, . _.V _ .< o M‘ > ' ‘ o O o _ _ - _ .. . . ‘. . _ o‘.‘-“ y. :w '_.:.Tl‘ _ “'1. ,- . ‘V‘ :1" ' ‘ .._ ' ~.- I 9 . .9” ."'. M. “*w 'fi . I i - . ‘ _ ‘A v . _ .- _ _ . ."~O . .I , W H ‘ . .-.. . , _ . 3 ‘ ' v , \r-n- (_~*‘.M.~W~y “f5; 9.13.1.6 "43‘... ~33 “IW’. 4'69. -.__.‘..._ ‘; _..-‘:,3. k THE DESIGN OF A PARALLEL CHORD THROUGH'TRUSS BRIDGE ' OVER THE CASS RIVER ON ROAD M-IS, TWO MILES 3. OF' SAGINAW CITY LIMITS Thesis for Ike Dem-ea of B. S. MICHIGAN STATE COLLEGE Gilbert Edward Diefenbaoher 1944 . . «1:3 71.... I 2x... "Sizzzéziw gr- .x:=£.£:§? The Design of a Parallel Chord Through-Truss Bridge Over the Cass River on Road M-l}, Two Miles 8. of Saginaw City Limits. A Thesis Submitted to The Faculty of MICHIGAN STATE CCLLEG OF Agriculture And Applied Science by Gilbert Edward Diefenbacher m Candidate for the Degree of Bachelor of Science June 1944 THE-"SIS Introduction This thesis is a design of a Pratt Through Parallel- Chord Truss Bridge. The location of the prOposed bridge is Sec. 13 T.II N. R. 4 3., Spaulding TWpo, Saginaw Co. on road H-l} at Station 182 + 16.5, crossing the Cass River two miles south of Saginaw City Limits. The dimensions of the prOposed bridge are;Two symmetrical lOO' spans, 20' high, with 26' center line to center line of trusses. The bridge floor is to be of reinforced concrete. The Spans will consist of five panels at 20'. The Specifications which will be used herein, are from "Specifications for Highway Bridges” issued by the American Association of State Highway Officials and Specifications given in the A.I.S.C. handbook. The object of this design thesis is to give the author some practical eXperience in analyzing stresses in structures of this type, and to acquaint both the readers and the author with methods and procedure used in the design of a highway truss bridge. The author will not attempt to give every phase of the design because the time alloted is not sufficient to include all details. In conclusion, I Wish to express my appreciation to Kr. C. A. Miller of the Nichigan State College faculty and to Kr. Nelson Jones of the Michigan State Highway Bridge Depart- ment for their c00peration and aid in solving problems per- taining to this design. Design of Bridge Floor The first phase in the design of a c'ucr:ts bridge floor is éhaterminiang the Lmu 3 ‘I 3 o 31 SOC \ .iv j 3‘ 1. ti. -iia '3‘ LO u.~ 1. | q 2 u I; -1 L.) I; _ - 21 d ...I OIIJ. 1 “ ' ' I {\I' *vw‘ - I. o . 1 '1 ~ J. 3‘ 2qu , 1 , o “ ' ) ) 3 , tli' 3L3. I 1.0 5 -l\/' O .‘_ ‘8 3 \L ' L‘I L 1L sJ I. -4. L I J L; Lil -L -‘ o _.| L. ,_ , ,i. "I I K“, (I ’1’\ ‘_ ‘ q _ .‘1. ~ 1 A1\ 1. ,3 __p F ‘_‘ (11.341 '33 ‘f J— —\ LIL/.1 til \J/‘AA 13? Li I) KJ. ‘J.l.'/ '11 J./ .0. T" “’3 ‘ ‘r° 1 , ’J‘fi‘f‘ '%11 \ \nti‘." Ir ‘ J! L 3 If)’)j j C ‘ " are --L I . j 1 ‘ C J . J ‘ - C 1 ‘;,‘.,_ n_- .1 '_, .4 vi 4. J. /v k.) - ’ ’ . ‘ 4‘ / ‘ . ‘ V V V ' 1. ‘ I 1 f‘1 (Ar 1 1 fIiT‘I l: o.) CJICLC sir n l '*Ic‘ . _l2 LIII odfuh L _ 4 . 4 V w ‘ rfi 1—. . L~ ‘- -1*‘r) f‘ x" 1“ q « L \ * i J J 3p ’11 Cd.) .133. -4. (J L .J.i3 -- J ~(1 Ak} C LOP -') I-J O ‘6! )J Lu J L. A .J [.J p‘ a (“x k I \J \v .JJ ff 0 J \J :I H O r‘ ' t *‘5 t-_J "5 O *‘5 COHC?JS“QSBH the sari: H no.9:fi ‘ue ht 4T3 cc certrx 91 lo 1. yr! Vn ) :r2(w_u3) _ '14‘3 vw- _~; _»3) m L O 2... (L+L1 _'_' "' L: A it ] hn'l -)“1 A I' .- I II. \ —' — ~/‘ {I \‘i In our gas; u : Ll : 3 ~10 . : 9 _ l ,otor. ’3 low, writing tie three 1~13nt equations we have: (1) T'f4”"+*"'- 9L (k-k3) (2 x“+4:"'X4 = PL (2k1-3k12+k23) (3) Y”'+4V4+V5 : -“L (kl-klj) - (Chg-3k22+k23) (4) ”4+4"5+TT6 :-DL (kg-193) (5‘. 1.:5+47'6+’.f7 : -"L (21(3-51:32+1{33) Allowing 2 to be unity and k g .5; kl = .0652; Re : .9348; RB : .5, :e obtain the follcwing five simultaneous equations: (1) m'+4:"+:"'= -.375 (2) x"+4u"' m4 = —.1173 (3) m”44744 (4) fi4+475+36 : -.1178 (5) m5+436+97 : -,375 In solving these equations we find that: "I \‘r _ O H .q I fir" ‘F 1"- "' , ‘009#35 I ON I T“'= T _ -.0024 :14 -0033]. Taking moments about support II and considering the forces to the left we have: x" = RlL - .5 ”L : -.09435 *L R1 : .4056? : R7 Hext, taking moments absit Sugport III and succeedip , \- . -. w 4.1.“ sui'crts we f no bAlt: a. II 0 O\ V.) I-J ID ru-d R 2 R6 3 R4 m II .3025? R 5 .2014? -' ~ ." p, I»; f» w": I In checkins these~resultawts for a total of 47 we met tae My,“ ’ following: 2 X .4056 3 .8112 2K If.) ’25: 1.0-" 1 x .2014 .2014 Total ’.0000 his gives us a check on our resultants. .u—‘p Own.p‘m "111-. ' . v‘ I W 1 'w‘ - 1 - " v-r- r "1 f lne lafllljJ no_ent occurs at .il-span 1-2. \ ” I, : 04056? X .E‘L _ 02 ‘28 ’; (T13X1HIIY'I) Lonent at nid-span 2-3, M -.O4‘4BL Korent at nid-s an 3-4, 7 - ~.0143PL The position of the wheels in Figure I shows a proximate maximum moment but witi only one truck on the floor at a tine the actual naxisun gositive moment will be: (1) I:I+1+$:"+:-"' : _(1:_1{3) : _.375 (2\ ""+li""' 1|.“ -"r- - ~(2IC 5" 21'k13) - - 11'78 I ..-'- 4 ..- _ 1" 1.1 _ O I \ 2 .-"I _ _ 1,. _1‘_. 3 _ fr- (3/ I‘I ~24. +7 -5— (111-1 ) - NO 50 O (5) f5+436+f7 = o ,I I--_ .- (4) ..-4+I‘-..D+i6 Solving these equations simultaneously we find: 2' z :7 z o; "" : -.oe<27; “"' : -.01ooo; M4: -.01975; I -.00015; "6 : -.oooa. T“akin"r moments about suveort II in solving for R1: RlL- .SLP -.6962 79L; R1 ; .41373P The moment at the wheel on span 1-2 will be .5; x .41373? -.20€’3) 32L, which is the maximum os ive mP“3~to T1,“) as: :7 q “n L "a.1~ ta t“ 1)}‘;i"_" '7: “ 13-” C7171 f3 .. c loul if“ i3 o ii iii“ l'cr is 1 a“ C5 f?“ f‘ “3'0 "t“"io l‘vs 1“”1 U H“ $73 I T‘- 3 -55 L4” +iJ'. T 3 u n .. '7/ 1 2 4 4 * n _ . s ,— 3‘ r :0 T __ 1 - , J — uniforl looi nor f>ot In one“. 4l70; L - L1 uq' ' — ., ' o L . 1 n ' H 72 L‘ + 11A + .LA' - ~-L '3 L. Tune, the nsfinnfi “o‘itivs ”3 ‘nt in feet-fonnis d, to t hi n w . ‘ 'p H . “ ' l 1,4 vwri .r- :‘1‘1I‘: 119' ‘.- \1 LL\_A..- .1— . ‘ ffi 1" r- - a Jeeisq of :loor glob. .- 1 a N .. :‘fl' ,. . (1.- 1,0 .1 -1 f1 k.) L) i 2‘; U' \‘> 1- 5 v5.1,” L153 1‘ (17,4. . ‘ 1,‘ . ll " , I_“ f‘ V \ ’ P I I-QVIL..€ ~13‘Jx :' .. g ’ n "\ "' "‘ ,1 ,~. \ ~~ -”‘ also — 8/1; x lSu - 130 lbs. FLT 53. I . I I”) 0 FJ (7‘ U 0 5 i C) ) O H) (3+ 7? n d ~11'hr1- Ilour ccv3iin5 ~ ll H l m) ILL) |.__J cf 5 j H (23 3 O H) d O Tetfil “. _' j __ _fl , O a " A" _ ’1‘. a V V Bron i091 loo moment eqnntiOtS we fist for “OelthC eni I I H \ U 0 \fi N H N D H \N 7') ‘4 ‘J H H [0 II \ F0 f0 H L- *4. TS Q 3‘ J O i J) 0 Live loads: 7'? q 0 U . 1‘ 1'7 K n” L-QO loadinj for live loei throne out :0 :et lc,OOO Uoi \—' ,3" «J l—Jo I F L "S J '3 (T) cf Ho 0 :3 N U) “1 Ho 4 () ounds for rear w eel loom '73 ( luei we obtain for maximum positive enl UGthiVL momen FJ n—V'w _ o. _ 067 x 16,000 X 3.0;; x l? - 152,200 inch eonnfis. +L = . ‘1. ./ , '7 ~ _ / . ' =5 Y lo,COi X 3.33; x l? - -o9,§OO inch oonnis. I ('3 \0 4:5 \ :4 -1'5 - . Since we have considerci a strip of slob only one foot‘ui we Will have to allow for wheel cistribntion in the nose of th live loci. Iva k+ 3 str ......... inge ' a ip 01 have: “V." .LL), Sjub L; : lEfideCfiL'u’; 2 3.5501 iI‘act stress on (3.853 + 125) hEVG for the tot; L = 42,8JOHM I = 16,7OO"W 7‘ - r: u I]. ‘ - 12/00 g , ”f 01,010 otel ’ ”3 3&311 00281” d slab 13 e leer3 fiietrib stringwro, 701 = .7 (3.83 “e eff ctive r J = 1.25 = ti , a strip 555? l 1031; théfl, I Z .399 1 19,63 noxiru: ne'etivo l =«19,5com, I : “7:630”% D = “2,21f'nlf “Q'- ..L' . . ution, if .5 he. +1.25) : 3 iatn, 2.) :- 0 int}: f0 1 f3. Wide li'fie 109 x 49 8 {37‘ +L;" :) 7| \4‘. . _I - 1 J, 9 Li av :- -765 o "F’."‘V‘LI‘I“1H ".A,... -..‘ , _ -. film A ’3 K] L I. " ‘ - Jw- - H "..o y AI.Q-._ f1 / 3 C. l. diCtfiflCe between H : x d-V - d‘l 0 1V l'j‘|r" \14 I. .LA~A\4.. - {3. th '1- g. -4. ;‘,"IW. r. :. "..A_ ll .-/1:ic} V “CVI. ,¥«.J. L k +— AU. \ 'er '- s. 4. no H. 1; a) \l. \ L. N f.“ 1 NJ. 3 .. — N . It .‘ 7/ .r. T 0‘& Oxl BL. 01,. O. .L . a. Q \ J» 1 I «.Q Us 0 31.» f _ ~ 3 A t . \‘g. ._L T.” 1 ; L I .l a .x. .l :1. «r l 3 pi .1... :4 r-.\\ .1 T all; 11 ‘mv A (ml ‘-' ,j') ~ C P. H 03 AU Go I! /C at no C nl V i U ‘ fps -—\J "7. ‘LL 77". t o L) Vv .7. ‘3‘ ,— . -. l f ' .1 A. J ' F.) 117’ v U .4 ' D ‘(Nfi " "\(. J\- _ .;’)n (3. ~ v A 1 . w ‘L‘- 1” I +3. 7, I“ C1 , r .‘F 42// .1 7/ b ll'. 3 find my . Y.‘ ‘I r‘fi ‘IJ- LIL I cove for ’3" r. A); 11 r./ AU 0,. n; dd nb AU 6 i; «If. teel .3 C' ancCinfi. w AK f 3f \ .-:> r. +- u stount re“ . +L—\) “ X s A: C. l r ..-x ‘2‘. nnnher of br ".1" J . 1000 v ‘5 .L O, Pn/ 0L 1 C/ r-fi —~. . ~ 0 - N '< N . ‘L D -‘ u I a-~ . Un?xgt1tuf¢uu* tin»63 VWJYNK, 1n 1913 _OIWJ1 a, 1&3 (gt- - " ' .1 ' x °~ .afi 1- 1 4 .‘ C a .2 v - 95 p.801. ‘. ilk] . lg 11:1? ‘T‘ tha flilO-v'bl‘éie Uq I'o-ox... ll‘f‘k‘n I I O O _ 1? 3“”le10‘tlU13. strinfier De91”n: rr‘ . . ,- ~ I“ f- . 'l'. - 7.. .. , ‘ liyg b11¢1"3 ‘“‘:n 1x3 to hrs lufll ft“ 1a1;_ :lt?1 “$49 fw*le ; C: "“1 . - s K . ‘ - --~. » 1-. ‘ - ° —. 20 ft. Lnerefore, thu fipfirflilawtw lax tJ of tge strline: will be r“ ‘ - ‘ 'fif‘ ‘ V . 20 ft. Lhis len“*n till he accur?+ flgdu h for mu? Cfilculntlons. ”1"“ “‘ 1‘ . ' ’ ( -. “ r‘v a' ' 2 ‘ >A - — " in; burlnd_ 3 ulll no “jacefi at / ft.-1u Ln. 1vt rvnls. First, conuiaemin" the "325 131‘ upon atrin"or: “= finfl: On A ,. ' , . u cancrete floor 1b0u par ,3. 1n. 131 A , . ". Y Y Y ' -1nor eqvwrlné dOJ " ’3 A " Total 149” p r 3'. Ln. 0 w W O U31n5 )'—19” $35 in‘, the “er“ 13¢] :f cornmch in? 01V~rihn v 43 4 7 O 7-. ' f‘ - / .1 per foot IL oar: “111 b3 ;.w;) 1 1;? - 495“ -cr ft. ‘7 I. ~ A "\ fl ‘ v - ‘ V ' nbcnnefi 4t. OI bCQC - ,5; p»r ft. Tw '1 - and n-» 9+ ax, \JL - / Vt- H i... ‘A‘ J. L; . 7"" _ I '1 . h‘ ‘3' « ,7 u , . '1. r: r f ‘. ‘.» Lihrelore, the g3¥1_u4 Awnént on strluger ‘ue to J39” loci ¢SZ / 2 — 4 r FAA f)‘ q - 7P‘A' ~ A” u 3 1/; l )JU I LO X J; - )qu,33d J. mafi‘ r ,' ' “v 'v .' -L ' 'v x . .. .12 H , ’ IVA’N u , h. ;né .lfilflh ilVC no an» Lil 00 H? ,u», t%~ 1a,“;a” rcur wheel is it :i‘-:trn. vi? é f“? fraét'fl‘ CT the ’E‘al 10f“ lCJi” ‘0‘ 4‘ " 1 :n v *I -: 'W ’ L -( . VI ‘ "N A ‘_ . v’ " ‘~ . ~ :- ‘ ‘ 1" v I ' U) n tA‘u -1? . 9r ;' the Sb 1“ rs pynclw wLJL1QT J 4.5 “J get far ‘-Ii@‘ live 13ml *0 th .. - A 'A»/‘- 1 O ‘7 —’ :A‘ ‘ 1 P - H I/ ' lb” " "‘ - 1(i . v —’ 4': ( 2‘ O —‘ ‘ ‘ ) 1"" 4C J “i — ‘41—!) ’ 0"» O t-l/H O \ .~ 9. r; (i ( l' I ,J J r?“ o _ . \ O ,’ q'A. _ .“C‘r‘. {\f“ ihgn for ‘ nmct we have ( f? ) ulo Qua — 5‘;,JJO”J ‘ ’N -. '\ f.) r ‘ ;Lfi_) ) 4 _‘. o 'I ‘\ "‘ 1 r- v" V \J ' L‘ .LO-LOQOJ. ‘L \r I J. L 1L b I I "r-‘I\ ‘.)l NU :Y‘I' '4. 0 Jr -». «.r «\ f L. _ 3‘] I ('3 . (11-0 ll 0 J. ‘Hfi 3 fi~'t q” . h; . ,; ~ 44 , .- " ‘ 1, ‘ d . \' . a T1 _ ._, . «L \ x \ -b 1 b4, 0 U '31 v’\ "J I \ \+-Ivr ) I o fiv.r -L. fx‘fi .4 Q fir} . -vb‘ LV‘II’ a”) ll ". I“, , x I l L- jxfifim'vl A— n+vx ./ k} f 3.7 ‘1 wt ‘ f N /6000 ¥ }._J 2-0 | WT" P _ ](,u::© ‘ v A‘x1-) ll. g3. be I "Lj H L) O "S Q J D .1 D Q J 2 i m . -. “. ., A u-n: 4 «‘y‘ .r‘ r I »~ c v-\_, lho loo fflirof tam floor*lmral Will be women him»? a: t 3 ° . l , . A o . - —. A" ...1° ' l J- m( ‘ fligtqnce from o_- 3) of trumch ufllCh 13 ooual to cu ft. For the fieoi load per ft. of intariwr boan we hqvo- Floor 120 x 20 = 8400 r per ft- I 7‘ .. ° ‘. , , - 7- ' w h -f‘) K ‘. f \ D striorers x )3 / QJ -g07” per it. — I“ ; "" "3 .i ‘ . ..V r- :loor deem (”SSULofl) lvO fi'h , _ .0 _ - , _ 1_ , ,-. ,-. , q , ~ 1 ,\ . 'V 133 gax1mun mouent on floor bacn ouo to ieqr loai 1:1 The position of the wheels shown i1 Jifuro I? will :ivo us a maximum henfiino no ont fo” tho oomcontrotcfl live load. _ I , . ".0 ‘ a 3/ P E, 5 I 33/ f; 11)? ' ' ’ r ~——— 6 ~—a-~—*4.7.4* ’ i F —,Fg4g RF 1&1" T” " -./‘ / '1" / I: ;?.2,}"?0~P Fm: L: $4.2m komonto about P4 = 4.75 X 2.1154? 3 13.039' I. '7" 1) 1:10.75 2,: 2.1154? _. 6i : 16.52P' I l—J \, O \J \11 k n H P X 1.8846 II C\ O {\J \fl l I H H \1 C I O '1') .. ’3. '1 U' 1" v wince :10 “’BJ C.) P.) C) u. d J {:5 i U H H ’D -3 y 61‘ '3‘ U) .) 93 ‘ i (“1‘ 0 % cf 6 H) '1 g C+ 5 D O F4 loofls will also act upon the same floor Knox thot the roor wheel loofis act upoh, because the frond waoela arm locsted siy ft fro? 'the (Nijncerfl;:flooI-lx?on3. TFhus v33 have: 6/20 x A 0?? f = 3/40 F, actinfi Upon floor beam flue to from. Wheel 15,0CC loads. »-0 l. v... The - A - 4 O 7 J. A y—W '\ ‘J H - . o - ‘ T.‘ ‘3 ”-i 'z’w'r , swbotitntiu' 3/4?: for i in :i"uro Li, '9 73 - ’ - 707') 'i - ‘ 7“. — +— fib011fl A- (j ‘2: AN- - 1 O 7/;“ \"‘C.«-':o) . *1 {1. nt mill fhwn he: 17 nor/"5 ’3' " .«_ Jl} A " 1 20 II II 07/4 r“ i O ’7 C‘O "D iOt’rl 1. 0'31.‘—- 'H 't.. 'v ,. *7) - , n- . t1!» ‘tlf‘.' for - «'3 il’l'a ' = x " ,- 3r ,l m V 1 _ I ' A 1 ' 10— 1 4 Q _‘1\-".' ..,. ”\I ’ 1”. I AM ....’_ /\ , 01/ , ~j -,..\ ~ ,. - 4— 4- 1.4 fl A ' .- .. ° 1 l oat lo.:no it ill; “ulJ' gill b:: c ) 2 4 2 ofiq = mo: roan“ ( J'q / ’Ll/ ’ .L .. 1- ’ ul' / , ‘-.,}\_,' ’ {39:3 1033 "Kw.ent, tol”rv* "o Pfit‘ 'fixn ; Pg i c. ~ 7". v.- . l- , ’5' - — O ' n/ —’ are 4- l ’ .C‘ 1 1 b \ . :52 -' ‘11 ‘- f) 74’.) 2'- ._C‘ = .; 9 L. ‘ 5" .- !" fjr‘ 30'! .- — )r_),0., I" l ow) + -JL? V _ 0 too tgffll TLT‘?Ut V111.Lu‘2 m 'r - r-C‘_ .o n 1.2.J. . - .1) 2/: 0‘) 1‘] f 7'. "- oil 1'1. = 3,0]/,‘;l; .1- T 1 no: rt, o” '5. = L,K¢”/ "/|r)l's. " l-HJ'51 - 419/9371'” .4” I O oforo, tho section uolnln? reiniroi will be A 0’3.“ n fin” _ ""7"? 5 _ ‘3 {'L‘A'll‘.]"41 — ‘--/'/O "' J ’3 “5‘,“ l...- :1 ’ ,IJ‘k/lv " . - ’3 ll “Al/q 7' A. -:“-‘r r‘ . cmlJ_i TDT'Elli7 x ii“%t l F2r) 123‘ E' / / / / V / / / / J / / / / / . / 1 I4" 5/ 0 C9 [2” A a a t/r a - lg. 6%; #27 x.” F' , ,1 ____ - _‘ ,»/€%NLLjngz%J,kw9 ad ° /‘7c?.¢2t; The bottom lateral system will be double intersecting, as shown in (Fig. Ix). For determining the stresses in the laterals, we have: 20 tan. D 3'56’; .77 see. c : 1.262 Then P sec. n.: 9.300 x 1.262 3 11,720#. [2 . i , a .5“ For loadings from panels A to C we obtain 63'. 3/5 P sec. ¢ : 3/5 x 11,720 : 7032#’ ft ‘%s i: ilV for maximum stress in lateral CD'. Loading panels A to D we obtain: 6/5 x 11.720 : 14.064# for maximum stress in lateral DE'. Loading panels A to E we obtain: 10/5 x 11720 : 23.540# for maximum stress in EF'. Since laterals are symmetrical with reference to center of span, the above stresses are all that are necessary for designing the bottom laterals. 22. wind Stresses in T0p Laterals: From preliminary calculations, it is found that the area of the verticle projection of the upper half of the truss is about 2.38 sq.ft. per foot or truss. Thus the wind pressure is: 2.38 x 1.5 x 30 : iota/Ft. of span. However, the previously stated specification limits the minimum to 150# per foot of truss, so 150# will be used. Then for the panel load we will have: P e 150 1.20 a 3,000#. Hence for determining stresses in the laterals we have tan. fl : §%’.'e77 Bee. ¢ : 1.262 Then we have: P sec. ¢ 3 3.000 x 1.262 : 3786#. Q Q I g I Q 1‘ , 15 L? ”)c' ”W5' .A‘ ' 1 , \ / , g l ‘ / / / I t, / / 1 i Q. / / / ( 1 £ / / ’ I / / / F 7 / 'A .E C7 C' 5 2 a; a e zz/gé 1’ 55" /oc> fie. X Then for stress in lateral CD' (Fig. x), we have for loading from A to C! 3/5 x 3.786 3 2.272# Loading from A to D we obtain stress in DE’: 6/5 x 3e785 3 4e544# The compression in strutt DD' is: 6/5 P a 6/5 x 3.000 3 3.600#. These stresses are all that are necessary for tog lateral design. 23. Hind Stresses in Bortals: 'lj rom (Fig.X), we see that there can be two panel loads (5,000 X 2 = 6,000?) applied to the portal at either panel point 3' or E. The end tosts are usually considered fixed. If this is the case, the ‘oint cf contraflcxure in each post is midway between the bottom of tie portal and the shoe joint LO. By drawing the clearance line, it is found that the portal can be 6'- 0" deep. By consulting the draning (Fig. XI), we find the total length of tie and xcst is about 28'- 3 1/2” so we have 28'- 5 1/2" minus 6'- 0" ; 22'- 3 l/2" for the distance from the bottom of the gortal to the shoe. Then the point of contraflexure is about ll'- 1 3/4” down froa the bottom of the :ortal. For convience we will use ll'- 0". Then the case will be as shown in (Fig. XI), where, C and 0' are the points of contraflexure in the and posts. The and rests are consideren to have equal resistance to horizontal shear. dance, we will have a shear of 3,000; - at point of contraflexure as indicated in (Fig. XI). The 6,000% load also causes a positive reaction at C and an equal but negative react on at 0'. By taking moments about either 0 or 0' we obtain : 61000 X 17 2 3,923# 26 for the reaction at 0 or 0'. Thus it is seen that there is a horizontal and vertical force at each point of contraflexure that holds the 6,000} force in equilibrium . . fl .. 0 II F J {V m . .II J M. _ m 5 3 , f , MN. / i. 16 1 I|_J.&r m . 9 z m. , i m I GO . a o 00 Q. 13 x [D . I i I . o . o o . a . _n . 1K .0 IIIIII t wrm l xxx . MNQM. fl. , xx _ \\ lull/W \\.....III|||‘\ / . \\ // _ \\ I‘IllxMWWus.\\u||n'-_ /I—\\\ 5 \ n‘ smash, l! FMZZ Sections: Intermediate Posts: Since the truss is only 20' deep, I—beams with wide flanges may be used. This will greatly reduce shop work. For posts Ung we will try an 8" - 31# I—beam. r = 8.01 L a 240 = 120- which is just the r 5751 slender ratio limit and hence the beam is satisfactory as far as the slender ratio is concerned. From A.I.8.C. specifications we find the allowable unit stress to be: 17,000 - .485 (Egg 1' Using the above specification the stress is found to be 11,020# 87 5 5 3 2.5 SQ. in. fifdgo' The beam chosen as an area of 9.10 sq. in., which is excessive but still the beam is as economical a section as can be obtained and hence will be used for posts Ung. If angles were used, additional shop work would be necessary and the added details (Lacings and Tie Plates) would bring the weight up to that of the chosen I-beam Hangers U1L1: 86,725 = 5.1 sq. in. for req'd section. Use an 8"-31#’I-b;:5~and considering four 7/8 rivets out of the flanges, we have: 9.12 — 7/16 x 1 x 4 - 7.59 sq. in. for net section, which is excessive, but considering the saving on details and shop work the 8" - 31# I-beam is an economic section and will be used for hangers UlLl. Diagonals Ung: 115 040 = 6.76 sq. in. for net section 17,000 A 6" - 27.5# I-beam, considering two holes out of the flanges, has a net section of 8.09 — 7/16 x l x 2 = 7.22 sq. in. This beam will be used as it is as economical a section as can be obtained. Diagonals Ung: 33 170 a 1.773 sq. in. for reQuired net section. 17 000 3 Since this is a very small reQuired section we will use two angles say 3%" x 2%" x 5/16 angles with a section of 1.78 x 2 . 3.56 sq. in. Deducting one rivet hole from each angle we obtain: 3.56 - .307 x 2 a 3.946 sq. in. This net section is greater than the required section of 1.773 sq. in., but this size angle is necessary for rigidity and therefore will be used. Bottom Chord LOLg: From table X in "Highway Bridges" by Kirkham, we find that two 6" x 7/8 angles are practically the required size, when considering one 1" hole for 7/8 rivet deducted from the total area. The net section will be 9.73 - 1 = 8.73 sq. in. Therefore this section will be used for bottom chords L0L2° Top Chord UlUg: Since the allowable unit stress for such chords is from 12,000# to l3,000#, we will consider 12,500# as the allow— able stress. Thus we obtain: 203 350 = 16.25 sq. in. for required net section ‘2‘”1 , 5‘0 0" This will give us some idea as to what size sections are reQuired. Let us assume the following section: 2 — channels 10" - 20# = 11.73 sq. in. l — coverplate 16 x 3/8 - 6.25 " " Total = T7797' " " Then for approximate value of the radius of gyration about the horizontal axis, we have: rh a .39 x 10 a 3.9 and for the radius of gyration about the vertical axis we have: (assuming the back to back of channels to he 9.5") IV = .55 x 9.5 g 5.22 Computing the values for the radius of gyration about H & V we find: rh =3 400 As is seen, these values are about the same as given above. Testing for rigidity we find: 1' 4".0' Then from curve given in article 21, page 11 of "Highway Bridges" by Kirkham, we find the allowable unit stress to be 12,600#. Since this is greater than the assumed 12,500#, the section chosen will be all right to use. 27. End Post UlLO: This section is subject to cross bending due to wind. Therefore, the unit stress due to cross bending shall be added to the direct stress. For section of end posts, we will assume: 1 - cover plate 16 x 3/8 2 - channels 10" - 25# Total 14.70 6025 830 11;}. 20.95 ” The and post is 28.28' long. By taking rh = 4.0, the same as for top chord, we find: .11 = 28028 X 12 I 8408 Ph 400 then from curve A article 21, page 11, in "Highway Bridges" by Kirkham, we find that 10,450# is the allowable stress. Then for required section, we have: 206,2?2 :19074 sq. in. 10,25o Since this is less than the assumed section , we will use the ch sen section. Although there are many other items of design necessary for the complete bridge design, the author feels that he has sufficiently covered the important designs. This statement is made in consideration of the fact that the alloted time was not sufficient to cover a complete bridge d n w..— BibliOgraphy .;3941 "Introduction to Reinforced Concrete” by Hale Sutherland and Raymond Reese. pp. 61 - 77,82 - 92 "Elements of Strength of Materials" by S. Timoshenko and Gleason H. KacCullough. pp. 205 - 221 "Structural Theory" by Hale Sutherland and Harry Lake Bowman. pp. 159 - 173 "Highway Bridges" by John E. Kirkham. pp. 268 - 288 "Low Cost Roads and Bridges" by Victor J. Brown and Carelton N. Conner. ppo 91 - 153 "Theory and Practice of Reinforced Concrete"by Clarence N. Dunham. pp. 39 - 138 ”Design of Highway Bridges" by Milo S. Ketchum. MICHIGAN STATE UNIVERSITY LlBRARIES | HHMH’ !| WI 3 129 ll 3 0307 My 1 3