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t i i i AAE 204 Fall 2011 Homework #5 Due start of class on Wednesday, 23 February 2011 The purpose of homework assignments is for students to gain further understanding of classroom principles through application to practical problems. Although discussion of assignments between students is permitted, the solution must represent your own efforts and understanding of the problem.
Blatant copies of the solutions will not be accepted, and repeated evidence of copying Will lead to failure of the course. Please do the following problems in the AAE 204 textbook (J. M. Gere and B. J. Goodno,
Mechanics of Materials, 7th Edition, 2009, Cengage Learning). Do Problem 1.29 Do Problem 1.213
Do Problem 1.43 Ā«'7
Do Problem 1.66 Do Problem 1.83 PāPPāN!ā For convenience, those problems are duplicated below. 1.29 A pickup truck tailgate supports a crate (WC =, 1501b);
as shown in the ļ¬gure. The tailgate weighs WT = 60 lb ' and is supported by two cables (only one is shown in
the ļ¬gure). Each cable has an effective crosssectional area
A6 = 0017 m2. (21) Find the tensile force T and normal stress a in each
cable. (b) If each cable elongates 8 = 0.01 in. due to the weight of both the crate and the tailgate, what is the
average strain in the cable? %. WC: 1501b PRQBS. 1.29 and 1.2ā) mi 1.213 Two gondolas on a ski lift are locked in the position
shown in the ļ¬gure while repairs are being made elsewhere.
The distance between support towers is L = 100 ft. The
length of each cable segment under gondola weights W3 =
450 lb and WC = 6501b are DAB = 12 ft, DEC = 70 ft, and
DCD = 20 ft. The cable sag at B is AB = 3.9 ft and that at
C(AC) is 7.1 ft. The effective crosssectional area of the
cable is A. = 0.12 inz. (a) Find the tension force in each cable segment; neglect
the mass of the cable. (b) Find the average stress (a) in each cable segment. i , i V z/2. *1.37 The data shown in the accompanying table were
obtained from a tensile test of highstrength steel. The test
specimen had a diameter of 0.505 in. and a gage length of
2.00 in. (see ļ¬gure for Prob. 1.3ā3). At fracture, the elonga
tion between the gage marks was 0.12 in. and the minimum diameter was 0.42 in. .
Plot the conventional stressāstram curve for the steel and determine the proportional limit, modulus of elasticity
(i.e., the slope of the initial part of the stressstrain curve),
yield stress at 0.1% offset, ultimate stress, percent elonga
tion in 2.00 in., and percent reduction in area. 1.55 A steel plate of dimensions 2.5 X 1.2 X 0.1m is
hoisted by steel cables with lengths L1 = 3.2 m and L2 =
3.9 m that are each attached to the plate by a Clevis and pin
(see ļ¬gure). The pins through the Clevises are 18 mm in
diameter and are located 2.0m apart. The orientation
angles are measured to be 6 = 94.4Ā° and a = 54.90. For these conditions, first determine the cable forces
T, and T2, then ļ¬nd the average shear istress rave, in both
pin 1 and pin 2, and then the average bearing stress 0,,
between the steel plate and each pin. Ignore the mass of the Ć© cables.
TEN511EāTEST DATA FOR PROBLEM 1.37 P
3 ; M
i , Load (1b) Elongation (in.) 1
g _
1,000 0.0002
2,000 0.0006 Clevis and Q 6,000 0.0019 ā pin 1
3 10,000 0.0033
12,000 0.0039
12 900 0.0043 .
ā d 2
13,400 0.0047 an pm
13,600 0.0054
13 ,800 0.0063
14,000 00090 Center of mass
3 14400 0.0102 , of plate
i 15 ,200 0.0130
2 16,800 0.0230
18,400 0.0336
20,000 0.0507
22,400 0.1 108 , Pans. 1.6ā6
22,600 Fracture 1.83 A horizontal beam AB with cross~sectional dimensions
(b = 0.75 in.) X (h = 8.0 in.) is supported by an inclined
strut CD and carries a load P = 2700 lb at joint B [see ļ¬gure
part (a)}. The strut, which consists of two bars each of thick
ness 5b/8, is connected to the beam by a bolt passing through
the three bars meeting at joint C [see ļ¬gure part (b)]. (a) If the allowable shear stress in the bolt is 13,000 psi, ā , bā>[ [<ā
what is the minimum required diameter (1min of the bolt at C? i" :(b) If the allowable bearing stress in the bolt is 19,000 psi,
what is the minimum required diameter dmin of the bolt at C? Beam AB (b X h) Bolt (dunn) ' i
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