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Unformatted text preview: ENGR 213 Winter 2006
Final Exam Name: K5 2 Instructions:
1. Do not open the exam until you are told to do so
2. Fill in your name above
3. There are 4 equally weighted problems on this exam 4. This is a partial credit exam. All work must be shown in the space
provided and must be legible for credit to be awarded. 5. The exam is 1 hour and 50 minutes long, so budget your time
accordingly 6. You are permitted three 8.5 x 11 equation/note sheets
7. No worked problems are permitted on equation/note sheet 8. Write your name on your equation/note sheets and hand them in
with your exam Do not write in this space 1) Shear and moment diagrams.
a) For the given freebody diagram
i) Draw shear diagram. (6 pts)
ii) Label the diagram with values at crosssections A through G. (12 pts) 25+51(x4)2 ib/in
100 lb ‘ 100lb/in )00
j ES"
CW, I W It” 7 v
X Uli’: :20 
47 IOO ~ £IOOJX+V"
PW W a  Ea  r 
gkj) v i;
3: V,
WZF =0 ‘ 7— .
too “(0100 Jx g, 7.
+[as+ 51(x4)Jx
/ G 4+V=OJ DmazAM'. A—7E3 ) CaNSTAA/r Pas/T'n/E 5L 0P5 ® ﬁat) H0£i30NTA¢ (1471)) mm. N54. SLOPE @ 0915, thaw/imp 4‘1 EiayF/ 1+d2120N779~L
F767, mama/Um; @ b) For the given freebody diagram and shear diagram
i) Draw the moment diagram (2 pts)
ii) Label the diagram with values at crosssections AB, and C. (5 pts) 1000 inIb. 2) A moment of 2500 inlb is applied to the triangular crosssection beam as shown.
The centroidal moment of inertia is 0.04688 in‘, Young’s modulus is 30 000 000 psi.
a) What is maximum tensile stress in the xdirection? (5 pts) b) What is maximum compressive stress in the xdirection? (5 pts) c) What is the name given to the location of zero bending stress? (5 pts) d) If the answer to (a) was 50 000 psi, what is the minimum magnitude of axial load
(a force along the xaxis) which would result in only zero or compressive stress
acting on the crosssection? (5 pts) ' e) If the 2500 in—lb moment was n_ot applied, oould an axial load of 2500 lb be
applied without buckling occurring? The length of the beam is 120 in. Show
calculations to support your answer. (5 pts) M = 2500 inIb M = 2500 inlb I
A'L AX
+9 55“
d) 0;)(134 c :48 ' mirth: ozx’m‘ + ﬂail GET}. g 50 000 0 =Wm +— 500004’9/
n. >. max. *4 Pt” ‘ n‘iTﬁ'EI
_ ~— 4/ 2 n
9) PM L1. '5» n=\) Yner \ npp\xc.A—H€. TT?’ L30 X/0‘>(0.0 4é 88) +92 “94"
/:Lo1 ER = 9M )2; F7: CR ER < 2500M +\ A/U/ BUdKL/A/4 WILL Uch/Z 3) A transverse shear force of 2500 lb. is applied to the triangular crosssection shown
below. The centroidal moment of inertia is 0.04688 in“. The equation to calculate the stress caused by a transverse shear force is Assuming it is desired to calculate this stress at y = 0.5, answer the following: a) What is the correct value of V? (3 pts) b) What is the correct value of Q? (10 pts) c) What is the correct value of l? (3 pts) d) What is the correct value of b? (4 pts) 6) Where on the crosssection (ycoordinate) will the minimum shear stress occur? (5 PtS) _\ \4/2 X Q=jA via ‘49” *5 "I a; O ,m Q—(m(t mimics}
€1 ‘ ' ML,“
5 = 0.0277813!“ M 4) A cantilever beam and its corresponding freebody diagram are shown below. The
beam has an elastic modulus of 30 000 000 psi and a centroidal moment of inertia about the zaxis of 0.005 in“. The internal moment, M, is constant and equals 144 in
lb. a) What are the two boundary conditions needed to solve for the deﬂection? (4 pts)
b) What is the slope of the beam at x = 6 in? (8 pts)
0) If the slope of the beam is given by the equation slope = 0.01 x
what would the deﬂection be at x = 6 in? (8 pts) ‘
d) It’s been a fun term, have a good break! (5 pts) @ 144 inlb y t
144 inlb 144 inlb () View 4"
CV) v’(o) =0 907530 M
['9 GEL/:_ M = M:‘0,0009é as? _  a ’ (soxlo‘XmaE) W6“) if _ 096 1“ (if
6"“ Mﬂdx' 0'00 'X C' J 0’“ \
{/0pé @ X26 )5 ¥\OP’[email protected]
"0.00576, ...
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 Spring '06
 Keil
 Force, Shear Stress, pts, Compressive stress, Tensile stress

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