homework3 - mam. Anfimhumdhyplmmubjauadwabiu-...

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Unformatted text preview: mam. Anfimhumdhyplmmubjauadwabiu- Hucofnmuinmlnana-afiu, - y,- r.Ir,-0}.lehodu|in-mll|¢y.8-126Pland r- Mi. Dmislhosmoxlld frll". - mind a,- Immom:mumsqgmwwimaqs.1m SolU-Hon‘ .pm gals. 2.35) excfiwx-ch) 'VL 5!‘#‘¢*"‘"°—1}] “Vim ' W” ev-vay‘im—fi‘fi'xl 67"“5’diw'fvzq’) a. [fitter-visa) v}, Viv: (av «26.) - onwaqu 9% - o.olbb44b W tr,- mm mm rY- “).M MPbu Prob. 3.3-4 A column in a IMO-le1]! building ls fabricated from square structural steel tubing having a modulus of elas- ticity E - 210 GPa. The cross-sectional dimensions of the two sogmems are shown in Fig. P3.3—4b. Axial loads P4 - mo kN and P. = 300 W are applied to the column at levels A and B, as shown in Fig. P3349. (a) Detenuine the axial stress 01 in segment AB of the column and the axial stress a: in segment BC of the column. (b) Determioe the amount 3 by which the column is shortened. JED/‘6 :6 294 ,' flél flxr'a/J/‘Wrrcr. Egan/flows»: ,' +fZF =0 : 400ml ~F—-o 6: 400141 ' —zao w -J’00£u— 5 =0 6 = 'fOfléM fl 3 Few: J71 /€If c; .‘ Orr 53' (2,) ,LT —200M ’ = = _ : u! ,0/ AW 6; fir [K/mell-K/mnl‘] 6! if ‘1 g P334 F 350 4A! r fizfi—_ flaw—.— m ' [mount—076M]? “ a:=44.amrc) 0; 243'; ¢MPé/t} {/0} «ma/[(5,315] a/ 69/an , 55456:“! f6!th JCA’VMQ, (“As/Ib/ .' ~61- =fi€=é§ifi : xii-)1" 051, {* 4¢.0/¢fi7flsJ/J’m} E; = Z/Od'fat 6221: _ (—meogmamm) f; ‘ aroma éfdflw/fiz I; oéérméflfi‘fll’ /=—/fi/c}}=/,¢zc9mm 6? ‘ hagzggmm 6"; = -. ~59. 7i/J'm». “Prob.” AflgidbeemAB issupponed by vufimlrods etiueudamditsuppomadownwardlued atCofP- 60 W as shown in Fig. P338. The diameter of the support _ red at A is d; =- 25 mm. Both hanger rods are made of steel (E - 210 Oh). Neglect the weight of beam AB. {3) If it is - found that u. - 2m, what is the diameter. d1, of the hanger rod at B? (b) What i: the corresponding diaplaeement at the lead point, C? Solvh'mi Euf h'bv I'Um. 5E9: rigid Exam AB +¢zpyso:rl+rz-p.o k” +JZM3=0= F.t3m)-Pf2m)=0 F. P=bD F2 :1: 33;? = 40 km U ) AQ:L FZ'JS-P= zokN 1m 2m Elmer?!" Form- Mamba Bern VFW 9,: FILI } AI: TIE: -._.— AIEI 4 €2= r'.2'-|-2- ’ Ag} Tm; A152 4 Gm; 09- ngafim As,st small displaccmflé ml 2E1“. LT‘I‘WH Given L15: Mp el= uh . €3=Us" 9443" 2-3: (and?) From similar .mhhg 1c: uc‘ {Avflus-whfirw (3c) Combine (0 4(1) *3 [317) E"?- "—‘ d2 = FzLZdF' ._. 0.0§02| m A259. AIS: ZFILP dz: [0.7.1 mm uv gtgwmm Us: [2.) Probt 3.4-7. A steel pipe ls filled with concrete. end the resulting column is subjected to a compressive load 1’ - SD kips. The pipe has an Outer diameter of 12.75 in. and an inside diameter of 12.00 in. The elastic moduli of the Steel and concrete are: E, - 30 x 10‘ ksisnd E. I- 3.6 x lO’ltJi. (4:) Determine the stress in the steel and the stress in the concrete due to this loading. (1:) If the initial length of the column is L as 12 ft, how much does the column shorten when the load is applied? (Ignore redial expansion of the concrete and steel due to Poisson's rstio eflect.) Soluflorl = (a) normal S‘fYCSS S‘hrairn dls+vibtrh'm 1 E (Y? 7 6 = Corns-1am SHYESS dJ's-lm'w-h'ow r5 = ESE, re :Ece YeSt/H-anIPMC’S? replace. U'xwrxcth PS)?” Pg u’c A¢= § eecttzm in)?" ' m4 ' -I ‘ <15 d5: lE- i9} =) P6 EFS Psgqrs AS _ =g.éE$[( 1135:301- (12.00 inf] _ Fla—0‘ Colvmn geol‘fon Qm'librium 7 M 251:0: -P— Pa—PS .o 9: SETS [IzaTEc—ES) 412.151 5"] 5:- -AP 1TEI2‘(EL-Es)+i?..152 Es] =>+Yom smss dJ'SMWh‘on. Y L” a: ‘3}: "' _4PE°/Tl' L12‘tec— 553+ 12.161139? \——-v--".Ps = —. 0.34m?— ken: “'5 = _4pEg/TT[12;(Ec*Es)1113159551 “mot-finest; arc Colr'anCSSl'VeL SWCSSCS. Lb) elongah‘on _ 4 n. e‘ 5 es ” a ‘ 6L ‘ maimed “2.191551 = 0.013911 In. a: 4.394 “0—2. {W New: column Sher-tons. Prob. 3.4-8. A homogenons rod of length L and modulus E is a conical frustum with diameter d(x) that varies linearly [roman at one end to2d.nt the otherend, withd. 4:: L An axial load P is applied to the rod, as shown in F13. P34- 3. (a) Detennioe an expression for the stress distribution on an arbitrary cross section, 0(x). (1:) Determine an expression for the elongation of the rod. Solu-I'I'oni {00 normal swess _ ' by linemanng 160‘ do . d(X)-de l— x 1d. “LI am. 01th out I + 2%) X L 9 EELD‘ YOd Sea-lbw Qu'mmm '- LEFX=O = Pix? -1>=o ( Fix3=F flan—x => Fix) =P= jfiu‘ (Mk ‘4’ (MNX) (Haas P/Acx) 1—7—’| “ when» - 4P TdJ-(H-Efi- (b) C'Qflga‘h'otn e=jl thdx= 4P1}; dx 1 41: _L T: in ° A008 “Eda {14-fo)" 1E3} H23 0 1T; do}. 9,6 2-PL , Trad} Prob. 3.4-16. A unifonn cirwlar cylinder of diameter d and length L is made of material with modulus of elasticity E. It is fixed to a rigid well at endA and subjected to Mbuted external axial loading of mnyfitude p(x) per unit length, as shown in F13. P3.4-16n. The axial stress, a,(x), varies linearly With; as shown in Fig. P3.4—16b.-(e) Determine an expression for the distributed loading, p{x). (Hint: Draw a free-body diagram of the bar from section x to Section (x + A10.) (to) Using Eq. 3.12, determine an expresxion for the axial (a) (b) displacement, uh), of the cross section at distance x from n+1 5 end A. So IU‘HDH = alluvial loudly: m3: (Wyach mew? gm _ Lzaeowtxmwimxeex) 413,001 A-O VXanSflA _ «1.. 2900A fix gm”- min-“#J-u—ém fool” '5 {LE awed“ '- 3T." W T,(x}=fl(l-VL-). {Vow Hath) K A= £413 ,Pb‘) . 1T6} 0'1 4L. ’0) axial dfgglacemcm 1132'- wh'nacv segment Egggl'll'h/fggm «rm 12,2550: since «pm ' Train-i e consmm, L A fl —. Fifi} e Tl'd2 To (L..x) Rx) H... m.» ——x 7LT“ W o , Fm Eq 3.12, utmntfojfijo £25.93 -: To k L [E f [L- W015 ‘ E. (Lx - 2537 LE 2» ...
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This note was uploaded on 06/11/2008 for the course AME 20241 taught by Professor Wagner during the Spring '08 term at Notre Dame.

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homework3 - mam. Anfimhumdhyplmmubjauadwabiu-...

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