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Unformatted text preview: Name: Section: Strength of Materials Final Exam Fall 2004 Check
Problems
to be graded Problem Value Score Total: You are asked to solve 5 out of 6 problems constituting this examination. Problem 1 is
required. You may choose any four from among problems 2, 3, 4, 5, and 6. In the box above please indicate which four optional problems should be graded. If no problems are
checked, we will grade problems 1, 2, 3, 4 and 5. 1. Write your name and section number on all pages. 2. State all your assumptions and present your work in an organized and legible
fashion. Neatness Counts, points will be deducted if your work is not neat and
properly organized. Name: Section: Problem 1: For the beam shown below:
a) Draw the transverse (shear) force diagram (V) in terms of w and L.
b) Draw the bending moment diagram (M) in terms of w and L.
c) Given an allowable stress of lOOMPa, and considering that w = 1 kN/m and L = 1
m, determine the minimum value of b.
d) With b found above, determine the magnitude and location of the maximum shear
stress (both the position along the beam and the position in the cross section). lP=WL M=3wL2 Name: Section: Problem 2: A structural tube with uniform wall thickness of 1/4 inch is subjected to the loading
shown below. a) Determine the normal and shear stresses at point C. b) Determine the principal stresses and maximum shear stress at point C. 15 laps
meta. GEOME’ERY Name: Section: Problem 3: a) A tensile test was done on an aluminum rod lcm in diameter. From the tensile data in
the ﬁgure. ﬁll in the rest of the table below. 500. _ _ _ . ‘ u n L V _ mm:
450  _H g —‘ V —‘ _ A
400; : " __ N _ A H
W : V" Z‘  ﬂ — .‘ﬁ‘ A S 
350 _ _ . _ _ y
E a... “ j ,7 . ,
z . ' ‘7 I re tress W a
T; 250 "— . ‘ 7 — — _§ “ :
3 ' ; .
5 ma _ , .3 timate tress l' a
150 ; — 3 ‘ " ‘ — mo, , ~.' :. A _ ;: Porsson sratio 0.35
50... E — — —_  _ ;V ' 04 ‘ﬂ‘f' "'"':l:_ l. V"’ V :7." f_"_'"";;'"';‘
0 0.001 \0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
Strain b) Given the composite block shown below, answer the following question. Use the
properties for Aluminum above, and assume the Young’s modulus of brass is 70GPa. A force P = 450kN is applied to the composite block by means of a rigid end plate.
Knowing that h=10mm, determine the normal stress in: The brass core
The aluminum plates
E M s s (are Aluminum plates m3sz rude /. Fig. P236 and 92.37 Name: Section: Name: Section: Problem 4: The motor M supplies 20 kW of power, which is consumed by mechanisms connected
with gearing wheels at B and D. Note that the two forces shown in the ﬁgure on the two
active wheels are associated with power transmission and are equal in magnitude. The
force at B acts vertically, while that at D acts horizontally. Both are tangent to the
respective wheels. The radius of the wheel at B is R3 = 150 mm, and that of the wheel at
D is R9 = 200 mm. Knowing that the shaﬁ rotates at 360 rpm, ﬁnd: a) the required diameter, d, for the shaft, b) the relative twist of wheel B with respect to wheel D. The material of the shaft has G = 10 GPa and an allowable shear stress “can = 20 MPa. F Force F comes out of the page 0.1m 0.1m 0.1m Name: Section: Problem 5: For the cantilever beam shown, determine the slope and deﬂection at end A. Use E = 30 x
106 psi. Use any of the three methods: direct integration, superposition or singularity
functions. 1.5 in. l kip 2 kip/ft B A L—zﬁ—J—sﬁ—J Name: Section: Problem 6: Consider the structure illustrated below. Member AB is a horizontal steel rod diameter dAB = 20 mm and length LAB = 3.0 m; and member BC is a vertical steel rod dBc = 30 mm, LBC = 4.0 m; both have elastic modulus E = 200 GPa. The rods are pinned
to ﬁxed structures at A and C, and pinned together at B. A force F is applied to pinned
joint B at angle (9: 50°. A factor of safety in buckling Fs = 3.0 is to be used. 3) Find the critical buckling loads for AB and BC. b) Is this problem statically determinate or indeterminate? Why or why not?
c) Find the largest allowable force F. Consider the critical failure condition is buckling. Section Name lngularity Functions
he S Mom ending may 13 r
a S 762 Appemix 0 Beam Deﬂections and Slopes Maximum
Beam and Loading Elastic Curve Deﬂection Slope at End Equation of Elastic Curve P 3
=~ — LXI
y 6H0 3 )
w 4 2
= —  4m3 + 6sz
y 24151“ ) For a > b:
Pbu} — b2)”2 9\/§EIL u 4 3 >
__ _ + I
(X x) y: l yinax ...
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