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Cade, and other’hembers of the Civil Engineering Department of Micrifiqn State Colleqe for the assistance rendered by them in the writing of this pe— Per 0 100210 O A Study of the Stursis Hydroelectric Plant Sturgis is an industrial city of aphroximately 8000 inhabitants located in the southerstern pert of St. Joseph County in southwestern Michigan. Previous to the comgletion of its municipal hydnselectric plant on the St. Joseph River in 191], its electrical power was sup- plied hy a small steam-Operated generating plant. Due to the growth of the city it hecave necessary to either enlarye the generating plant or obtain electricity from sore other source. The St. Joseph River was already heing used by several cities further downstream for power purposes so it was decided that the feasibility of a hydro-electric plant should be invertigeted. Accordingly, the services of the firm of engineers, Ayres, Lewis, Norris, and May of Ann Arbor and Gardner 8. Williams, consulting engineer, were ohtained to determine whether or not a dam would he economical. It was found that not only could much more electrical power he develoned, but that it could he delive ered at a smaller unit cost, so a hydro—electric plant was erected. The canacity of the plant is 1100 kw. while that of the old steam plant was only 200 kw. The machinery consists of two 550 kw. gener— ators directly connected to 844 H.P. turbines and a 40 kw. exciter with a 67 H.P. turbine. There is agnroximately 870 square miles of the watershed-etove the den. This area con sins a large numher of lakes and ponds which increase the storage capacity of the area, thus making large floods less frequent, but which, at the sage time, decrease the ultimate runoff because of the large amount of evaporation. The river's head- waters are in the central part of Hillsdale county. The portion of the watershed in Hillséale and eastern Branch counties is very hilly. 5. In the central part of Branch county ani in the southern pert of Calhoun county, the land is ruch smoother, but becomes quite hilly again in western Brarch and Calhoun counties and in the ea=tern part of St. Joseph county. The distance fron the ground surface to bed rock varies between 100 and 200 feet over most of the water- shed. The soil is chiefly sand, sandy loan, and gravel making the amount of surface runoff smell. Rainfall over the watershed is moderately heavy since the area lies in the path of most of the storms soing eastward over the southern portion of Lake Michigan. Rainfall data is nvailelle fron Wrsefi station (see map) for the years of 1880 to 1920 inclusive and from Goldwater station for the years of 1898 to 1920 inclusive. Pre— cipitation records since 1920 have heer printed only in annual bulle— tins and several of these hulletins are not availnhle. The first eighteen years of the rainf111 curve represents the annual precipi— tation at thepi alone while the remainder of the curve represents the averages of the annual values. These values will he fonrd in a table at the end of this paper. Since the mean annual precipitation at Wasepi is 59.90 inches and at Goldwater is 55.92 inches, it is reasonahle to erpect a nean annual rainfall of 37 inches on the watershed. The curve of annual rainfall shows that the yearly pre- cipitation is quite uniform and that dry years are consequently infre— quent. There has been hut one stream gaging station on the St. Joséph River upstrean from the Sturgis dam and the records from this station are very unsatisfactory. These records were taken in 1903, 1904, and 1905 at the Marantette Bridge in Mendon (see map) and can he found in U.C. Geological Survey Water Supply Papers Nos. 97, 129, and 170. These records are of little use since the discharge measurements were all taken at practically the save gage height and hence do not determine either the shape or the position of the discharge curve. The measurements were taken at various times by different parties and the diScharge obtained hv one party at a certain gage reading varies greatly from the discharge obtained hy another party at practically the sane ease readine. These records were made even less useful by the fact that no readings were taken in February 1904 and early in March, 1904 there was an ice gorse at the hridge, im- mediately followed hy the failure of a dam above the stetion keeping the gage reading far above normal throughout the month. A part of theSe records, however, may be used to obtain a hare estimate of the percentage of the precipitation which runs off. The daily gage read— ings fron Octoher l, 1904, to September 50, 1905, will he found at the end of this paper. Month Ave.Gage Ave. Total Runoff Precipitation (in.) Reading Dis- million Goldwater Waseni (ft.) charge cu.ft. ' c.f.s Oct. '04 1.51 520 1,592 4.57 5.19 NOV. '04 .95 570 959 .10 .01 Dec. '04 1.00 410 1,097 1.87 2.22 Jan. '05 1.54 540 1,448 2.27 2.59 Feb. '05 1.52 550 1,282 1.50 1.41 Mar. '05 2.20 1250 5,295 5.64 5.12 Apr. '05 2.08 1100 2,850 5.5 5.20 May '05 5.01 2400 6,440 7.51 7.41 June '05 2.05 1100 2,850 5.50 2.56 July '05 1.94 950 2,540 4.61 4.51 Aug. '05 1.71 . 770 2,060 8.05 5.54 Sept '05 1.77 880 2,142 4.00 _ 5.18 28,555 45.14 55.74 Assume that an average of 40 inches of rain fell on watershed above gaging station from October 1, 1904 to September 50, 1905. 5. Then 7%.; x 5280 x 5280 x 844 _—_ 78,500 million cu. ft. of rain fell since 28555 - _ _ .351 78500" the drainage area shove the station is 844 sonare miles. or 56.1% of the precipitation run off in the year. In a paper printed in the Transactions, A.S.C.F., Vol. 77, Page 546, Joel D. Justin advances the following forwula which shows the re— lationship between precipitation and runoff. C _ .954 SJSS 32 " T Where C is annual runoff in inches R is arrual precipitation in inches 8 is slope : elevation of highest point minus elevation of lowest point + Varea T is mean annual temnerature. .155 . . 1150—827)12 57x57 . S bst — . Lav- ' mr 4 ..u P. -.~-——- .—-—-—-——— _ J . ‘ ’ S u ituting C._ 954 [ 4x5290x €80" 2_ 47.8'” 0 27 inche Then lgégz-‘:_.278 or 27.8% of the precipitation ran off. 0 From data taken for a sanitary survey obtained from F. R. Theroux of the Civil Engineering Department of Michigan State Collefie, the aver— age flow over a dam in St. Joseph River at Mishawaka, Indiana, for a period of 12 years was found to he 1200 c.f.B. According to an article in the Engineering Record, July 14, 1906, which describes the dim at Mishawaka, the area of the watershed above this point is 5000 square niles. Then the average runoff per snuare mile is 1200 - 0.4 c.f.s. 5290x5280x144 “' - per year which is only 14.7% of the precipitation. A larger percentage The runoff at the Sturgis dam would then he of the rainfall than this can he erpected to run off from the portion of the watershed ahove the Sturgis dam since the slone of the watershed from the dam to the headwaters is greater than it is from Mishawaka to the Sturgis dam, thus decreasing the chance for evaporation. One of the reasons why the percentage of runoff is so low at Mishawaka 6. is that the 1670 square miles of the watershed in northern Indiana contains a much larger percentage of water surface than the portion of the watershed in Michigan, due to the large number of lakes in northeastern Indiana. Considering the three estimates and giving each its preper weight it seems reasonable to erpect that about ?5% of the precipitation will run off on an average year, that is, any year with temperatures clos to normal eni not preceded by an unusually wet or dry year. Using this percentage as a hesis, the runoff curve was drawn on the same sheet with the rainfall curve which shows the variation that can be expected in annual runoff. Of course not all of this runoff will he availahle for power purposes since nearly one—fourth of it runs off during the spring floods and some of this must go over the spillway. Due to the lack of stream flow records it is impossible to draw a mass diagram so that the power available can only be estimated. Assuming that one-eighth of the flofi goes over the spillway in the course of a year, there will still he 57x.25x7/8 or 8.08 inches of rainfall availohle for power purposes which is equivalent to 520 c.f.t. Assuming an effective head of 16' then the average power available would he i29153fi§1§ : 945 H.P. 550 The size of the snillway is determined by the maximum flood that can he expected during the life of the structure. In some cases where the difference in the cost of making a spillway large enough to accommo- date a 500 year flood and the cest of one to take care of a 100 year flood plus the interest on this difference of cost is more than the cost of the structure and the damage that Would he caused hy the failure of it, it is more economical to design an apillway for the 100 year flood and expect it to fail sometime between 100 and 500 years in the 7. future. In this case, however, the capacitv of the spillway can easilv be increased l‘v lengthening it. thus decrensinf the necessary length of the earth dig at the south bark. An adequate Spillway is especially necessary in this case since the failure of the dan would undoubtedly Beuse the failure of one or more of the several dame below it, the first of which is at the upstream side of Three Rivers, a dis- tance of Si? miles. Of the varivus ferrules for intensity of flood flow the one which Hives the rost reasonable results is found in "Elements of Hydrology“ by Meyer on page 569. This fornula, 0.: 100 AG‘ in which Q is the nex- imum flood in c.f.s. to be erpected once in 95 years and A is the area of the watershed in square miles, is desiqned for use under Minnesota conditions. This must be nultiplied 1by a coefficient denending on soil, slepe, lakes, and other features affecting flood runoff which is .45 in the case of the St. Joseph watershed. Precipitation in hirnesota is only about 25" annually so correction must be made for this also. Then Q 3 100 x .45 x«§z x 870af: 5590 c.f.s. is the maximum flood to 25 be erpected once in 25 years. According to Pickels in his'"Draincge and Flood Confitrol Engineering",the narinum flood that can be eVpected once in 500 ye"rs is 1.70 as large as the narinum flood to be eXpected once in 25 years. Then the spillway should be designed for 5590x1.70: 6110 c.fls. The length of the spillwav required will be found bv the forruba on page 151 of Creaqer's and Justin's "Hydro-electric Handbook" Q;01h"’ Where QI: total discharee in c.f.s. coefficient of discharge depending on shape of crest and head on effective length of crest crest. C l h actual head on cheat, 8. The value of C from Fig. 77 0F sqge handbook is 5.94, using fit: 1 where h. is the heqfl used to determine the shape of the crest. Trensyosing 1 :_ gar-1": - 6110 _ ...w. - 9 f , Then 1: 5.943(5); _ 2 8 6913 The actual length of the spillwnv is 508 feet but the vertical T- rails, which hold crest gates and walk at intervals o” 10 feet decrease the effective length to some extent. The soi‘lwev is of the multiple-arch type, composed of 15 arches, 15 heing 20 feet long and the end grches ?? feet long. A hori7ontnl section through the face of the dam is a segment of a circle with a 12 foot radius, hence a right section is ellintical. . Y Au‘ we” Y ‘///5ggyflii'- 6 . '0 \ fi' 0 x X Abniawbl .fimfibn I annm'.fiwfibv' In the horizontal section through the arch when x.: / or — 10, yt: 6.875. Since the Sloop of the face of the dam is %§, when x:-/ or ~10, 15 , 5 17 the seznizinor axis of the ellipse is 12 x 1.1.511. ___ 7.9595. The general Y‘: 6-875 X .; 4.5487 in section normal to face of the dam and I formula for an ellipse is E: ; b:: 1 Then X25271 y’a‘: a2 b‘ Substituting 10"): 7.959517! 4.548727 e”: 7.02395‘e‘ From which 9‘: 148.5100 Then. 7.923952%; 148.5100 y‘ _—_ 7.9595‘ x 148.5100 And y‘; V9591.4518 - 63.0557_§: 1n 1OQA From this edustien a section perpendicular to the fece of .' the dam can he olcttcv for the.guroose of eualvsis. Since the luttrc:“es fire relfitivelfi thin it look? lesical th"t the arch shorlr1 he "nelv"ed in the tens LQZHDT 0" the arches of a two fig“; hridqe with a; elestic firr. For t‘is a ”1y”lfi, 9? "ection one foot 70%; is t"”en ”t AR (See section threw h sji‘lway) since this is the loTe“t ffi11 0Hill and he“ce h"s the vest oreeeure on it. Accordin: to the theerv of ele:tic fiers the systel is con:ldered free so: M47513 W MI to #0"e aloe? fectio; GH, thus nzkin? three cantileVerS out of the syster—~the tro arches festened to the nut°ide hut+reeses, hft free to move along lines ah and dd, and the “uttress which is fastened to the foundation but free to hove along sectien GU. The traneroidel section on the Puttress “hove GH and I‘et'rreen ah and cd needs to he con idered only in finding the resultant thrusts unon the huttress. Each eroh is divided into 6n even nunher dfsections such that 8/1 is conrtant for all sections, where S is the length of the section measured along the areh axis a“d I is the nonent of inertia at the section including steel. Since the c"ose—scctiana1 area is the same throughout the er oh, I is also constant and the_arch between skewhacks cen he divided into 12 oual sectiens,3.60 feet lone. The in heed on each rectangular ection was then found under the assumption that the x""ixun elevation of the weter *urface is 8?5.00 feet, Or 5 feet ahove thecreet. Now the tote.1 water pressure on each section and the portal conponent of the weight can he computed. These are shown for only half of one arch since all others are the same. 10. Section Water Loed — lbs. Wt. of Fect.-th. Norm. Com}. of W . 1-2 52.4Xl.6f21.03‘: 2100 lSOxl.60xl.: 240 180 2—5 62.4xl.6x20.25.: 2020 240 180 5—4 62. v1.6xl9.65.: 1960 240 180 4-5 62.4vl.6v]9.20 : 1917 240 180 5-6 62.4x1.6x18.86.: 1885 240 . 180 6—7 62.4yl.6?]8.78‘; 1876 249 180 The resultant of the wcter ore"sure end the nornal comyonent of the weight can easily he found granhically. Only the verticel com- ponent of this resultant needs t.q “e considered since for a given value of y, there are two Panel and ejjcsite collinear horicontel cocoonents which heve no moxent about 0. The followin; nelenclnture is used in the anqlvsis when hnttresses are concidered electic (see also Analysis Sheet No. l). .: coordinate" of any point on avis of left arch referred to O as origin XR YR — Sane for right arch in“ 5R - Mosent at any point on ewis of left arch end r5- rht erch resnentivelv of all external lords hetween joint in uestion end top of buttress. ,. ’3 “L: an -‘N:mher 0f S/I divisions in left qrch and right arch CL, CR — Values of 8/1 for left arch & right arch respectively. H1, V; :_Hori70ntal and vertical components of the thrust from the left arch on the too of the huttrevs. 1‘ :_To:ent at sectidn GE due to thrust from left arch. Hz, V, ‘: Horicontel end vertiC'l confluents of the thrust from the right arhh 0n the tOp of the buttress. v - Moment at section GH due to thrust from right arch. Point 15 P12 *0 '9 'U 1414+Atj+4 t0t314 79 8 ”U 5 S- Hr—‘N mmppmmmmqqmmmo H C" o (OODQOU'IDCNNI—H'U Tot.1 X 1.00 1.68 2,58 5.10 5.85 4.57 5.52 6.08 6.85 7.65 8.41 9.90 1.0.00 10.80 11.59 12.57 15.15 15.92 14.68 15.45 16.17 16.90 17.62 18.52 19.00 X 19.00 17.62 16.17 14.68 15.15 11.59 10.00 8.41 6.85 5.52 5.85 2.58 1.00 50.00 Diff. Loafls Sufi Increment of of of X's Lend? “Qfient O 0 .68 1960 1960 0 .70 1572 .72 2020 5980 1412 .75 2905 .74 2050 6010 2945 .75 4508 .76 2040 8050 4569 .77 6198 .78 2045 10095 6279 .79 7874 .79 2050 12145 7975 .80 9716 .80 2050 14195 9716 .79 11214 .78 2045 16240 11072 .78 12667 .77 2040 18280 12505 .76 15895 .75 2050 20510 15710 .74 15029 .75 20209 22550 1482 .72 16078 .70 1960 24290 15651 .68 16517 24290 218610 Y X‘ 1‘ XY m .82 561.00 .67 15.58 281610 1.64 510.46 2.69 28.90 186462 2.50 261.47 5.29 57.19 155558 2.78 215.50 7.75 40.81 126819 5.15 172.92 9.80 41.16 100421 5.54 154.55 11.16 58.71 76682 5.40 100.00 11.56 54.00 55752 5.54 70.75 11.16 28.09 58061 5.15 46.92 9.80 21.44 25908 2.78 28.50 7.75 14.79 15142 2.50 14.67 5.29 8.81 5689 1.64 5.66 2.69 5.90 1572 .82 1.00 .67 .82 0 Conti1ever Noments Hoxent 0 0 1572 2784 5689 8654 15142 17710 r’5908 50187 58061 46056 55752 65468 76682 87754 100421 112926 126919 140529 155558 170584 186462 202095 218610 inK 4155590 5285460 2515575 1861705 1520556 888744 557520 20095 165770 69915 21789 5265 O 51.424172236 882451120 1002476 15161758 nd' 179260 505798 557785 552557 514518 256118 189557 127125 74852 56555 15085 2250 0 2209216 11. 12. From the results of this table the six equetions used in analyzing archhs with elastic buttresses can be solved for the 6 unknowns. C. (15.237. 41.231174 V. 2):. y.- Em.y.) _-_ —CR(1.4.Zy‘—H,Zy; /‘J.ZXRy‘-£m‘yg Since arches are of the 5959 thickness anfl symmetrical 22y M. -2 Zy‘H. ,l 2 ny v. -2 Zmy ; 0 Then 62.84 :5. 472.48 H. .1628.4O v. - 4.418,45? ; 0 (1) 11.255 —H.Zx.y./V.Zx: —zm.x._—_ 0 14,234.. -H,Zx.5;. 7411.2sz —Zm.x._-; 0 Adding the two equotions, diviiing hv 2, 9ni snhstituting, 150 M. 914.20 H. ,1 1722.96 v. — 15,161, 758 3 0 (2) C.( mu. 41.231 71 V. Z x. - z m. ) :_ —C‘(n.l.1,—H.Zy,/V.2x.—Zlh.) Transposinq, dividing by 2, 'u1 substituting, 12 11.41.42 11.71150 7. 4,002, 476 _—_ 0 (5) Fro-r. (5), M. _-_ 2618 H.— 10855 v.,La5,559.7 Substituting this value of M. in (1), 7.97 H. ,1 52.55 7. —851,20”) :: 0 (4) Substituting same value of M. in (2) 26.14 H. {514.67 V. —4,501,601 : 0 (F) From (4), H. _—_ —6.56858 v, ,1 104,291.1 Substituting this value of H. in (5) 142.97 v. 4,575,442 _—_ 0 And v. _-: v. ; 11,019.44! Then H. :2 Hz :_ 51,912.5# 4nd M. ; 31. ; 47.714 foot-lbs. The thrust from the left arch acts M./V. feet to the right of noint 0. Since the force polygon drawn from this point 4.55 feet to the right of 0 does not follow the qrch axis, it is obvious that the arches were not designed hv a theory considering the buttresses 15. to he elastic. Bv ohservinq the ménner in which the horizontal components of the water pressure fron two adjacent erches equali"e esch other it the hut- tress, thus causing little or ro horisontel disilqcement of the buttress, it aopeers that the buttresses were prohdhly assumed to he inelastic and the nrches designed in the same manner as a single apsn, symmetricsl arch bridge. In this method +he erch is considered to be Cllt in the middle 2nd half of it acting ns a cantilever es shown in Analysis Sheet No. 2. The arch was taken from the sage elevation in the fece of the den so thnt the sections and loads will he th. same as the; were in the nreceding case. The following nomenclature is used in this anulysis. 8.: length of a division measured along axis of arch. nh': number of divisions in one—hwlf of the arch 1': length of spfin Ca‘: average unit compression in concrete of arch ring due to thrust tc-;_coefficient of linear temperature eroersion t numher of defrees rise or fall of temperature 1’. E C 12° modulus of elasticity of concrete H., V., 3.: thrust, sheer, and moment respectively at crown ”.2 normal thrust on rediil section X.; eccentricity of thrust on section, or distance of N from srch svis t — thickness of section I — moment of inertia of sectiwn includine steel: I.%hIs A — area of section including steel steel retic for total steel 9t sefition d — enhedment of steel from either unper or lower surfdce 1T - moment _-_-_ NK, m — noment st "Iv joint on left hslf of arch aris of 811 external 14. Pt. X Diff. of X's Loads Sun of Loads Increnent m of m rP6 .80 .80 2050 2050 0 0 6 1.59 .79 1620 1620 P5 2.57 .78 2045 4095 1600 5220 5 5.15 .78 5194 6414 P4 5.92 .77 2040 6155 5155 9567 4 4.68 .76 4665 14250 P5 5.45 .75 2050 8165 4601 18851 5 6.17 .74 6042 24875 ‘BP2 6.90 .75 2020 10185 5960 50855 2 7.62 .72 7555 58166 Pl 8.52 .70 1960 12145 7150 45296 1 9.00 .68 ___"._ ..1B§§2_ 55555 12145 55555 From these moments the congutetions on Analysis Sheet No. 5 were made. The vnlues of k and 1 used in finding unit stresses were found in diegrams in Hool's Vol. 1 "Reinforced Concrete Construction", on pages 562, 569, and 570. Ger the commutetion of the stresses in the buttfiesses Analysis Sheet No. 4 was drawn. The arch ring thrust normal to the face of the huttress at D is 12,150#. Since there is an “rch on eich side the total ncrndl thrust per foot st D is 2rl2,150.= 24,500#. The totel pressure can be deterrined by a pressure triangle as shown with but a smell error. The resultant of the water pressure and weight of the buttress were combined and their resultant extended urtil it met the base of the buttress. Then the unit pressures at the toe and heel of the dim were determined. 9 at B — 4 AB—6 BC - (4}‘40-941-513‘7450000 :. 9,000# per sq.ft._—_;62.5# per sq.in. ‘ '1'" d(AB)' — 2x1600 p at A;Vx 448—6-"\C -_ (4134.0361g2 450000 :22.50# per sq.ft.;15.6# per so. in. MAB)?" 2x1600 The unit stresses found to be present in this structure were all rather low so thnt the conclusion csn he arrived at by this investigation is that the dam is verv stable structurally. Of course the purpose of thi: investinqtion was to find as near as possible the method used by the designers as well 8s to cheék the stresses in the structure, so that . . H- O . - ‘ o ‘ . ‘ I ' l I . l I I“ - > A , I . | . I ‘. 7 , — 7 , I I ) ' ’ .I - . Q ' . ..u ' b O . t 1 f A, , A _, ' -. 7 , a I ' ‘ 4 ‘ ' ,_ 1 7'- , - _ , >, ‘ . .‘ (. __.. .. ,’. , - ’ a ' ! ,J . ;~ " I 'V‘ ' ‘ I (v { . l ,’ I 4 ' I _ _ . 4’. A ' '_. - . , ~‘/'_' - . - ' -' '. V‘ ‘ . AV ‘ "t , - '3‘ ' A 4' ‘i ‘ ' - I I ‘ I . 1 . ’ .r 1. I ' 1 ‘ s s2 2 6.316254 _ of the many things learned by the writer in the studying of this project, perhaps the most insertent is that in a strvcture of this nature the buttresses can be considered inelsstic. U1 16. Eiscellineous Tnhles Annual values of reinfsll in inches used in plotting rainfall curve. Year Wiseni Goldwater five. Year Wnseni Goldwater Ave. Station Station Ststion St teion 1880 46.75 1900 55.95 55.72 55.8 1881 55.88 1901 55.87 57.50 55.16 1882 52.05 1902 59.49 55.58 57.5 1885 55.27 1905 40.65 55.75 59.12 1884 58.21 1904 40.61 55.78 57.2 '1885 55.99 1905 59.26 46.21 45.5 1886 40.28 1906 57.54 57.89 57.6 1887 40.90 1907 45.59 40.19 41.5 1888 51.67 1908 41.58 56.50 58.9 1889 40.22 1909 46.49 59.05 42.7 1890 46.55 1910 54.18 28.40 51.5 1891 54.22 1911 42.25 51.24 56.7 1892 57.61 1912 55.60 50.55 55.0 1895 42.65 1915 55.85 29.10 51.4 1894 50.74x 1914 58.84 51.80 55.2 1895 50.68 1915 55.95 29.84 51.8 1896 58.60 1916 2.29 55.65 59.1 1897 50.55 1917 57.71 29.05 55.5 1898 57.64 42.89 40.2 1918 42.20 . 54.65 57.4 1899 54.76 56.46 55.6 1919 57.55 51.61 54.5 1920 50.17 54.06 52.1 ”Precipitation for March 1894 is not in records so this value was found by adding to the ?“801j1t0ti‘n in the other eleven months of 1294 the mean monthly precigitetion for Nerch 9t the st tion. Discharge measurements used for flotting discharge curve Date Area of Ween Discharge Gage Height Sect.(sq.ft) Velocity c.f.s. Mar. 20,1905 2596 5.00 May 11, 1905 949 1.62 July 5, 1905 550 1.80 July 8, 1905 487 1.70 augy 4, 1905 456 2.00 Aug.51, 1905 777 2.50 June 5. 1904 468 1.75 810 1.50 June 7, 1904 455 1.55 697 1.55 Sent.9, 1904 587 .85 522 1.58 Sept.22,1904 589 .79 506 1.24 June 2, 1905 512 2.15 1095 1.90 Nov. 7, 1905 481 1.50 ' 710 1.55 NOV. 9, 1905 500 1.65 818 1.70 17. HCOOTG‘. o o O 0 o .r—Q HHHHNNNr-HH OQOC‘OC‘OLOOC‘ (OFCDO'Z .985m 895 asses moms .om .pemm 'CC C (Kg.l>-b(.O(O(L OOOOOC 03(1) C. O; b—b—b—b—b—b—«Ju341uauaq>b-m>m.m‘dyd 0. O ‘ C1 \ C. C C 09.... O r-CI-ir-ir-ir-lr—‘HHHHHr-ir-{HI—irnHHHr-ir-ir.HHrir—‘Hr' OONWLCNOOCOOUDOC Oh.m ON.H Ob.H 3.95. LOUDLOIOQOP'O UiOWmP-(OQLOND . ..C... HHHr—ir-{t—tr‘r-‘HNNNNNNOTN Sgc>c>c>u3c:cac:c;u:u3c>c>c>c>c> 43%;“. ca ecmfl .H .poo rcsm 1 (SOC .00.... O wiririrfr4020102010202N3u3u3u3u3u3c>u3crc~c>c afb-b—b-¢)O.C O O ‘- c>c>usc>u3uaé>C‘u>c>c~c:c3c>c>c>uvc>c>cau3u3c>c>cwc>c>c>c> 1‘) UN U) c. O ommuubhbbhwwmmmmooooooc-oommd 0............ 02020202NNr-ir—IHHHHHHHHHHHHHNNOJNNNNNr—‘r—i (OQOWQ‘O .pp< ow.w mm.m mb.m mm.m OLD Q‘H o 0000...... OmOOI-DOOOOOOOOUIOOOOOLOCUDLOLO commwwwwwwmmmmwmmfimfimmbwm Gm. .995 sewecm mtwo HHHHr-‘Imr—I—‘r-II—iflPHHHI—ir‘JI—‘lr'i LOWLDUDQ‘Q‘LQNNNNK. om. .cmh fi‘ CDCDCJCDCDCDC‘CDC) -Or-1C\2Z W454.“ OOFFMQM 0mm...) 342. MZA. 0m. 3)....I M3>.—._OO .7, P- — ——————————————— I I I I w Weighf of I '3 Bufi‘reo's I I I ‘1 I I Real/fan 7‘ of 8: 0° W dfer Pressure 8 1 47' $1 . gl ‘0 I W I I I I .50 wk D A , c 6 E 4' Lg“ +0 0 d = wid+h of bufl'ress «1' base =Z’ ANAL 115/5 JHEE T N0 4 34191988” 1113534533 3A 1‘8 1, 8. 119.85.! "'9‘ ~. w- '5 C i A > . V 4 Ni 1 'n) 527 ‘1') “a? 3‘ "I . fir of Z_OI_Q>Z maid-m GOP—IMO” UMV>ZHZ m2... OT- 3>4I m:>.:0m V‘ ~D 0?,“ ‘ .g‘. . u; .. . _ . ,( ."I ‘ '-I ""'§ '0’? ' 5‘. 1‘ A MAP 0; 77/5 PORTION OF THE W4 7525/40 ABM/f m5 0AM “ALAN/1200 INDIANA OHIO I? 55%.? $193.11 771589-1199 5151:}: 99.9mm - '1: 91-82581: 31335: {MIRIAM T843 ". I‘m.”- . i,! _ --- ‘ m F . flIIIIII III III 1:08.98. IIIIII m. IIIII Ir o0 T I a a o 5 E a E 6 4 n H .4 IIIIIIIIIIIIIIIIIII 080:qu 5.. IIIIII w... ..u. . 5 u .. m 5 Z x w c/u . . .1 IIIIIIIIIIIIIIIIIII on 58911113., IIIII n v/ W _ _ L m . 4.. A m l . N u w A new m z .. _ «I IIIIIIIIII rm . u l _ E. . s .. - .- . . 7 , ., .-f l 6; . . M m. I l . 1. . I M .d. I ON 2 ,1 n 1f 2 n a , .. M15 I] m... w C .r I I. h [m .9 e W ..m 6 H5 E 5 4w N rm 00. V M 8 w M P... u... s. A/IML )I 51".; 51955 7' N0 5 Tempsrafure Rib Jimrl: 1b pa Tofdl s I"): K L Um‘f .SfrErses Pf: x: "j ‘42“ 32' m ms mg Haj M N v t . (scam) 14.5 M N M N M N ,1; 5, Cr. +IIZI 20078 -I680 H190 “(680 9215! ~2020 Lo .00182 +5072 £6978 299 £32 .0968 354- I735 / €200 2.55 8!..000 6558 53555 481495 135112 53,349 Mus ZH60 «4334 «254—4 4375 4058 ~I6SO [.0 .0018: ~4677 73:35 253 .744 .09 82. 33: 5q5 2 7.52 7778 5006’} 3,585 55:88 290825 67:72 36383 -652 21080 ~qu1 “He? 4480 4400 «I775 (.0 00192 “32!? ”825 .I8I 2pc 1.. 250 :13? 3 6.12“ MO 35.089 4.210 24873 153486 27,550 22,144. ”I006 206120 4848 ‘ -58 -5550 -7a 4360 1.0 00182 4134 17570 ,065 1.35 ,_ [54 _,. 4 4,88 5.2 21,902 334 14250 88578 9383 Izezo ~28? 20840 «(042 I +748 4610' Mac 4430 (.0 .00182 +1359 17300 .078 L43 —— /7z -- 5 3.35 .27 9.7735 .078 6454 20204 (13?. 5583 +290 20720 “454 H336 4065 +1600 ..lqyo [.0 ,oalaz +2226 £7075 ,l30 1.73 - 204- _— 6 7.59 .06 19,527 .002 ($20 2518 ‘11 12.4: +742 20700 -lOI . +2889 4975 +2030 «2010 /.0 .00182 +4461 77015 .252 .732 .04 82. 315 (.92 52.2; 8.39 241-887.119.425 135,858 1,815,481- 243,486 In, th. *‘”M’).9"2("7R ’"mey flssume C a [20 *5/57. 1'”. Hg: 2 ‘1. H _ __I_ cfpjflfi‘é; a 207.23 “(531.7 .- 2306),, (1’)] I 5.18,, Since mL= MR ”6 5 Z[”457L*(55/7 f/ - 5 x2x 243, 410,- ZXI38,85116._3_9 (+2 8:23:72! H5478“ 31x15) xpooooe ’60IKBOX21009°°°’U4* 79 ’20 20X 6 a" " l I x x 2 6x 11.425 - 6.357z /.6x I44x141 x 2 . ., . z I [ J [6x11 425 6.37] /.6x :44 :8 I442. 55.44 :4 . a 20 678” " ‘ “>90 a «30.20"I - . V5:- 20 678-1680- 2020 _ it 5 ./f 14:20”. "My“ 0 ’ 5"?" "7.:th H z 4828x9239 4'7" ”0””): H.027 " [6’5” / 7 224" Mc=--—°—L=~-————= +1140 ‘Foo‘I-lbs n 6 zoa4o-Iua- M2020 a! / h c.(,./. 4): 1.... -15, am :7- f- M gfém.+mg)~2% 2.5] .... [42027 [8 ' c 2 "h Ca (F’- I} 4 211‘0-4375- ,mzozo_ "650 /.5,/} /-I-.027 --——--- .. 2x135856 *2X20676X 6.59 34M” g f z . 01/ 2M 19%;- ”app... ak. I603 fir" ( e) = 4 “2' 4700+- lbs, fd/IO //¢ Ior Rib Shori‘onlflj 322g: ,20 _H‘ #or Temperofurc M a -- iii-fl _-10§O‘X68’ ‘12’5/ 3 floo/-/6S. Comp"85;0n over err’fre- SQCfiOH " (C =3 A k 6'!- Tension over par/ of Jec¥idn~ l2: .— wmswr , Snbe'EWEI/HVHA 0 ‘JW 1:75“ YT}? .3"'MU WMWW $3.824 PW WI ma o 9 .rn a... uh .! ! a,“ / «S .0 mi. m ,wa 1' I h 0.0 me . rW u o N... R x “ .... _ , ... n a _ a H W c n n - .... .H ._ 9.”. R . _ . .. \ _ . 3 u n , a _ _ IIIIIIIIIIIIIIII !|I!!l!!!!..! ! a ._ f3 XI. I0 _ - ‘|'|'|'l""' ...-lull llllllllll film. WWI!!!! !! a . 1 P. .! ll!!!!! !.!!|l!!!! .. II!!! IWWIUW IIIIII um. !! \ 4%. 20'00" H. = 3i, 912* .u .r. I !. . . ..l pruvyfifh‘tnfilig. .g. ..“uv...T((H.I.! .... ...!. l p... fi/VflL VJ/J Jf/EE 7 N0. 1 1.3 on. on’ an. 0.3 . .... - . ..‘l:€.442«3 14.1.4.4“ .. ......» 12.4.4345...”14.1....fluu.......ta...” m ...-.. 7-........ . .. . : ‘ ‘.-_-'~;: “...-.1; a ; '. "_ '3 A‘aé'.’ * “« '5'...“ <33 4 TL»: a” )fin vanit. . \t . r. vow .\. A w» ...< x... ‘ I . u . ‘ t n . . . . r . . v . . . . JAN“... .a. «. at“... Tat-UK .w‘...‘ , . , La . ,. . t