Hw3 Solution - PTOblem 2-1 9 2.19 Two solid cylindrical...

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Unformatted text preview: PTOblem 2-1 9 2.19 Two solid cylindrical rods are joined at B and loaded as shown. Rod AB is made of steel (E = 29 x 10‘5 psi), and rod BC of brass (E = 15 X 10‘S psi). Determine (a) the total defomiation of the composite rod ABC, (b) the deflection of point B. PoW'I'iDn P53: 4D “[01 Apt?) Ls: 401-73.) 0' = 2 £11.] Sin. A“ : gar = Eta? = 3:11.; a“) Em.- zqv/o‘ ,m' soups 5*“ Pfiffi ’ W = VLSSM no": in. 2in Por'lfo» 3c: Pk = — zouozfg L34 = so fa.) A: 3 in.) AM= EJ‘ = §C6T : 7.0626 :53 , Eh: LS'HO‘ p5; (on 5 r 5.5 + s“ = 17.55:? m)"— 5.csagu;o" 5r Imam" M45 3;; = 5.64 was?’ 5.1.14 Prob|em 224 2.24 Each of the links AB and CD is made ofalumjnum {E = 75 GPa) and has a cross-sectional area of 125 m2. Knowing that they support the rigid member BC, detenninc the deflection of point E. S OLUTION EB ' Fan USE mem bar at as q 'F'f'Qt. L—4— B ‘ s C 0.20m ' 5310” ‘9 2 ME = 0 4am) as + (awxsxio’ )= 0 an e sgsisué w 59 2 M3 = o (0.34) FED — (0-20X5xro?’ ) = 0 Fa, = #5625 no? N F09" (Pink’s AB and CD A: 125m: = HES—#04 mt x 1. =———-———(2::?£4223$;::: = = as 3 x 3»: "El-ii? * “‘9” “04"” : 8° :7" 5139,” e = 33;?“ 323$ '-' 112. '5. Ho" rm? 3;: 34+ like Deiormfian airman.“ = 60.00110“ 4- (0.44 XML: we") = 10?.5wto"m = 0.:0415 mat Problem 2 30 2.30 A homogeneous cable of length L and uniform moss section is suspended fmm ' one end. (a) Denoting by p the density (mass per unit volume) of the cable and by E its modulus of elasticity, determine the elongation of the cable due to its own weight. SOLUTION (b) Show that the same elongation would be obtained if the cable were hofizontal and if a force equal to halfof its weight were applied-awash end. (CU For ejemen‘l w‘l' Poa‘n‘l' 1‘ alow‘l'E'Fieal In, movelfnad’e y ’P '—' werak’! 0‘; Fof‘l‘l'un Pork/j = m A (Lay) _ P _ A(L- LL ’(L-) as _ fiL - awn. £33; a): 8 = SaLfi-‘LCELLQQ’V ‘- 193 (L7 “.Ji L); O ' 2. "- _ __L_ L1 =€§~<L %) 2 £2— “E T0419 wag/Lj- W ‘— L1 F-%fl‘ %‘% =%P3AL=%W "" probIe m 2 ‘33 2.33 Compressive centric forces of 40 kips are applied at both ends of the assembly shown by means ofrigid plates. Knowing thatEs=29 >(10‘; psi and Ea=10.1><10‘ psi, determine (a) the normal stresses in the steel core and the aluminum shell, (b) the R deformation of the assembly. 10 in. 1 in. LE? 1'; '-' Fori’favlo‘F 6146pr 'Force cam-Hes? LY sbeffi. Ps ‘- Porh'ou draw:th ‘Fbv‘ua cavh'ej gorse_ Steelcore __ PAL. : S g ' EaAe P“ L .— .— éAE 5 ER Ps- 2. 5 73"}af fierce P: 133+ P5 : (EAAQ... E5_As)% E. E _ ._P____ L * EmA¢+EsAs Delia-'- P 1‘ ‘40ka3 A1: fidfi—Jfi) = %(2.51-L0Y' :- 4.1233 ho“ A5 = JfiT-gl‘ - Emir 0-7254 ;...‘ E = —-—~————~m——fl93———-- ::' -ggo_q; we" (IOJ x10 ‘)(4. I235) + (2?xfo°)(o.785q) (cu Gs= E52 = (zexxo‘iémomxm‘) “Jammy-5: —12.o: ks:«e‘_ 5“: Egg -.~ (:ono‘Xmofimo") '-'-6.27¥/ng55 —s-27 la: 4' 1 (1:3 5-: La r (IOWGZOFH no") r “6.?JYID'3in. 4 Problem 2 . 39 2.39 Two cylindrical rods, one of steel and the other of brass, are joined at C and restrained by rigid supports at A and E. For the loading shown and knowing that E5 = 200 GPa and Etr = 105 GPa, determine (a) the reactions at A and E, (b) the Dimensions in mm deflection of point C. r—lso—T—lzo 100 100 A c Aha: 5‘.- 200x10“ Pa. ' ' ' ' A = E01011:- i.25éé‘f*f03Mm1-= {.25664filo—3 m1 EA: 251-327wo‘ N C+aEz E.- lOSleqPq / A : flso)‘: 706.86 mm‘ : 7oeiseud‘m E 1. Ass: 19:9, L=ISOmM=OJBOM __ ?L,, F 9.59.180) = H: gm- ————EA # zyhsnflos memoxm 112,. 8+, (1: P: Q“- goxioa .._L = L20 mm: OJQOM H 3 _l _ sen = @2531:ng = = a — Cf!» D3 P: 9,- 60»!in3 =' [COMM = 0.100.... '3 5.3;: gig—i" = (92532;: 265?“) = Isl-Insuo‘f'fi, —— gamma)" 9+0 5: [9: Qfi~looxgog L= I'OOMM‘O.!OOW\ 3 _ g = 3‘: = (9""°°“‘D )(f'mn = LEWSSon—qR, — l’b‘iflss‘xlo‘ “E E TLQZOKLO Mrs E: s”: emswsm +5”: assaswgo‘” 1?, ~— 242.41%:0" Since Poin‘i' E canno'i' move repdfve +6 A) a“; '-' 0 0:.) 3.85337”? Pr wax/112w? = 0 I3. # ELSSlxiog N 62. R5 = F3;- loamth3 = 62.8xtog—Ioouog =-- 37.2%0’ U an Sc = S.“ Sn; .— r.ra3<;7vzo“’ Pg — 26.348x10“ = (Llé’aéfiwiD—qKéZfiSlxlosiv 26.3%xzo“ = 46.3xto'ém “é-gfim” “ 2.46 The rigid bar AD is supported by two steel wires of 1'1"; —in. diameter (E = 29 x 106 psi) and a pin and bracket at D. Knowing that the wires were initiain taught, determine (a) the additional tension in each wire when a 220—1b load P is applied at D, (b) the corresponding deflection of point D. Problem 2.46 LB+ e be He N'l'au i‘OVI O'F bail“ Them 38 = i2 6) SC, = 249 58 = PfisEi—se p g EA See mew") $3") (12 e; EB Lee to = Ioenwlo‘ e D _. RF LCF _ Sc _ EA a. P “ Hwy, " (qulo‘H-(i-I (2H! a) CF _ _ 18 CF : l18_e$xjo=‘e Usinfi 'Fme boaiY ABCD Dir/1,:o 12fl5+24P¢e-3eP =0 (amoejmot 6)+(2+\(H8.63¥l0‘ e) -(36)(210) : o LLIZSSHO‘ e = (300m) 9 = IflISSXKo‘Z’ we; (00 P35 = (los.77xgos‘)(1,qlg§xlo-=) e 20%3 jb P”: = (ug_g,3,xlo$)(i-qias'xto'3) = 227.6 )1; G‘i.’ X Jo's in (B so = 36 9 = (as \(i.912§x!0“3) O, 06‘“ ivy L A ...
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