. 102 655 THS THE DESIGN OF A WELDED. ALL ALUMINUM FRAME GREENHOUSE Thai: for the Door” of I. s. mmn 5m: COLLEGE Stuart H. Boguc 1949 SSSSSS ‘ mum” ; 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 6/07 p:lClRC/DateDqundd-p.1 The Design or a Welded,1&11 Aluminum Frame Greenhouse A Thesis submitted to The Faculty at EIGHIGAH STAEE COLLEGE at . AGRIOULTURE.AHD»KFFLIEDradlfificfl by Shmfi Hay m candldnsc for tha‘nnsroo a: Bachelor of Selena- march.19k9 tutti; ’n t» 1—. A .1... .1 216864 Introduction Aluminum elloye ere produced in practically e1]. 0: the tone in whieh metele ere need: plate, sheet, her, rod. wire; tubing. ehepee. tea-31m; enemas, and ingot; as well ee rivet- end eeree machine products. Shep” my be the “undue et‘rueturel shape. or they my be or specie). design which an be pruned only by eta-hue». II'he mines rem ere rebrheted into finished new and etmeturee by drew- the, weeping. ”inning. hemering. manning, welding; brew- ing. riveting. end, to: name purpeeee, soldering. Eeee er tehrieeflea end finishing the metal in one at the reeeone for the choice a: alumna. duper-1.0:: of on“ should be made on the finilhed mule ee aede tree the different: peeeihle "term” not en their ”have prieee per henna. Since the volume or new in “all: substantially the em. the price per pound at denim would be divided hyehe ratio or the epeeifle greviuee (epprexmeeely three to; meet or the enema motels) when emu-ins the materiel cone. In «Meson. economies frequently result tree the greater eeee with which am on he taunted... penned or “hem-e finished; end eke tree the lower out crush-nutter: rude possible by the lightens or the eeeel. bequeath; these «nuance ere more than settlement to overcome en untenable eon commune from the “endpoint of mete). nine elm. ee; to: maple; with omen grade: or steel. In such when; the higher «rep nine or elumlnnn. when the ertiole is finally discarded, in elweye en eduntege to he considered. The out generally recognized oherneterietioe or the elonlm alloys are their light weight, resistance to cor— :oeion (both in eeeeoeet end indmtriel erode.) end high etrength. Then quelitiee ere largely reepoaeiole to: the etreotml epplinetione o: the elenlnnn elloyo, mtionlerly in the trmportetion industry and in erehiteotnre. am or the very higha-etrength. he": motel elloye otter einllu strength-duels” retioe but the thinner notion: result in lee: rigid end leee rugged etmotnree end preeent handling yrohlm doting tehrioetion. In eddition; moot of then elloye latter in the coat oonpeneon with the light elloye. The nodulne of elasticity; which in the retlo or otneee to etreln in the eleetie tense. mie- eoneehnt. depending on the composition or the materiel; in generel, it inoreeeee with inoreeeing want: or elloying element: from about io.ooo;ooo to ehout 10,800,000 pound- per some inch. to: molt preotleel mpoeee. however. the nodnlne my be tehee ee 10,300,000 peonde per eqwe inoh. Beeeoee or the lower veloe 0: thin content on eonpered with that of eteel, it ie neoeeeery to nee deeper notion in eloninon alloys in order to ulntein the an detleotion ohmeterletiol when the: en loeded ee been. It is “hell: with to deeign e etmeture heting the eene deflection under load end eetnelly higher ultimate etrength then would be obtained with etmetnrel steel, end, It the me time. to reelize e eating in‘weight or more then e pound for each pound or eleminnn elloy area. The lower nodulne or eleeti- oity in en eeeet‘when inpeet loede ere to be reeieted, einoe. other things being eqnel. the lowerthe modules. the greater the ehility to eheorh energy without permanent net. the lover module. is nine edventegeone in rednoing etreeeee prodooed by misalignment, settlement or upper“, or other fixed de- tieotione, eooidentel or intentional. the nodular of rigidity ie ehoot 3.900.000 ponnde per eqnere inoh tor aluminum and ite oomneroiel elloye, eorreen handing to e velne or eon-third for Poieeon'e Ratio. benign 0r iterie The new ellweluninun treme greenhouse wee designed for durability, A full wind load or twenty—nix pounds per equate root and one-half minim snow load of thirteen pounds per equere root were used to resist bad weather none ditionl. Sinoe double strength glue in used for the win-s down e weight or two end thirtyutwo hundredthe pounds per lineal root was necessary for the eonputetione, Since the deeign was chosen to eliminate all interior euperetrneture e true in the tom of e gable bent wee eeieoted. The , vex-ions membere of the gable bent are to be welded together in order to deteIOp the full etrength of each piece. In e riveted structure the member: are weakened to e certain ex- tent by the rivet holes. The ends or the truss ere welded to e bearing plate that in bolted to e ennerete roundetion. Since the ends or each we no bolted amen the m... u statically indeterminate. Therefore. to oompute the moment! and reaction: due to the loading. Gentleman". theorem we used. It etetee thet “when t etmoture 1e noted upon by an equilibreted force eyetem whieh produeee as total internel etrein energy 9. the derivative or U with rupeet to any tone zine the diepleeenent in the direction at that tone.“ Ehe loading on the gable bent wee broken into three who to: the note of computations. The load! were broken down ee relieve: the vertical eide or the greenhouse wee eon-leer“ to reeiet only 1 wind load or four hundred one eighty pounce per foot: the horizontal component or the wind and em ioed which ie two thousand one hundred and eighty pounds per root; end the vertical component or thirty-two hundred pounds per foot were considered to not on onoohelt or the met. It on deoided that it the etrnotnre no no. eisned to reeiet the maximum loading on one aide it would to study enough. The tint mentor to be deeigned won the tee oeotion gluing her. It In eoneidered to be a oontinnoue team with five euppoi-te end a uniform in“ on it or tour and choc-hen pound; per foot. The maximum negative moment was found to be larger then the maxim positive momenta; therefore... the neutive moment governed the deeign. The notion modulo! required wee 0.15!" The tee eeetion ohoeen was an two ineh by one end one-vital! inch notion with a notion modulno of 0.195. The notion wee oheoked tor eheer and found to he entinreotory. The who won the next member to be designed. It we] denigned ee e einply eupportod been withtoonoentrated ioedl at as little leoe then two toot internist The loading eon- eiderod no the once and wind lend. the weight or the sheet the weight or the toe eeotione; and an assumed weight for the mun itself. The total loading designed for was two hundred thirty ponnde et lone then two root intervals. The mum. moment wee need to oompote o eeetion modulus of 3.93. A nix inoh ohnnnel notion with e notion madame or 5.06 m ohoeen. The ohennel m checked for oheer on both the In: nie end the '13! exie end found to be satisfactory. rho true: flee the lest member to be designed. The moments end reeotionl determined hr Gaetigliene I theorem were need to select a section modules or 15.99. Anflaobeam; *with'e eeetien.modnlue or 15.06 the selected to make up the 3‘31. bent e the calculations etc :11 eonteined in the engendtx. ‘Eerits or This Design This aluminum frame greenhouse has many advantages over the iron pipe end wooden frame houses. who most outstanding sdventege of this design is the great decrease in maintene shoe. The aluminum structure‘will need no painting. Palate ing s wooden greenhouse sorros more purposes then for Just looks.d Wood must be kept severed so it won’t dry out end rot and be e collecting pines for dirt. on big problem in the flower business is disease control. These disease orgen~ isms thrive in dirty pleeee end are harder to eliminate or fumigation it they have s plane to hide. to: these reasons e wooden greenhouse oust be well meinteined st e large cost. the aluminum framework will eliminate the yearly maintainsnoe and make the sloshing oonperetiveiy simple. wooden houses must have metal Joints and due to the high humidity required for flowers these Joints will rest quietly. The aluminum frame house will not rust either in seeeoestel areas or inland areas. Glass meinteinnnoe is also another large item in the greenhouse business. In addition to the regular repieee~ nests due to broken panes a greenhouse must be realezed about every ten.yeers. In the wooden Irene house this represents e his project. It eoneiste or removing the old glass. pulling out all the glazing neile, removing the old putty end then the whole prooedure.nust be repeated in reverse to repleee the glass. Approximately forty per cent or the reglesing time.ney he eeeed'with this new nluminum.design. Removing the old potty; which was emotions hard as rock, meant lots or ecraping and even shavings were removed from the wooden gluing hers trying to remove the petty. scraping and nail- ing are eliminated by the new aluminum glean clip which in spot welded to the aluminum ginning her. To remove glue simply push the clip in again“ the glazing bar and pick the glass out; to replace the glare push the clip in. insert the glass and let the 0111: spring back into place against the shoe. ‘ ., The aluminum design will allow no sagging or the root after any years an the present houses do unless they are rigidly ssinteined. A sagging root can be a large expense _ due to heat loan even though it may not be noticeable at the time. Glaze has a tendency to elip when the root cage and this is an added sorry during the bad weather months. i'he perfect greenhonee mid be one that had a roof entirely or glean so there would he no shadows inside what- soever. Since this is impossible, the next best thing is a house that will allow a minus: amount of sunlight tum. mus alaninun design mism- ens.- qualitioation. It '1. designed to hold glass that in twenty inohee square rather than the standard sixteen by eighteen inch alone. The elini~ nation or the interior super structure sill also reduce shadow area. Since sheds lines are kept to a minim the sun will penetrate the frost quicker and the winter eon is able to shine through longer. ‘ Inside the greenhouse space is very impel-tame.p this means that the bench arrangement nest be such that a maxim number my bat used. In the wooden homes bencharrangod mutt was rather limited. because of the intarior supports that were neoosaary. The“ aupporta are oliminatéd 1n the no: design and will allow any bench arrangement which would be the moat protitablo. A ploamt appaaring greenhouse is alums: a prerequisiu to ba successful in the flower business. The aluminum tram. greenhmmo would mun). this requmment to every want. the gable bent eliminates the need for any unsightly super», “mature. the aluminum will never rant 0:: requiro painting, we most important or all; it will look Just as good an: ton you: 01' carries an 1% did on the tint day. musim mm um insignia t3 amt": nth“ this by m w Aim .; M «1193* it s. gins swam tion is him i must mi. in can it is a summit may, the amiss in teams by this him 8. this tamper Mimtwn mm: ' its my hush”, aspirated was as by .- imam. ms whines! isms“). moths“ at wilting Wm m: 0.} W “lass, shim imam. the us if fist. ' I mu m. “mun ass annual swim are, and “min W m. inst. (a! tinnitus ”mum. whims. which mus» up“: my and but! that ”with mm. ‘ mu mt «1am» 1:in manual! in noon at a ”mainly sass alumnus. In maths:- mm is alien, this V j await an hut ”wuss; hut this viii hat to was int-i whims-1m hm. him as ii hisirnbis in an s must-1 with higher «um. summit m finiu‘bl. teas num- w. mm 52:: u mamas. m mm mum that am. ' sari difficult: a «mum rm mm in m m was, sad for on»! mitt it is imam is has tn“ as m min and In 011mm” m is £3.11“; with . i m at» its waning pm: in the amt-3i 'M its him;- Wm‘ in but was omm prmms amiss mm at m mu Mine; was and 1m in. museum. 1a «mums. am Mama it than: Saints am mm in: 1113:5310 as m an as mm: m in mm. imam iii-mm m In mom in any wines, am, that M“ of manuals and that guilty at tho «:3th joints at «33160301: tutti: than: the finding in portal-mid in tho :1» position. Wilding 1n the martini position is very difficult and mum to until-sly mount: 1: mama. Mutua- u'u tilde an to ma. with standard. I)...~ Gs ”ta—gonintar nit! ‘ and for welding; other utarlali. Propu- polarity my ti ditemlnod by trial on the joints to to undo. Approximate «mint sittings ind elutrodo am to; gelding various thlikniam m in” mile-i: tax on 0131131; inch thinning, a on iishth inih rod may hi and with appsonnstily slat: mums; a on. quarter inch wild would sisal" 3 thru autom- thi or one gm inch roast two hands-alumna: mm the am rods my to units: a on. half inch wild using a scant a: about truss hundred, amp-rah Commercial oliitmdsl with a hasty flux coating, its always and. The flu: outing has two pm‘DOflli to rim. that Mn” and. from thi fills: natal and tron the 9mm metal and.“ “still” and «arm. the m to tho and of tho doatrodi. Elwtmel my to attained made from «musician: pm aluminum or from in alloy sustaining ninityurin per «at aluminum ind tits par ”at liliimu hi silicon allay slut- rain I", usually as“; harms; a this ”out in gratis mm m making affinities. Tho pm llama clout- rMis would M and only am ”sari tumours sonioi soul-- “on: m twisted or to than a bitter uolo: mtoh with am if the alumina alloys. ' The preparation a: butt Join” for mom-m "lam is comparatively unplc. Boom“ or flu «is with whim pens- tntion m to obtained; no «a. preparation in new“ on material up to one quarter inch in thickness. Heatier materials should be partially beveled to within one quarter or an no of the bottom of the section. This preparation can sometime be dispensed with it the material it between one quarter and one half inch in thickness it e weld depoeit can be laid dun from both sides of the notion. Striking the are for this welding is very similar to lighting a match. The electrode metal melts very reridly in the are and; similarly; solidifie- quite rapidly when the are ie extinguished. In View at thie fact, it will be round that an attempt to draw the era by touching the rod to the work will, Ill-oat invariably, result in burning feet or freezing the rod to the cork. Artervctrikina the arc near the point where welding ie to etnrttthe are it brought to the starting point end welding is begun. During the first tee seconds or welding the arc my be somewhat unstable due to the lower temperature or the parent natal and during this time an no elightly longer than normal should be held to and et in bring—- ing the perent nothing: to temperature. The are should be kept as short as possible to improve its» stability. An ere length or one eighth to three eixteenthe or an inch is moot natiernctory and it should never exceed one quarter of en inch. 'me are voltage is from twenty-two to meaty-five volts. don. eiderahle molten notal is thrown about in the form or splatter it e 10:13 arc length is held. in are too short will be ex- tinguished frequently by short circuiting of the electrode and the weld p001. The rate or harm” of aluminum electrodes in from two to three times the rate obtained on the name size or eteel electrodes: furthermore. e considerably shorter are ie held when welding aluminum. In View of this fact an Operator who in familiar with arc welding of steel will require acne pract-o ice in order to produce good weld in aluminum. Weaving or the electrode is not necessary on in welding steel. In welding thick plate the electrode can be moved forward and backward or moved slowly from side to aide to build up the desired height in the weld. The low melting point of aluminum. on well an the him rate of diffusion or heat away from the Joint, requiree spee- ial consideration in chooeing the exact current setting to be used. Small parts or material which has been pre-heeted require considerably lower values or welding current than would be used in melting a similar weld on parts of large eiee or on cold material. It too high a value or current is need, the operator may find it impossible to keep from turning holee completely through the work. On the other hand... it too low a nice or welding current in need. incomplete penetration end e high and narrow head will be obtained. A good wound tonne» tion to the material being welded in very important. A poor ground connection 1will be indicated by difficulty in starting and maintaining the are. When the are in extinguished en in- eulating rune flux coating is termed over the tip or the elect-s rode eherply on the work. After this coating hoe cracked off. the are may be “struck. coins the hatch striking“ methods. In making multiapeee eelde it in important that the eolidii’icd flux be removed from eech welded heed before proa- ceoding with successive heads. Failure to remove this flux will result in welding difficulties and with anti-upped flu: in the welds. Wold Design Botm tho “out or wold noodod at oooh Joint out to determined it in nooooooxy to‘knmv uhioh load conditions will produoo o maxim wont. Thio woo dooidod by o trial; ond error nothod. A loading no pioood on tho otruoturo ond tho memento woro oomputod. It no team! that tho loud duo to wind oouood tho grootoot otrou. the moment duo to tho dood load woo nddod to that oouood by the rind load and the lumen moment no titty-4‘8 thouound toot pounds in Jointo “b" and “d", tho Jointo who" tho root Joino tho vor- tiool mambo: at the trm. By this “no method tho maximu- otonant at tho pooh Joint ooo round to be oixty-ono thousand root poms. Tho void ot Joint 'b" no the first to ho oohoidorod. A oomph“ butt wold botioon tho Mignod mambo: and tho vortiooi no undo ond tho root or the otronsth no providod by a oovor ploto on both the top and the bottom of tho Hugo. Tho butt wold would mist o moat or floaty-too thouoond toot pm; thoroforo. this loft thixty thousand to 5. man by tho oovor piotoo. A width or tivo inohoo woo arbitrarily ooiootod and ortor finding the moot of inortio of tho ploto, o thiokuooo or one-hon inch Ill round to to satisfactory. Tho voluo per inch or o m: inoh wold io too thousond tour hundrod and oovonty pounno. With o plate otrooo or sixty thousand pounds. county-tour inohoo of weld uro noodod to provont to iluro. Hanover. toonty-oight inohoo woo providod for o margin 0: oototy. Rina inohoo or pinto with o throo inch “Y” notch m uood on oooh oido of tho Joint. nu will. provide a rigid connection for each or the lower joints and yet it is not too ccneerietive. Since the Joint at the peak has a larger maximum moment it will require a thicker plate and.more weld area. The butt ‘weld between the two‘B-aecticns will take twenty-two thousand toot pounde on before, leaving almost forty thousand to be taken by the plate. By the cane method of calculation a five eighths inch plate wee round to be necessary. A five eightho inch weld with e value or three thousand pounds per inch of 'weld one used. With a plate tension of seventy-eight thousand pounds it is shown that about twenty-rive inches of weld were necessary. he before, twenty-eight inches one provided. A five eighthe inch plate, nine inches long, with o four inch '1‘ slot one used. A'wolded connection.oee also used for the column anchor- age. The maximum moment that e nix inch H-eection can resist ‘uae chosen on the design limit for this connection. This moment wee round to be two hundred.end eleven thousand inch pounde.. Tho ciao or bolt necessary wee tiret determined by finding the bolt otrees conned by this moment. The nine bolt necessary wee_e one and one-half inch stool bolt. The bolts 'will be anchored in the concrete at the time or pouring. allowing about twelve inches to protrude above the surface of the concrete. ‘Hext the size weld desired must be chosen. A three eighthe inch weld one chosen with e value or less than ninteen hundred pounds per inch of weld. With this value and tholmexinum bolt stress or ninteon hundred pounds, e little over five inches of weld were required. This value must to checked for sheer from direct pull and shear from flexurs and also the resultant shear on the throat of the weld. It was not found to be sufficient therefore a length of ten inches was chosen and found to stay within the limiting stress. A four by four by three-eighths inch angle was chosen to complete the connection. It was checked and found to be sufficient to take the stress. The angles must be ten inches high in order to provide the necessary weld area. Computations and sketches are contained in the appendix. An estimate was made on.the electrode consumption for the construction of this greenhouse. There were about fifty- four pounds of three eighth: inch electrodes necessary for the eighteen butt welds. There are about forty zest of three eighths inch fillet weld in.the column anchorage. This will require about forty-two pounds of electrodes. In the cover plate welds st Joints ”t” and "d" there are about one hundred and twelve feet of one-hslf inch'weld but three passes are necessary. therefore, the requirement here is about one hund- red seventeen pounds. The tsp cover plate needs four passes to fill the five eighths inch fillet weld and since there are fiftywsix feet of sold it will take almost ninety pounds of electrodes. These figures will give the prospective builder e rough estimate of the amount of each size electrode necessary for the construction of this greenhouse. Bibliography: WfiRigtd Frames-- - ----a--A. Miriam Graphic: Stgtics x- - - ~ .. - - - ~ - Charlésfi. Malcolm Stating: Indeterminata Stmcgureg ~ - - L. C. may: WQdigg and 2 razine‘ Alcoa Aluminum .. - - - - - - - 191.5 App. nu: ‘ N- 7’“-.._.-<‘.._,... *.«.- .4]. ‘ . . . .11! I. ../r I ,1 . / . // I /v . A // V :O\\UV./J \RKCUK) .. , meOQ t wwkw w E UKIK oibtztg T kOub QOKJNGJ WmOxU \GU.\Q\\\N| u\ .BQ mwx‘..wc\,3 CQQOuWJ NW C ‘ l2.65' D #7? ———.—- 8 ‘1} :21. A i T1 M. Va H av“ 17.65” a T MC MC Va V“ fva [765- HQ 5419+...) Mb Md pvt—— T “ We. Md m 5'HQ 1765'”; b : H ‘___/7.65‘Ha 0* Me vMa q?“ 5o/u 71.00 Ar Nome/773‘ If“? GaK/e 5077‘ la' a}: /6 j, imp/Ft WY JZLIJHI , l265 ' X. / 1 ‘jL ”#7 A Y 7:77 5:? I cons‘l'an'r __ = 5525)" ”3251224) ‘ [2.5 ,_ 249:! x 9 I y 21.0 - no .69 A:/O*44‘54 1‘2’ Load: % 5. ‘I‘J-izjéLflz'lISB . 11 =5(Isz):§J£._ H . —|938 '62 [K I,” = 2[,~'é(5)’15(7.14)‘+7g (22)(12.45)2+22(/.635)‘] -.- 21:10.4! +258.4 + 293.4 1 58.6] = /242 Iy-, = 2[§/‘(22){/8}27‘5{/6J2] = 2[237€ H620] -' 7332 M” = (~//aa)(-/. 53) + (new/“z a) Mr, =(-//aa)//15) fK-a/oMZ/sJ = /a/a r 5820 -' 7638 ‘/6a407‘5c720= 3062.0 A B L017 v?“ Mx,='Maf//O.X - 2 1"—H°‘5 aM- _/ aMa' aM . .._.._Hq am.‘ x 1"“ Va 0 M6 : Ma "' 5117/0. 7"/2..5 c» 3 a: 9‘ BC A 5Ha§ 7“ ”bl V0. Mn = ”M5 '(5-IA/(575 x)'t€ (8/8X2’KS75X)1(21M/ Mn “/7. +5/%'/2.5-2.87JX7‘.575%xza/azx 1/55 x2 dMXa __ am. - aMXz 3H; ‘ 5t57JX 6M3; Tn. ‘ 18/6X Me ‘ Ma. 77.65/74. 1- mm 1- ”165 “Vi/£1 c D m 43 Huh/146-14 x,(a/a)+/zé5- a)(.575)(3) \7/ ”(Mb/245M, -/ol/¢ 755.65 -. 6/8 VaX; +/a/5 X, -. 575 ”EX! =7% 1‘0. 656/. 4514 455.55 26/8 M» X: r /o. 15X, -. 575 flax; 3M1” BMa'-/ 3M!) 3H0 : [7.651575X3 aMx: _ '3 Va " '/3’.6/8X3 Md " Ma'Vz 6.5/4 H014 #55245 Ham‘zez/ Haas/h : Ma. “5/110. 1‘ 36%. “67.45 DE fiyva T T Mu ‘ 'Md fK/zas-fl.l(x4) [265' (1 x4 -‘ 7%, *5/24 7‘14 “7.45 +07. cJ-fl.) x. ._L -- . - Ma r554 16%. f6245f/265X4 - 5’. X4 am; _ 3M0 "’ aMu aha ’5'X4 a MX4 M‘a’ U ‘ f 251x MOM: d ”3% A Mil/2m; W: ¢ (17¢ (jg/T df/a flE—f 00‘ 0% f E] 0" Gin/.2757) E] .15! .. _ 5 , a’l‘fa— o'.[('Ma "I‘I’ax ' '5' )("/)0/x +f(-Mu5ha- -./25 a2375x+.-575Mx a/an -/65X‘/(‘//0’X 22 "jo‘ (‘Ma r17. “flu/6V4 “/5165? 6/6 16.x: f/o./5x3-. 57Jfiéx3){-IJ)1.1/1-€'/ 1:10.:f1C/1 23.3 230 “5 1 111111 1 v 1 -1 1 -_ 1 ‘1’ L——-} kjl'Per .. [1”.-- .. -_- -. ”—1 . ,,, -_ ~ .-- .-..--._..._..~Jr-_—. DIO"/1’.l/H ———l _ 3/ _—_L—__L____1-920 I f“ ' - - (j £3 /“ OJ!” }" ’I k; \ ’9‘] i- . f - . - ~o— /. i J // I x: /1. 1‘ hr--- 013 17/9/11 "I '1 , _ O A /#-' __ .//# /1.’f1/(. (Ala/.11. ‘ 4/1JC1 * 41,}2/3" ‘7' _ /1>’1 ‘4' 92) 1’“) — —: = M = 4.92 \/ /O/0;J'~D.7 ’ r l‘ ' 1 n -. . 7 " r / / I / J (9 x ,6 0:4 C/111/.:2/ 2;. " 1/ Of; / 1: X'X : /5o /gq Z7./ 9 L ?7 ”\ Of 1-)“ 2./15 '3 C _ J4:- : —;.€...;......--....-4; 4/5 ' 71‘ A ‘32” X , 64‘ - vx-x ’ :0 15.12:.31 1" : . 7'1"; I‘J 1‘1 far). f/iz‘. C/Td/J/M/ 1'5 {.119- 02519-17 025 7'22 jecf/on CAP/1501771 [Odd = 4.5x/7Cf 2 Max + 1/70/11. 3 .077W/ 2 ”lax " 1770/77. ‘ ./07 W/ Max She-91’ ; .607111/ Max. Mom. = .107 11.13 = 13.6 " VQ - 1.35 1' 119.1. 5 - I b - 1269‘ #53 530,081 T/Wre/‘ore 7‘1‘12 52,-:7100 13’ s- Ci“ .0.56“/.:T,- dead 160d L1 1 1 11.11.111.111 .1. 1....11-.-._1--1-1..--1..-1.._1:..-1.--L_1_‘J /"c {2 b \ d 03 .. _ a K .. 2 “[06K LML’E : ,45 /+‘f «LOGK 1.5.5A 1 K ‘1’ 1‘ LL® : 21/8K/ffi L55 2.68 1 269" £113} = 3. 2 “/16. G/CLSS '-' 600fl/7‘ru55 7ee'Sz'cf= /36#/7“r(.153 3f . Che/1nd: .300 /7'r¢153 1/7“ baa/'11 ‘ 463“ 2M5 : 2-68‘(5'/105) : 2.63M 0/912 7:) 0/1200! /oadl 2: Me = (/06"/765)+K086*/3*9)‘2.éé-0.55 1/8)“2"r 25.1: ‘ ' (2.3365) +/4.12~5)+4.75 +202 4511 0.45) -2.62 52m Max. Mom. due To ML."'D./.. 2 M0 = (2.33 ‘/765)+/4./2 ~1765)+4. 75 + 20.2‘17765",45*8.82) — 2.62 = 6/. 33"- due 70 1'11. +0.1. 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