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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 crosssection 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 xy 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 crosssections: 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 NonSymmetric 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 crosssection? (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 crosssection. (5 pts) AAE 352 Summer 2010 Exam 2 Name: 4 NonSymmetric 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 ,
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mow/V ¢ AAE 352 Summer 2010 Exam 2 Name: 5 MultiCell 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 crosssection. (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 MosW566,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 VarLiczd Sha‘tght w‘abs; (éSZgf/‘ZQL :”O.6q OI; C64" 1'— N/w
(5,01, = mm as zouzwuzasm) >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.;
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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
Ergoi 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'“ bademes ﬂ ﬂyzgooo 63,: I760 g“ + 500036;; 94,159 AAE 352 Summer 2010 Exam 2 5 MultiCell 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—IOﬂ ...
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