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Unformatted text preview: ENGR 213 Winter 2006 Exam 2 Name: Instructions: 1. 2. Do not open the exam until you are told to do so There are 4 problems on this exam . This is a partial credit exam. All work must be shown in the space provided and must be legible for credit to be awarded. . The exam is 50 minutes long, so budget your time accordingly . You are permitted two 8.5 x 11 equation/note sheets No worked problems are permitted on equation/note sheet Write your name on your equation/note sheets and hand them in
with your exam Do not write in this space I) For the stress state shown below, answer the following questions using the 2D
analytic expressions as necessary for stress transformation (NOT Mohr’s circle). a) What is the maximum normal stress for rotations in the xy plane? (5 pts) b) What is the minimum normal stress for rotations in the x—y plane? (5 pts) c) What is the name given to these stresses? (5 pts) d) At what element rotation angle (from the horizontal) do these stresses ﬁrst
occur? (5 pts) e) What is the shear stress in this orientation? (5 pts) YA ._ 14’ NV];
‘2) 0;“ Rama (y 96/ :Wt
. /z{‘(
(1) PRINL 9% 577255555 xb X47 W (9’ )
‘2’ _ o a ‘v
abefémdmgig =1 9.2 l g 1133” 2) a) For the strain state shown, plot Mohr’s circle, labeling the axes and points P and Q<§ts> _ P+r P PW} mm”
ay=0.003 5x=0~001 M Q l, .‘ F;
5 ‘ “009 ourng H 3 (bf/MAJ
rag/2::O‘OD3 . yxy = 0.006 ex 0.002 b) A state of strain and its corresponding Mohr’s circle representation is shown
below (the usual conventions were followed in drawing the Mohr’s circle
representation). Draw on the Mohr’s circle representation the strain state
corresponding to a 30 degree counter—clockwise rotation of the element. 5’ +5. yxy = 0.004
(0, 0002) 8X 0.010 c) A given strain state, 8,: 0.010, sy=0,yxy= 0.004 is shown on Mohr’s circle below
(the usual conventions were followed in drawing the Mohr’s circle
representation). Calculate, using basic geometry and trigonometry, the strains (8,,
eygyxy) resulting from a 45 degree clockwise rotation on Mohr’s circle (15 pts.) In order to save you some time, I have calculated the following for you; é a [j
Center ofthe circle: (0.0050) 4 U 55" 6
Radius of the circle: 0.0054 ’1 l/IN / 1 I Mb'
Angle 20p =  21.8 degrees (a w {b é‘“ [1 [:0 007/
V?” ’= = 0.00577» 0:90:41” ’ '
g {X CK + R cosﬁi — ’ 49544054532 0,0029
\7 g): CX ’ 726054:  amps—0 3)
a) The 3D stress state shown below can be evaluated using 3—D Mohr’s circle.
Explain why. (5 pts) if
b) Using Mohr’s circle, determine the principal stresses ()0 pts)
0) Using Mohr’s circle, determine the absolute maximum shear stress ( pts) 3.
2.9 x / 00 &A\\\ at  60
z a; ‘3 “M0
/— 40 20 Nxaf’ _;&
MPa
i L F— or ‘20 60 MPa 7
/ xv“) 7W0 ‘ﬁrﬁﬂﬂé, SAW page; MA Eel{‘0 4) Two thinwalled pressure vessels, one spherical and one cylindrical, of identical
inside radius (R = 24—in) and wall thickness (t = 0.125in.) are connected by a tee
ﬁtting to the same pressurized input line (i.e. both experience the same internal and
external pressure). Both vessels are constructed of a material having a strength of
100 000 psi. Assuming failure will occur when the maximum nomial stress in the
vessel exceeds the material strength, answer the following: :1) Which vessel will fail ﬁrst? Why? (no credit without explanation) (10 pts.) b) If the inside radius of both vessels remains 24in., and the wall thickness of the
spherical vessel remains 0.125in., what wall thickness of the cylindrical vessel
will cause both vessels to fail simultaneously. (15 pts.) \\
a) 72:34
,5: was 
9 Mo 000 P50
17 —’EE
“at ll 07mm
5F)» %\m3mu~i a, .
in) 77,Q.;\$ ti‘lt‘S/ MA'Y‘ dw%$ m lmaer n vavw‘i') 9 R=94“
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165 0,135 Far ﬂmul+nn£W5 gﬁbm‘ 03AM :. 02am
SFhl . 6% ...
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 Spring '06
 Keil
 Force, Shear Stress, pts

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