AE 525 EXAM-III SOLN KEYS.pdf - LAST NAME FIRST NAME Total 100 1 The cross-section of a piece-wise homogeneous beam is shown in figure below For the

AE 525 EXAM-III SOLN KEYS.pdf - LAST NAME FIRST NAME Total...

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Unformatted text preview: LAST NAME: FIRST NAME: Total: / 100 1. The cross-section of a piece-wise homogeneous beam is shown in figure below. For the given geometry and material properties, compute the following section properties a) Modulus-weighted cross—section area b) Location of Modulus weighted centroid * c) Modulus weighted moment of inertia [22 (15 points) y El =40 Msi v1 =03 a1 = 5x10'6 ”m” °F E2 = 10 Msi v2 = 0.25 in/in °F use ER = 10 Msi a2 = 50 x 10’6 ,.g All dimensions in INCHES , {P r... m/ it”; ‘5'”-—/ «4/ is ~ ,. EVE A? A ‘7’? %' 76% ‘7; Ari 2' V"‘?’ 12%: ea 0; 95 if? 25' (m. fig mm? 3 é z; a 0‘5“ {a '3__ «$4,225; g5 «wfi m." . 2w ? ‘7 2 . 2. ___: 1; as»? Mam)? +5, im— a mi 2. A cantilever beam is subjected to surface tractions and an end load as shown in the figure below. The cross-section geometry and location of the centroid are shown in the accompanying figure. For the beam, obtain expressions for the statically equivalent running loads 1% (flap); (90mg (mex Wm); M and mz (X) (24 points) 3. A homogeneous cantilever bearn with unsymmetrical cross—section is subjected to an end force (parallel to x—direction) and a running load as shown in the figure below. The cross—section dimensions and location of the centroid are given in the accompanying figure. Obtain expressions for the internal loads P(x),Vy (x),VZ (x),Mx (x),My (x) and M2 (x) (24 points) 1000 lb? Dimensions in INCHES W me [/Wégfizo?) n ”la-Q? {bfl’i’i is: aw i”; Mm {W M .m , =33 ‘9 W1), W 724%; (x; [Q13 Paw‘yz: “WWW ‘ a”) = Kg ) W 3 %GE'% ' ( Vyfjm)m E 0%ij 0 ~90 3 2:» “gm ”2%”!W) ’99 Mx 05‘“) 3O £09 a} '7" fiat? MYGW .w wt‘Zéfifiwm Mx CK)” M>flqgm)fl 5%xa/2U M OWE tig’imllscm ”431”) (so a 15%? I?” a M 0L): ”fl?L%“5m)ib"M Fogfi Wm>*§/é&b X . 7% 9 (m WU}$M7 5’30} “§C%fl%>370 Poo .5, wm lbs 25% m {3 (34,, «‘9 W a W A“) a - M 01 1 ZLW "‘ gmgfié‘; Z i ' V7591); V V5.03) «Sflféé‘x/ t 7 ) {ESQ (so *2. WM) era §M7 (M a 213:0 fl if]; (flaw) gym ‘50 4. A homogeneous cantilever beam is subjected to an end load 012% lbs parallel to the z—direction as shown in the figure below. The material and section properties are defined in the accompanying figure. Compute the free end deflection v0 (20 points) [1:22.311'11!2 [W222.5in4 [22114411114 52:24.81? E:1Msi ‘ _5m/in a=10 , OF Dimensions in INCHES 76 9 :50 WK awymm%fio 5"" lb M (f :2. 46% very”) "M Him) an asset» Me 5*} =' Mei”) _,. g {me Mow) *5 Mfimw $0 0 7;, O Mit (3“) w, o Pfl)$-'E;Zaog VJ «clam gr l ”‘2 POL) *0 a 13,431.: elm % %3W+ M‘ij‘z’ei “a?“ " f; GTE; Oi): Jéflfi‘“)m+6‘9£§9§ ‘ i we “‘3’ “lfg QM? $55 :2 50126:; ("£2”le («J 5 "2L “Em-é’cfigmw gm 1}” «1:, $932!? @3930) ”gag , 3 Veg} 2:. a}? £%,é§m} +4313”; "éwéfiaxm @331" g . 2. A“ C“:- “m‘ifiva— Cm 3 (20‘:- O \90 2:0 $ Cr; :; b60122 Cm%)% $63: 7 5 ~ we (90> -..= 1'50 1:? [ax—60> _. @a + @323 €33: 2: g; 6 wk {2% M 5‘9 a 501w [0 -~ @5931“ CW) +£7.22? \90 L. ) WWWM “E. 5} w % {WE 44:}: a» 23% m [a “my a?) .4 4%; m 2;; g 2:» 42;; I N f ’2: % gigging? 2%‘8 gm% 1 ""5" (,Q—Z‘59CQQ'Q} “124$?” [9155* 5% we 2 i 19,4 flew m @5325 "mam; ‘L g 5. A cantilever beam with piecewise homogeneous cross—section is subjected to a uniform temperature change of -100 “F. The material and modulus weighted section properties are listed in the accompanying figure a) What is the stress at point A on a section at a distance of 10 inches from thgfree end. (17 points) / T 1 3:30 0' y* ? E1 :30 Msi 051:5x10_5 mlm °F 52:10 Msi . /. a2=15x10'6 m m °F ER=10 Msi A”=8m2 z: _ 4 W=O.67m I;=8.67in4 * ..._‘ , 4 Iyz—Om T M . ii “EWM (ESL; «MW k5} AE 525 Féfight Straflures-s Fall mm. LAST NAME: FIRST NAME: Examwéli M115 l. The cross—section of a piece-wise homogeneous beam is shown in figure below. For the given geometry and material properties, compute the following section properties a) Modulus-weighted cross—section area b) Location of Modulus weighted centroid * c) Modulus weighted moment of inertia Iyy 7/ (15 points) ¥ 0: =5x10‘5 m/in 1 OF E2 :10 Msi v2 = 0.25 a2=50x10"5 "1”" °F 2 L34 2, All dimensions in INCHES 2. A cantilever beam is subjected to surface tractions and an end load as shown in the figure below. The cross—section geometry and location of the centroid are shown in the accompanying figure. For the ' beam, obtain expressions for the statically equivalent running loads px (x),py (x),pz (x),mx (x),my (x) and m2 (x). (24 points) Dimensions in INCHES 5 w w.» al} a. as :gwmm Y ca O W? 1:; EQME grwa I?“ g ”mag, blswyl’xclse (”filiéwgéflflfi 3. A homogeneous cantilever beam with unsymmetrical cross-section is subjected to an end force (parallel to x—axis) and a running load as shown in the figure below. The cross-section dimensions and location of the centroid are given in the accompanying figure. Obtain expressions for the internal loads P(x),Vy (30,172 (x),Mx (x),My (x) and M2 (x) (24 points) 1000 [bf ‘Mvog f; g??? «"60 Cfiwgm) w ‘3‘ were ; z 1 Maw 743W '" ll <7; *fiW” 4. A Homogeneous cantilever beam is subjected to an end load of 200 lbs parallel to the y-direction as shown in the figure below. The material and section properties are defined in the accompanying figure. Compute the free end deflection wo (20 points) 14:22.31}? I”, =22.5 in“ 22 :114.4 m“ Iyz 224.81%4 , EmlMsi Dimensionsin INCHES - - _ ,6 m/m a — 10 °F Jag: lay.“ a“: Q QWCZEW my '._ - .39 L3“ warti— ELM-1&3; 7%3 Wx~mgrwmmg 7 ’3 4:) 'EE'L 7 PLW)3%,QW)$ o marge}; a» 2% E}? Mg Lee} ‘6’?" New) t" Q Wig: M): area) :3 wine lb-ma C, :gfitfigmg «wiw‘ew {ifffi- ”2%:1 rxrwwa; (3 Pugs-«Vatwmfl 'Jfi' {M + s “” $33 2.2., “VT? {20 : _.,,_ 2% a”??? Mawfi” ‘9 ”WC EEK g, 9 aw ' h meow l“ “3‘0 9%aw i —> C1? +2mfl73¢ C15???“ WWW WW; i as 7’ 5. A cantilever beam with piecewise homogeneous cross—section is subjected to a uniform temperature change of —50 °F. The material and modulus weighted section properties are listed in the accompanying figure ' a) What is the stress at point A 'on a section at a distance of 10 inches from the free end. (17 points} E1230Msi a =5><10J°' in/in 1 OF E2=10Msi a2=15><1046 mun °F £=mfi I;=0.67in4 I:Z=8.67in4 1:50:31“ fife firm 7 ' a ' 2,, _ T We ‘3” was” , ”i i 153i “5%“ r a??? a ‘2’"; M%§ $2 MW E 20 ‘5’ 1 *5?) 45M one“ @539 e G :2: [0 i5 9., ”5e wég-WE) at»? tzzem 0 Q X “’30wa +L§®m '2' W9 2 ‘9’ ?&2* m“: "$0 E1” xfim to" ‘2:er @Eufi fig “9‘3 I’VE: _.,.. +5ffiwo ib-vslsm P? If “gage“? Txai Wmiéflfi%>'§mii "=53 flfi" if.” ’3 Wm . ms _,_, 3 {mfigm W (Eta) Cmtfim}[email protected])£§XEQ/) Cat-W % , AE 525 Flight Structures-E mi 2014 LAST NAME: FIRST NAME: Exam-Ill £55: me 1. The cross-section of a piece—wise homogeneous beam is shown in figure below. For the given geometry and materiai properties, compute the following section properties a) Modulus—weighted cross-section area b) Location of Modulus weighted centroid a: c) Modulus weighted moment of inertia In (15 points) E1 :40 Msi v1 = 0.3 a =5><10‘E mm” 11 1 OF E2 = 10 Msi v2 = 0.25 Z ' a:2 =-50><10iG m/m °F use ER =10 Msi All dimensions in INCHES 2. A cantilever beam is subjected to surface tractions and an end load as shown in the figure below. The cross—section geometry and location of the centroid are shown in the accompanying figure. For the beam, obtain expressions for the statically equivalent running loads 1349099.,(x)apz(x)»mx(x)amy (x) and m. (x)- ' (24 points) Dimensions in INCHES 7;: 7;: 0 "(7m +2.39% 9.4% sc 5 . g \- ‘f‘ 47%;: $55” Q i9 :7" £523.55; 2; “Walk ... 7 0 EM 2? ”yr/17¢ mmgro W tug-ms G .w—a- ‘? .4: {agar-QLZDJs 7 \J '2... 5 __ 2-C9”1‘9~l3 ’2... M...- 3% max e; +l2tn llama 3. A homogeneous cantilever beam with unsymmetrical cross-section is subjected to an end force (parallel to x-direction) and a running load as shown in the figure below. The cross-section dimensions and location of the centroid are given in the accompanying figure. Obtain expressions for the internal loads P(x), Vy (30,172 (x),'Mx (x) ,My (x) and M2 ()6) (24 points) Y 1000|bf Dimensions in INCHES «323% W <9 G . «a MK : w/WO L5“2*§2;>: — 21%“ - £15m . ” 1% i7“? r ._... M 04.) '3: wfiéfi-Q ”M My W mafl \‘f 10:59 70 PW}: WWW WWWW Maw): iflmflflmw Mxflaopgo Mcuw§5w2§20 [Mi (6’9 O M%C€Cfi}:. +20§Q @“W 'Wfi}; gwa “E, {3450 mefmjéfiy / w 9 l W 5:43 PM): 9 a; «95.2%, - em La A .. o “i" a. m . {We}; macs «i»- (a; Mom) digger): V5335} _.._ 5 fig??? 2.: “£33 (dfiis‘afly {so ’0" .3... :0 $434») {2 {x wfiifi wwng 1' as)“ H; fixéfiw gm E K. E [i .3... 33 m 7"“ >6 .i E. .7??- i. i 4. A homogeneous cantilever beam is subjected to an end load of 200 lbs parallel to the x—direction as shown in the figure below. The material and section properties are defined in the accompanying (20 points) figure. Compute the free end deflection W0 M 6525‘ A m 22.3 £112 I” a 22.5 in“ IE 2 114.4 m“ Iyz = 24.8 i214 E = lMsi 6 in / in °F 05:10— M7 it?“ x £62.: Lem g $434.2 {37% Mg; (.59): W 4 {3.25“ {(2%}; ”mm? {km 5. A ca ntiiever beam with piecewise homogeneous cross—section is subjected to a uniform temperature change of +50 ”F. The materiai and moduius weighted section properties are listed in the accompanying figure a) What is the stress at point A on a section at a distance of 10 inches from the free end. (17 points) E1 = 30 Msi 0:1 =5x10'6 m/m °F E2 =10 MSI /' a2 =15><10‘6 m m °F ER =10 Ms: A}: = 81312 1;, =0.67 m“ 1; 28.671314 3 _ . 4 I),z —0 m ‘t '1’ MD KM") T «um-v?“ '1 M?“ a E; sq A} Arr; Pf 2}: My. ya Mtg i 30 V 2 +673 “two“? 0 O «to»? ?"5m 2.7 (O {5: 2 +523 +L§m O *0 “it?" ...
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