(I um W“ I b — N 7 h — — __ — — WWI/H“ . o‘W“\b '- 1 -fi '— nmm‘W'v.”-r? 01 ywmr“v‘r-~r. _,A ,_ ,7; .: ‘__ var ’2“ I‘ "5‘!- . L... .o'o .. -, ,.." 2‘" 1‘“ "¢_ JMML‘Q‘T m - 0 -~;.- "‘ ’-" \L‘ ‘*v‘.-'~.='r\r- onw‘fl Tpax‘vE-‘RS ;« , .. A ‘. ‘ .I ‘ ~ ‘ . ' ‘ I . ‘- ' \_) L 3 . .' h , v. -“ ‘ - ‘5 s b, , L? \4’ . k} ‘ L ‘2 v -. "Mrs ‘W 3 ~,-+«».:.v-_~z7 v: H 5‘ u A 4-. ‘ v c . l _,.\ § ‘: ' \. m .4 ..... vfi . . .' L J o ‘ I . ."J'lf‘dl" ~33 .C.!'.;‘I.;2LLL'M"M5 - W ‘l——- .Tf‘w'" “‘YVF "if”m'J‘V'rfil'fl-a P...“ “ “ 2;; .'I.-.'~6I .‘r‘ ,.:).- -,.-v) r-.-. g-‘F t 'Pfi'l v- ...” ..'. '3 z 3 u l.- Q) 0 tx\./' \ _ SUPPLEMENTARY MATERiAL ' N BACK OF BOOK mum . m 814!“ ms: U “W". S ””— flfi/f QL,J_C.Q,.¢.4 LL] QflJ 4.4.19] “Luff—CI Ltéc‘é‘ W ‘ / v The wishes of the he has in due writer of this thessis in this note to thank the members of the faculty Michigan State College for the help received during the past years and concideration has written this thessis to show his appreciation. _‘ ’0' xxx. .\ 1" h V V"(‘ l '- "r TT\‘f 'j“ J . I .. . . A . ‘ [11“. :J— ‘4-1 f1 . I A l ‘4‘: J I; i) b ._ J 4.} k .4 1"".* \ - 1 ~.-7' i_.\‘1_‘ ' r Infiri. Aifl‘ira {9-1.0 Lib 11-111.11LJIHLLJQJ. Jr. CLO.» LID Ihesis submitted to the faculty of . «J; ' 1 ,I‘ ‘- "j. ' -,. ton. lieison M Candidate for the hearee of bachelor of Science 0: June 193 THESIS Analysis of Two general types Flex Towers, Flexible frames are heavier than poles and are intended to take care of longer Spans. iheir chief function is to take care primarily of transverse loads with a small margin of safety so that under u usual conditiins of service they could provide a little resistance in the direction of the line and distribute a load coming in this direction over a number of supporting structures and transfer Such a load to the still heavier structures placew at regular intervals in \the line or they may transfer all loads coming on them in the direction of the line to a point where they will he resisted. ‘A Rigid Towers digid towers are the largest and heaviest struc- tures made for transmission line supports. ihey are intended to hafe‘strength to carry loads coming upon them either in thedirectio s of the line or at right angles to this direction. They are usually desianed for a combinatiOa of hoth loads. ihese towers are luiit i* tria eular rectanvular or square dependinv unon conditions. ihe width at cr>und line varies from one seventh to one third the total height 103? '11.? qoadings, 1 head load of the wires together with anJ coating on them also dead weirht of structure itself. 2 Mind loads on the wires and the saruCLure transverse to Lhe directia; of the line. 5 Eulls in the directiiz of the line caused l1 deed load and the wind lwad on the wires. ”9% 99. Q3 .\ 30.x 53.x «3.x 5.3.x tow. 33. 30.x S: as. Q9 be. we. .63me Ste $0.28 hhmeKh. .ocu QVh, «ox «flux m\\v.u o~°§ ho. 58V ”00% 90. «no». «3% hoo.‘ A... $00“ flaw QCOQ NO. \0. \k bexflfl \QO.\ .6: QOQN O h-‘Jl‘ - .- — --. n a pAJo.-- I ndnnl w- .l- .“Mlll‘ -An'I-nu-A J- K 1! u)\\\.« \N\‘ ‘\\ \‘;J\\1 \x\ .V \N\\ .\‘ \\~A o \\\_ MN“ \ \v” ,u.\\\\.. 21>. ‘ ON m.\ m\ N\ K\.m.b Sv\ nV\ ”Kennvkk \. w\h\$\h\m.\\\ox.mmkvlo \V \R\.\ at \V n LENOO hum QtSCQ ”N NVXM. .NmeQ >\Q Nth, .0.“ka 3%. \K\b%\%\‘ .Q>\\\= VVVNKUV goSo QNKVQ\Q>\\ . ‘1 .0\ a. . - 30W _ 0* mos, on on 0” om. OO\ O\\ 0mg Lefcrence for use of Ihomas's curve Formula stress factor 3 Stress in nine heneth of Conductor x ‘t. per ft. Stress factor is ordinate for both See and Stress \ baa :dpan x abcissa of sag curve Length ‘ span X abcissa of length 0 rve bind pressure on conductor It has been determined by many experiments that the ' I - wind uressure on circular objects - .OOBSV“ In which V 3 velocity in m.p.h. The two curves indicatea and actual velocities are based upon ex eriments. The indicated is the velocity used by the U.5.N.s. As a result of consideralle investigation the corrected velocity times a logarithmic factor equals the true velocity. 3: ”a: [odd/n} °"’ 3g F/.x 7‘0 wer- \ —_ a: 4[_. 6“ “,0 ‘ , K win]. ”0 A ‘4 ".53. , ——> 32.0‘ Jifo o 1430 h . \ ‘ \ * 3 ——+ .390 0‘3 :70 : \c ”° 1-: ’ ‘ ‘ ,_ ——» 34° 2220' {V 3220 3 ': é —a- 34°” 0 cu M N 4~l 30° 42°“ ——-)- 1500' 1:00 \ \ ___,_ 5-30it ° \ Q \’ \ xx ‘ t. a 6 __,. 5'60 ' \ ..\ 3 " ‘ \ e ‘ " , \ ___,_ 570 o E \i \ \ U o \ ————,-. 6:30 ‘ \ \l \J \ \ fl \ ——+— ‘70 2 \ \ '1 J \ \ \ \ __). 670‘ o \ \ 'I \ 5. \ \\ o \ a. j Q —-——-1'~ fé u LIL-:- 1'765' ' conJuefo" 1 390° 26 :42 Max Zodd/nj on Jae/tor 73m”- [300- Cor-id. L “90-0.1. 6.5'00‘ Conducf’ar 420 M51 1300‘. a Job-Dd. Q «900 ~ C. $467k W 1.“qu ’00 ‘Mc (“5‘01“ C. fidr‘ py 25'0 0.1. A veer“ IV ”'0" 0.1. . Ho'u’ 37o'o.L. 600 W 400‘04 66'0-W 450‘0A- V 760“}? Ultimate Gauge ” a S Diameter Area Tension 500,000 .819 .5924 5,540 Load per ‘ jax. load Lin. ft. vert. Lin. ft. hora. Plane resultant head 1/2" ice 1/3” ice 1.535 2.545 1.815 2.64 hengtn of conductor and see lower Span 550 ft. stress equals 5,500 From Curves stress Factor = 5,590 4.17 Sag = 550 X .051 = 17.1 ft. Length : 55J X 10002 = 551052 ft. Max. vertical stress 1,500 Max. horizontal stress 670 Tower Loadings Wind Flex tower 20% per sq. ft. Anchor tower 30$ " n n Flex towers are designed to stand max. stress perpendicular to line Anchor towers are designed to stand max stress from all directions 412) x 42 . “-,._ 2 X 45.95 180003 + 5hTJ x 45.5 5+110 X 42.5 :1 ..V’. "'1: f.) 0 Z 544,503 + BJMD X 51 H) ,.:,‘ .— L4 1; UL’O bJBLJJO + 2590 x 55. n H 7:. (1'7-0. 5 5 ‘1') o R -_) L. 777,700 + 1792 x c .25 2 X 66035 HUIJJJJ f 365 if 7J.CL> 75755 eeJ x 77.s5 E K dlol5 895,252 + 255 X 77.M a? I: X {37.235 ,547 + ’; -.- ,- w ‘ ‘V: ,:. ‘_1'-l- \) 4c %’£.>Jll‘ 9JJ,;3J7 + 51.5 x 100.55 2 3-: 154. :J 9J5,777 + 5:5 x TJe.e9 2 X 111.79 Stress 5,450 Allowable 4,550 " 2,600 " 1,582 " 2,220 5,170 6670 4750 15.1 6.6 11.2 7.5 11.00 m 5.0 13.1 5.0 7753 8540 9550 9010 pJ7J 7900 7340 L) U -.-l .) 5723 H 110 X 1.46 160 + 110 X 4.25 + 7520 X 2.7 233,108 4 755C) X 4.9 + 59".) X 2.3.1 56,878 + 772) X 4.55 + 4783 x 2.1 99,778 + 12,500 x 4.25 f 540 x 2.1 15w,695 + 1384 K 5.45 + bu84 X 6.6 256,615 + 16424 x 6.85 + 550 x 5.5 549, 465 + 16954 x 7 + 560 X 5.6 46J,025'+ 17514 X 718 + 670 X 5.6 087,8/5 + 16064 x 7.8 + 620 K 2.9 753,795 + 15794 x 5..5 + 570 x 5.9 889, 205 + 19574 2 8.55 + 5/0 x 5.7 455511 DIVE: 1‘ (iL1755 | I ..~a 150 5.5 + 1.45/5 40 20,108 56,878 99,725 156,695 256,615 549,463 460,025 007,5/5 730,795 889,205 1,052,685 + 5.9/5 + 5.9/5 4,270 11,150 18,800 26,500 55,600 47,600 57,80J 66,800 76,800 87,800 90,500 1—! (JO 21},1CR% 56 , '(57 5 99,778 5‘ 155, 93 555,515 £y49,465 460 ,ka?) 587,875 750,795 1,952,555 11.4.10 40,000 H .4". ‘J J. .iJ-c And 530 X 11.12 + 6931') x 4.573 35,730 + 7420 x v.75 + 794 131,7JOI+— 880,JJO-+ + 667 ,05-3 + .7 1.31.: . 11.1 55,783 151,703 205,0J0 440,633 697,050 783,533 1,050,390 14,450 x £3,530 x 8.1 4 4 82,150 X 9.5 + 5 25,460 x 10.5 + 24,360 x 11.5 + DIVIdOR 5.12 + 8.73/7 n.75/7 7.5/7 8.55 + 9.0/7 11.La+10/7 15.ce-+11.1/7 17.21 + 12.1/7 J K 7.625 + 7040 4.575 '1’ v r ‘—' .,' 4 (4(1) 4‘. a O '1 a ,- ‘{'r\) 7: 4:05 9‘30 F: b o x.) 660 X 5.5 f‘.‘\'1l}' ‘LJ ‘ \Iflfi; .‘L- ‘ 54.1-. 4...") i; , 6‘.) 15,53 29,0w 57,70 Q U 0 C) X 4.57* '. :5,750 131,710 Lnb,uw g; 449,520 _ ,7 9/ 0'1 C\ C?! L; ’ 1 00 ()1 7 8-1; , 1,060,033 f . ‘) 1'." i {1 g- .11“. .1 ,4-) 511‘ .. 4‘ 3." 50,919 H 52,730 M /I‘ 1 J ‘ g ) . .7? l 139- A «1’. L 19,2.5R) (5“ 7-10) 6983 F 6.75 4 704) X 15.5 + 7143 X 34.:5 2; X 2.7 .5.) 6135 x 11 5.5 10,580 :56,9)J‘+‘420“¥ 31.75 4930 X I4: ... b )2 QUQU 80d 7,t)“-}_) .g93,533 + 543 X 43.6 4153 X 16.7 1:: X ’é'tbol 1101‘ 5,763 ,"7 1/1 H LC . J 1 ,- 71,&53-+ 670 X 53.6 5&5) , a x bb.‘ 14.0 4,983 4JT,55J + 063 Y 6I.6 5530 X 23.5 a x 97.1 17.5 a A) .nTV ,. '.L... .115) All rivets in towers are in single shear allowable 10,000 Flex tower Max. stress in cross arms 9 910 1ofojo‘ flax. stress in channel 96,500 10,000 Anchor tower hax stress in cross arms 5 1 J 00 ._._._...L_...— I 10, O 00 Max. stress angles 53,700 Io,ooo 2 rivets IO rivets 2 rivets 6 rivets MICHIGAN STATE UNIVERSITY LIBRARIES O 3 1293 ll“ llll lllllll 3174 5213