-aeweeeeeeePee eee ee Bae 121 769 THS THESIS INVESTIGATION OF A TWO SPAN REINFORCED CONCRETE ARGH HIGHWAY BRIDGE C. E. FOSTER & E. E. PETERSON EB ea a. Unenncan Cone ey on te sare wa ~-eee - . . tee IS / ~ (™ : f~ \ N ~~ ' ’ ~ Were ss sy T eC ses e oe wo eee ere ae d ! sf fo gee el ane en wt tee Oe da wn tn et a3 3 j ; * a ty ~e gv ay on < « t s mit é gég°° N BACK OF BOG;. This thesis was oontributed by Mr. C. E. Foster under the date indicated by the department stamp, to replace the original which was destroyed in the fire of March 5, 1917. —_———— plot tower tet ww wet: tiLsryI TTT. . . pres + } + -_ =a ~ — wwe ow —eawr ti et ee . SETI SIT Try eres ere eae 7 . 7 . - a a ee ~~ oe ee . ywwere re rt PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES retum on or before date due. DATE DUE APR 0 7 2001 DATE DUE sa3 wre 7 a we we Fs Fut oo > ¥ = FETTTTT = . - = ~ : sES 3s ls ss 273 rtrt. z tT - z - ta : a . sas 2. i . a . 2 an > sa ta “ 2 “ *37 . - .. a7 ae . : : sige : - +! 2 .2 . -—- on o- . . -7 ° Bist Ls este ee soa ltltl . nen a -t. 1100 c/CIRC/DateDue.p65-p.13 ee MICHIGAN AGRICULTURAL COLLEGE hs go Ora atel CANDIDATES For THE DEF BACHELOR fa) ee S| at 1S WATE: ) ‘ a ToREWORD.-~ PURPOSE OF THIS THESIS 15 TOENAGLE US TO BECOME More WITH TRAE ANALYSIS OF A RFINFORCED CONCRETE ARCY —— MN Be ee ee — a CESSARY TO DETERMINE REACTIONS HAVING THE REACTIONS THE THRUSTS, MOMENTS AND rs ‘} INTRODUCTION. ITERS OF THIS THES\5 CAME (N TOUCH WITH THIS MROVOK THE AGENCY OF THE MicHiGAN STATE HiIGH- MENT. THE BRIDGE was BUILT IN 1914 BY THE D6e COMPANY, OF CHICAGO. THE ORIGANAL Dod chy 'TED BY AN INDEPENDENT BRIDGE COMPANY. THE EN6- HE STATE Wiénway DEPARTMENT SAW FIT To CHANGE OF THRE ARCH ,MAKING (tT HEAVIER THROUGH-OVT. For THE WRIFERS HAVE INVESTICGATEO THE ARCHIW AN DETERMINE- THE STRESSES INDUCED IN A STRUCTURE yo TYPE WHEN SUBMITTED To THE LOADING6GSPRESCRIBED IN SPECIFICATIONS. SRCH BEING UNSYMMETRICA AND FIXED AT THE SUPPORTS BY THE ANALYTICAL WERE DETERMINED GRAPHICALLY. STRESSES WERE- BY THE USE OF ‘INFLVENCE LINES ViSH TO THANK, TRAE STATE HIGHWAY DEPARTMENT, MR T AND Mr.H-L. BRIGHTMAN, ESPECIALLY, FOR THER KIND NCE IM PROVIDING DRAWINGS , PICTURES AND INFORMATION. , FOR THE METHODS INDEGTED To PROF C.A.MELICK IN CHECKING THE WoRK ere yaa t Chet THE CARE TAKEN = u' 0.206 01455 Wath Wohl) ePIC So ee <— aed pee ee eee on ae =——— ee ee eh BD MRRP NP PR ARN Were 0 0 | y 0 \y 0. rt i} y 0 0 Y S32 ool> a te hee eee ee oe oe — eb ee he ta hi te Leh > pb pp Oe pas 289 O50 ran ’in' hed {.264S515¢ 0.63225 15 Fae) 6-16 hoe Amat 19.4376 ee ea 0.649 £365 Zo foe te) 1.6406 ee: 1oe eS 12 S$o4206 0.b25Z100 A oar ae ye ee 0.0400 7), 3844 13300971 nee t A.o2 al | Wy Toke: Wl hax g a wie}. 1.20 88384 044 195 a = } 4E71648 32.50 -0,.60 \4.4A4A00 eee Cr he ee hole OLE IEC: 4b — 01% 23.6)46 _ 5416 44.)/672 - 1.332269 0.691 6132 ea - 1.00 }3b%00 err 14 6400 libTo2ZI4 onthe dae ye ee 22.6576 eat 3 Soe 7 j4 6° merely J ro 0.691422¢ 4.2000 4.0000 AAAOD san 2 eo) 8) 44000 4.7000 4.6200 4.02 00 4.8200 NTN 48000 3.1000 . 47600 4g000 4A 0400 39600 1.1800 1.3600 0.6400 0.1600 04000 02000 -01Z00 - 0.2400 - 06000 —0.7T4A00 -|.0000 - 122000 — 1.5200 ~|AB00 -720000 ~30-05 -I.2600 \-J3 0.14 54 lO alae heey 7S - adidas ~ 0.0682 0.1146 0.)7T4Z OY A Aa - 0.2184 le ol aa aa ~ 04173 ~ 04462 09971 Re kee 0985! 0.9740 0.9605 eye ome Pad, 08949 fe} sicred¥) 19096 | 25498 an coy ORE Dh mass) im - 26177 | °.54999178-3.547q ) ésictias -0 3242 Z were re ; Ae eee “Ay Ae A bs dh Tree rac eee sa 1(033752-/2047 a7 3.30065(9 - 19983 | 31054499 -12748 | 31026483- 1266.6 | 1.1949483-623B66 Rel ee wey 4-2 ea APY ee errr sl | 2487766S-30749 | 2;0192)4- 172645 0.242447 -J446S | Ce GRA ee Ta eS TERT ea on KoR te kot-) = 067135733 | 04824-5156 -30.370 | 9.948470] - 0838) 2272919 - 168.17 | 18262542. - 67.337 39721 323-13785 | 37080383- 510-SS| 20172253 -(1944 | 17420684- 55.716 25446792 - eared EER ke 69 2 a) 0655)76T Coe oh ron hE) @ y Re yA ate) 0.2296818 153- 44832 | 0.0779/AT -11905 | 03q04980 24576 2.33/6080-Zj4.59 | |9D5247Z -Rb148 | 14811087 - 3Q277 4/407 - !loob3 | 37925797 -62027 | 2.$717194 - BT3.0) 31°75/-17060 | 20390509 -j04.41 | 22078389- 161.37 vt acres yen 1 ec mee eI 1 | i T22S2 - RX hkl S522\ - 19299 | 18439524 - 69.816 G il yaya Te) e) 4 eats ee: 2 eras) 00461043 390999 -|1342 ppirade Z1Z73 | 98791052 ~ 31941) CES Mee Re 2m We Cae 4 Mee ee S| ee Lr area Be Ata ee Ce tye ee 18270340 -67.148 | 29973402 - et ] | | ' | | | ] rr ernT 13324848 -21502 | 98622946 - 0.1283 | | i 62) -8./699 | ISZ7TSI8L- 226 5 433 - 3.1 364 4759312 - 29913 ie were AP] @ omy. hee oe-s i) 520784 | 61043 05967581 -39S1S | 0.5390260- 3454 972)586 -99571| 2.210TS5AI - 16246 2 | PEC EL) Mees ke ee a ee 291 TZ36T ac oaes EC yal aa a 4745333 VAC ile IA /4S 9 - E9026 my Ze Lo°| Tr YE ae a) 4 0 ee ee) ‘| qZL0— yh oe [3 a “Al! 2B ; o7t$'} kg hol eR) erie aaa hes ey? Pre ee €bLUI ti) rte +07'0l 88959 of 40lb siti Cy 900) s71— Sto- (S112 O799zl jos L$9zi | Lizz ee see ae Se De OS GLeb | cLe 39! Te Te oe CIZEE |OO-GoLi | O¢90011 Ob: sie ho'0- at eS es ye) oe) Ta yea! ih ee Ce EC7 LE | CCELI! | pbpybBL | 001531 eae 7 eed ae oe Ty i9'€ ora, Cine ee ot ae Ty by cE | beebb | ogloce Pa Ciena By) (ae ce ay. yA ya nee a en fe ee Ei ay eee A ay aan Wee dy 1 ee ee ks 2 (abl < BA aha aC) oa a2 meals aE ow ees | Ths a pL LEL aT oo ———— bf- OIL IS¢Zi a es me] Ab: oe 4 ae a a heat Lk ed Al 5. el CET yee Pas Po ee ee ke Ce tab et oa (eae eee ds ee el ae eS ee So ¥ ~2ZbLtS9/ 2) ee) ad es ee e2 - e [TLE OL | belberl! CMG ZL | bOL20OO ory ae eee ates FIL - €b7bisgi | rie fees Aa ae eo et) YI) side ALE’SS = FODGHLI | 9¢S9l-ySLOET OT (2°Cei — SILLisiz | aces 654-7 OL9'1 LbesoLLgl OOTE SLI! a Ae eee doe 2 ae i ae ae ae LE Fy Tia e CE ke ae Sa a ce ee ra s.r er ee a RS a a ce ee 2 ee st ee RE de Oe a gf td am Ae od hk Ae a oe ae eae oy te ee ed Sa Ae SIBIWET! Tred a Atty is 4 A a A es os ak a Wet eee ee ol 184 ea ee s aa ae le SE ee SS a fe iILGS9- sobggive | FETI~LeyLgrre | C9US -ss LyT9B-STHLSE BI | SPIl- fopgeloz | vowel - osgiziz | vyirel . $s) CITLEBS! FRET IES! LOS ea $7 eit a a sae 99 TEL ~ TETOSISZT | GSi-TZLEsTI7E | Re ee ey hoe ied a ae te) oa RS a 4 ee ie oe oe a Uae el ee SR hold Ss CD yee eS a) ee ) Se 5 ie A) Ad ae 2 eb De 2 eae ro oe eee oe hh ee eee COE = The Stve |. Se a pe eons ~ Fbzbv IST | gZILOb— 7 nis tT. a re ee ~LOELLOLE | yrwby- CEILS LIE » Ae Al el’ ae ek es 2) 2 Cabseobil yLISI°- =ogizz7t | YSTO. Logoseoz C9LOl - 47 1G1E9 Ad Zhsiegel eis ye as ae “1I0L1S ¥' ab eae dh [ € 17°C Weeds =o -. rf Son om ie oe Ki s4 et 2 che es he ee aoe BWCOCS -beG +See Pays tee eke yg idl _Ch°9DSTE bESOD -STRiPGL'Z LITOS-~RIGpoLEe £ xlo-x) -VGEOLLTI | CLE'B7- LIVZTS HI Vhyb- 00%, Lb? | $7¢°99~ OsLaizs! 3 6 tole Terie PIE Le Tee ae CvOxe1gi . eplze J path AT a Se), ee SIL ater -ZLiitows?2 '$togi -Laressrv 2 S€959 -POlDIeL) GOLA Shir tfoxz POCIE- (RE LOISE | S80gs - 9€999S7'€ ts ba ae ay A Se be a ede et ho a a 2d ed OL LZ ~€b>eLlL esc 1 af ee Oe ad Ea a Ae a IbTbhtbhO ata oh 2 ee ie -a°3) 'a| e con a ere Na ge SOL | o hed " A Pa eee ot" ee as Pe ee ae ae 5) ee P°SIT -VHSSREEE |\SECCL -LHELESPu orzsspy - VioT$sS9E SyHPIl —zyLLBVE bETLS - OwILE ES! | boblUl-ssypesit racic’ oe Jae 2) ee eS eee STIZIL | BERbrIeT? | eid ee Lay Tbu Lx ee Scab Rit re 09°L9 ro ar 1 ee eer se tne Se ek he a) ee es gt. ew Wed Tar SLLITZ ome td be 4 oo A leS3i- Liti g9tE a SF bs he a / Oe ae + koe ee eA a bie ks Ser ae Ane ee ee SA ee ee ee ee a) ee ee ee oe ae 4 ae 2 ae Ste aa Le€is 9€bo ehitbeki Det ay ee yas ae oS 0} fe ae | - a | be 8L'C9 de dt ae] “bb esslo oS Te ee oe) ee rn 2 ee a Ae Ss ZY CiMbI ZL Z TL OOL -pietseP et | LIBLE _L191109S Phyl _ LyIZyP € oLivt! (sO Sboy te lbp - CSoselL il | LeveS- bPLeitLi oA) ie See eee aS ea eed ee Td hee te ad TT aa St ae Itpeg OL + i ali al, lew re Sad se BLbS | ba Bo ag Ped a 93999 - DZLOEPLE SOpbhl -IbegboPVE (98 b-Togie Ibe! A ! TELLB - LbISOShI he 1 ea Pee 1 eee Ae a A BbI IIL boolLyL! oe fom Tne a IPS” te 9SS C44> ae bem ee 28¢8C-RLIStS HI | gigiz -iLesves lt | logpi -2O%CbiLi'l gStib -pILZ09y't | so Th9 - LoisOpgy IbSLY ~fE7SLLIZ eee te ek oe Ye So. a ca) co oe Dy hd eae oon a ae a eS Ma Ag SR OL3i | Ty sees i ce ae a ae oe a Ys A A LYLol - oLibreo? Radka Se ay eee CLE Le oe eee SAE : — — | ioe a oe cyeL Ts ce S299 OT aa oe «A eB ca Tm a bLS OY -S9OTZE btF | wEZS a Ph 4) A ee 2) Ye oIis?l -oOLosItI¢ ZEVISS -SzSst- ST 1 OSL + Z - Stborbe'l hed eed oe hed Se ase La i eh a See Pe hal ae oz | Le Eyed ee 2 on ed Ee 5 } = — ae yee se ale ey coe ky se ee ee oe eo ee oe are a) ee de a) ee ee A Oe a | Qt wi -8e ie TSll |99es7-obc+ HEE’ ‘ae 9S - e E o ae | ie bei gcibo bel Boy tse yt) a At 9€LL ~ | eat ee eh ees gSTtIb -yiLzogy't Sturt eee a) a2 ey ee Lslpe -19e0€3€ ! A eee eS oe bLSvbTt a a Ae syplotyl a> ir ee ee ee ee wE2STZ - CSS Y LOVE av et 25) OL {ZOILM+) Poa la a Ae a yee 1 See ‘ihe 4 Seek a al ee "oO Ff sc sd ¢ ! wI8 LI - IT ee ae eae -\Losre¢'! A ee LolsQp3t $ETTB > GIPISHbE SsItlLvEe vl a Nr at 4 rake Coad Tekan SLE'NT - ae CIEL RIL LI bf peed) : ee a ee ae) OLthrec€ grey) - Eeelesi eb ae 109) LaDy | eee We Be oisal - ey eA ae 2 Te ee ae 4 heh ole ro Taw Say | Bh a 3° VY -SSlLtrrt! bb°9%b ey ae Oe ee eet beigeib? ore ee | — a rhe 'bS LI 4 er ed 9- | v b96l / eer, Sy Ad a OUssY a3 4 ay ae } deh | rita 5 L $20 erry. marys 7) Tx) eee p ok c iy a rT) nr 7] es ye) a eT oy en eo 2 2 rea eee aT Ta 7s) | La 0S 2p2! oLlyZi yk Tt a es | orga eeayea es es a ta =— os SS - | : eos n sae ty PA rd he aA) oP) Seen eed Be 1) G'19L9| Pa ae rey ae | ¢€b7z9 era GTA Nanas o2g 9¢\ 03 ose | kt ee a |) | ETT) LL ne oa te) ogae2zi | S8tIS |S Cm FEI any 1 ee ¢g.90! || oojs2t | Vy 86| ez! ap rot <> ae ays rh CL wey TA Tory ole orL4 es ah gSb€Z argle ean ae oe ee ee opotr Lay ‘aj Sy ae ae CZI'Z¢ - he AD Lt7 KE< EE Tee Sl ee ee a en ee S27 ll =| 29E GE - Oftll +teyvl wetv- 6 39¢) 6Shbt => N20 - acy) ean a 7) ee T) ek 1 SELZ¢ sus aye aa a aaa L2€31 OO GING = NZ ren aay im keg wks Shi x4 A oh) axa ie Lr XL es ae ss) a | oo a a. 246 ear Pot Or --0 | ) 8 ao GSTS Bri9E = GOBLS QCZLE — SIL ZL | LOB AT loviG@ 1168 LozlZ SHS aS) ya 47 | 2X9 Keka ol ee a ee, lee 7. x Lo Te se aA IC LbS ani ieee ah 4 a ae Oa Aas ae ae 122°9€ i ee A. S219 i I NED ivove’ LL’bL + Ml ah ae ied bh Le oP die 6SLY ce 7909 ee 2 a) Paes ad gcFg Bl OIF Ol gg «(094 etek aa OLIG wi) oan koa a Me daa + Ade) hey C5 3si-¢9 | A 1) eh 1% is LYSLyohb 3 30 Arh ded 4 b Al S| ibe A a] Till bhyd as Ao (4) ia Abel. CLZI00T ZE0S7TIVb b lie Jee, Ae oe em eb oh Me na ao] ad 2 Oh Dee a a 7) Lay a a) SvbElIb 'b wae bl || 1llbL¢)o eo A 'y 997 ea re ee STVEITIE veebslov \€OL LOE’ BLA eh D2 he's PISLLOZ ‘vy VECZROL 4 OL by 2S Sk ae rT y bof030°0 ‘wa ya ae Aa a eee De oe 1 a Tod 2b$£3°0 O1G0LI Aa { aa VbLLb'l LoLgi ‘2 a2 ey A $LCLe'l a ke yi ae a aoe emer Tt! SbIbLIL! ee a = aT ey ae he 0998984° OILE LHI’? aoe To) ae \EIZLOLE ErtwEewe a Arey Ta $C Zoe Oty) ZIZZboT'E CvSOSTI'Y obbyghte | SboSULbE < = = } 4 ‘p Pie €1gseosz | oaks a eae Lhe 0g 0 | ke a SUbsr | SLbLE'2Z oh eh ee by399 ¥ Cie te) rae a 4 A TLLOCT Wa 4a oho eB id ae ode Rey: earl BY 2 ea) oP eS og Eom elt Ee ats 2 NES ILE $19 004+¢'0 $9L1 699 ‘0 oh ie a ys a a a es lan Te) ' OR Vy " - 5 A lad) Soe ea b's eh Sd ad ‘th ey ae 3 SLEIQL L@S¢Lol - 93 IE CEl - S¢Ctbs —— ras | OBBS°O Treats SEG CS 8 Ree ee L TE LIne La Re em ik De AL ) ee ok od (el ee LL xen 7 Ales TAS Siete 4200S nt A eT e aa ose a eC es Dl a ee aL etree Sea eaese ees ora eT ee eA eee te or cb COR arc eae ay oe ee ASR dL Sea Bk inal ated aa ale iT Reale aad oa De TT at ee ipa eer yee aa Lache ae 7s) aed ec EL Le Gn ene er HE* otboOl C4stLO+ 9¢¢Gby¥_- ISL0Sb90 iogtbo, svioln'b TTT ele FONL* igre ll Legge OC HIbS-| StHSEELO phases yer racer hata k af a ae ra) teen pecans POSS See aap al eee a - kvz"H (0001, TA) yO! ao ‘q a Tae an Ee W ea Frat en oh DY a) | ee ao Ye Teoma aT bytvI0- 4954. 999 Eee a AT 4 2 ee op as ed 2) Sak TELCO MMe y7eS e TT ee Slo) Sef yl 2) ry 2 22) 2:4 92% 7 a oe 1 ST i Sty 19 -| bt€-Lz cAaaa gioshog']| syltLe’ | b2io1g-b) LEzé$90°2) <9¢-221 -| It09y | buses tT), ce a aT inc a eT oe re ILEbbL’ = 9DF4HLEb| WOCALE D> Glad -) LOLS oP L eT era) maa IDLZISb'b 9Ob889¥°2 BIC HbZ - | Se Ta) CEPA ec) 0c) a ee 2 eae S9b2bbbb| OROBIIS'2| 7281 97¢ - Renee a ee SO4¥wL - [ M BY Die dal De ee CFb'S + ily eA Py WS be aie POb¥ITZ ~ otgsyh%— OvlL9i + A Bia iy a ool OS + 1 ede Boe CtTSL + iad 0%Z90L~ | it ow Ml i Ao bsStt Bla de 2 Cr+ Iter Se Ee 5 do QteIl+ aoe W389T + mee beet | 2) ees A \ . . a tye & yh ae aes a Be 5 AFB - Sy ae obel - aH al | fi i Oe LSEL+ Rita ce: Peri. a ae LSE 4T + val ee eras TS ak tee irae | = | 1 09S bZ- | de ea ae ostare| ¢ eae TT Ae a PT ean yet) eae sa eee ee Oe ey 4. ey aD) eR Lae mee iM A i 2-70 i wae s we ee on he ie en oes eoS8 (tr 900 TT + OOLIZ4+ PYM ie ae 090)1L + eoLoL ~ Sot | is A Oot OE # ‘waar tone 209 b- gS = “Be oh aa + OLS + °sSsTt + oi 9et?c! evIrs Seer, ee) “ay ET | Va ae Tree Es eT ae oe 2SG - 2OS| - esit— Col: = esi St + Core Aa c H T a Ca aee oo CFT +e Ce ia CS 195° + ok De kia J90€ 95 + PINGS |, oS var toe e cr as bbe Dai 2949S + ran + ee TT aes he nd RE ooos + 9SL SS) + chee Tes eer oP | tt ii i ae | Poa Oe eo a eo pee ae i in ks ee oOTZ + Ce a a x M- oe ies ol 1 3 ay COO14 Ol + OS(|( biy+ I i BS dame OSSLY + aSlti+y + pace i Ke Bas eZ Sane OY ie oh Ss ae 9° oy re +— +—-}—- LOADING Live Loap UNIFORM - 100°/sqFt Roa KOu.eR, 18 TON a ete) oD a iN DEAD LOAD -— SES TASLE—- WEIGHT OF CONCRETE -1S0*% cu. ft WEIGHT oF BACK Filtt- 1Zo™ cuFY. a) GA) ea Ly i Tote td Bole Ce Lo |\a Seo Th 5.3 b+80 122890 (3 S00 21600 o279Sa ae ——-10 po eh Super FOR INFIVENCE Lines: AG Naas Pasa FoR 3 SFction) Sie hd by Sabeccncatiet a ee fie ord od a) ec tae ae Blo ee oS LAS Pi ht lr iat a 9 =) WYLNO2Z S04 lel) ee Gh he Ve. R fi m 4nyv3OC J ca ‘olelelels 30O USOT ODNIAC\A zao = ” a FAN} AINANOIAN | 4 = PS Laem ton Me al cele! | A oe WeP h or Ar lod i a a mell 3 Soh hoa Loh A hom | te Phe fame Bal Mie i re) EcT: Tr z mor’ — 13423! 4+ 3coAc tiegoc 77 5 : a ore +2S 600 Sees 21 Aa e) too accel es oS To PIU pS OAL lob 69t id) _229!0 ee s 9432 BARBS 3480 | -\2950 z4o00 ni se SS werereae { rere vy —— | ese) Se el atl (Py ot ee Co : 2 T = | 14066 + 32360 TL) cll ea Peo ae et es in — aS Case (ay - DEAD LoaD Moments & THRusts Li.-i “TivE LOAp THRUSTS, WITH CORRESPONDING Moments LiL-Z2 MAx. live Loan Positwt MomEtnts & THRusts L.i..3 MAX live LoAd Necatiwe MomENTS & THeusts R.R. 1-2%3 Roap RovreR LOApING SAME AS kb 1243 ConcLusion \T 15 TO BE NOTED THAT THE ALLOWED MAX UNIT STRESS oF G50" 0" AS SPECIFIED IN THE STATE HIGNHWAX SPECIF\CA TIONS 15S SLIGHTLY EXCEEDED (2%) AT TWo POINTS OF THE ARCH SECTION. HowEVER,, siImce THE GACKEILL WAS ASSUMED AT 120%)/ CUFT THE ABOVE DETERMINED UNIT STRESSES ARE CON SERYATIVE- IT tS AY\SO Te BE NOTED THAT, DUE To LACK oF TIME THE SReEcT OF TEMPERATURE AND VIER TARYST FROM™ THE OPPOSING ARCH HAVE BEEN NEGLECTED. LT 15 ESTIMATED THAT THESE WOULD SLIGHTLY EXCEED THE CONSERY MARGIN DUE To THE AGOVE ASSUMPTION OF THE WEIS6HT OF GAcK- FILL THE EFFECT OF SHORTENING DUE To THRUST 15 ,HOWEV FULLY CONSIDERED IN THE METHOD OF ANALYSIS. {TIS FOUND THAT THE MAX SHEAR AT TAE CROWN !: ZS5%*/SQ1N. AND THEORETICALLY REQVIRES No STIRRUPS Que TOA LACK OF TINNE— ANALYSIS FOR. SHEAR STRES HAS NotT BEEN MADE: FINALLY, 1T 13 COMELUDED THAT THIS SAFE ,ON THE ASSUMPTION OF RIGID ATINKE was = AS ica = VUsED TA . | Al< R UAL ETTLEMENT iy dh < (on ad Sat | SECTION \ ho Ges 7 Tae ee Ry te TTC 352 five | Cas2@j)& bk 2 _ _ 550 Part Casew) 5 as S50 gtr | Case 4RR2 _ Soe le Ee eee Cee Ce Pee Caselay & RRz eet mae Case fay - DEAD Loap MomMENTS J tae ee in 7 A a Pe ert UN ee LL-2 Max. lve Leap Posimv& Moments & THRYSTS eee eS ore oro) am fet oe alta RR. 1-2%3 ROAD ide RO Ss Pye ae See oro oN Cae Ny) lt \5 TO BE NOTED THAT ae a ae) aa STRESS PROM load SN oth = ot THE STATE HIGHWAY SPECIEICAT TPR PM SO Sh i (24%) AT TWO POINTS OF THE AR cr SECTION: HoweEVER , SINCE THE GBACKEILE eat) ASSUMED Pe My Ad aS a ABOVE DETERMINED UNIT STRESSES pe CON SERYATIVE- Ir ts ALSO TO BE NoTeED THAT, pue To LACK oF TIME; THE SReECT OF TEMPERATURE AND PIER TARYST FROM THE OPPOSING ARCH Have BEEN NEGLECTED- IT 1s ESTIMATED THAT THESE WOULD SUIGKTIY EXCEED THE CONSERVATINE- MARGIN DLE TO THE AGOvVE ASSUMPTION OF THE WEIGHT OF Gf. ol THE EFFECT OF SHORTENING DYE TO THRUST 15 HOWEVER, FULLY CONSIDERED IM THE METHOD OF ANALYSIS. IT 1S FOUND THAT THE MAX ois batate BOE TAS CKOWN 15 ABOUT Z5%*/SQ\N. AND Sat tte) 4 a Seek oon RERQVIRES NO Po al --20 oe oe 9 aa a Sia a a at 6 SHEAR STRESSES HAs Nor BEEN MADE: FIVWALIN, VT 13 Patol» i on OR a Oey a OY on i Th AwecHW 1S ENTIRED >), hl ae seo AssuMeTtion OF RiGiD AGUTMENTS t aa fe ed BEEN USED TOA weicasi: TE ne UMERUAL SETTLE MAENT SO‘ Ee 2 ie id eh APPENDIX 7s ae. wd. THEORETICAL ANALY 5'5 ola ona FUNDAMENTAL FORMULAE: — Mae 354 isa) Sale ee ern a a dns MNPQ BE ANY Peete Moles Lt ady PING. LET E,0N THE LINEAR ARCH BE THE CENTER OF THIS SECTION WITH COORDINATES (x 4) MEASURED FROM A. LET THE CENTRAL ANGIE OO BE SVOTENDED BY THE PX an ea at THIS SECTION OF THE ARCH RING WILL BE ACTED UPON BY SOME RESULTANT rh ta) ee eee hs Sa hd RESOLVED INTO A RADIAL Snean 5S, A NORMAL Paoee anette an OS) 3h id MomMENT Je> M. THESE SHEARS ARE SMALL IN ORDIN: ARTY ARCHES AND ARCH Sita) Mtoe THEM IN THE THEORY OF STRESIES, Nay CMI nS ae THEORY OF FLEKTUR FOR Phy Ee ia N , THE TWO AGENTS ites % BENDING MomMEN SECTION. THESE NT SECTIONS OF THE ARCH T SHORTENS THE 5 AMOUNT 782. A RISE OF TEMPERATURE LENGTHENS THE SECTION DB BY AN AMOUNT ye a 10a A ay isla cae ee oT 1 en eed Pe ee ae ola VALUE of M WILL CAUSE bey 5 alia DB To DEFORM IN THE DIRECTION DB’ CHANGING Ao BY AN AMOUNT 49. Rl ae URED FROM THE CROWN Positive TO THE LEFT, NESATWE TO THE RIGHT. HENCE eae een PEE EL ts Segara By Sean Oe a aac Spe cd Pee 4 eo Mb a td Adis NEGATIVE THE FQUATION HOLDS TRVE FOR S| Now IMAGINE THAT FOR ANY ARCH LOADING, STARTING AT A, EACH SECTION 15 bet 4 ORDER AND ITS EFFECT ON paar tan as “Aca SEPARATELY AND IN TURN. THEN MP MAY BEREGARDED AS FIRMEY aes since tal eked DEFORMED SECTION PRECEDING AND THE SFEECT OF THE DEFORMATION OF MNPQ ON THE PORTION OF THE ARS" BO 1 ae ae JET US FIND THE EFFECT OF THIS DEFORMATION OM THE MOVEMENT OF THE PANT C, WHO COORDINATES ARE Cm") THE CHANGE IN ee AC ANO TEMPERATURE Wilt pRroDUCE AN EQUAL an i ool C Also THE CHANGE IN dd pue To M with PRODUCE A CHANGE AT a al ae lo Fal ee THE SPAN-™- QUE TO a TEMPERATURE ON THIS SECTION ALONE re eh Ok dl eh ae < a a Td ali Risk.n. DUE To THRYST ee 318 toll ea SECTION ALONE * so) e =< <'siNO=-BS S¥= oS eee Stn ont 2S el M DUE TOA POSITIVE BENDING aa PUTT cd eae pith aot t- ae rah HENCE Oxy aCe mero Be ee THE INCREASE IN RisE.m-av& A POSsITWE BENVING MOMENT M wit GE- Pde as Pee TN oh ee aa wi ZREASE iP heer ee aa te eed ee ae) . 2 1s . TEMPERATURE _ os ak ie | Pe Va ae! .)- APOSITIVE GENO TCM tah Mm ACTING ON ‘at mae +d,= 0 fae) ~4 ne r Wh rm mA rs eo igor 0 ,0K ah TITUTING JIN 152 re ( ¥ tl Gee Va DS a ar She oer WEL. et UNC ES No THE rie FOR SYMMETRICAL ARCHES A= 0 no OLLOWING ITEMS ARE CONSTANTS IDEPENDENT OF THE LOADING HEIR VALVES FROM ABOVE, ARE La ar a ae ve ee: a t a eos ray D3= 7 ” F AIN6 TERMS ARE DEPENDENT HEIR VALVES FROM ABOVE ARE- la ae Lig-—&) O5 \ c a rat " A an TD Mins al Seon ES re RS yes ne es Perr hy 2 ee vA Fa ana , Beesd | oe a b= Oa yi ee Ws. ‘+ THe FoLLov oe . ae Bi Se — a rm bY Cos 5) J ae Vi hot NTRADQOSE DRAW TRVLE ABU" LEFT ABUTMENT ANT DIVIDE } EACH OF THESE PARTS NUMBERING TH raw. ye FORMULAE.- Un ~ Yn-1)) - 5 BEING CAREFUL To USE ~N » - By Some ara | S THE ABOVE CENTER POINTS SCALE THE DEPTHS OF THE- AND LOCATE THE STEEL. COMPUTE AREAS & MOMENTS oF RANIFORMED SECTIONS PALCULATE AND TABULATE FoR CENTER POINTS VALVES OF ee 7 7,¥ he shcos 054 reo er ae oe uh bi 7— > i 7 For A alee LOAD AT POINTS; 1-5-9-13-11-21- 25-29 - 33- CALCULATE %& TABULATE VALVES OF aia ) Sale aoe , ay a 3. Sum OP THE ABOVE a oa AN) MAKE A TASLE OF AR(H CONSTANT), KS 7 on re rn STE ey ara: By 3 ee deh ae 8, Vaan FoR EACH OF THE LOADS THE VALVES OF THE ONSTANTS d,, dq dg, 6,62 ry MAKE A TABULATED seLUTION FoR M.,Vi,H,,.Ma. WHERE Mr m -HLN - fee) CONSTRUCT ON THE LINEAR ARCH THE TRUE EQUILIGRIUM POLYGON FAcH LOAD. RESOLVE EAcH KEACTION INTO ITS THRUST & SHEAR PCNENTS rs POINTS (- S-9- 15-17-21 -259-29-33-37 . ABULATING VALVES SCALED FROM sAM E- {7. PoaT INFLUENCE CURVES FOR MOMENTS, THRUSTS, €j SHEARS 13. Finp 4 TABULATE VALUES o= AcTUAL DEAD LOADS , UNIFORM LIVE LoAn % EQUIVALENT CONCENTRATED WHEEL LOADS. 14 MAKE ATABLE OF DEAD LOAD MomMENTs THRUSTS & SHEARS NTS eae 37 E A TABLE CE LIVE LOAD MomeEeNTS THRUSTS & beter For st MAx. ¢, Positive. MoWLENTS MAX- ,C, "ing MOMENTS MAx,- Phal S POSITIVE OR NEGATIVE, Pua LOADING 4“; PosiTION OF et - ALCULATE Baia €,f, FoR THE FOLLOWING COMBINATIONS CF LOADING RE SULTAN" RESULTANT MomEeNT wary Osea Be SHEAR ON CONCETE- TEST FOR Sipe ELEVATION C-SPANS , BO CLEAR hyp ae ann 2am ted motte etetiete eet AL TOME So) S oh a] te \S ve TE CLEAR CENTER PER LE id SET A a 7, Ae Caen 2 Tea ETO QNISSOMD FOO lad J 47 - as er Shae fll r ei Aone Ysa) Sak fl 3929 snc cas Pe ED pa rae a Luan