E... _ 1.11.133: . fizz-virgin. . .1ft 1 E ..«rhk,..:.a,l;: H.“ ,5 ..irl=(~.¢l11.2 .1. Thu-31$ ,,.«-"“‘ m. Jag 3* - 'a-m {in _ r, i. "31"" .c- ' ’ l‘i. my; 31.4 a” duo“, m~ -w-n‘v“ .‘v WEI" . .. . ‘ " ‘ ' - a _ _..--q _....:..--_:..:_.~. -,-.4..:.ab- H - CI.- - I a. ' D u ‘- .a = "‘ aw” _ app-WW'W‘WJ 55“ u. . . .Irp-ctnn-wnlu"l 'l'lq'lll'D-.' - ‘ . .. _ .. . up: ‘. I.‘I~O‘ ' w.“ Computation of the Strellec and Design of the Logan Street Viaduct Lansing, Michigan. A Theeie Submitted to The Faculty of MICHIGAN STATE COLLEGE of AGRICULTURE AND APPLIED SCIENCE by . Collinl Erxihggnton Candidate for the Degree of Bachelor of Science June,1928. WI}- I nuns Design of the Logan Street Viaduct This viaduct which is to be built in the near future consists of an arch section and a beam and girder section three circular arches being used to cross the Grand River and the Viaduct portion making a grade separation over the Grand Trunk and uichigan Central Railroads. The total length will be 1,180 feet and the cost will range from h50,000 to a half million dollars making it one of the greatest projects in this section of the country at the present time. It is to be built of reinforced concrete or steel encased in concrete. Because of the nature of this thesis the material consists mainly of computations and a complete set of computations of the stresses in the North Arch arc given and results from the other two arches while in the beam and girder sections sample computations are given and results are shown. In the design of abutments and piers the maximum stresses producing maximum thrusts were used and the base was assumed‘ and a graphical solution was used.1n the piers because of the number of times the computations were repeated the final results are given. O In order that the reader be more familiar with the project and the prospectiwe design an architect's sketch is shown drawn by R.F.Rey, City Structural Engineer of Lansing. There will be a 39 foot roadway and a walk on the west side of 7'9"and a curb on the east of 3’3“. It being necessary t to construct in this manner because of prcperty lines and clearances. 1039341 The Oldsmobile Company on the last will have an under pass and entrance onto the viaduct portion just below Isaac Street. The Grand Trunk Railroad Company will lower its siding to the Clds. h' in orddr to facilitate clearance while the Olds have complied by agreeing to lower their platforms. The wearing surface of the roadway will be 3' brickor a i inch sand cushion. The abutments are of a semi-gravity type but reinforced for expansion cracks. The oiers are of elastic type reinforced as shown. ‘Carnegie I beams will be used in the Steel Spans of which there are 3 at about M2 feet. In designing the Arches the method of Unit Loading or Influence line method was used and the outlins followed was that given in Hool's Volume III of Reinforced Concrete Construction. This being suitable for Open spandrel construction. Reference books used are Hool's Reinforced Concrete Construction-All three volumes, 0 Roukes Concrete Practice. Ketchum'e Handbook Steel Construction, Spoffard's Theory of Structures, and Boyd's Strength of Haterials. An attempt was made to maintain all specification set forth by the Joint Committee at their last meeting although 6505 concrete was assumed which is below and only 16,000# steel stresses assumed. For other specifications those issued by the Michigan State Highway Department were used. The Arch Section is composed of three arches. First the South arch with a span of 61', the Central arch with a span of 76', and the North arch with a span of 90‘. The grade over the arches is 5;. In fact this is the maximum grade on the structure. The arches are circular segmental and reinforcing steel is used in too and bottom with extra steel being used at the branch and.soringing. . I This viaduct is in a portion of the city where a bridge of shapely contour is necessary being bounded on the South by the beautiful Scores Park and Shady River Drive, and on the North by a commercial district composed of the Oldsmobile factories. So as an arch gives this desired effect it was thought advisable to use it merging into the beam and girder section where it crosses the railroad tracks. The following sheets contain the actual final computations in the design of the Logan Street Viaduct ()1 Loading Loadings on the Structure consist of a 20 ton truck pulling one 15 ton trailsr assuming the wheels at 12 feet apart and distributing the load over k the road way, that is, assuming h trucks side by side on the road way. At points, this load for convenience was transformed into a uniform live load of 212 lbs. per lineal foot. The sidewalk was designed with a front and rear wheel load of the truck resting on the sidewalk. Impact was taken as 25% of the total load which is in accordance with specification for a structure of this length.- Computation of Stresses in the soars ARCH . oo.mm~ - w. r mo.w:a mm.a .-~.- a m mam. nuo.m~ oo.mm~ mean nous cu «easemenenuea .uk.m .wam tom .uo . oo.mmH Hm.mu mom.em m. - m» m~.me~ H N :mH. 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Vm ouog . «as. uvm Aamavm Henna .uo nounnoh .aeoo coaocoa .nsoo neaoume .ano nodocoh .nsoo Homm.oan. a nude Womo.m nanoaowmo «own. mflu. A opwa momm. oauumoaoweo umpuh wagon flux “V nuanced H .02 ~H.~ -.m ‘ sz.e mo.n no-oa m~.m mm.m 3mm. mm.~ noon: m :H.: mm.m mm.~ mm.m gauoa Hm.o mo.z :o.m ~:.m noon: w mo.H om.m nm.m mm.: “one; mm.m om.: ow.m mo.m among. N mm.m o~.w mm.» mm.: nose; . om.HH Ho.m m:.m mm.m yuan: m a .m an. mm. mg. “once m m:.oH mw.: . m m mH.H mm.m : “can: m om.m mH.m o~.m mm.m nouoa m:.m :H.: mm. o~.o~ ww.m hogan a Hm.“ m~.m mm.H uonoa Haw. oo.m om.~ umaap n O N . msm. :m.m mam. mH.H “one; Ham. oa.m mmw gonna m co.» mm.m :m.m ~m.m uoyoa mm.~ am.s 2:.m mm.~ amonp n 0m.HH Hm.m oa.m H o.- Hosea . mm.~a mm.m 0:.w ma.m umanp .uam Amm.mvm AOH.NVN auto; an.vm Aom.figm neon: .uo goflmaes .ano seduces .nsoo ceamcmh .QSOO grammes .neoo Hom:.mn.a up“; HOHM.=uwwoacmom Homn.mu.q o «a Homm.:nomoauuon Honda padom \V. msfiomoa.u .oz H~.m .m om.~ mw.m unsoa mm. n.u nu.” Henna aw mH.H mm.” A oa.z m~.n. nouog. mw.H ma.m mom. a “can: on . 0N a04mnoa .aeoo cramcoa .QECQ :cflmcoa .nsoo canMoa .aaoo Hom:.wu.a op“; Ho~m.:nfiwoaoauo Homm.mu.a mp“; Howm.sanm0Hocoo Honda acdom \V “IN waanmoq H .03 mo.HH mo.o~ om.- o . m w ma.m am.» mm.m mOH. mm.m mw.m mm. mH.H 0H.m OH. 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Smaaomcmufi.SNISmmoGRH. gm. 3&5 atone maoauocm "an an hanq¢ on a once moana-m< madame; on can no-uouvm Inluuda .aaoo H on . nu ammmmmwu my Hosmawa.m-HOHmavn.aHn om w . . HommzvH.mcflomnmvaa*aomomme.nq.ommo~.~.maHHo we vnw»nammwmmavmm m unto; «cannop H mam“. com mu :- on undouoa w .o- . m «H. H on mm.HH om m nu.mo “ommzvg.wHAommmvma.m¢AomomVflmawuwmmmwamm.awwaammoflwm.“ ounmavmfl.uc noun: nouuaos H mm H onaumml 0 WM on w ”.mc om m m.- oHn Hn.mH .cummv“.mn.ommavaaHAommoammmwmwaomowvmaan.omm avnmw.naommoavmm.m nonoa .. .3? . 9:33 aoamoouaaoo H Hmm I .mmmqmmm: u on a .o- Honmmvw.ancaoammvmm.Ha om w mm.-HHOHm mu.mu Hownmvu.wmfiommzVaa.chommoav:H.aHAommwva.WcAowanVm.uwfiommoavma.uc nouns muumnuunm maoduoom Han an hnna< on a code ma«n:-< wadvuoa 0» one nocoouum Influx»: nod-cop * man u .umamemmwa n m» N 8.? m a. 0: T 47.33 m. .. Aommgvam.mm«ommm.~m.meomwmvHmfiwuamwmonvsz.u$aomwoauwmmowuaounmnVFW.N «.30; God-non 5“ m3." "gleam" I 0-H mad—3.0..— w .o. m m.m* o~n mm.~* om my m. a “ommavgz.m*Aommmvnm.~caomomwwwmu~wmmou um.wwnommowvmw.Hwfiowmmavzo.ao. u.nap 3‘38 % Hm ...Iflfimbo: m... ... my “camwvmw.ma ca mum.* om.» Nu o~m mm. omnm m.mc Aonmawamwm‘aom ouwaw.mwaomww.~:w*w~omnwavummo.nflommoav~m.m «one; u a. mndoaoa .naoo m mam n o o u. on a .ou Aofi m m.w* om w mm.~* cum m. u Aomnmv::.m*Aommzvnm.~afiommova.mwaomowvmm.wcaomn Hymawwxfiwmmoav:o.au gonna a endow ouoaaoum Had an hann< o» a omao waueanu4 mnduaoa 0» can con-ouum asluuna 32- .nioo m mud n ONmumm I mu m m .m$ osn msm.* om m n.m* “owmzvnaw.mmmmmwvm~.awaomww.mn.mMAommwavmm.H.Aommoflvuo.m nonoa .naoo * man a la; n ow a . Moamwvn~.no .oawmvgo.~*ao~mzv~:.mvflomnmvu.ncaoum:v» .*Aommmavm:m.sxaommo~vm.m nouns .aioo m ma u "mm n mm A m: m .n* om m mNm.$ o~m n.m* Aommmvwnm.-Aommavm~.owAowmwavmm.mmA wnmavmm.am~uwmm~vuom. none; ‘ x . .naoo * mam u_B; «wmmau.om . com . m n~.~: m o.a$ Aomsmvfizm.*flo~m:vfi.muaommmmeamwwmmofiv mu.ww~omnm~vm.~ noun: muaoaoa w .0: wudouoa H .on N «idem unoaaoou Had an manna o» a once manna-.4 mcauaoa 00 one unaom an con-ouam luluum: .mmoo m «mm a omsumw u my . o“ m un.m* 05 n ~.m‘ cum v fl. a AomnmvmmJamacmomwmmmawaommowvstwmoamomvwomfimaownma mag. unto; .980 :8 .. 3m 3» u on Ofi m so.ma om u ~m.n* cum o.u$ Aomnmvw.acaomomvmo.w ommouwmnmu~ommoawHw.uw~omnm~vmmo. gonna «2.53 _.v 92 u Inlmnl H 030 0:0 u .u A m an.m o~n ~.m* omn.m a. ¢ “0mm.avnm.”*Aomm.oavmmmuu Wmo.m“ m.* wwn.mawmo.uu~wmm oavmm:. uouoa K .N .38 ¢ mam .- «WWW u on m. No.mn o~n. ~w.m* omm.m o.u.* - Aomm.avm.nuflomm.mwwmo.w*aomoamVuzuwflown.mavauawaomw.oavmmo. «can: 9:33 m .o- n anaom uaoavoom was an uann< o» m undo maniac-d wnuuuon 0a can uo-uouaw anluuna "O N .csco A sum u o m A :m o vom.m u om w A. *0 0A. mu Aomm. wmw. .gwA ommvx pm :om. m.MAVMA.Wonmw omvmm .-Aown mAvmmm. nosoA mmm maAnuou .nfioo m w I o g cm m .02 m.A mm.m omA .w A. a omm o~.oA* A. .Awm 0mm. .: 2v A.won mnoAvmuwaAowm mAvaA.o nouns mmm aoAucme w mam u o a mu m. mm m on m. 0AA. A m can m o». m. Aowm. .Aomm :WA gum. mnAomo mVNAAWonmnAmAvmw. .cAomm.oA.~mm. uoaoA AOAN.AVAA.N§ ANA A A0» Aom. fiA omo.va uaAnaoq A .ca .anoo m mmm u AOAN. AvuA. -AOAN. NAA *AomA wvm o:m AVAA A- omn.mvos. oA* 8m. .Avwm. .monmm.CAvoA. AxfiomkovAA. AquwmamAva. .A*Aomm oAVmAA. Mean: A AnAom < unAcnoA on one numoonum eaann.A H undo waAanun< m .nsoo A mmA u .mm%.mw.n mm A AA .ALAOA AoAm w AAAoAA.A A w-Aom A AA * owm.A m. AomA. .ALNA.A*AOWOAALAo.~-AommwoALAw. “*Awmm.wAmAAA.u~A AwmALmAA. no.0A ‘ mAw aoAncwe A Am u A n I on LS .uAOAA. m 0AA omA mu -Aowm. A. A* o. .LA.A*AomW.mALAAmAcAomw.koAA.AAAmwm. .mAmem.u nouns aoAmceA A Amm n._mmmAmNo u AA AOAg A:-A me A cm A .m- 0AA.A omA m m . XLNA.cuA emu. komm.mon 0AA me. AAAOWE AwAm.quwm.wALmAm. «oaOA maAuAOA co A mom u u my A .0A AoAm.y mm. NAAS groAAAOAfi AL% -AomAmL A A‘ Aomm. .ALmA. AA m.mwfi mA:Aow% mLAA. AcA 8A6 WwAA.A*Aomm.oAmem.n nouns m unAom anoAvoom HA» «a haaa< o» A ooao maaanmm< mnAunoa 00 can nonconam aaanmA .naoo m Amm u me.m OHVHom$A0mm.ofivnmm.0aowm.mHmmdm. Halon aoAmcoe m mm a ommmma H on AOAm. mm.m* oA .w m.AnAOAA. Lm.AAA omA.m o.A:Aowm. LA .AA AomA. wAm.Au omm.mwmo.m*ACAAAOALAA.»:ACAA~0ALmNm.*wmwAumALNAA.u Awnam AoAm. A.As 0A .A m. A 0AA.A mp.mu omA.w A. A owm. AONN~vaMcM—*Awmo wvwfimHIAoWWap A v w A a m aoAmcme panow A mum u =nmmmw~wu u my AoAA.w AA.AvoA~. m. *AomA.A w .maOA.A oAA. 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H~.Hufiom .m -.m* Aomm.:vmmu.*Mwmm.mvwo.m*flwmm.oavmo.mwwomo.oavm o.wfioun.m~va::. nouoa madame; n w . nodunoa ¢ mm : omm.nn u ou ~ on A m mo.aa*~oa .w m~.*Ao~m. m~.m* om .m -.mu Aomm.:vsm.mquwn.mvmm.mawomw«oavmn.~u~wwm.oav owwxflwum.mavamn.o "can: m «cannon * s: u mumunnwu u my 0H .m m~.mnA m. m~.~* om .u H~.Hn cpn. -.m* . Aomn.vam:m*.wmm.:vmwwz*wwmo.mvmo. $Ame.mH%mmo.u~omm.oavazs. “once madame; H .0— fl 0 .naoo * man u mummwmw u on A0H04m mo.au*fl m. m.*Aom .m m~.n*Ao~n. -.m- V Ao~n¢VMMm.u~wmm.avmmw -womo.mvma.mm~omm.mavmo~.*Aomo.oavsmn.u gonna m «aaom ..noamoon Han an hanga o» H omuo wcaanmu< wadvuoq on can nonconpm nasaua: u mmmHommu . my .naoo * 0H: . .Sméaé- Hogm.avaH.*.omz.uvoa.:*aomm.mvmm.m*aomm.oavzm.m *omm.mHV~mm. “one; noHoqoa * :m I m H1 u on A m. HHo.HH*Ao~m. mm.H* Aom:.mva.mu.own.mvmomd~.~wmm.oavmdu.mu wmn.mavnm~.naomm.mavmgo. Henna .naoo *wm u _¢umammuu my moam.mvam.mu .oammvaH.*Hopn.:voa.:*aomm.:v m. *Homo.mvam.n*Aomm.oHv-m. nouoa “ O .naoo *omn . uwwwpmH u on Aon.m Ho.HH*Homs.u mm.H* HoHn.:VmH.muHoum.:vmow.muaowo.mvmaa.~sflowm.oavmmm.-Homm.oavw:o. gonna unaccoa N .on wnHuuoa H .OH OH anHom uaoaaoou Han pd thnu o» H ouoo maaasmud mnduooa a» can sandman m . .gnoo * Hg: ".mmowmmflu u my Hosm.:vm~.mufiomn.uv~m.s*Homm.mvmm.m*fiomm.oHVo:.n*Homm.mHVn:m. Hosea madumomon IRIIIHI o ASH-non. * mm H 00H m u H HonmgvmsdoH*Homsmvmm.-.omsmvn.*Homm.mvmmuw-Aomm.oHVm~.~1Homn.mvamm.1 gonna .930 § :m u oo~.~mu mm Hoammvm~.mufio~mgvpm.:*Hommavmm.m*AomomVo¢.m*aommova:m“H young .naoo cogm .u oga m m.” on madufloqo . z HonmVm~.oH*.o~navmm.-Ao~msvm.*¢ommavmm.muflomomvmm.m- Homm.oavmm~.nnaonnp . 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Hauouo pay no wchouuonm pHm H m.mmm.m* u. «Hawmmdmmmmv * - waaaouuonm wancouuos- wnuaounonm mannoauonu 33H can and can can .nama moouau .nawa no HHau .nam» mo onHu .nsmu no HA6» Dan Dan nah Duh : OH I n om. “Mammy ohaauhmnamh .muHouoa ~.oz n c waHnuoa .waannoa «.02 I uanmoq .maHuaoq H. OH n any uaHuaoH .unaoaoq H.oz 0 Adv unuuwoa caoHuoon Had «a HHano op Houno uuaabmu< monuOHam Sneaum: H6909 Maximum Stresses Due to Loading Point No.1 Losding No.2 Loading Upper Lower Upper Lower Cr 131# 915% ~10} 509 Spa. 286 -39 -336 12a 1 216 76 -225 508 2 219 -1 39 285 3 313 -56 ~58 “15 h u93 -150 -78 #31 5 u59 -1h3 -110 nyu 6 u72 ~65 ~159 hat 7 “23 -S2 ~159 “96 8 M15 -60 -15u #53 9 230 9a -76 u76 10 1ho 190 -88 has Central Arch 0! Viaduct The stresses in this arch may he considered pcrporticnal to the north Arch and to the South Arch using values for the thickness of the ring in porporticn to the other two. To show that this is feasible the arch relations will be given Span Lengths South Arch 61 feet Central Arch 76 feet north Arch 90 feet Diff. 15 feet ' 1% feet Thickness of Arch Rings South Arch Cr. 15 in. Spg. 2.5 ft. Central Arch Cr. 17.5" Spg. 3.095 ft. Horth Arch Cr. 20 in. Spg. 3.71 ft. Ratio of Crown to Springing South Arch 2.0 Central Arch 2.25 lorth Arch 2.5 All are the some type with porportional cclusn spacing and due , to these facts it was assumed that the stresses would not exceed the values in the other arches. Arch Axis Spans Large Arch 92.7' Central Arch 78.15’ Small Arch 62.6' Hexinum Thrusts Large North Arch 57.9785 Central Arch 51,692# South Arch u5,uou# Crown Thick 20' 17*" 15' 3-35' 2.73' 2.1‘ €5' Thickness Q Spg. 3.71“ 3.11' 2.5' L_with vertical no degrees #3 degrees ' “6 degrees Design of South Pier Division for Constant g I D ..- 1‘ L‘to make §_conetsnt 2- 3o 3.u 3.9 h.“ 5.1 6.3 8.0 O‘NO‘Ulk-‘U-INH 60h Summation x3 I YR " KRYR .. ,3 s yfi Summation XL I 1L ' XLYL . XE , 2 Y1. Summation YP e 1% Design of South Pier . 97h.6 § 301.1 a 11738 g ”6229 3 ”170 g 72h.6 = 209.1 g 6165 3279325 = 2216 2373 Summation MR ' MRXR Summation EL ' HLXL MLYL 3,1“6,180 1,361,870,000 26u,5eo,000 1.087.530 366,360,000 67,811,000 OP: 6.0". “P g S pi. ,I". I rs I .monaaum «meow no nonaoe opp Hp copHou one: osoHudnoo omega smo.o:m.m - H>mmm.m * HmHHmH a Ha:.Hm u Hum -Hmvw.mHm * Am: a H:V~.nm: Amy ooo.mm~.mHm . stam.mm * Hxsmmom a HsHHmH u “mm . Hmvmnm.:H * Hm; - szm.mHm “my Hem.mom.wH a N>Hm6.m * memowH a msH.mo u :mo.o:m.m s Hemmm.m * HmHHmH u H==.Hm “so 0 u ooo.o~w.HmnH u mpmmmm: * NmmMH.HH . m:m.:~m Amy 0 u ooo.OQH.mmm . Hpmmn.- * HmmmHm o Ham.zm~ Hm. «Ho.mmH * ~>msm0H a mmeomm * mamomH u ooo.~m~.mHm- Hpmsmmm * ngmmom . HzHHmH HHV anoaadsam saoecsaansum Nam uoHa mason no amduoa Design of South Pier Values of Unknowns by Means of Least Squares 5'550'9 1:2 .-. ammo? 3'9OO” H2 : 21,500fi 12u0# V2 : 20,370 :EESO : H.5' x0 . 6h uoo- 3.15' 25.375 Design of South Pier p a 000 (1 - ,100(1 1.1 ) iii-g— £..:.u.x6) - 5 t 3 P = 11,000# per sq.ft. compression on Left P': 660# Tension on Right Steel in Stem wall I : 17,u00 x 31 112 = 5,352,800 in.lbs. d : 7' : 8h” - 3" for covering“: 81' to steel p : .0077 be2 : 6 2 800 : 59,000 1202 :59,000 a? : u,920 d : 70' A3 :pbd .0077 x 12 x 70 = 6.“ sq.in. steel Design of North Pier Division for Constant S Div. L to make 8 constant 1 it I 2 h 3 M it it 5 14 6 U. 7 u g .__l_§__ : .123 I 32.6 Sumnt 103 XR s YR P ' XRYR s XE s 7% I YL ' XLYL . XE . YE Sunnltion 1P 2 I YP Design 1057 396 18173 57ous 7152 9711.6 301.1 11,735 06,229 u,17o 98 1821 of North Pier Summation MR : u,35o,eoo cR :3.7 W quR 2,01u,593,000 MRYR : 559,9h6,000 Summation ML : 1,706,110 0L =6.01 - sLxL :6eo,935,000 . HHYR :132,290,000 CP :.123 I~ Mn '11 K“ ”L :11 ..urtflrh phayhfitz kc Chi-Itch AOHH.m0H.H a Hemam m HmHom u HaHHVHo.m n Hmmmm . Hmmm * «a» u HavamH. Ame Hooo.omm.mmH a prmH.HH * HmoeH: . HsHoano.m n HmmHme c HmHme* mama . Hawmvan. Amy Hoom.omm.= c N>HmoH * “mean u msHHV~.mu u OHH.m0H.H . HpmHm * HmHom u H: HHVHo.m “an o n ooo.nmm.:Ho.m u m>mno.Hm x mmnHH.mH u m: smoH any. 0 u ooo.mmm.owm . H>mmm.m=* HmmnH.HH . H: mHm Amy Hooo.msm.mmma manH.mH* mammHHo mamman.mc u Hooo.omm.NMHs HpmnsHH* Hm 0HH31H: .Hoano.m AH. .mnacson uncaaszam sooossaassam Nam uon nano- «6 eanon Design of North Pier Values of Unknowns v1 : 11.2oo# v2 : 33,200# X. z 101 ft. X2 : 2019 ft. 1 to left to left 7.5" North Pier 0.0. of Section 28 x 7 x 150 : 29,6005 12 x %_x 150 : 1,800# 19 x 5 x 150 : 1h,250§ 2 #00 12 1800 x 6 h 2 Z 11' P I 100,143: 11575 (1 £6 ) : 3120(1 t 1.76) . 8,600# per sq. ft. 92 : -2,350# At Ease of Stem Wall p : h8,200(1 t 6 x u 8) —_§—L— pl : 153# per sq. in. compression v 3 12000 g g z 5619‘ x 2: x . A. :square root of #8200 x “.8 x 12. .0077 x 12 : 1.25 sq.in. 12.1 Use if ¢ 2 12' and fife between for A. moment varies as cube of diet. below tap 0 lM' the reinforcement necessary : i that at the base. So carry for 1h' up. M if Viaduct Section lhis viaduct section consists of beams and girders of reinforced concrete with the exception of 3 steel spans over the Grand Trunk Railway. The lengths of these spans and the angle of the bents with the roadway are shown on the layout diagram. Sample computations are given and the other beams have been worked out in a similar manner, so it is unnecessary to show all of the computations. These computations have been checked twice so they are assumed to be the correct results. . The depth of the flirders are limited because of clearance over the Grand Trunk tracks as shown. Slab Design d : 5% in. d z 7 in. Use ;” sq.bars U" c. This design governs all parts as all other scans are shorter, and in order to keep a uniform slab 6% inches will be used. 7’7 Span 37'-O" (for intermediate spans) D.L. Club : 7 x 150 : 10503 beam :2.2lx2x150: 663 - IX 1 150 : l 3% 17307 L.L. :3; of h Trucks : .737 Of One Truck .737 x 28.030 x§,: 25.0003 .737 x 20,000 x3,: 18,0003 l Truck ; (30.53015.5f12,500xl2).6 3 273.0000 "2 : 1703 x 3'72 : u D.L. : Shear 0.L. . 23,000? b a 6' V O 7 .1306 ‘UBO d3 : 29' U : h l 0 3 1213 ---Use stirrups 2 x x A3 = M : 1 000 = 15.5 BQsine a8 [33 -I E) ' - ' ) II 2' Use 12-lésq.b1= 15.18 sq.in. x : .36 1 : .392 p ; .00622 to : 000 : 15.650fi 5,: .293 . x. 9212 d to : 6 O z 5665 Investipation at Support ' u : . = - -23 K : .h28 3 = .855 12 bars in Top at Support 12 bars in Bottom at Support 1 .9: . t..., .. ‘Ltlr. ..l ‘11:...1’.‘ «q “I x. . Span 37'-O" Stirrups Use 1%" p - .392 Concrete will stand Vo : wbjd w quzhx675x29 : 2h,h00 f 8p. at support sjhnfgjg W. V i u 6" : 6e32' ,’ §&.¥§é ’ 35.5%8 7' tax stirrup spacing s .350 s 13.1" S e 7' : ' 6 00 : 9.h" , s X "’ s e 101f: 3§a.000 : 12.1- / ’4 I. t . Mar bent up bar spacing “a 5 aa : 25.h' Spa 9 7' {fr13' 9" for53’ 13' to beater bf: do : D.L. 37' Span Outside 10% 37' ; an" h6' Iltb : n.75 x .75 x 150 : 535fl rs%x&x1502 19 been 2 2 x 3.533 x 150 81150 1 x 2.12 r 150 : 318 slab : 1.25 x 1.25 x 150: 23k rail s R1 . 21.250fl . a Truck : (21.250 x 6 5.78.750 x 12).8 : 195.000 ft.1bs. a 0.0. s w a? z 2896 3 :12 3eu,000 ft.lbs. uu11. a 6 z 108 5 31? - 32,000 ft.lbs Walk lOOfi/fto - 673.666 iEeIBCe ""6¥§E37000~fi R1: 17500¥12500x§§f12500 x g, :: 29,2009 R1 : 29.200g DeLe : 2806 X 17 2 “2.100 VD.L. : 76.900# T-beam - Outside 37' - Span Investigation at the Center A, - u - 6 RS 000 - 12. 00 sq.in. " 7:11:55)“ WV Use 12 - 1- ¥ :12 sq.in. §3k§=‘255 pzfi: W5 .0065 Di 6 agram K : .360 to : .36 x “2 2 15.1“ f : I : S.QH§!%QQ : l 005 a I s33 1 x . x 2 5’5 fc : 7f: :1;5?02 x ’35: 580# Concrete takes VO 3 wood : ho x 2% 1.88 r #2 : 35,500 stirrups ' ‘ S 0 support : Agfgfid : h x 6000: 88 u : 11.2“ or 12” V Max. stirrup spacing: .b5d : .hS x “2 : 18.9“ Max. bent up bar spacin : h z u an : 35' any 36" 8 $5 5 IO 35 : h 6000 88 u z 20" m. p - x 3' from sUpport. Spa 5 18' T-beam Outside Investigation at Supports Sending Six Bars 3'. = 11%": .095 p’ : p = 63:23.55: .01100 Diagram 8 K : .365 J : .886 r: -6 11800-1 ’03: 9 :fi-‘fitfiefiv‘ 5”"- f 3 K g 60 60017 c 'H%f:?) 1515?T:¥§6%§5': 6 bars may be bent up from each side Lap bars 5 intermediate supports so as to provide 12 sq.in. Top 12 sq.in. Bottom an; tits V .K. ‘ u , a t . ., . .IHW. .. ,. \ipinlln vinoJ.‘ , t .f... t . ,. - fl , ‘ . \ I . ¢ , I u L . . ‘ ‘.‘I f s 01* “PM Jan“. It.“ Lit. . y 1 . ,. 5.. 1 . 7;...krwtwfip. 2,511.3? .3, / 1 t 1‘ ...NO 3 .I;A? 1| . bl , . . .V v . . ... a. . w .- (Itun Ill . .A‘l' ‘3”: ‘11 ‘ x x ‘ 1 . _ . ‘ x ._ «Pb, . 4.41. :73 rylg.“ ‘ j \ I { 1 \- T-beam Outside 37' - Span Negative Moment at the end I,: w 12 for dead load on fully restrained section. u truck : (21,250 x 6% f 8750 x 12).5 = 121,500 ft.1bs. ‘ID L = w 12 : 2806 x 322 : 240 000 ft.1bs. ' ' 15 1 351,555 ?t.1bs. 13385r¢5:37 “"‘ET336}000"# Bend up 81" - sq.br. : 8 sq.in; g} = n z .095 p' = s p = A = s = .0079 d I? 12 b5' EEEEa 3 Diagram 8 f8 = “lghOIOOO = 14,650# x x 2 £0 = 14,650 x .gal : 625# 15 1-. 1 r; = 1n 6 0 . 1-.0 = 7,100# T-beam ' Span 37' - O" Negative u @ End Supports it . fig for dead load 'L.L. q35_b0f 4 Trucks 3 .737 of 1 Truck .737 x 28000 x g: 25.00% .737 x 20000 x 3,: 13,000# um“ . (30,500 x 65 {12500 x 12).5 - 12h,000 2mm. 2 D'L' 1%15 313,505 1%.Tbs. 000x12 : 9. 660g. in. necessary 'rr-m We Bending up 8 bars 3 10.12 sq. in. . if 12 bars are used in Investigation over the support bottom. '- h :- .138 p' ...}Ma 13‘ . £0.12 ... .01n5 g :9. . D I 153%: .0218 X Fro- diagrams x . .h61 J : .sue 15.12:.gfigng .10 g l 00x #61 3 870# -—--Is allowed because of extra fail—.5515 . . concrete in knee. 1;: ;5.300§§u6;-,;381 : 6mm! 9.27.,“ 0..-.rixuflawiauikrngvflaf-.}i I Fizi- . . . .. x s ’1 -.. .. Infiflulfihim‘ .5.) “I VO’JI. 9 ,jfl \ v r. P Tabulation of Beams according to Span Lenathe Reinforced Concrete T-Beams Inside - The interior beams s.uv Span - Over Arch; - a Cl C- bf _ 25 d0 - 18," de - 16" Use u 1" p bars - Stirrups - Sp. 6“ uniformly 20' Span bf = 5' - 0' d8 = 20” (1C = 2“" Use 10 l”sq.bars Stirrups - 6' progressing to 11" 22' Sean bf . 5' - 0" d8 3 21' dc : 25' Use 10 l"sq.bars Stirrupe — 6' - 11" at center 29' Span bf . 6'-O" d8 2 23” (1c 3 27“ Use 12 l"sq.bare Stirrups - 6' - 10" 31' Span . u I bf : 6 -0" d8 3 2h do = 28 Use 12 1 %f sq.bars Stirrups - 6" - 10” 3h' Span - bf . 6'-0' d8 = 27' do 3 31' Use 12 1 %f sq.bars Stirrups - 7' - 13' at center 37' Span - See Sample Computations Outside Spans - Sidewalk Side s.u' Span 20' 22' 29' 31' 3m 37' dc : 32” d8 = 29" Use h a} round bars in Top and Bottom Stirrup - 13' Span do a 37" d3 = 33' Use 6 l”sq.bars Stirrup - 15" uniformly Span do . 38” d8 = 31*“ Use 6 l”sq.bara .Stirrup - 15' uniformly Span do 3 #0" d8 = 36" Use 10 l'sq.bars Stirrup - 13.9” to 16” at Center Span do : #1“ do : 37" Use 12 1”sq.bars Stirrup - 12“ - 16' Span dc : #5" dB g #1” Use 12 1'sq.bars Stirrup - 12“ - 18' Span.- See Sample Computations (PE: Lively)?! . z . ; , r . .- . A ..- M114. wan... r therapiehnxhu. 6.11,. Curb Spans T-Beam 20' Span b, : 2n» do :37" d, . 3kg" Use h l” sq.bare Stirrups flax. Sp. 15.5" 22' Span ,b1. 3 26' do : 35" d8 3 35.5" Use 6 1' round bars Stirrup Max. 16' 29' Span do = "'0‘ d3 = 37.5. Use 7 1' sq.bare Stirrups 16fI Sp. 31' Span do 3 ’41” dB : 38.5“ Use 10 1' round bars Stirrup Sp. 17.3" 37' Span - See Sample Computations . vI‘L on. I I... I.L‘Nssurlahiw‘r‘.zrln.nrth.i 1.: .o . at. . M Jufibfifif. ‘25.... ,..A. »~ u » 2.3%....‘0 3.2K V . ._ 115.1 ... . . .. ...; chInUriia‘r. “0' Steel Span Outside D.L. slab. ”.75 x .75 x 150 : 53“? beam : 2 x 3.92 x 150 31175 7. 19 I-beam - 160 rail 3 . 2 2 “D.L. : v : 2H 8 x ”0 : “88,000 ft.1ba. +2—17— lull. 600 1 H6’ : 120.000 ft.1bs. #0 H : P1 2 IZHSOO x I E;. 00 ft.1bs. L'L' E , t. be. Use Carnegie 0.8. 272 27' l60# Beam u : 675,150 ft.lbs. flax Shear at end section : 208,570# Allow. Uni. Load Fired Free 135.000# 95.0009 (2u3s 7 600)h0 : 121,000 --Fix ends TOp Flange stayed laterally at intervals of about 15' or 17', if at all. “0' Steel Span Outside Use Carnegie C.B. ZUM 2h" 3 : 500,u00'# Shear End R ; 159,180fi Allow Uni. L: Fixed 100,000” Shear D.L. slab : 600” beam(c).h88# I beam - 1‘0 12133 L.L. : 90% of wheel loading 215.7505 & 11,250” MD L.: 12- 121siE03; 2hh,000'# M :19 12518f7875x12;EM15OO'5 truck . u total 1, i Section Modulus S : #215300xl2 : 328 l O 130# S : 3}" Free 70,000# 31 :1575071125012 11250x&g 28,100# 0.1.. :1218x2 iamgso V 8 3 Suggest 2’4" 0.8. e 120!)l Providing 301.9 Steel Spans 40' Span Outside Use Carnegie 0.8. 272 27" 16Cfi MO' Span Inside C.B. 25h 2h" 130g “2' Span Outside 0.5. 272 27" 175% h2' Span Inside C.B. 2M” 2M" 1303 an: Span Outside 0.3. 272 27“ S 190# uh' Span Inside 0.3. sun 2h" 2 1u0# I’ll nutu..l.Il . Io. Isl III-voila. . ls l il‘l}\oivd§\.£ - , . It'll} fl-m—v-w /— 00 /amrz De/ér'é P/YGSI‘d’r Defer/c , ;..Z.?,’ ' O O .3.er i 1 I T/P/CA L CFPOSS “JEC'T/OA/ 0f ‘ CW/YC'PETE BEA/‘18 \k \ \ N \\ ‘mll I ll I! ll ‘ 61/sz 7e ,Defdf/s LOGAN STEET‘ V/ADUCT' l—AN JIM {‘3 " 7’0 '~6 ' Sewa- 00 TJ/P/C‘A L 0905.9 sneer/0M " «1977554 JPANJ’ Fer.» .- x ' ‘ it [gr '3" , ’4‘?” of pas?“ Cry-a4" 7‘ Bow as . .. a . I a ‘ y ‘ J‘J/ we éV/rccf W/Y/ 6‘- r/o/cc/ SSSSSSS "WInull“!HEM“fififlfljflfiflififlflfifl'fifllfl 1