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Unformatted text preview: ENGR 213 Winter 2006
Exam 1 Name: )4 1‘," 2 Instructions: 1. 2. Do not open the exam until you are told to do so. There are 4 equally weighted 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 one 8.5” x 11” equation/note sheet. . No worked problems are permitted on equation/note sheet. Write your name on your equation/note sheet and hand it in with
your exam. . Some problems may include “extra” information. Do not assume all given information is required to solve the problem. Do not write in this space SSwEAVN 0055+. MOOHO 3m>z
5% n2 3 ﬂv 1. An circular crosssection shaft made of iron has a length of l2in. and a diameter
of 0.5in. Iron has an elastic modulus of 30* 106psi and a Poisson’s ratio of 0.28. The shaft is subjected to a compressive axial load of 200le.
Remember to include the correct sign and units in all your answers. a. What is the average normal stress on a plane perpendicular to the shaft
axis? (5 pts.) b. What is the average Shﬂ stress on a plane perpendicular to the shaft
axis? (5 pts.) c. What is the normal strain parallel to the shaft axis? (5 pts.) d. What is the change in diameter of the shaft? (5 pts.) e. What is the axial elongation of the shaft? (5 pts.) P = ' g . .7 —s
= "3. 395 XIO C
9M“ —w
A AD: —\)£. D
AD= ~(o.28)(3.39§X/0—5>(0'§) AD= 4.753 x /o*“;n.
9 5_ _P_L __ “2.00022 AF— £(0,5>Z<30><I06) g — 0.0004074 *2 e’n, "'I 3'de "/ ﬁnal and» NY.
*1 3110 2. A force of 500le is applied vertically downward at the end of the rigid
horizontal bar, AB. The bar is supported by two vertical links (BC and BD) and
a pin connection (at E). This structure and the corresponding freebody diagram
are shown below. Using notation as indicated on the FBD, answer questions (a) through (e). a. Write three independent equilibrium equations for the structure (3 pts) b. Is this structure statically determinate or indeterminate? Why or why not?
No credit without explanation (6 pts.) c. Write the compatibility equation(s) for this structure (6 pts) d. Write the constitutive equation(s) for bars BC and BD in terms of the forces Cy and Dy (4 pts)
e. If bar BD was removed from the structure, would your answer to part (b)
change? No credit without explanation. (5’ pts) 0») {Ego LTinz=0 6’
Ex=o 500+CJ*DJ *Ej ‘0 ( gi/j‘p/R ®2M5=0
500(30) + Cy (24> D_7 (24) = O b) INDET'EFZ MIA/ﬂ re , 3 nay/L. (saws.
4— UNKNoa/A/j ’i’9 M9 ’3) >155, w/ﬂvL Arr [SD/unknown DJ J;
dwmaJ—Vi H'WX (3,> 2N¢J 3 agnj. #7 /
Z uhknawnf, . 0
OP 6"“ 5 Q/é/
\ «X i (M B
/ V0, VJ
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ﬂ 9 3. The steel bar shown below is subjected to the distributed axial load, q(x). Given
that Young’s modulus is equal to 30*106psi , L is 12in., F = 75lb., and the . . . 2 .
crosssectional area 18 0.25m , answer the followmg: a. If q(x) = 100 x lb/in., what is P(x)? (10 pts.) b. If instead, P(x) = Cos(x), what is the elongation of the bar? Be sure to
include the correct sign. (10 pts) c. If P(x) = Cos(x), is the bar in tension or compression? Explain. (5 pts) ér)=/oo \ \
Z X mléﬁdi} 1%er
{pk _—_o 051/ “(KM
17. ,
«— P<*>;flooxdx ¢— 75
’9 x
3“ /
{39‘} J78): 7Z75—50XL Karl
9 \
x? ' WV“ 0 . L, 12 /’/:;‘
‘40:» 6%); 9 =fniglcj : c0596 olX ___)7‘)54,(10 .m
5 4 3— PrE. x (0.25)(3ox;09 A—ag—«g
34ng \8( \LM . p I .[ﬂN/V‘} “ff/Jim
%J\\ 9 ﬁnd le)= Cpsy i 7:. 0—?l7—J P6X) La))l alﬁMSZ/ IA SyéA' 77nr%¢ln.5 01m AN M m ‘lfznhw o‘l’lwﬁ M m (L: {>(gsjlm‘
O/A/e’” . A shaft consists of three sections; a hollow section (A), a large diameter solid
section (B), and a small diameter solid section (C). A Torsional load is applied
between sections B and C. The shaft is made of steel (shear modulus equal to
12*106psi). A drawing of the shaft is shown below. The diameter(s) and
corresponding polar moment of inertia of each section are as follows: Section A Outer diameter = 1.0 in. Inner diameter = 0.75 in. Polar moment of inertia = 0.0671
Section B Diameter = 1.0 in. Polar moment of inertia = 0.0982
Section C Diameter = 0.5 in. Polar moment of inertia = 0.00614 Answer the following:
a. What is the minimum shear stress in m section? (9 pts)
b. What is the maximum shear stress in m section? (9 pts)
c. What is the m angle of twist of the shaft? (7 pts) ...
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 Spring '06
 Keil

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