# HW23 - Prob|em 4_1 4.1 and 4.2 Knowing that the couple...

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Unformatted text preview: Prob|em 4_1 4.1 and 4.2 Knowing that the couple shown acts in a vertical plane, determine the stress at (a) point A, (6) point B. 20 40 20 For m+¢n3ﬁa I = 7:: {0173 Ou+s f): Md’mape 2 I‘ = fi- (80}(12 D)5 L: ILSZXIOG mmq r 1/.525/0“ m“ CUfoc/IL: I2 = 2‘: (4:2)(80)3 I; = L7oca7xro‘ rm”: Dozen/o“ n." Dimensionsin mm Sed‘l‘fan: I 2 II - I1 7 iglgssxlo" my _ - -_ M _ _(Ls‘xn>3 )go.oqo)__, c (a) 34- wmh- 0-040“ 6;- 4“— ; iglaggilo-‘ — 51.6on 1%. km an: R WW3 51:41.6 MP1 4 I 09-] ja=_c0Mm-"L7,060M \ ng—m 2 _ 15x105(.;o‘060) ‘— I 7.81333vlo“ (“ﬁx”) Pa 4.1 and 4.2 Knowing that the cou pie shown acts in a vertical plane, determine the stress at (a) point A, (b) paint B. V‘o = \$0.5) = 0.8M. Q = {:(Lﬂr o_é In. P g (C?— VD= \$00.2”— 0.6”) = 0.2:qu in” .. . __M _ (Siloa’chs) __ 3 , “JJA‘QB-n— 5}- —I¥‘~~ my,“ — 13-1%“: ,aa. 6} ‘43.}? (61' «an 3 T . . 6=_ﬂﬁ = _ (SKID3](O.6) : _ 3- N 3 ; (b j“ 0 6 m' ‘ I 0.7494: I 6" Io 7‘ 6-3 * 43.4? ks; Problem 4.8 4'. 7 through 4.9 Two vert icnl forces are applied to a beam of the cross section ShOWn. Determine the mwdmum tensile and compressive stresses in portion BC ofthe beam, is (—5-) Ya '2" Z ‘ [gag- = H.778 I"? Neu'hm.’ men's Pres 4.778 in GJaove ‘Hne base.- Q . 3.22: I. = iii 5J1? + AM.“ = r’dsk’rFs‘ (83(2722)‘ : 59.95. in V 4.713 4* J In 715b,hf+A,J:= 55(I)(€)3+ (gm:st : 21435.1" In = Hi 5.1%: + Ar’; = FH‘HMS + (4)(4.278)‘ = 73.54 in” I = I, + Iz + 13 = 547.?“ 22.43 + 73.57 = 155:1: m 34.1, = 3.2512 in j” :—4_773 ;,1 P 43M M - Po. = O P (1-4 M: PO. = (2.5)(10) = 500 lop-m. 6%: - Elli” :' " W = — k5; (CoMPNSSl‘OM\ '4 6hr 5. - I‘ll-XL": : '- g-tTTLg-fﬁ—ga) = [5.40 k5; (+6n51‘0n3 ‘1 PFOD'em 4-23 4.23 It is observed that a thin steel strip of0.06-in. width can be bent into a circle of 3}- in. diamem without any resulting permanent defamation. Knowing that E = 29 x 10‘ psi, detemine (a) the maximum stress in the bent strip, (b) the magnitude of the couples required to bend the strip. =92 = 0.00254... (0.3 61.. = EFC - “ﬂngng = was “IO-stv‘ —. 1933ks/ .4 ‘ -t1 (5) 2 qu'oo)3§:5”° ) 0-0433 15- m .1 4.24 A 500 lb ' in. couple is applied to the steel bar shown. (0) Assuming that the couple is applied about the z axis as shown, determine the mmn‘mum stress and the radius of curvature of the bar, (b) Solve part a, assuming that the couple is applied aboutthey axis. USeE=29 x lo‘psi. (0..) Bancl;ﬂa adLOJ" Zuaytlﬁ. = ﬁloh’ = i‘;;(c}_at5)(0.7575 = taszosxto'z in,” I c. = H. = 71(935) = 0.375 in. 6' = P1; = g5w.)go‘37s) r “\$9,031”; I I5-8203 «10“ 6‘=IL85'ks.' «6 i” 2 ﬂ 1. L f I —3 .n-I F El" (Q‘lxlo‘)(ls.9203u(6") ’ "05"“ ° ' {0: \$15 in [92755711 4 Bertaan aloodl‘ j—aﬂl‘s I = 7% b"): 2 TE‘ :1‘ “’0‘; l'nv c = ill = ﬂaws) = 0,2257%. 6 = M19 = gquslﬂoéﬁzi) : Hitsuo’ps.‘ 6:17.7§ksi-a J— : A -_-: = [0-3 -'—I F El (2"?XIO‘K56953H0'3) 3'02? Y m p = 330 in. /o=27.s‘¥t .. 4.39 and 4.40 A steel bar (E, 2 210 GPa) and an aiuminum bar (E4 = 70 61’s) are bonded together to form the composite bar shown. Determine the W stress in (a) the aluminum, (b) the steel, when the bar is bent about a horizontal axis with M =60N-m. Use wtuuminUM as Hm: V‘CZFcremoe Wit/hawk}. PW JUMKI‘UM h: 1 For Shae)? ‘(‘I= Es/E~= IUD/70 "' 3 Problem 4.39 (OJ Mam-Mum Y1=| ) j:_(OMM= "O-DIOM _‘_40j(603(_0.o:o) F ‘ _ ‘— MEEIMIOH.‘ 7» HSWRMO Pa. 6:; 45.1 HR; (Eh Shae? n= 3, y= 6mm: 0.005.“ 65=__ (QCQoXOth) 2 gugoywe Pa 6;=_3L\Mpa ‘I'bﬁlzxfO‘q Problem 4.42 steel 29 x 10‘ psi. blowing that the beam ' of momeatM = 450 kip - £11., determine the maxlmum stress in (a) the wood, (6) the steel. Use. Wma' as +Ke reiereuce Maiewn‘aﬂ. For wood I): I For s+ee2 n: E‘s/Eu, = zen/La = "5.1111 Tran 5 1Eon e51 seah‘on — _ Hams! “ Yo ' 1:2. ma : 3.153 tin- The ne-J'l'r‘up a-ycl's ﬁres 3.753 in, aLauc He wood-s4”! {NEH—Egg. r, = ngﬂ n,A.a,‘= gamma (723(6- 3.752? I C“ in q I1 :' '95» b, hf+ n2 A, a: = -"—;g”—’dm{o.533_,+ (no. 272 )(3353 + 0.25? : 641mm“ I= I‘ + II = 672.77 m" M = kI‘P- £51 5‘: "gig-41 ca.) Wood: n = I y: 12— 3.752 = 3.242 in- 5.“:— LEW : — 1.97:, to...‘ (pie—1.479 ks; 4: (b3 She-ﬂ: 71:16.1!” = - 3.753 -o.5 = —‘|:258 In. (tam!) 45o) — .2583 6; :- mad-77 ( q = 15.43 ksi 6;= [6.43 kso‘ Pro Hem 4-50 4.50 Knowing that the balding moment in the reinforced concrete beam is +150 kip - ft and that the modulus of elasticity is 3,75 x 10‘ psi For the concrete and 30 x 106 psi for the steel, determine (a) the mess in the steel, (1:) the maximum stress in the concrete. _ aoxw‘ ;, ' 3.75am; 8'0 = i; 15% 4 mm? = 5.11% .1.“ nA5= 2.52133 rn‘ LocoA'e. +Le neutral? axis (303L930 + 2.5) +, 712x é: —-(25.I33)(Ie.5- x) = o @ ISOx + 375 + 6x‘— LJW-6‘? 4-25.133x =0 n ./ L ' A’— éx‘+ mass»: -3‘f.€‘? = o 309% 4;» x x 7 (2K4) f6-5- X = {8.275 in. I. 2 i’akh.3+A.oIf : #303? + (soksxmasf : :42: .3 In” 12: gage: amazes? = 0.: :n“ = 0.225 in. 13,: nAﬂol‘,z —- (25.:32.)(14.z75)‘ - (357.1 .‘n" I = I,#I2+I‘3 = gouge“ ‘ "DI—M‘x when. M?- !50 HID-H g IZOO kt‘P'iw (0.) s+eei7 n=8.o , 3,: 415.275” ,‘n _ (goﬁl’SOGM—Jcﬁw) 8083. 5' (b) Concre+e n = LO) 3/ = 5, 225 [h 6:- 3W 8083-5 6 : 2 23.0 Vivi d = —« 1.163 ks; 4 ...
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## This note was uploaded on 05/09/2009 for the course ENGRD 202 taught by Professor Petrina during the Fall '08 term at Cornell.

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HW23 - Prob|em 4_1 4.1 and 4.2 Knowing that the couple...

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