.67 OX 767 = oO 46.00 FILS X767 = 164,9 6/.37 BISX BROOK F3X76? = - F24.3 76.67 BLEX BH BFF FBX 390,675 ZIFAF 9.90 PLSX £3267? & FBX 600 FI20,F JO?7.39 BLFK CF OIOKF FAX/22.67 O75, 2 J1$:00 x Y MWe fey wx #04) Mm Fez oO oO “FILE TGS A) (SBF FeIF ae 745 3.23.2 OQ —-437 -/F 306? B/PG " 246.0 6465 o 494.) 162 F600 POFO “ GASES 969.7 164.9 (1009.9 230 @1,.33 U?,S/4 “ "4nd 1297.8 F242 1739.5 3F4- 76.67 U950@ " 17875 16/6.2 2/9-2.9 $9224 264 —t Pa.00 #76 “ BS7?3.8 (9 3R4 4IZ0G7 346.1 Ss bol (OA%F3S B99 §* 35034 22625 6758.3 -1F39050 -4bF } J1$,00 44,00 \" : i | thruk? » £ Pisin + He cos & | x YéP 2 Psin % tte Cos % ™, Fez Scale: ("25 7) oO ; Oo FO 1$,33 OQ 7] 709 90.9 FO 9067 0 0 546 4.6 320 46.00 245 a G74 93.7 a/ 61.393 CFS 29.4 £46 109, 0 3? 76,67 1027425 46.9 w1.2 130.2 4-t 92,00 1505 76,6 280 566 $3 107.939 | (92H /12.4- 7HF 146.68 63 11$,00 x Not... Mot, Fe lupper edge) fE(,ower eae) 4 . Loading: 15,33 24/ -—6@ 235 2tS Dead Loading plus Livé Load 30,67 294 +194 FAG GO over sere rhird. 46.00 250 569 6/4 -I/F ONG? 263 437 700 -/7a 12,00 398 66 3 66 E36 Leaged Thousand -Peunads Pramatas Ordinale x tive Loag He oF Dead LoaW/= 625, with no Eccentricity 107,83 320 ~ 447 127 76? Columns weed lead tive Leet! os Me He Ve th He Ke Me ef Live sead = 71.4 ‘etal Mae 115.00 A O47 i] 647 753 412 F450 ~ 7 ai TVot@e/ Pte = -— #38. 4 - 4384 a 62g 0 CPF 4,62 LR BSR Te oe Fecentricity ef total He*-z7e_ c o2/ FLEE FFG -f.9/ OG? BES ~Fl/ 22.9 FF ao GASES 43 407,86 ~-3B2R B76 60 -1IFLF 327 7.78 a 66.8 4s 409,F -33S5 92,83 b76 ~144%0 22.5 473 & 7.9 3 112.9 -20O0 0,27 086 - 6b.0 1466 B36 - DATA TAKEN FROM THRUST Cc 72.9 Fs A159 -2.67 9.08 .O/ ~FF EF 3.4 o.77 Thrust 6S5/ -F3h, F PAF BLOF Section Total Yegin. fecen erm, VsG 77 0.00 7/6 S40 = ome —FFHR “IFS 7.67 7/6 2 to “70 - 72. “24 Zz2020 722 242 7,50 + ser 1/4 27.33 7FHO 27 +/30 962 32/4 53.67 773 2Soo tIGO 4-70 F FO F720 22 > +170 ie at +- SF FR ZF FF72 276 r/e0 FFS 2 es | 979.067 72 Pa - OF0 2s3 SS a 11500 ISS 32, -2ptO° 2290 750 — = = O25 P/F = 71GB “62 , Seley fhe crow”. pper 4age Aewer faze. GIS 27/6 3EO Soe 7FO 73F S7F 4&0 ~-F 20 Tee StS FFs 2GoF LF € - 66 -FFO —-4¢-SF ~2.2 8 ELL 7O7/ fe. BSR WE T= (oes, CALIF. INSTITUTE OF TECH. MATHEMATICAL ANALYSIS No +Mire Mo +M,ive Ei lyper) Fe (Lower) Scale: ("= 8' section Mr NR “ coal CO sees PEE (F.393. -690,/ 90.9 Zs ~ ere Pw | 259 50,67 -7IEF ELS 2AF “239 oe FIZ 46.00 -7646 G7, + 24s -2 27 PSP 6497 “awe F 54.06 256 mee gd st? ee 76.67 “er, f 5/3 ZE3 ~“ 23 240 2&6 42.00 146.0 740 273 AIS XE {SF 107. PF fOZ2.S5 74F ZF2 253 Sées~ O 115100 Loading : Dead Load plus Live load over lerr third. GRAPHICAL ANALYSIS TT Ariusth Fe Section Total wr a) Fecen Me 077, eg, in, Uzper edge Lower eolge. oO 7/6 270 —62 “FPF —SAS 76 3F6 2@7 7/7? 2F4/ -,63 ~4S] -/47 T4- FSS 723,00 720 242 -,90 -~GFS ~ 212 i) FSF FI FS 7 FO LFS —,70 -6S57 —2I1S 270 460 $3,67 74S 2S0 ~6S ~ FES -I$F GH 409 o%,00 7 66 as? ~ 29 ~ 253 ~ FF 127+ F40 FRGPZ F257 277 20 +165 SF 33/ es P67 Fb F 290 +, 70 aor IGE FEI 92 11S, 00 5 bF 29O +110 GSO BI/ G0/ ~2/ TAESIS H. BARNETT~ 1923 CALIF. INSTITUTE OF TECH. S5action 30.67 46.00 61,33 76,67 92.00 107.33 MATHEMATICAL ANALYSIS DATA TAKEN FROM koad fom Dead + % Live (Rt.end.) -14 Live@.end.) ~226 RD ae Lr) 142 bk Ww) ~“26/ D 3G L (pr) 330 i. () -250 D 3 L (&) 3 $4 Ke (UW —J/S9RB 2) oF tL (R) 26oF L «ay — iF 7 D 2/ L (R) 1S tL () OF D' 27 L ®) -— FOF L. «.) 262 ANALYSIS OF BRIDGE WITH Le eT THIRD LOADED fe N 211 36 30 2Ilt 30 30 re a/ 29 226 3? 2g 2 36 4-4- 27 2F7 ea 26 ZS? 63 25 f. upper 39 197 SIS S 36 SIE 456 140 Fe lower 503 35/ 160 FG G/ /P bo SIO Loaded Columns SyMoaVHd Thousand - Poun ds Scale: /"=/00000* Scale: /*= 5" LOADING: Dead load plus Live Load over Loth end rhiras. GRAPHICAL ANALYSIS Crdinares Ord o@e x Le Liue 4004, Dead lead 4Aive Lead Total Me Ste We o@/.7 Oo C47 7,53 Ld8 = 67.7 Oo 62. F 162 3 — 63./ 2LS FF. 6 ~19 + OF7 ~ 4106 64 FF 107.8 -322 08.76 —136.46 66.8 43 10946 > 3.35 O83 -(F 4,05 O99 #3 JIB.G -2,CO BaF? — £600 72.9 43 VISG% ~-0.67 O08 -—-F8.F! OFS. / — 436,38 For bothents ~&76,76 He of Dead Load = 675, with Pe ececntricity Pte He of Litre Loail= 163.16 , Tetol We+bFSE+/P2/F= £07 ~ Tefol Me =-F 76.76 3 Eccentricity ef teta/ Ke = -F7b6. + FOF =-1/, below rhe ecrewn, 207 F2.69 22.77 DATA TAKEN FROM THRUST LINE 146/ Thrust? Fe Se age Section Total Yegin, Fecen. Wem. Vgin leper Liye Lower eage. GI 59 g.2 #07 27/ -/.¢ ~@&@%6 -297 -/F S60 LEG3BAMSE 7-67 PIO 272 Og -7370 -239 ye SIO 2300 S/F 27S -0.6 -49! -/6/ 336 436 3BEFF 3S 26/ $02 $167 +55 “S17 226 F267 G66 292 +o.E +t+aoF5 +227 60S” és 69.00 P/F 807 F410 +912 +296 S47 e F#.39 972 327 +20.7 +680 +222 BEF JOS7 7467 J OF 0 250 +O¢ trlaore + BF a i A B/C W1$,00 4040 350 -¢f -//#% - 37 FF7 THESIS H. BARNETT- i923 CALIF INSTITUTE OF TECH. MATHE MATICAL ANALY 31S ae nalai tM fen te (upper) te (lower) 1/35. Dea ; +8 2Z at Live Aas) + 18F ie + SO/ -/4AS pe Live CL. end) ~ 14 Zc , Scale: 1: 100000" Sum 4/78 *#7BLZIZ : 30.67 Dead + 22 RIF Live CMidd/e) AAS BS + 558 t/o0o L (24. end) +/62 30 Sum. #229 +329 46.00 D - Bo 2/9 +682 -6 L oe 28 Z 1330. 3/ S +44 +338 @/.33 D + 5F 226 : en Z cal ke a Bs t+ 654 +48 L +384 37 oe re iS) +303 FBS) 76.67° D t GF 236 Li =779 Be S582 SF Lea gees a ST ee ay nh +269 44. . - : a B t+ 2IF- 368 92,00 D For ZF7 + 472 + 304. ae b - AB 8B 6 + GF +388 Scale: /=5' 107.33 D 42d 2S? be +279 B87 +239 i SOS : . Zz. - 468 63 s —-/68 4.07 Loading : Dead Load plus Live Load over ler t+ and raddie rhirds. y GRAPHICAL ANALYSIS ea Loaded 7 housand ~- Pourds Ordinates Ord nate x Column LiveLeaa Columns Dead Load Live Load Total Me He Ve Me He Ve He ef Dead Load = 625 with roeccentric/ty- i-~ G Let? 72.9 FZ 115.9 ~,66 107 018 He ef Lite Lo@~d= 33h Total He =E625° 433/, | = 9861! F 699 43 112.9 ~2,00 .27 OFS total Me= 26F./ ; E 66.8 43 109.8 ~3.34 $3 S10 - Eccentricity ot total He= B26RI = GS6/= 24 Dp 64.8 43 (O78 =3.22 176 180 He 8 applied 28'@love fhe crown. c é3./ 43 106.1 -/ GI GF Pos B 62.4 43 [OEF +161 LAB BSF , | A Gh? 43 (04.0 4755 (18 450 | DATA TAKEN FROM THRUST LINE | A -keght 6s? a (047 4755 1.18 - 450 T brust Fe Fe B 62.g a /05;4 + 1,6/ 142 - 3.59 Section Total “Eglin. Eccenr. (Yorn, 5G. in lpper Lage tower Edge. Cc 63./ 2/5 64.6 —/91 GF =BSSES O 957 $22 > +.28 268 66 4/0 2Z3F 7.67 F62 323 4.65 625 2oF S27 1/9 Z300 978 3279 ° +.80 782 256 SBS 73 38.33 /002 336 4.85 B52 278 G/F £e 53.67 040 350 49S 780 255 605 os 6400 /088 366 +, 50 SFF L7z. CFF /88 B4,33 HF 38S +,/0 14 37 F2z 272 GF.67 V/4E 385 —-,30 -343 ~—//2 273 TT? 11/$,00 4210 4 06 ~/,00 -12/0 -39S /f 6a/ fo) THESIS H. BARNETT= (Ses CALIF. INSTITUTE OF TECH. MATHEMATICAL ANALY S\S Section Load te fe W % fupper) te (lower) (F.338 bead +6 2// Live Utiddle FIBF GZ *+2E9 4BS7 - Oo Scale: /"= /00.000* a (L.end) ea 22 30.67 D +22 2/4 Z ES SS 4 /2S + S22 £:: —~26/ 30 3 -— {FF 32a F6.00 2 ¢Y FF 2/2 2 - 2S BE + 1/00 4572 Le " =F£:50 ZG 5. ~2 36 336 6/, 33 D FES 226 yi -J SF Bs + G69 AFG6SS ZL —-/92 28 ~] -273 SHE 76-67 D +t EF 236 ne tite Z. -/19 eB +209 + 49P —— a — oe raed ne a S ~f Fh BSS ° rea a eg | 32.00 2D 5 eee A Pe as — ——e ’ nel | 4 + /8 eB LAGF +228 i _ nT | . ” 7 ae : ta is ee /O7.33 D -2/ os oer . i i a 4 +279 e7 + 93/ -/93 | ed 4 +262 es oS) TS62 349 aa Loading : Dead Load plus Live Load over left and riddle thirds. DATA TAKEN FROM THRUST LINE 7 Arust Fe section To ta / WEL 17 Eec€én, W701, 49. Ja ip per Fave Lower Fdge , ? IS 7 G22 + .28 268 ie “Oa i 7.07 BS? 322 + FO 38S 12S Fd? IO? 29, CQ I6F 329 — AS APS 9? 277 37/ 328,33 IGF F3/ —~. 70 6 SF PAS 706 3SE6 43.67 /OCO7 339 —-7. 00 /O0?7 3297 10 668 6200 1030 FFG -,90 oe Bog Mahe 650 G4 33 SO SF FSF —. 20 2// 67 ZOS 9 23 92 @7 // BB F777? 4+.PO E78 Fe 677 es 118, OF MRe 77 F200 FEF O 7? FO JA O7 —3 53 THESIS H. BARNET T— 1923. CALIF. INSTITUTE OF TECH.