The Economical Spacing of Roof Trusses Citation Wong, David Yue-Kwong (1933) The Economical Spacing of Roof Trusses. Master's thesis, California Institute of Technology. doi:10.7907/hyhf-hy15. https://resolver.caltech.edu/CaltechTHESIS:10112024-180914262 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: (Civil Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Civil Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1933 Record Number: CaltechTHESIS:10112024-180914262 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:10112024-180914262 DOI: 10.7907/hyhf-hy15 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16789 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 17 Oct 2024 18:29 Last Modified: 17 Oct 2024 18:39 Thesis Files PDF - Final Version See Usage Policy. 8MB Repository Staff Only: item control page

THE ~ NOMIOAL SPACING OF ROOF '11RUS$ES The.eta hy David Yue-Kwo»g Weng .l a J?@tia:l F-ulf'illmtmt of the Reqµirements foi- tlle D.a gree of M.a.ater, Qf S-ci~ OAL_IFOHNIA INSTITUTE OF 'l'ECBNOLOOY Pasad.~,1. California 1. lntrodue.t i.o n. Truea: Dlag:ram. 1...2 , .a•. Dis.eu:a_ai:on 4-9- ~. Results <,f U(lSign 10-.16 4.•. Dise.usaion, of Re-.s ulta 11-~ I!i'.TRODUaTION The eeonomical spacing of' roof truss-es is usually affected by a great deal of factors that it has been quite imposaible to develop a theoretieal formula giving the exact spacing for diff erent spans. Howeve,r ,. ae a common practice and :from the expe.r ienoea of different engineers, the spacing of roof truasea usually varies from about }§ of the span for shorter trusses to about~ o:f the span for the longer trusses. The object of this problem has been, therefore, to try to eonf'irm the at9.tement above by actually designing trusses of different spa ns at clifferent epaoings, and to eae wh£>.t are the factors which enter into thi s question of economical spacing of roof truasea. In so doing,. the author tried as much as possible to keep everything constant except the span and spacing. The type of truss used by the a~~r was the Fink steel truss with a pitch of 1/4 as ahown in Fig. 1. The roof covering O'O naisted of corrugated steel supported on purlins. The specifications of' the A.I.s.o. design of the members. we.r e used to govern the Three different spans were tried at 4o feet. 60 feet. and 100 feet. The apacinge ueed were aa follows.: (1) For 40 1 span, spacing at 8 1 • 1/5 p.n 10 1 • 1/4 span 121 • ,110 apan 15 1 • -,/a span ( 2) For 60 1 span, apaeing at- 10 1 • 1/6 span 12 1 • l/5 apan 15" • 1/4 span 18 1 • }/10 span 20' • 1/j span 22.5 1 • ;/8 span (;) For 100• a.pan apaoing at 15 1 •ID 1/6.6 apan 20 1 • 1/5 span 25' = 1/4 span ~o• ... 1/;.5 span 1 A/ V V D1AGR.AM Fi 1· 1 TR.USS .Spa Y\ == i s y v I ~ " v :l:: _l_ Cl.. -4: -\st- T I ~ DISCUSSION. In the diacuasion given in Hood and Johnson"" s "Hand• • book o-£ Building Construct.ion", Vol. 1,, the theoretical spacing of truaaes for lea st total coat of trusses, purlina, and roo.f' e·o verning dapenda upon the relative cost of the component parts. Let X ..,:· tota l eost of' oonatruoti.on per 8'UB,re foot of roof., ( l) for truse~ t 11,l cost of truss per square foot. of roof. k • constant a-• spacing k t•~· {2) for purliru p = cost of purlin per square foot of roof. n ·• constant. (;5) for roof eoveringt o = coat o.f roofing per a'!l,lal'e foot of' roof m • eousta.nt. then k 2 X•t+p+o•-+mt 8 +ms To obtain the minimum unit cost, with respect to diff erent spacings,, multiplying bys According to the equation above then, for the lea st coat# the spacing of trusses must be such that the above equation be aat.iaf'ied. Hood and Johnson mentioned#' however, that the relation gi.tten a bove can not b.e ueed di:reot.ly for the determination of the trusa spacing because the spacing does not appear in the equation. A.fter designing t he 14 t.ruaaeal the auth-01· has made a study of the dif:fer-ent factors which are involved in the determination of the va lue for t# p.,. and th The-ee factors as found ae~ed to vary a great deal With respect to local eondit_iona and requirerne.l'.l:t.s,,, and t-o the time when and plaoe where the structure is -to be built.• The oo,at of steel structure,s. mey be divided into: ( l) eost of material (2) cost of fabrication ( 5) coat of erection• and ( 4) co.a t o-f transportation. Under theae items there are the ooat of drafting, mill details., shop l abor, placing, bolting, hauling" f'alsework,, ete. In ord• to make a simple inv.-estiga-tion,, the. :J.utho.r has neglected the minor costs and chosen the follmti.ng onea to find t, p, and o.. A. t• the coat c:i,f trna.s per .s quare foot of roof is m.ad'6 up of': 1. -co-at of material of trus:e. at 1.5 '/lb0 a. c,o st of shop labor~ table l 0.55 - 1.1 ¢/lb at. o.~ I/lb Total• 2.41,//lb t.o 2.95 ¢/lb- B. Pa the coat, of p-urlin per aqua.re :f'oot of roof is made up ofs 1. e.oat. of mat.a,rial-I beams and channels '" ~o 15n at 1 .45 ,Vu, •• cost of layi1~g-punchi.ng holes and erection o. o, the cost of roof'ing per a.qua.re foot Q:f roof ia made up of at 2.0 -/lb 2. eoet of laying at 0.9 - 1.49 ¢/lb total • 2.9 p/lb to ;.49 ~/ lb These values were obtained from M. s. Ketehum 1 a 11 Struetural O· Engineer t .s Hand hook3-.- The o.oa.t of' sh.op lab.or wae ca.l cula.ted for th@ atrue•t u.re as a whole . The following c•oats are haood 011. an a ve:1·age. charge of 40,i per hour , and include d-etailing and ahopwork. In lot.a o.f a.t least six,, the shop coat of o.i•.d inary ri vet~d roof t-rusae.a in vt.1-iioh the enda of the members are eut, • off at right angles is a bout as :f'ollowa.s Total weight of truss 1, 000 # Coat in cents per pound. 1.15 - 1.25 i 1.;500 0 .90 - 1 . 00 , . 2, 500 0. 75 - o..85 ~ :5,500 - 7,500 0 . 60 - 0.75. d. The values. in Table I were obtained fro:n the above figures The cost of erection include.a the ¢Ost of placing and bolting and was obtained from the f ol:towl,.,g figures: ( 40 ¢/hour basia) . Kind O;f stru.ctur:e Coat of erection. in dollara/ton Mill building f'o:r 01~dinary condition $6 .. 00 - iB.00 St.eel office builcliP.g $5. 00 - $9.00 Steel buw i 10.oo - $15. oo Iiead fra.rues. $12. 00 - $18. 00 For this particular prob.lem t,he author chose the value of $7 . 00/ton for the coat of erection. See Table I , on t,he following page.• This amount.a to 0.;55,i/lb. - 9- Table I. Values o:f t ( t == the unit cos t o:f truss :per :pound) Total S:pacine ,rt . of trn.ss Cost of Cost of Uost o:f Labor Mat eria J;lJre-c,, .:;, O"l t .1I, 1 in ¢/ #- in ¢ / ti- in e.:,, 1r SJ?ru:1. ¢/if fj ¢ / 1~ ¢ / 1·~ ¢ / If- s• 1290 1 .1 1. 5 o . 35 10'' 1290 1.1 ti " 12• 13(,6 u n ll 2 . 95 15 ' 1 393 ti u ii 2 . 95 10 1 2250 C. 85 11 n 12• 2273 0 . 85 II ;i 15 1 251 3 u H 2 •.95rth· 2 . 95 40 ' 2 .70 2 . 70 18 ' 26~~ 5 o.ao o.so 20 1 3202 0 .75 22 . 5 1 34,lo 0 . 75 15• 6219 6,.70 20 1 7318 0.60 u n 25' 92·16 o.55 II u 2. 40 30• 10295 o.5 5 II H 2 . 40 2 . 65 GO' u II .. ,. .., .. ii n u 2 . 65 2.GO 2.60 100 1 2 . 55 2 . 45 Results o:t Design . -10- RESULT The result of the d.e aign as shown in the ta.b lea below showed the economical spacings as follows: Span Eeonomiea,1 spacing = 1/4 $pan 4o.• 10 1 601 12 1 !Cl, 1/5 span 100 1 15 1 ~ 1/6. 6 a.pan Accept.a bl& Eeo.n omic spacing. 12' i:a, 5/10 span 10• - 1/6 span 20 1 ·= 1/5 .s pan Table I .I . Weight of Tru.sses 40 1 --s:pan S'spa.c. 1ofial '1'-'>nPU of pt'eces 10 1 wt.in # wt.in # 12• 15' ••il wt. 1n 1r wt. in rr ~ Chord mem t>ers: 1-5 41! Ctb 2z.r 369.00 369,00 442.00 442.00 l • 'l 41! <!) 13. 0' 166.00 166.00 166.00 1 66;00 7-7' 2t_s -(3) 1.i-:O' 95.50 95. 50 95.50 95;60 2-6, 4-8 4/J ~ ,t__ 7' 3.7 1 I._S @ .s: 3 34-.50 34 .50 34 .50 34 .50 52.00 52. 00 52, 00 52,00 3-8, 3-6 41._s ~ .s·. 1' 75 .20 75.20 75.20 75.20 4£! 6) /.!. (}I 153.00 153.00 153,.00 153.00 7. o' 28.70 28.70 28 •.70 28.VO 9 74 . 00# 974. 0 011° 1047,00# 1047. 00#' 67. 40 67. 40 67. 40 90. 00 ..... 12 ..00 12.00 12 •.80 12 .80 - 40.80 40.80. 40.80 40.80 - 57.50 57.50 60.00 64.50 - 1.7. 90 17.. 90 17.90 17.90 20. 40 20.40 20.40 20. 40 100.00 100 .00 100 .00 100 .00 Total con a.ectiam: 316 .00# 316.00 #= 319.30 11' 3 46 . 40 # Total :r-ru :3S Weight 1290.001;: 1290. 00tf 1366 .30# 1393.oo,i- 1 5-7 Sag tie (-< @> W,e ight o f members: eo:nne·e tton •Factor: Foint l u z JtASTef f/s . A. 2 ,- 1 n 3 2. tf 5 I 1Y 6.8 4 n 7 1 5AaeL V " w ~ . ~ she p/4-f,o_,' r, YGJ1s efc . -12- Table III. Weight of' ·Truss-es 60"'-spau .10• 12• 15' wt. fh Wi. tn t,vf ,;/( :# fh -it 18 1 20' 22.5' t,,vf. ,;, If wr-. 1325,.0 1528.0 1580.0 th II tv#IM Member: ~·•• ·. 1-5 4Z..S ::.974.0 2- 974.0-~ Ulo.o 1-T 41..s Z44.,0 ~46.0 282.0 354~0 ' 388.0 4.88 •.0 7.7'' i:_ (S 120.0 120.0 126.0 136 •.0 184 • .5 :\04.5 2~,~..Jl 4!! 1 L_s 58.0 58 • .0 58.o 58.0 58 .0 58.0 144.0 144 .. 0 144 •.,0 144 ...0 144.0 1A4.0 3.a, .3, ~6 4/J 115.,0 115 •.0 11.5,.0 115erP 115 .• 0 ~15.0 5-V 4-4 227 •.0 227.0 227.0 227.0 227.0 227.0 Sag tiE I<- 45.3 45,.3 45..,3 45.3 45.3 45.3 3 ..,7 Weight o,f memt t927.3 I 1929.3 2117 •.3 '?404 .3 2689 ·.3 2841.8 Fc:tcfar .' C' 0'1 necfio>1 Jt. l. 63 •.8 76.4 112.0 112.0 153.0 168 •.0 n 2 t!l: 13.7 .13.7 16.7 16.3 16 •.3 18.4 ft 3 36 •.7 .36.7 36.7 40_.o 40.0 .58.0 ff 5 57.2 64.5 72.6 83 •.0 . 99.0 108.6 ns 8 20 •.4 20. 4 20.4 20.4 20.4 . 2'1.2 7 27.6 27.6 33.0 33.0 36.7 46.0 104.6 104.6 104.o 125.8 146.6 148.3 322.0 344.0 395.0 420.5 512.0 574.4 ' u s./i.,e I., .!,l·· U•· , • :,~,, •?/. , r,'ypJ'i etc-. -.P - Col'lll . ractor . .- l,'i,ljaJ. I 'I;/-,;;;, 0 :rrUf s ,. :2}24 't. 0 ff' # 2273.0~ ~513.0.ff 2625 .. 0 . 3202.0#' 3416 .. 0~ Tab1e IV• Weight o~ Trusses 100•.span 15' 20' · ·2 5 ' 30'.. in fr wt. 1n 1/' wt. in '1P wt. in tr 2925 .00 3830 . 00 5400.00 6040.00 1-7 906.00 9'18.00 1252.00 1551. 00 7-'l' 539 •.00 539.0 0 539.00 576.00 2-6.4-8 200.00 200.00 200.00 200. 00 3-7 416. 00 416.00 416,.00 416.00 3-8.3-6 426.00 426.00 426.00 426.00 5-7 100.00 100 .00 1 or: . oo 100 .00 Sag tie 176.00 1'16.00 176.00 176.00 \'It . of mer 1ber s 5688 •.00;;,( 6665.0 ~ 8509 .oo :tt 9485.oo.it Joint 1 lVl,.,OO 151,00 181.00 186.00 " 2.4 40. 80 40.80 40.80 40.80 " 3 84.oo 84. 00 84.00 84.00 n 5 97.50 121.50 153.00 191.00 ft 6 8 32.60 32.60 32.60 32.GO II y 33.60 33.60 33.60 ,t 3.OO 17'7.60 1 £0 .• 00 212.00 232.40 603.10-# 6 53.40 :11 737.00:ft so9.aot 6291.00-f 7318.40~ 92t16 .00 if 10,294.0<J wt. Members:, 1-5· ,, - Connection Fac t or,: ivt. • o:r Oi ~nn. J!'acto ra Total Vlt. o:r Truss -14- Table VIII. Comparison of Cost 4o' .. span cost per ~-rt.per unit sq.ft. cost #- ¢/ # ., Roofn, . 1\,v<I,~ __ 2.46 1 ...64 \.'w,, 2:p 2p -t C sq,..f't. ¢ 3. 49 a.Go 1~80 2.95 t Spacing ¢ 5. 90 14.5 11.9 s•· 'l.78 16.38 9.5 lt' - 11.-90 4 e03 2.95 Cost per s CJ. • :ft . o1 roof~ Z3.45' 3.49 8.60 'P"'r I,;,, - '-- 2 .16 1.80 3.89 RO •11 YI,- -2. 4 6 '' w , 1_ _ - 3.2 2 2.95 9.50 / True a of Cost l)er s q .ft.-o:f roof= z1.q 9v £co,.,;;,n-r 'ca. I Spa -my loofi"' .. --2. 46 1 "PIA.r / ,·n .. 3. 4, 9 8.60 -.3.00 · < l;l •.80 .5,.,.40 2 .95 8 .. 38 ,, I,() ,, Cost 2.84 10.ao l.9 .. 4 a . -38 ·<12' 14 . 40 23.00 5.- B5 '.I1rua: :per -~lq.ft. ( :r roof 22.36 (tf:' Roof i"' 1---2. 4 6 3. ,19 "Pl,\f ,,;,., .. ,! - 4 .. 00 l-0 ,~ ~ - .... 2. 32 8.60 .. 1.so 7.20 2 . 95 6.85 Cost i •:f Tru.s: per :hq .ft. cf roof t:.zz_t,S- 15 1 -15- Table IX. Comparison of' Co s t 60 '-spa.n ... tvt ;per unit cost Sp%- sq. f' t. cost il:J.g 1,1: (/ / 'ff. sq..-:ft., . 46 3 . 49 8 . 60 ¢ 2. 28 1.80 4 . 10 R.~,&fr'>11 • 'PIA 1 f I;,, • • 10 1• 2 per 2:p 2p s . 20 1 6 . 80 10 .12 11.10 1 9 ,. '70 ' 8 , 54 C t . ,, w ' ~ - 3 .75 2 .70 10.12 Gost Tru.s~ per S\ • ft . otr ro df = 22. .82 ,C ~ R.otif""\1. 2.,4 6 3.49 8 .60 1,;, - -3 . 08 1. 80 5 . 55 w 2 .70 8 . 54 Pl,tr 12 ' ,, Cost olf - fj•~<tao:i 1 5• TU'.\"P '/ 3 .16 - ? +. _ n 1-P CH'l , 'Pl\ri-f' .: z.( . (;, q \,,, v/:cono 'rJ?tc al .Sp, C 1'rz r R••fi'o'l1 -2. 4 6 3 . 49 8 . 60 - 4 .,00 1.80 7.20 .2.ao 2-.65 7.4 2 'P1,1.r/1~ ,J test ot ,, w - : '. 1 4 . ~10 23.00 7 ~4,2 18 . 00 26 . 60 6~45 22 .• 00 30.60 6.94 26,.50 3 5 .10 6 . 58 'J'russ IDer sq .. ft .. o:f roof' =2.3 .2Z. 18' Ro o(,'ri1 2. 4 6 3 . 49 8 . 60 P'-1.r ,,~ - 5 . 00 1 .80 9. oo 2 .. 43 2 ,. 65 'Pu 1,;,, •. 6 .12 L ,80 i.l .•.0 0 2 .• 60 6,. 94 ,, ,, l..v 6. 4 5 ~rru.ss per s ~ • ft . olf ·roof' =z4.<'.1~3,.49 8 . 60 Qd•f 1·. 2 .. 46 Cos t 0~ i';\ 20 • cl ,, w 2 ,. 5'7 coa t olr :i.russ per s g . 1·t .. ~ ~l_:;-4 1· 2 . 4 6 3,. 49 8 .60 '{)(.(.,-1,;,, •.. 7,. 36 l ,. 80 1 3 .• 25 {<_ddfn 2 t2 • 5 I ,1 ,, lA., 2,. 53 2 . 60 6 . 58 ~os-t of i'russ per sq. :rt . ~8-43 ·- -16- fable L Comparis-on o:f' Cost 100"-spa.n Spae• ing Cost ( f 'rrtlSf. wt. peJ unit cost sq.ft. eost per # ¢l# sq.ft. 3.36# 2.90¢ 9.'15¢ 3.67 1.so 6.60 4.20 2.55 10.vo 2:p 2p e t 13 .• 2 22.95 10.10 per 8( • ft. .( f roof=- Z 7. o:;- \V Ecor, •.r.>11c.,.I .,5 lbact'nJ 3.36 2.90 9.75 4.90 1.80 8.82 17.64 2V.39 8.95 21.60 31.35 8.85 31.08 40.83 8.25 3.65 2.45 8.95 Cost c:f' Truss per s~. ft. cf roofs 17. j-z 3.36 2.90 9.,5 6.00 1.so 10.80 3.69 2.40 8.85 Cost cf 1'rusE per S( • ft. Cf' roof- 29_40 3.36 2.90 8.64 1.80 15.54 3.,44 2.40 9.'15 s.•25 Cost cf Trust per S(_l • ft. (l~ roof, 3 3 .s1- Discussion. 0£ Results . -17- D,lSOUSSIOM _OF BJSSUl.TS . Mr. M. • s. Ketchum in his' ttstruotural Engineer•11, Handbooktt stated that he tried thi.a problan of economical .apaeing for a 60 1 a.pan and fo.und ·that the least weight waa at a spacing of 10'. The aut..hoi~' a re-ault show'8d that this valu-e was the aecon-d value for the- eoon-cxnical apacing of a 60 1 .s pan trusa. Aa it can be noted f'ra:n. Ta.bl-es Vlll> IX,, and X. the results did not check With the thaoretk-al condition in the formula t • 2.p + e by Hood and Johnson. The estimated value of c wae much too great to give the value of 2p -1- ea much larger value than that .o ft. But in every case except the 60 1 span,. the economioal spacing oceurred when t '7 2p, having a surplus for the value of C• However~ c waa kept a constant value and thus did not affect the equations to give a different economical spacing. \7e can say then in this parti-eular case that the -e co:1omioal spa cing of truaae.a oocurs when the value of 2:p ia juBt less than the value of 't. Besides the di.f 'ferent factor.a affecting the coat. of the structure,; there iJ..re minor factors in the design of the component parts themselves. Roof covering eoats vary with the nature -18- of the covering. In the design 0£ purline and members of the truss, if 1t were possible to obtain rolled aec.tiona which would provide e.:xaet.ly the required area.a for all members,. the result of the- problem would have come out t10r.e accurate. But aa could be ee.en from the designs above, the sizes of many membera. were determined by -the apeoifioati-one andyby the requirements of' standard praotica• and For the web members such as 2-6• 4-a. 5-,,6., ,-a. the designed members provided muoh larger areas than were required. The author the-refore ma.de a study of this factor# which he called "speeification .factorfl. He picked the members which were aff•e eted by it;J the percentage weight of these members to t he total weight of the whole trues is tabulated in the following table-a s T!:iblee XI, XII"' and XIII. These tables also give the percentage of the "Ooimection F'actor", which includes the weight of' connection plates,,- shoe plates, et.a . 11 The sum of the nspeoification Faotor 11 and the 0011:neetion Faotortt thecrefore give:e the percentage in the roof construction that is fixed by apeeif'icationa and standard practice. Subtracting the above sum from 100~ gives the percent.age that the designer has a right to vary the sizes and forms of the members. The relationship between these percentages is shown 1n 'l'able XIV. As can he seen, the values of the 1 Spooification Factor• varies with the spacing, decreasing aa the spacing is- -19- increased. The aoonna.etion F'a.ctortt seemed to be qL1ite a constant. percentage ranging froou 2;.1i% - 25,. 7% for 40 1 spa.n truaa 14.,% - 16.8% for 60 1 span truaa 7~88% - 9 .6% for 100 1 span t l'Uas,. -20- Table s below give val.ues o:f the "Specification lfactor 11 and the"Connection li'actoru in percentage o:f the Total Weight of Truss. Table XI. 40 '-sl)an 8' 15 4 12.' lO' wt. o/;) 12. 9o.:tt I 007o \ 1..10~ f 00 Spec. ]'actor ss-3 12..8 ~--;r3 42. .J' 5'.r3 46 ..f s.r3 Conn. Factor 3 I (p 1.-s.7 L~-- ( ~,j 2 3. wt,. }'b Weight of Tru~ iS '3 \ lo Table XII -. wt. % Jo ( 3 (p'tf- I oo J'o I 3 'f 3# I Od ./o Truss wt. 31-7 1 34{, . 24_g wt. ,. 20' wt. 'fo vrt. % , .., wt. / tJ ,4 I ~ . ,;),1 8·,i, ' / 1 - 22.5 1 . . wt . % ,/4 2.273+ //JO /4 2.. ..qJ I oaJo i...1,,1.s* too 7o 32°1-# I Dd /4 ~ 1-1<.* /00 /4 jt- 1.1..'fi* JOO - Spec. Fa.etc r Conn .. Fae. 15 12' wt. % ' 60'-spe.n •• 10' }"i> 1r1 t , qs-3 42.1- f:i'3 42.0 322 14. 'J 344 (S. • Table XIII. s-~1 .u.5 n"j .2.i.. r .s--s-, I&= . 1 3 <.,2. ,o., I 3H, ,s.¥ S74 100 • -span 20' '1 5' I G, _o 1i.o Sl 2. 420 26' 30' ro wt. ? <jo wt. l 2. 1I I DO /o 73(¥ I ~o Jo 'P. %:ff I Oo Jo :i.-7<c,3 4t.o ('i-~-7 i.r .4 I~ l r 1-f,H &-a 2 7. 't Conn. Factor G,03 q. ~ (..s-3 S: .13 7.c,7 S-/0 7. f.-8' v-.rt. 'l'russ ·wt. .:#- s :pee. Fae. :-41 <ftJ \Vt. 137 10 21! / Dd ;o I (p _8 -21- I C cr I ' " ' ,Q ,.~ ·II'\ ~ v V) 'o 0 ---t m,. " ' '" lflll l Ill " ~ .C , Q_ ... Q N ' (5 ~ f/) ~ '" r, "' I... 't--~ ., <I (\j - cs ~ a.. ~ 0 ~ V) '° r I ,.,, II 1111 C\J I f ,til l '" \J ~ ~ ...... ~ I C II ~ -~ ~ '½ -~ ~ -.,:::_ ~ <..., ~ <u IJ"I:: I::: v ~ 0 ~ " (..J ~ II ,I) ' ,, " 1111 ~ . (" ' 6188&1!1 <:) ' ~ \.. "" '(' ~\.) -~ ~ ~ ~ ,;: ...... :..::: ~ ~ 0 ,, I,,, ~ ~ {} ' 0 I 1111 • ...... ".J ...... I'" I ·o I II ' ~ 11, 11111 I II I" 1111 '>' '\.-, co Cl"') C 0 ~ CL V) .s .v ~ V ~ ~ ~ ... ~ . .C ~ Vl \\ \ 1\r 111 I11/ i/1,jj .d.., 0 z In the calcuh tion of e.treBae.a,,: w was obtained using Hmve' a formula: W• _ ___._...,_ pL _ __ 150 + 5L + pa/5 there are.,. however, dif ferent formulas to determine the value of w. Among them are the following ones taken fr001 the discussion of .Mr. n . Fleming on »weight of' steel R0of' 'l ':russes by Empirical L • span P . = loadinr.:,:, of truss in aq,. ft. lbhori z . area Qambria. Steel oo., for spans of 75 1 or least Carnegie Steel co.. , 19J.7, for loads of 40/} or more per a q. f't. w• P l r. L 40 • 5 (r L -t 8) Fowler,. 1909, for F'ink tru,;iJes up t..o 200 1 span w .., 0.10· L + o.6 for heavy loads w• o. o4• L -;- o•.M for light loads -24- Johnson, Bryan, and Turnea.ure w- L 25 .. 4.o Jones and Laughlin" 1916 Ket.chum, 1916 Merriman, 1911 L 'l' • ¾Ls( 1 -t- m) Ricker, 1912 L L 2 w :ill 25 ... 12,600 -25- The values calculated for these different trus ses are shown in Table XV on the :f'ollowing page:. The auth or h aa taken owt Howes'• Jones and Laughlins'$; and Ketchum~a formul a s and compared the values obtained by these formulae \'li:th the actual designe-Cl value,s of w, ·t.he curves on pages ( 27 ) showing the relationship. In every case the actual \V is belov, the ealeulated values from the formulas a-a shown. For shorter spans, the three c.hosen formul a s do not seem to deviate from each other very much. For longer spana; Howe 1 s formula seemed to give values closest to the actual designed values of•• 3.5 ryrrel I Hc,ndboo~ 2.264 2.6 Jr-au t w ·, ne c~.,,ne 71e l .73 R.,cKer-, /912. 3.05 3.9 4,5 6,5 4,8 5 . 86 s.o 1.87 R.,c k'er-, 1961 2 . 69 8.25 5.25 4 . 45 4.87 5.49 3,75 3,14 3.28 5,48 5.6 4.07 5.S Merriman 3.41 3,54 3.6 5.0 a .65 4. 07 3.66 3.4 4 .27 2 .73 3 .8 4.0 8.6 4 .2 2.a Maurer 2.95 . 3.0 3.4 3,14 13.2 5.0 Tr-;,~,,_ LQrql-d;v, Jones j3.5 8. 00 6,4 5. 6 I.T. + I 6.60 4.2 3.0 Fowler 11'. I 2.265 Carnegie ~ 4 .50 3.05 5 .0 4. 36 4.7 3.2 3.35 3. 48 3.70 Cambria 3.94 4 .12 2,91 4 .13 5.4 3.8 3.44 3.14 3,31 3.69 3,5 3.65 4.2 a.oa 2 . 67 2 . 43 2 , 795 Howe 3.16 3.75 2 . 32 2.84 30 ' 3.28 25 ' 4.03 15 l.. I 22 . 5 I 15 a.ctul 12 ' 10 ' 12 ' 20 ' 20 ' 100 1 ,span 18 ' ' 10 ' 15 ' 60 1 span a' 40• span Values ot w from different fcnoulas eompa.red With actual w. TABLll XV - 27- f Lo.rCJhl,n +H _E::t _ - ,:...i: ♦-+ s~ form.._ -28- In calc:illating streases,_ the weight of the truss is usually ao small com.pa.red with the weight of the co-v e.ring and the snow and the wind.Ii that an err,or in its assumption is negligible. Table XVI on tho following page ahows that the actual we'ight of -truss to the total load on the tru.ss f:or the determination 0£ stresses in different merabere varied from •7•55% t.o 10.,6%. For different loadings the variation in weight ia usually from 25 to 7ff/4 of t.he variation in loadi~• o- It &hould be noted that the personal equation .of' the designer and many fae.t.o rs ente_ring into the weight of rOQf truase.s may c.a use a var.lat-ion of 5 to .25% in the same trl.laa. Thus the d-eaigner must baae on hie own judgment and experience. Truss wt. as % total load span 9.4 fa 3774 355.::lt- 8.34% 2,262. :ff- l0.6J 0 9. 62 /c, 8.8 Jo H#H· 14,428 11,325 251 8327 7 .02/a 7690 540.# 22.5 1 1270 7 .55 l, 6653 502.-if 20 1 1090 9.65 ,% 4860 470. "r- 18 1 882. 8. 69). 4792 416.;#,- 7.55% 2,884. 210 .o:fl 15 1 •total load • iJea4 + 1/2 en + Wlad ( vertical.) Total load 100 1 Truss wt. 10. i,, Truss wt. as 'I, total load span 309.~ 8.7f//, 8.45% 3098. Truss wt. Truss wt . as of tot.load 1,965. Total load 'I, Total 1,456. vert. Jioad 12 1 166.~ 188.5 10 1 60 1 span 40 1 ~ 127.5 Truss wt. •'"'7 8' 5 F'"' c. Panel loads ' The Ratio of Triis Weight to Total Loacl.• TABLE XVI 7 .85 fa 18,175 1425 30 1 ~I