AAE352_Summer2010_Exam02 Solution

AAE352_Summer2010_Exam02 Solution - AAE 352 Summer 2010...

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Unformatted text preview: AAE 352 Summer 2010 Exam 2 Name: AAE 352 Exam 2 Due at 11 :00 AM on July 23, 2010 No late exams will be accepted Mailbox is in the AAE main office, 3rd floor of Armstrong Hall Mr. A. Ritchey (Office: Arms B144) NOTE: You are only allowed to use your two page glossary for reference. Do not discuss this exam with anybody other than myself. Only a graphing calculator (scientific or four function works too) is allowed for computations. Failure to comply with these guidelines will result in no credit for this exam and a report to the Office of the Dean. AAE 352 Summer 2010 Exam 2 Name: 1 Short Answer A. Indicate if each of the following fit the plane stress, plain strain or neither condition (5 pts): 1. The skin of a balloon that has been filled with air: r r 2. A long drainage pipe subjected to soil loads (external pressure): ~ '. 3. A narrow beam with a large length and rectangular cross-section subjected to a pure bending moment: ’ . ‘ 4. A hollow tube subjected to a pure torque: ‘1- B. Name the three conditions that must be met to guarantee a unique structural solution (5 pts): 1. r 2. Cr 3.' C. State St. Venant’s Principal in your own words. Please explain how it applies to the shear lag phenomena (5 pts): ,‘ fl ,r D. Will the effective torsional rigidity (GJeff) When Warping is constrained be higher, lower or equal to the unconstrained torsion rigidity (GJ) for the following cross- sections. You need a separate answer for each section (5 pts): AAE 352 Summer 2010 Exam 2 Name: 2 Elasticity Given the displacement field: Please perform the following: A. Draw a unit square in the x-y plane before and after the deformation (5 pts) B. Determine the strain (6 components) in the cube (5 pts) C. Use the stress—strain relationship to determine the stress (6 components) in the cube if it is made of Aluminum, E = 72 GPa, v = 0.33 (5 pts) D. Calculate the strain energy stored in the cube (5 pts) i“ ,7, [\- ' AAE 352 Summer 2010 Exam 2 Name: 2 Elasticity Answer Sheet AAE 352 Summer 2010 Exam 2 Name: 3 Section in Torsion Consider the following cross-sections: b = 200 mm t=3mm A. Compare the torsional rigidities assuming both sections are made from the same material. (5 pts) B. For the closed section, determine the shear flow due to a torque (T) applied through the center of twist. (5 pts) C. if the maximum allowed shear stress in the material is Tallow, what is the maximum torque, Tmax, that the structure can take? (5 pts) D. What is the twist angle per unit length that results from the the maximum torque, Tmax? (5 pts) .«r [‘13. AAE 352 Summer 2010 Exam 2 Name: 3 Section in Torsion Answer Sheet AAE 352 Summer 2010 Exam 2 Name: 4 Non-Symmetric Bending Consider the beam in the following diagram in which V2 is applied through the shear center noting that Vy = O: b=50cm z VZ = 1000 N X y h=100 cm t=0.1 cm l<——————»l L = 500 cm b 0cm A. What are the moments of inertia of the cross-section? (5 pts) B. What is the orientation of the neutral axis for the given loading condition? (5 pts) C. Determine the location, x, y and z coordinates, and the value of the maximum tensile stress in the beam. (5 pts) D. Draw a diagram and label the values of the shear flow in the cross-section. (5 pts) AAE 352 Summer 2010 Exam 2 Name: 4 Non-Symmetric Bending Answer Sheet U1 f AE 352 E C“ a Ton b 4 R ,z —— _ 3 z A 3 \ iy‘ (kiwif— + 229% 1;; : £(O,OOLI;ZHZL.506) + 8333:33,3cbcm4 M 3 :2 3 , .12: «17% “9%) “gnooqa 4-5125» 0.008 = $300M" 132: wax-3) + Emmi/23: Jan/60) : @500 My " :I z 233131 f “ w}; an“ f1 I( 0 0L; ‘543 Vt \l7. N518 1 T’s; -L tug A “y rm)! fig : VZL :'500/OOO N—CM .— _ = ' ' .«LI Ll .. ‘igzmg‘ ‘___}_2_Mg L K31 Cm <7“ 13:14:42 % 13:24:32 Ml: é‘qozéé_g Cm“ 02x: 552 g -3 5-2. ‘ @ “Pt :1 (3,1)[email protected],503 021x: 350 3%; 3 55m?“ @ ’Pt :2 (51.1):(0, 50) Uxx=~lfl£0 £5419“! a£“"=—I;75n<>q é} (0.50) or UXC“’=+l-75Mpa M0750) l6L:O (£5: V137, VZQZ—VlZV—Z is: (V‘gz Q2 - V‘ngyvz 1A |—>;2 Q3: sigh: 55, Ga:s\t(b—§fi:55\-D.O5sfq In 6H3 (323: BM 991%? :32) GE $0105?" ‘35 at}: $150 + 553 — 0,05 55 In Lb—va Gaf’ts ELL azr-t 35—23% -553+0.056§2 P22 775:5.0L105a‘q(55fi0.05 sf“) — (aims-H 5 5.)] woo £5 *0. C705; 5,9 +0.17% 9‘ N/m Tn in 353 25, (1,0H05e-‘1(125)- efloflegcozsmga $0553) (000 is: 0‘0035 egaoswsz _ LI...%53 V/m‘ In ‘193 fisfl‘l-QHDS‘L‘H (‘ 553 4” 0/0595) *G-?D3écfl-Ss3\\ I 060 (CS ': 0.0051 H53? —0,.|7ng33 v/m akgg 4—: .1 N/cm *7 —\ CkeLH 7 0 2+3: 0:9~§f@.00525f—0.17485, (is. _ . a 3 .nH 9. 50 -OQ(Q_9.g_5’SI_‘O__§:ZS|)L 2: al—i N (I o comPM f0 1000 N Applt'ed , 7 IOD 3 r1: 1000: 50 «0,0035 35 +0, 3454 5g + H. 2e53 0L5? = WM! mow/V ¢ AAE 352 Summer 2010 Exam 2 Name: 5 Multi-Cell Section Assuming that the thin webs are ineffective in bending, analyze the beam box shown below: 3000 N 5000 N h h=50cm A=Scm2 t=0.5cm A. Determine the moments of inertia for the cross-section. (5 pts) B. Calculate the shear flow in each web. (10 pts) C. Find the location of the shear center relative to the centroid of the section. (5 pts) 1AAE3456? 4£XM\QSO'.W ! ? a + 5‘ gince, webs W Mos-W566,in 'm bemoiwtg (90:25 git 3005») 2° '= 9.6 cm mew/“fad ‘Sli‘bm low Sirlhagr 1&3 H Mg”: fl(6)(615>2= 20250004” I2: HA(%)"‘: ’2500 w” Cut \oo’tlfi Var-Liczd Sh-a‘tght w‘abs; (éSZ-gf/‘ZQL :”O.6q OI; C64" 1'— N/w (5,01, = mm as z-ouzwuzasm) >20 '2... 9.3 Sam was ma 2 2:2: Zaa+i~9 I 5009(3)):02ng +02ng34+°742ng 1:3 ‘ ‘ien * if “423 asqooo =2<¥§Wf§fieb €23 3" Q61 + 21: +0? (igg—ngQoaJ’igq) €24 ' kW?!“ m 56é5°))(%o;+ 24,) 4,5, = Zofiiq', 2 SQDd)‘—”+ I740 30, 6000309- 5/4, 15? 71,1000 =- 1750 is. +5500156a .AAE 353 ’ Exam 5L gamma We 5 Pa. :1 CM’ 999.; ‘ _;, d _ 4...:— $5 any, fieufz‘s - acgamgégw} t f / (Miaééi meta-03h} h: [ammzaswzngm r “Ll—Mo [QM-lemma —(~g0,+iw5501= figflMwh(-2o.+zaa>+<z¢a-2o3 ‘ Wis 31 0.05:[ 103.5 cam —50202~ 0550] : -20] Mg; _,60 4,130.54: -7.5535iol+ (9.55%;Z = 204 +‘g—OOOZoQ A‘y awe” { «5‘70" 14%“ [ ‘5 50m 7 Ergo-i Us 'Zm)(550w,3~ Usmwwfio / 11 FL: 8cm]: (nqxuycsocmal masofl +(95 “ZAMEOMX = €000 A) 2 7. £4; SOOON(50w\:'(25)27r(M\ +1515032+75$o>2 5030,0130 =O’H7, EH 3 250, 000 / )6) Kb“; MM VZ=3OCDN to 56‘ £6 Fight (5? 2 W "mi 645'“ bade-mes fl flyzgooo 63,: I760 g“ + 500036;; 94,159 AAE 352 Summer 2010 Exam 2 5 Multi-Cell Section Answer Sheet ‘4 ’4- " ‘I \\ A, #3, \QWOC o». «W 1;} 500 ( on if?" v’ cm” 16;“ z \) O- z "' W" W“ \ Name: 111*: (L, Scfeci—I-Ofl ...
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This note was uploaded on 01/18/2012 for the course AAE 352 taught by Professor Chen during the Fall '08 term at Purdue.

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AAE352_Summer2010_Exam02 Solution - AAE 352 Summer 2010...

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