- DE- ont‘F—"mP-m-n—‘ XQOH quvmoa anaona I II I I II 7’77 IIII Mil I _l N (JO STUDY OF THE STRESSES OF A MOVABLE DAM FOR THE NEW LOCK IN THE SAULT STE MARIE SHIP CANAL AT SAULT STE MARIE, MICHIGAN Thesis for the Degree of B. S. MICHIGAN STATE COLLEGE Eugene H. Rook I942 Study of the Gtreasee of a Movable Dam for the New Lock in the Sault Ste fiarie Chip Canal at Sault ate Marie, michiyan :fiv‘ire A Thesis Submitted to The Faculty of MICHIGLN STRTE OLLEJE of AGRICULTURE AND APTLITD SCITNCE ’ - Eugene H. Rook fl Candidate for the Degree of Bachelor of Science 19112 K Tera-S IS Table of Contents Definition Conditions to be ms t Diagrams of placement Description of first dam analized Forces caused by water Stress in wickets Description of second dam analized Forces acting on sections of dam Panel loads of trusses in sections Calculations for length or diagonals Algebric analysis of trusses Graphic analysis of trusses Conclusion 143101 10-11 11-12 19-15 15-2o 20-21 22—29 90—45 46 Study of the Stresses of a MOVRbIe Dam for the New look in the Sault Ste Marie Ship Canal -at Sault hte Marie, michigan Movable dams are structures that are built to partially or totally restrict the flow of water in a channel or canal for a period of time, usually short. They are entirely removable from the place of restriction of flow or are collapsible so that they are out of the way and permit the flow of Water by or over them. Thus, they recieve the name of a "movable" dam. It should be thoroughly understood that they are not permanent dams such as are made of concrete or masonary, but are either wood or steel structures that are used only in emergencies or tangorarily for the purpose of making repairs, adjustments, or to re ulste a water level. There are many types of movable dams such as curtain dams, wicket dams, needle dams, shutter dams, rolling dams, drum dams, and so forth. However, most of these are useable only in shallow water, up to about 15 feet or in places where the water is restricted before its full head is attained. These types would not fit the conditions (which are stated on succeeding }ages) under which the dam I am analyzing must Operate. This dam must operate easily, quickly, and efficiently under a full head of about 55 feet, and at the beginning of placement most of this head will be converted into velocity. Therefore, the design must be more stable and stronger than the types listed above. The data for ship canal at Sault Ste Eerie, fiichigan is listed nun. -2- below. This data was secured with the kind help of fir. H. . Rook*. Upper pool Low Water Datum —-- 001.1 ft. High Hater Monthly Mean --- 605.04 ft.‘ matimum hourly change --- t 4.0 ft. Lower pool Low Water Datum -- 579.4 ft. High Water Monthly Kean -- 505.65 ft. High water hourly extreme --- 505.22 ft. Lowest extreme -- 3 ft. below Low water Datum All of these elevations are based on the low Water Datum at New York. Elevation of canal Wall -- 121.00 ft. This elevation is based on the Sault Ste Narie Canal Datum. The relation between the two is: Low Water Datum . 605.04 ft. at the Sault ¢te yarie Canal Datum . 117.57 ft. Depth of lock sill below Low Hater Datum = 51 ft. or elev. : 570.1 ft. width of canal directly above upper lock gate 3 50 ft. This is clear distance between bumpers which project one foot each from the sides or the canal «all. Length of lock between inner service hates : 500 ft. The data as it was obtained is of no use; so to put it into usable form, the elevations must be converted into differences of elevations or heights. The averaie difference of elevation of the upper pool and lower a Mr. Rock was, at the time the information was obtained, Principle Engineer for the U. 8. Engineer Office, and is now a it. Colonel in the U. 3. Army Engineer Corp. .5- pool is 601.1 ft. less 579.4 ft. gives 21.7 feet. This is not the extreme difference; so the difference for the mavimum hourly extremes of both pools will be used. This difference is found by adding both the maximum hourly change of the upper pool from the Low Water Datum and the extreme low water level from the Low Water Datum of the lower pool; thus giving 21.7 l 4.0 % 3.0 or 2o.7 feet difference. This extreme is not likely to occur as the lower pool is usually at its highest level when the upper pool is at its highest level. The reason for this is that there is a power and water level control dam above the rapids connecting the‘tro pools other than the locks. However, the extreme conditions are possible, so they will be used in the computations. The truss supporting the wickets must be placed on the canal wall, so the elevation of that should be obtained. The elevation is known, but it is given on a different datum plane; so it must be converted to the Low Water Datum Plane of N. Y. The relation between the two as offically recorded isr Low Water Datum s 605.64 at Canal Datum : 117.57. The elevation of the canal wall : 121.00 ft. The difference between the canal wall and the reference point is 121.00 - 117.57 or 5.6j feet. Therefore the elevation of the canal wall with reference to the low Rater Datum is 605.64 { 5.6) or 607.27, and the difference between this and the extreme high water in the up;er pool is 607.27 - (601.1 4 4.0) or 2.17 ft. This I believe is all the conversion that needs an“ evplsination, as the root can readily be seen frOn a vertical section throught the lock. However, before the vertical section is shown, a general plan of the lock will be shown with the position of the dam indiCPted. This will give a better understanding of what the conditions are. Hr ale. was. ax \. \‘t §EU§>R \and n\t.\nk N\¢%NOO% VGQV. 3h\¢\ \hhd‘fiixk \Ofiuh \hk\§ l. \\\\.\ \tttou , 1 G t.“\\.\bm1.\b\\§kr “buxtm bh.\\.\bml \bxx‘N. . .n £3“ th\\~.\UMn \fi‘bq h.b\§.w b.u.<\\bh. \U\§Q event \chtox flax. 33 \e\ \othxw which \\R& W VUOV 3U\< \0 kUvnK VQKUENU n... J I, yea. .I/ I... [at w I. . (.Ivdax w? o O V. fVu . . 0.). .8. . . v n A finlrv 1‘ .r J \J I; m...“ . a / a r 1,1570 J Ir-.. '1 7/ he -1“. l . I I-IIII-I‘|| I101.-. .. I . l. l) t/r/AuJ/Mr ,1. IVA“)! A14 V x J at}. 1.9.1.30. I . mile 1.01.1, v 1// .' A .f / «no I, .J AA. 09 #4.. ‘I .. «04.31. .751“) .I.\ r not...) .rJ J... nuljwvr kn. NWJ [WNW/mil; a. nH/ . ' IIIII'I ll-llll |' TI: |-I ' XIV} ..... M...\~/v .f.l./ Hot.../. -11 I I .2... h... at nor}, .1... ..., L J .. .4! 1.. e. L. .r V} .b; at .t D i. {U I,» ,- - .49 4.4 Jr... 1“: p . a..._.,/ J. 0 .— I’). .H .V .11.; J .r— -HZA7' firemr we» WWI-T 2/2227 - 7:2.— “ - ‘J J5” _zgeé&;_‘;;.;.€£r_é?§4 .Zondlgggw- ‘TuflrxJUIM‘ {- . J . 600'; Evil/0M dflkyrcgepercfis/rw 217’ :x' .flksl 2’04 4/ cal/oat This gives the conditions that the dam must conform with or over- come. These conditiJns are much more severe than those for most of the movable dams designed. Therefore, this dam must be much stronger than most dams of this tyye. To overcome these severe conditions I have chosen the type or dam shown on the following two pages for my first trial. The dam consists of two horizontal trusses held tOgeather with two vertical trusses. Inside of the bar formed by the trusses is glaced X bracing at the panel points. Then upon the upstream side or this box is hung sheet piling. This piling cantilevers down into the water to the bottom of the canal. The dam is constructed so that the truss box can be put in place first, and then the piling put in piece by piece until the whole canal is shut off. ‘1 \\t\.\ (3% as .0 \nw. \\e\A - 11;. . w ..-. . VIII, 33.0% atozu0\ Q h.\§s\§0\ my Main sex a l1 M§.\ h; thfimxx .ani 0Q .UIv/U ../ l.J\ 4/}, (Jed? X W; 9 {fr NvW/UV till ll. i’lll'lf it‘l'I It I III1 I.‘ III 6 ‘ill II‘IIIIAIII'III.I| .‘ul. " u / i x . m \ _ _ _ . a x . + \ / \ a / . \. m n . \\. i . .\ m \ . .\ u x u , \ / . x .I ll. II: it 1 ill illilolilllllll Ill bulllllllllltllu. - Ilul-l.lllil. .l .21. Ital. -.illlv.l.ill1 . Illerlllsl a (II. .I llllo. illuIIA : I .1... .ll: 11.: 14.. N Nl/vl/ / bun/nu I W} +J 5 I .I 1.. I .. . I «My ,. . .0: J .J l 0.. Luz. 19., a. #0.. 4/0. . .P. /. k .../. \. .\ . ~ \ x \ ~ \ . A \ . x. \ x m ~ .. z \ . x \. I _ / X i \ \ / . \ _ _ . . r \\ _ \ x .z _ / 7 \ x , . . ,_ \ Ill'rl ll Ill 0:.» . ‘Illl. ii I9 I I 11 J il! Ill I» I'lll I. “I..." will- II. I IKI. 4| [Ill Iii. til flllllii I .lllll'llr I...I..Iu- ‘i‘l Illilvllvlll .1 ._ I, r/ 4.. n. . —l i I II Vang/J 40.1.; 4U. V V x...../ flea... ‘5‘ §0\\ Uh“ MbeQKQ N§§wa~ «\N. 8.»me QUNKNWQtoOQ “hukk Son.» 0% \Qb\ “bk \0 \tb§\ n\ bkt 39*.2.‘ but qufik §0\§ then. UQX n.\ “\Rk thxm. Shhkmud?» l . . J flaw/Oz». 4 ..vz$.. /-l.l- ./ are/l1. -—-—.._-.._ IN w//. J aft ..l. o I: . I. It .r f a .r- 3.. .3. 7.- 7 .9 0....w you oh 5.1.9}... nevi .N zfl/A I77... .f/xu nun/U .. .U .0 9 v... v..».....,...c a}... $4., a...) / , Jud ./u “a VHJ ..w/ I I 9 ‘.~Il.7 if (”1”; I -9- The first thing to analyze is the wickets. However, before the stresses can be found, the pressure exerted by the water must be obtain- ed. The forces of the water acting on the wickets is shown in the diagram be]; 0'. height x width x average water Pas = pressure : 55 x l x (62.8 x 5§_£ 0) Fac .' 2 This force acts st‘ég or 11 2/5 ft.‘ft0m 5 the bottom. P50 3 6.5 x (62.4 x 6.§_g_0) ; 1,258 #/11n. ft. 2 This force acts st‘é;2 or 2.1 ft. frum 3 the bottom. The resultant of these two forces is the difference of the two or 58,220 - 1,258 and is equal to 56,982 #/ lin. ft. The point of application of-the resultant is found by Varignon's Theory which states that the moment of the resultant of two forces is equal to the sum of the moments of the two separate components. Therefore: 56,982 X a 58,220 x 11.67 - 1,258 x 2.1 X x 11.987 ft. approximately from the bottom. The point of application of the resultant from the top of the water sur- face equals 55 - 11.987 or 25.015 ft. The forces acting on the wickets could possibly be worked out by the use of velocities. However, there has as yet been no failure of the gates on any of the American looks at Sault Ste Marie, so the velocities have 01" l ‘ ‘ Y e s w , e . _ . o - I u . e . . , a , . e . . « . _ . u . . I n s . . . . n A . . v . . . .Y‘ . . s , . . V . . ,l. _ l .l ‘l v a . . ‘ 'l r x at I . V \l I . n . .. ,1 . . p . e o n , A _ . . . , . . r _ .i U u l . v , .. A . . . . .r A .. :( . I e . I a I I .U a ‘1 r L .a s .. . -10- not been determined. The velocities could possibly be worked out by mak- ing use of the static head: and then from the veIOcities so gotten, fig- ure the forces. This would Just mean that the head was changed to velocity and velocity back to head, and as there are frictional losses the result- ing head would be lens. Therefore, there is no point in this type of an analysis. Now that the force crested by the head of water is known and the point of application of the force is known, the next thing to be investig- ated is the stress in the wickets. These are usually made of sheet piling. The type of section that I will try is the Carnegie Section M I10 which has a section nodulue of 20.)# in.’ per piling or 15.26 in;j per lineal foot. The other properties are shown below. 'a“ k . V - a U I . a . ‘0 / / " ‘ _ 4' 7" 7‘ 771/: I: {we/3179': The forces acting on the piling are shown in the two diagrams below. TI‘ /0’ amrcav” ‘ I7" ’1 ‘ ' "‘ 274/“ of (Mo/M/ ' v f. '\'.. e "i 2 I. ‘1 .9. .I o u- u «on. .9 ' ‘ ‘5 .f. a "- O- a I c .1» . I A: "a - h ‘I o of. 5 r.“ l')( '0 '5 e, ' l I rt- I-.. J I ‘. - - 4.1... - -_---- 2.“.\.>\ Q‘ébk '¢.\ ”3'3? '5‘ I': ‘\\.3. p" ‘N m .e \\. \ u I w\ .. 5\ . on a e e. \ t t \ m. a w in W ("P w. 0 I ' Illl-ll‘l I II..- \\A m .1 ”pl (new ”.7 WIZLIFI . II'FAI xv a."_- ‘ t. I -'. 4&0? X ‘\\ “ \\‘~"3 \'\ ‘“ “KN :& -11- Taking moments about the section o-c or at the bottom of the truss box, the stress in the wickets can be found as follows: Homent co : 50,982 x 25.085 - 949,808.706 fi-ft. / lin. ft. or 949,808.706 v12 . 11,397,704 gain. / 1m. ft. Stress : EOHent ; 11,221.Z04 ; 740,900 # / sq. in. Section Modulus 15.26 This showsthet with this type of arrangement, the wickets acting as pure cantilevers, the stresses in the wickets would be so large that it would be uneconomical to reinforce them enough to make them safe. Therefore, this type of movable dah should not be used under these con- ditions. Also with a little bit of comgutation it can be shown that if the wickets rest on a support on the bottOm of the canal, the stresses will still be too large. Then too, if a little more cOmputation is done, whivh I haven't shown here, it Can be shown that if the truss is made so that it will project down into the canal about 15.5 feet, the stresses will still be too large to be economically overcome. With the same idea of using trusses to overseas the force of the water, I am going to tryfdrOp sets of two horizontal trusses each into the canal. The outline of the trusses are shown on the following page. These two trusses, as can be seen from the drawing, are to be held five feet apart by two vertical trusses. Upon the truss shown as the front elevation will be placed sheet steel to hold back the water. There will have to be six of these five foot sections and one of siv foot depth. And as these trusses need no center supports, they can be placed over the canal with a derrick and lowered down ioto the canal with CPblOS from the sides. Pecause these sections woxld have to be slid into the water I have plated the sujgortr on the back side of the trusses. Also I have made provision so that rollers can be used as the sulports so that they a. -12- to \\\\U\ [V \ko \|.\ abhflbklm {\O\\00. \Qt Oxmk 11 \Odq II ‘0 40 d} \WI.\\ 41 J1 dt _ I Z ‘I 0 a b~0\m. £§bk-fl¢3OQ (csfibaixh. {000. can b sect! the; out. on t‘ the «co—.“fl. i e I Iflu A. h o l ed 0. I II ilillil [if‘ Illnvt I _ \ \ i / . I I- . I I H \ .\ . . \Y. \ II _, II}. I 1 I a \ t I: . I u . III'IIIIIi .- If I .. .I CI..III II. 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V; .« :81. in. .1 ,9 ... I I1 I- II. II. .« IlI rilrI II I III - 4 IILIIIO II III I I I].-. l I .lflIiKIII.l.. ...1I.I-.. (Ill I’lllll I. .I. .||..l III I.I I F . \t . u w I V _ \ . . I .. ; _ w . I # \. .\ v \ . I . I: / F \\ + a ‘\ ~ \ . / . / . / n _ . x...- _ w ~ ~ \-.\, w \ . .~I I g \ u t .‘4 /. . I . a . _ to ~ I II-I ‘I- I I I,lI.y tr. ‘I IIIID.. I.lI III-||.|1I.I'I II...1 l? L. I. -15- can be lowered easier. The following diagram shows the relative positions of the different sections of truss units when placed in the canal and the derths to which they are subject to when the full head is obtained. From this diagram the pressures that s lineal foot of each section is to take was worked out. You will probably notice that I did not use the 6.5 feet of water on the back of the trusses as I did before. The reason for this is; this is more of a substantial dam than the other and me; be used more in the winter, and possibly in the summer, for making minor repairs on the lock. If this is likel; to happen, then the lock would probably be drain- ed out and the back water would not be there. Therefore, I have disregard— ed the backwater altOgether. 7;f 0/ CMO/ M/ :7'09- I ..,.-r Semi/on 7 , “-17 Q 7 45¢un6dbr¢7 1) . + 5“}1935— %; .Skaaf/brl4‘ 5 cc Illa/t Z .Sirar9onL! Ell/{01" o/(‘oro/fl/ Rec -‘\ i.) \\ \ .\ .) u‘ ‘X v Q. X, ._. ~ -‘ at.) A‘NAQ‘; .~__ W. '3‘“. \ -115... Section 1 Pressure at 55 ft. = 55 r 62.4 . 2184 # Preasure at 50 ft. 3 50 x 62.4 : 18 2 f 056 # Average Pressure per lineal ft. ; 4056 x 5 3 10,140 # / lin. ft. 2 Section 2 Pressure at 50 ft. 3 50 v 62.4 : 1872 # Pressure at 25 ft. 25 x 62.4 : 1550 a 5552 # 1 Average Pressure per lineal ft. : 4 2 v 5 z 8580 5 / lin. ft. 1 . 2 | Section j Pressure at 25 ft. = 25 x 62.4 - 1560 # Pressure 81} 20 ft. = 20 V 6201* '_' 1248 7? 2808 # Average Pressure per lineal ft. : 2808 x 5 : 7020 § / lin. ft. Fection 4 226 fi 2] 8 5? Average Pressure per lineal ft. ; 2184 v 5 : 5460 # / lin. ft. 2 Pressure at 20 ft. Pressure at 15 ft. 15 v 62.4 Section 5 Pressure at 15 ft. 15 v 62.4 956 # Pressure at 10 ft. 10 r 62.4 - 624 fl ' 1/ C Average Pressure per lineal ft. : 1560 v 5 3 5900 4 / lin. ft. 2 [o R? Section 6 Pressure at 10 ft. 10 x 62.4 _ 624 # Pressure at 5 ft. - 5 r 62.4 12 # 956 # Average Pressure per lineal ft. = 956 x 5 z 2540 g / lin. ft. 2 Section 7 Pressure at 5 ft. 3 5 v 62.4 g 512 # Pressure at top ; O x 62.4 u 000 f $12 fl Average lreseure per lineal ft. = 212 x 5 3 750 # / lin. ft. 2 From these loads per lineal ft. for each section are found the panel loads for each section, that is for each truss in each section. Cection 1 J This diagram show how the 10rd is dis- tributed over the 5 ft. section. To obtain A and B, the load was broken up as shown. A‘v‘Bg5x1572fialsoAzB 2A : 9560 0? A : 4580 # also 8 : 4630 $ Sum MB : O ""—B % 5 P : @12 x 5 x'g v 5 or i Z 520 # 1.. 2 fi 1 4 Sum “A 3 O 5 B : §12 r 5 x‘l v 5 0r B = 260 i 2 5 Load on tap truss -- per long panel Reaction B : 4680 g 260 = 4940 # / lin. ft. . -~“~ l ‘ A.“ .—.—-_. - .. .— w“ “" ’ -16- Panel load I 4940 x 11.5 3 56,310 # Load on toy truss -- per short panel renal load 3 4940 v 9 2 44,460 ? Load on lower truss ~~ per long panel Reaction A g 4680 1 520 3 5,200 # / lin. ft. ?snel load 3 5,200 x 11.5 ; 59,800 # Load on lower truss -- per short {anal Panel 108d : 5,200 X 9 : $1,260 # Section 2 Afro" I? To obtain the reaction A and P, the lead was broken up the same as in A Section 1 . 2A ; 7800 or A 5A 3.2lg x 5 X‘_ 2 Sum. MA = 0 5B; 212x?) Y 2 load on top truss -- per long panel A‘ B : 5 x 1650 5 also A z B Reaction 8 = 5900 # 26o ; 4,160 i / lin. ft. Panel 108d : 4,150 Y 11.5 : 47,840 # Load on t0p truss -- per short lanel iancl load : 4,160 v 9 : j7,440 # Load on lower truss -- per long panel 'Reaction A ; 5900 x 520 = 4,420 e / lin. ft. saws-«r ~—* ->—. i k‘.-_--. _ , . _.l\ o 14..-... . _* V v--- \. i . 0 \. ”1.“ ._. ....__ M - 4.. . -A--.‘ l A *J.'.. h“ .‘I -,V --.....-_ .- J .~’}- _-------.~V_ —_‘Z . 2 4‘7.“ . «- - - ----—-- ad 1 1 “$4...“ _"{.‘-- To ”P‘- Fr: ft' eac‘r -17- Panel lOad = 4,420 x 11.5 :.- 50,:150 # Land on lower truss -- per short panel Panel load 3 4,420 Y 9 : 59,780 # Section 5 ‘3 30 obtain the reactions A and B, the load was broken up the same as in ”actions 1 A as 2. A {B : 5 Yl,31+8 8180 A a: B A a 5,120 ,4! and a 5,120 ,9 Sum. lflB :: O 520 #/1in. ft. 5 A a 212 r 5 v.2 r 5 or A 2 5 Sum. “A 8 O 5 B : 212 Y 5 r‘l V 5 or B 260 fi/iin. ft. 2 5 Load on tOp truss -- per long panel Reaction B 3 5120 / 260 z 5580 # / lin. ft. Panel load 3 5,580 x 11.5 = 58,870 # Load on tap truss -- fer short panel Panel load g 5,500 x 9 = 50,420 # Load on lower truss -- per long panel Reaction A : 5,120 - 520 = 5,640 # / lin. ft. Panel load 3 5,640 x 11.5 : 41,860 # Load on lower truss —- per short ganel Panel load 3 5,640 x 9 : 52.760 # To simplify the work of figuring the panel loads, a ratio was set up. From this ratio we find that the reaction 3 reduces by 780 # / lin. ft. each time and the reaction A reduces by the sam amount, 780 § / lin. ft. 1. P639] 1 t c 9v 8 \_\. \\\¢\_ “ m M x. _ d _ s _ n n l m . u M ._ m m . “lfnlth. a ‘- 3.) ~..‘\ t l V ‘4 . .d—-- - -—_--.J ~.-!. —— --—--— — ..— .1 3.. ft. Also the long panel loads reduce by 8,970 # each time and the short panel loads reduce by 7,020 # each time. with the use of these ratioa the rest of the truss panel loads can be worked out. That is, all but section 7, which is a special case as it is six feet deep. Section‘h Reaction B ; 5,580 - 780 g 5600 # / lin. ft. Reaction A = 5,640 - 780 g 2,860 f / lin. ft. Load on‘top-truse -« per long panel Yanel load : 58,870 - 8,970,: 29:900 # Land on tap truss -- per short panel Panel load ; 50,420 — 7,020 g 25,400 # Load on lower truss -- per long panel Fanel lead . 41,860 - 0,970 = 52,890 # load on lower truss - per short panel Panel load ; 52,750 - 7,020 = 25,740 # Section 5 Reaction A a 2,860 - 780 2,000 # / lin. ft. Reaction B : 2,600 — 780 1,020 # / lin. ft. load on top truss - per long panel Panel load 3 29,900 - 8,970 2 20,950 # Load on tap trusa -- per short panel Panel 10sd : 25,400 - 7,020 3 16,580 # Load on lower truss -- per long panel Panel load 3 52,890 - 8,970 3 25,920 # Load on lower truss -— per short panel Panel load a 23,740 - 7,020 3 10,720 # .—. -19- Section 6 Reaction A’: 2,080 - 730 1,500 3 / lin. ft. Reaction 3 a 1,020 - 780 1,040 ‘4‘ / lin. ft. load on t0p truss .. per long panel Panel load = 20,9507; 8,970 : 11,960 # Load on tap truss -- per short panel Panel lead = 16,530 — 7,020 : 9,560 # iced on lower truss -— per long panel Panel load :‘25,920 - 8,970 = 14,930 # load on lower truss .. per short panel ranlo load 2 18,720 - 7,020 3 11,700 5 Section 7 This section must be worked separate from the rest of the others because it is siv feet in depth, and is only hold- infi back five feet of water. Sum. MB 3 0 6 A ;‘2lg x 5 x {g_:;2 / l) . A :56) 1/5 # / lint ft. "um. MA : 0 68:21215Xl15 2 5 B 3 216 2/5 # / lin. ft. Load on tap truss -- per long yanel Panel load : 216 2/3 x 11 1/2 = 1hg950 = 2,491 2/5 # Load on top truss - per short panel ~20- . Panel load : 216 2/5 x 9 : 1,950 # Load on lower truss -- per long panel Panel load = 565 1/5 x 11 1/2 gm 3 6,478 1/5 754 Load on lower truss -- per short pinel Panel load a 565 1/5 x 9 = 5,070 # Nos that the panel loads have been obtained, the exact dimensions of the diagonals of the truss must be worked out so that the stresses or loads in the truss members can be computed. These loads will be com— puted algebrically and also graphically. The graphic solution is used only as a check upon the algebric work. 8 ' The graphic solutions are drawn to a fairly small scale. This was done because the stresses in the members are so larre that in the larger stressed ones the difference of 500 pounds will not mean much in computing 1 the area of steel needed. Therefore, I believe that the small scale is Justified 0 Below are shown the computations for the lengths of the members. ' 6 Fuel: 0 ”1‘ 1—59 ' '17 371 o ' '7 ‘ , h TFie diagram shows the end Jiagonals that must be figured. This is most easily done { ‘ i by breaking it down into simple triangles. 3 1he side "a“ can be shown to esual 4.5 y .. feet by simple geometry, so it will not be A. ..|I|IL.|I|| 0 II... II I I, n ,1, // . / I; r /1 /, I llllv l.’ . \\ 2 . . ,2 _ It . _ / u _ I . ./ ,/ . . I _ I fill!!! it; . . 1 I, \ — l .\ I \ . .. a. . I! . J / -21- provsn‘here. b2 a 92 f 122 b”: V 81‘ i 1411“" ; 15 ft. 02 I 4052 f 62 ‘I c = —\/20.25 ,4 5c? = 7.5 ft. The diagonal "d” really is the same as the b diagonal "0", but turned around in a slight- L~—————__.J A 1y different position. Therefore: d z 705 ft. The computations for the main diagonal is the same for all of them so only one is shown here. e = V1411 / 152.2? .. 16.62074 n. a _ This is a very awkward number to use, lL—MTJ off. .lhis can be done as it will only cause an error of less than one so the last three figures will be dropped tenth of one per cent. The algebric solution of one truss is show below. Yhis same method was run through for each truss, but as it is evactly the same, evcept for the answers and figures, only the answers are given. \ ‘ \1. .l .. lull. - ulln- — ~‘ I 'A . v0 I '1‘ c . I... l I‘ \1 .\ ill . z. . 1 1‘...l..¢tll.|.i|1|uV P... A 1 _ a . \x is \J. .. \\ . A .2. \ . \\\ n .x .. I» w u \_ \.IV \ _ . .p . .\ _ . re -1. -1 My? ... o . H II. — _ I . H N x ” ac. é . _, _ . . .. . m . fl . v... -..__..-__.._- _._.——_-_. W \ 1- i111 Ilull olll I‘ll». 2 W Faction l -- Bottom truss 1 - 5 ER 7’ ‘3 ‘1 . . I: 6’. , . II; 4: ' 45 A, , a I J’ 6’ .9 lo I! /4 II c t ,j i A l 5? f' f5 c 37 [-1400 am £9,809- 493a; 53800 5.1000 «Isaac 63300 11400 Reactions 8113.. ML 3 O ' .. 87 a - (25,400 a 0 / 55,500 a 9 J 55,800 x 20.5 % 59,800 a 50 / 59,000 x 45.5 / 59,800 v 55 % 59,800 . 66.5 ¥ 55,500 x 78 / 25,400 a 87) 3 0 a = 226,200 4 Sum. M3 : 0 p 87 L - (25,400 v 0 # 55,500 3 9 / 59,800 v 20.5 % 59,800 a 50 #59,800 x 45.5 / 59,800 a 55 x 59,100 r 65.5 ,1 55,500 x 78 / 25,400 x 87) g 0 1 : 226,200 # Jointla-b-l «lszhe’l ‘, 6 (l—b) - 0 : 0 a M‘*“’ 1 (1‘b) : 0 # (lea) - 226,2 - O (l-a) : 226,200 # Lomp. A. '2” .3~ 1». . 3' ”and J int a-1-2-k /”'d I J oint b-5—2-1 sumo szo (1-2)" - 226,200 ,4 25,400 = 0 (1-2)v 3 202,800 (1-2) - 202,800 _1_5_ (1—2) = 255,500 # Ten. 12 "um. F‘, -; O (1‘2)h - (2-k) : 0 (2-k) : 255,500 f_)_ : 152,100 # Comp. 15 Sum. F}, : O ’ (l-b) ~ (1~2)h % (5—b)n - (2-5)u : 0 = 0 0 - 152.100 / (5-b)_2 - (2-5)_2 - 15 15 15 \O (5-b) = [(25); r‘ 152,100]_1.§ Sum. FV : O - (1'2)v / (5-b), / (2-5)v : 0 ' 2021500 / (5'13) _1_2__f (2'5) .13, IO 15 1 - 202,800 ,1 [(2-5)_2 / 152,100? 15 15 "9'" (2’5)}_§ / (2‘5) 13, : 0 15 _ 15 (2'5) : 0 f (5-5) : o ,1 152,100 x_1_5_ 9 (54>) : 225,500 3.4 Ten. Y _]__2_ 7‘ (2'5)l_2, : 0 15 15 I'll. IL Joint 1140—5 Joint 2-5-4-5-j-k J 01111. 5—6-1-j -24- SUI! 3' g 0 " (24?» 1‘ (5‘4) : 0 (54) -.---(5---b)v : 255,500 13 15 2—2,800 # Comp. Sum. Fa : 0 - (5401-. 7‘ (4'13) : 0 (“-5) 2. (543)», : 255,500 i 152,100 79‘ Ten. 15 Sum. F? = 0 (4-5). - (5-4) ,7 55.500 = o (4‘5)v:: 2.21800 ’ 551500 = 1493500 (W) g 149,500 16.62 _ 207,058 # Ten. 12 Sun. I“ I O (Z-k) 1‘ (41-5) - (5-3) (5-1) a 152,100 ,t 207,058 11.5 16.62 (5’1) 2 295,371 # Camp. 0 Sun. Fv _: 0 (12-1),- (5-6) : 0 (5'5) : 59.500 7? 00mp- 9un. '11 g 0 (5'1) '(5‘1): 0 (5’1) : 295.571 1’/ 00ml“ «Inn-— 4 _‘_. ‘ J amt 4-5-6-7-11 J 01m. 7-8-11 ' .6 k ' .,' 8 Joint 6-7—0—9-h-1 -25.. 81m. 1" a 0 (ta-7» % (5-6) - (it-5),, : 0 (0-7),, a 149,500 - 59.800 -.- 89.700 (6-7) ; 89,700,;gggg : 124,255 5 Comp. Fun. Fh : o 12 (7-b) - (6-7), - (“-5), : 0 (7-b) : 152,100 / 145,271 # 124'235‘%%f%§ (7-5) : 581,555 # Ton. Sun. 2, : 0 (7-5) : 0 5...!“ = o (3-0)} (74’) = 0 (8-8) 3 581.53) £ Tbn. Sum. P, z 0 (5‘9)v '3 (0‘7)v 1‘ 591500 = 0 (ts-9), = 89.700 - 59.800 . 29,900 (5-9) : 29,900 19:92 = 41,412 £ Ten. Sum. 17‘}, = O 12 (6-1) #0551), 1‘ (ts-9),, - (9-h) = o (9-h) = 295,571 ; 85,962 ; 41,412 11.5 16262 (9-h) = 409,988 # Comp. .‘ ‘ . ‘ - . ‘. 6 _._ - -.__....___. ..,..._.___....’. 1"- ‘ \ - 1 7 x +\ . 7- ‘ . ‘ .‘ ‘ ‘ . x " \x“|‘ x-r- v. 1 ..,\ t \ , ‘\ l‘ i 314’ .. \ /' .. _-. ._.._.... . m » \ I .— , ' - 1 -. ‘ _ -. ’ ,__. ’ 5. u - . - «— \ 7 / Y ) - ' ' r_ :. ’ \ r . ‘2 - ' 9 a- , I ._ 3. x I i r .\ r; h . —.-... -._. -- —_‘.3 ;“.—.—_ - \\ .-. ‘5 4,. o‘- a 0—. up w v . ‘ n . 1.5:,» .y: c, . \ "‘ -_ | ‘ up \. _ I I Joint 9-10-g-h -25- Sum. F“ : 0 (9-h) - (10-3) : 0 (IO-g) : 409,988 # Comp. Sum. P‘v : O (g-h) - (9-10) : 0 (9—10) 3 59,500 fl Comp. gum. Fv 1’ O I 0 (9-10) - (8-9)v - (IO-11)v - (10-11)v _ (9-10) - (“~9)v (IO-11)v : 59.800 - 29,900 = 29,500 (IO-11) 3 29,COO 15.62 = 41,412 § Ten. 12 Sum. Fh : O (11-b) / < 10—11), - (8-9). 2 (a-b) : o (11-b) _ - 41,412 11.5 / 41,412 11.5 % 581,555 » 16.02 16.02 (ll-b) = 531.525 # Ten- 1ype Section 1 Section 2 Section 5 of Top Truss Bottom Truss Top Truss Bottom Truss Top Truss’ Stress Stress Stress Stress Stress Stress (l-b) 0 0 0 0 0 (l-a) Comp. 214,890 192,270 180,680 158,540 147,050 (1-2) Ten. 240,825 215,475 202,800 177,450 164,775 (2-k) Comp. 144,495 129,285 . 121,680 106,095 89,865 (2-5) 0 0 0 o o (5-b) Ten. 240,625 215,475 202,600 177,450 164,775 (5-4) Comp. 192,660 172,580 162,210 141,960 151,580 (4-8) Ten. 144,495 129,285 121,680 106,095 89,805 (4-5) Ten. 196,621 175,999 165,646 144,857 154,587 (5-j) Comp. 280,602 251,065 256,297 206,505 191,991 (5-6) Comp. 56,810 50,850 47,840 41,860 58,870 (6-1) Comp. 280,602 251,065 256,297 206,586 191,991 (6-7) 005p. 118,025 105,599 99,588 ' 86,964 80,752 (7-b) Ten. 562,266 524,762 505,067 266,888 247,867 (7-8) 0 0 0 0 0 (8-8) Ten. 562,266 524,762 505,067 266,888 247,867 (8-9) Ten. 59,541 55,200 55,129 58,95; 26,917 (9-h) comp. 589,487 549,072 527,990 286,619 266,492 (9-10) Comp . 56,810 50,850 47,840 41 .860 58,870 (10-9) Comp. 509,4 7 549,072 527,990 286,619 266,492 (10-11) Ten. 99.941 55,200 55,129 28,988 26,917 (ll-b) Ten. 562,266 524,762 505,067 266,888 247,867 -23.. Type Section 4 Section 5 of Bottom Truss Top Truss Bottom Truss Top Truss Member Stress Stress Stress Stress Stress (l-b) 0 0 0 0 (l-e) Comp. 124,410 115,100 90,480 79,170 (1-2) Ten. 111,540 126,750 101,400 88,725 (Z-k) Comp. 85,605 76,050 60,840 55,255 (2-5) 0 0 0 0 (5-b) Ten. 159,425 126,750 101,400 88,725 (5-4) Comp. 111,540 101,400 81,120 70,950 (4-b) Ten. 85,605 76,050 60,840 55,255 (4-5) Ten. 115,882 105,529 82,825 72,470 (5-3) Comp. 162,405 147,685 118,148 105,580 (5-6) Comp. 52,890 29,900 25,920 20,950 (6-1) Comp. 162,405 147,655 118,148 1C5,580 (6-7) Comp. 68,527 62,117 49,794 45,482 (7-b) Ten. 209,705 190,600 152,555 155,457 (7-8) 0 0 0 o (8-b) Ten. 209,705 190,600 152,555 155,457 (8-9) Ten. 22,776 20,706 16,565 14,482 (9-h) Comp. 225,464 204,927 165,995 145,479 (9—10) Comp. 52,690 29,900 25,920 20,950 (IO-g) Comp. 223,464 204,927 165,995 145,479 (lo-11) Ten. 22,776 20,706 16,565 14,482 (ll—b) Ten. 209,705 190,600 152,555 155,457 Type of Stress Ten. Comp. Ten. Ten. Lomf. 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(7: ,1/ .46- By having the stresses of the different members of each truss com- piled, as on pages 27 to 29, there is one thing that is very obvious. The amount of steel that would have to be used to construct a movable dam of this type would be very large. This conclusion is drawn by check- in the com;ression members. These have the largest stresses of any of the members. As they are compression nembers, the unit stresses in the members may be reduced to as little as 16,000 # / so. in. This would make the size of these members very large, and the weight a large amount. With this large weight, I believe the project would be economically im'ratiCnble; as light wei ht is:requisite of this type of dam. Therefore, another type of dam should be tried. The only other type of dam that I can think of is one where the members would be mostly ten- sion members. This would be something like a folding drum dam. That is, all of the dam would be placed under water until put in use. When it is put in use, the folds would pull up from the bottom of the canal. The folds, of course, would have to be anchored to the bottom of the canal by ties or some simular arrangement. However, the objection t‘st I have to this type is that it could not be easily inspected. In fact the only way that it cowld be checked would be to raise it into the position that it would be in when in use. In conclusion, about all that I can say is that more reserch must be done on different types of dams for this canal until some one is found that is more economically suited to the conditions than the ones that I have tried. This may not be possible, but it should be tried. Further investigation and experimentation has not been done here as time does not permit it. «\ 6 I II. .,1.’Io‘vlqn. fl uyifl ,‘ MI. “W. I 1. ., al" I f..F-. _ i 9 All 8 8 8 6 4| 3 0 3 9 2 3 ii I l _ ll. . III 1| ll .III II- I'- ll. " -i' —- - A. ‘1 L4- g- “l‘m‘ _"