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HW2-Soln-Composite-Materials - .J" .0%A...

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HW2-Soln-Composite-Materials

HW2-Soln-Composite-Materials - .J" .0%A...

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Unformatted text preview: .J" .0%A composite with uni-directional ber reinforcement is made using twounknown constituent materials, Material A which is the ber and material Bwhich is the reinforcement. The elastic modulus of material A is 150 GPa andthe elastic modulus of material B is 10 GPa. ' If material A is 40% of theoverall composite by volume, determine the elastic modulus along thedirection of the bers. In addition determine the elastic modulusperpendicular to the main axis of the bers. - ' 2.F._____-J._____._ --'> E3: reamTM = IDGPK_______________.:0. 0\ *4AL on; Na F\BE(L (1" b RELWIBQ)560mm,: 15';- V: "' Em 147= (/50)(ov)+[0/a}/0160)= (00 + (aE == 6.6: GPACOM r- lQDHVDIULAm 7:. g- Fgeg (Zbzzecr/oidxE0451:EMVF + E: l/m-m/0{0H) + m (M)Emmy-2 3 .. #93:- Afr-" 1/ + 9052W.z = /5 W524 1%) Gm 112" EC, = HOGPQ6 c: '40 M90SEEL,d=\M, 090 z rmqeooc53 = 905%;6 s = 2370 we09$ '5 {GHQ/"c,Pg?EC: ECVC "' as, UsA": Trf'z 1- W9 1: MMMZAS : 1027-: 0795sz.AC = $,l(4O.7QS=- 2,555sz Va: 2- 0.75 273%\/g 5 EC: l)OO.7+ZOSrO,?= 82,51 51,25 : 155.75%f(5:128 @= no 6% ~ (.27 (05 2. 55w? + 205- 2740'? 0.793% 1'3 328.01% 20%? '- 533W \ 40:013*(XC'035)~' VCEc, 6 . -6 -G -6 _____._ a, ai: :100 4 (n' (O "0 0 )\+ 0.5403? W10OTISWIO Describe what is meant by the phrase 'critical ber length'. Explain whathappens if the ber is longer than the critical length and what happens if thefiber is shorter than the critical length.I: " 1,. nclu-Lwc.(it #44,... I #44472 reivrr;aj 7/c tit/{0 f/Woux/ m @QWhen in use, a shing rod can be approximated to act as a cantilevered beam.Assume that the force (P) is applied to the end of the beam by a sh while the otherend of the beam is rigidly held by the sherman. The defamation (A) of the mod isPL3given by the following equation: A = E] . Assume that the length ofthe rod is xed (i.e., can not be changed) and the cross section ofie rod is square. Thedimensions ofthe cross section can be varied to answer the questions below but thesection must remain square. You Should assume the behave as a linearlyelastic material.3) Develop an equation that determines the mass of the shing rods in terms of thematerial properties (e. g., elastic modulus and dimension. , section geometry (e.g.,cross sectional. length and length), and the design inputs (e.g., load anddeformation).L l...on... _ V lowly Lm...was not? war gamebe en.n 91? a 794:} we: was 255 575.6"172Am Pt? 1.3% m mfgW ma k?" MMMe) (if) (e) (toEm" @ nan) M 7%., AW! amwm A... aan! gad IVA-{Md IJ' rja/gnd#2:,_________________ _ _ 7? b) Using the data below, detennine which of the materials shouid be used if wewanted to make the lightest rod. assuming that all the rods have the same stinessc) Using the data "below, determine which ofthe materials should be used if wewanted to make the most economic rod assuming that all the rods have the samestiiaessNate 1 tonne-'3 1000 kg83 7g bw/ V320 Mwld way/4 7gb{/maml {712%qu (1.6- 74er gr M In * .5rm.wws w W'th :9 N (2.3%- NAumtsuvm Au 9 3 (3:3 311;:Famwmbnaw g 9. zxmx{la}: wvwmaw 2.6m 1543(.6. [tidy-83% rad/3 (fa/gala Adda?Mm ata oiymawa} fags?" if? mwmq wgdmm 7'5 Mdrx/wmtw} @ _A shing rod. is formed from a composite material of 0.5 kg of glass bers embeddedin a matrix of 0.5 kg of epoxy resin. The glass bers are assumed to belong,continuous and unidirectional. To achieve a greater stiffness it is proposed to use adi'erent composite that is comprised of long continuous carbon bers that will be .embedded in. a matrix of 0.5 kg of epoxy resin. If the modulus of elasticity ofthecarbon ber composite is 10% greater than the elastic modulus of the glass bercomposite, estimate the mass of carbon bers that will be used to make the carbonber composite. Assume the applied tensile stress is parallel to the direction of thetong axis of the bers. The epoxy resin, glass ber, and carbon. ber have an elasticmodulus of 5, 86, and 350 GPa respectively and a density of 1100, 2500, and 1800respectively.mm0: S 3 216.5353:51!ZQBNstrya 2.31m nah? 34MItem can" PNA/$ 3 V M or:V MW 1%:ng23w ka/mVsm: a 932./ / o a 3 laxV'f'mae "T" Vague 4' Vm VxwadMWWWW em \wcgm :71. VemeuVgeewg Va" Saga. 1.: aViewer 3 W! (59 12.geWeeiy m Vfm' $5,455 7" lgmv gin?e: (317.) (away (Mm/)(SMQ g gel/Z mewsm 3:4 E m? if/ym 5i}am?33.526173m m 03WMlic {a may; amok praaadcm A rod made of composite material is placed between rigid-8119mm (TmS could beState two potential advantages of coating bers before using them in a composite. w ({L'll; a m flag 7M 74%(9:) 7g; / (mm/0 m am 4:, ujZaM/c. e (.1 naar 76 554s5:; 507% :i'kzy [(0794: 73d 24?. (An/m' go (we, Mo/Vchm, 76" ca. crab /7l at) am#1: 765% a m m 'delOw bum]M 4m K1,, mtxakdxogimiiar to a frp composite bridge deck). At 250 the nod ts perfectly behwecn therigid supports and there is no stress in the system. What temperature would thecomposite need to be cooicd to in order for the composite to crack if it has acoefcient ofthonnal expansion of20x10'6 mlmm/C, a $trength of 20 ksi, and aneiastic modulus of 10,000 ksi. Assume the composite behaves as a linear elasticmateral....
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