4 LN AUNTUTTULAULTULTUALYIAN = IMM MMM Hc FHI HiHiMMIAATA NA ay AN ANALYSIS OF A CONCRETE ARCH CeCe) a a Reto 1), be =P eL Ns ChiCh ACT aa _ G {PPLE : mw “MAT: IN BACK OF soi PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE lath i om CONCRETE ARCH 2 KENT COUNTY HIGHWAY. | As A Thesis Submitted to The. Facu Ly of THE MICHIGAN AGRICULTURAL COLLEGE ye J. VanBuren eianes TBDimmick Candidates for the Degree of afore tala Oy MEN era Tel ro a A a ae A 1.04025 FORE W rt er a, a aa eee of ae RT ie fe) as fe Lecome at a enable IT1O re familar ad ee AY and analy sys oy 7 Corncre fe arch, INTRODUCTION THE WRITERS OF THIS THESIS LEARNED OF THIS ARCH Bi IGE THROUGH THE AGENGY OF THE a Ah Oe nh Oe UA) TATE HIGHWAY DEPARTMENT. THE BRIDGE ‘5S TO BE CONSTRUCTED THiS YEAR ACROSS PLASTER CREEK ON THE GRANDVILLE AVE ROAD IN WYOMING TOWNSHIP KENT COUNTY. MICH. A DESIGN OF AN ARCH BRIDGE Was SUBMITTED By AN INDEPENDENT COMPANY, BUT THE ENGINEERS OF THE STATE HIGHWAY DEPARTMENT AW FIT TO DISCARPFD THAT DESIGN AND CHOOSE ‘HE ARCH HEREINAFTER ANALYZED. IN CRDER TO DETERNINE THE STRESSES ACCURATELY AND TO BECOME FAMILIAR WITH THE ANALYTICAL MIETHOD OF SOLUTION, THIS SYIETHOD WAS CHOSEN IN PREFERENCE TO THE GRAPHICAL SIETHOD CF SOLVING STRESSES IN AN ELASTIC ARCH THE REACTIONS WERE DETERMINED ANALTICALLY, HAVING FOUND THE REACTIONS, THE THRUSTS, MOMENTS AND SHEARS WERE DETERMINED GRAPHICALLY. UNIT STRESSES WERE COMPUTED BY THE USE OF INFLUENCE LINES. WE WISH TO THANK THE STATE HIGHWAY DEPARTMENT, MA.L.C.SMITH, MR.CVU.DEWART AND MFP. CHHALL, ESPECIALLY, FOR THEIR HIND AISISTANCE IN PROVIDING DRAWINGS AND INFORMATION, WE ARE QEEPLY INDEBTED To PROF. C.A,.MELICK FOR THE NMNETHODS USED ANO THE CARE TAKEN IN CHECKING THE WORK, UVAN BUREN, 7,.B.DIMMICK. 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Stress ( — a 5 ara -MxAS_O since the ferm ie ER tres ee sae oe so pear Eee : ae Ha From the figure below Pl a eft ed -a)x ra-W,(y-b) x>@ ers Cos g +V sino tM, eg Be) SIN @ x>a Seok ety MX pei ia ae a va Le A Cate A tes Bae Os nak Hy. ge - WS BEG oh eee (y-b)as oes oe 2 pee ee ie a, poor rpg nae ee 4 Xe Re ae oe oem a ax (aca Wye aie <0 3. as a oo peeeet, ~y sages eee peer Crees aia aoe ees aL aoe pee eereey aa SEE ag eae a Rewrifin ng the Ore ee ay vals A eae eee lead S or H,=-= 4 te eae mara ee oe 16} Pe ee Fee. 3. Pah rs aA a 76) CT ey) 2 cet seen he So ‘ # A ee ae solving the last Two equations gives(Z-%, LF d ar M, 7 or ae a a hae S Rai ane x2 ie = a, nae or M, ae) or DV, =E, BA ee | mn) CMT ale Leelee er ae per Vale a The following terms are constants for y any g given. laa MeC iL Mala Lee the Yoading. te a Pe ae ir values = 2 ¥) 4 Ke o- gees a ~ THEORY OF THE ELAST/IC ARCH-CONTINVED : -s “xyAs eer ae me a im —— 4 LK: C, 25 eT Ry verre i PS