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Unformatted text preview: E MCH 210H Statics and Strength of Materials
Fall 2009
Exam 3  CONFLICT This is a closed book exam. Show all of your work in a clear and logical progression. Partial credit will be
based on the clarity of the work shown. If the instructor can’t read your work, you can’t get credit for it.
Clearly mark your answers and include units. Check your work. The exam has ﬁve pages and a cover sheet. Let the instructor know immediately if your exam has less
pages or if anything is illegible. Good luck!
Fm = rdm
1. of10 I AV=P+wangx Ix = IyZdA
2. of10 P=Pa+pgh AM=C+VAx I _ sz
3. of10 V=6ly'A, A=6LVL y—Ix
4. of 10 I = 1m, + Ad2
5. of 10
TOTAL of 50
0' = —_M._)_).
I
F = ,uN
X___h )5 x h x
h/2 ‘I’h/3
b
b
A=bh A=nr2 A=bh/2 lx = bh3/12 Ix = m4/4 i, = bh3/36 NAME: 1. Determine the magnitudes of the reaction forces at pins A and E. Neglect the mass of each member. c::::::D——>Ex
ﬂ/BD Egg TF l[Ev C3) FEDS /
BO \
ZMFto: 60w30°(o,z\= E\,(o,z
ZMA=02 BDAIMéOMBX= 250(03» EV: 400 ]
BD: L'QZ N ZJESHN‘DLU ZF$:O; E)‘: BDMBO %@
iFy‘O’. AV: Bum/Moo” «7,50 = '50 N Ex: 27“
0 ® .—————”"—""'
2R: ; Aw BDCWO 43‘ "‘ [gm/Exact} = 4m N (D : Ayf— + Av '2 215 '4‘ ® A: ”bl N 51$?»— NAME: 2. Determine the moment at the base of the cantilevered retaining wall. There is salt water on the left
side of the wall and oil on the right side. Specific fluid weights are given. Do your calculation for a 1 ft
unit length of wall. mgmm’f arms Q) R0
1’3 14/3
MOE—4% ee(q\=224 6., magma @ louse 01/: A @
RN: minim : leex @
R0 : %,(2qu(4\= 443 (23 M: ”29... — Mo = %(Ise%l'%(448\= 306' ”“6“” @ M = 3060 lloft/wc’c NAME: 3. For the shaded region, determine (a) the distance from the xaxis to the centroid, (b) the second
moment of the area about the xaxis, and (c) the second moment of the area about the centroidal xaxis. a a ﬂu;
A=S\ic\)t'\fajxlzdx:m '57;
O
O
A= 3—503 ®
a 3
a “ axl _ Q.
’A=SO\/cycix’§o Jim‘d)‘: T‘o' Li
*A ag/Li 3a
.— L— 2 5 “'—
\i; A 203/3 g C2)
3/
Ix: i‘lldA a 3 ﬂziﬁzr ' a’iléaeh
 L 3 I = L Siﬁfii Ax = 5 Hz 0 '
di‘t: achLy .7 $ 0 Za‘i
13L: T— ®
1“: IL + Adz
Li 'L 3 7'
2—3;:164'7361 ‘2?) w 46 ii aoaaba” NAM E:
K03 b3 3. Determine the distance from the xaxis to the centroi , the second moment of the area about the x
axis and the second moment of the area about the centroidal x—axis. (0
y \{r SVdA
x
A= 5cm
dA=$dy=®r %)d‘l
Z. L
:S(a_£)d1:a1%=Z% 3/
o 3 3 3 ., qA, 0‘4
_ Q 3 , $_§—:g— [75"; Za
\{A= So (ml—5&3d7' 7’ 4 4
L‘.
a 1:! 03‘ 92:: ET“?
I¥_So(a\f‘ “361 = C? 6 ‘==‘
1%: 1c 4 Ad;
£3} = 1o + 1&1?)
3 q 231”3"g 4,1:(1
(L'X'3‘5ﬂaq =<IZEV771§0L "Wat E9...
IL' '6 i L‘ NAME: 4. The beam section below is subjected to a positive bending moment. The maximum tensile stress is 75.5 MPa and the maximum compressive stress is 55.8 MPa. The second moment of the area is 457x106 mm“. (a) Sketch the flexural stress distribution as a function of y in the space provided. (b) Calculate the
bending moment, M. 300 55$ V 150 All dimensions in mm ’65.? @67me 6 g
: . =— I 3 __ :+7_oo)&l0 N~MM
Q» \l l’l7 ‘3 CF 65% M IZ’ll‘: O 15.5 (“67540“)
472.6 @‘lwnm Q‘=+765 M:  =*200 “09 N'MM M: 200 \<N~m NAME: 5. A 20 kg block rests on a plane inclined at a 30° angle. Is the block stationary or sliding? Calculate the
frictional force. pa = 0.5, W = 0.35. MjN ll 20(qsmmza' = IMF? M g
" ° , N 0°: '
Ei‘fto3 F = MG‘M'SO — ZO(‘I,XI\M“3 Gig i kl ZFn=0L N: M3 cw?“ MSN= 0:5(20Mi‘8l360035 = $6.0 N (2) F > MSN ——> sliding CD 'F = MK M = o36Qe¢ﬂ§= 5‘15 M @ ...
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 Spring '11
 C.J.Lissenden,

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