Sustainable Energy
2nd Edition
ISBN: 9781337551663
Author: DUNLAP, Richard A.
Publisher: Cengage,
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Chapter 2, Problem 6P
The total world population in 2012 was about 7 billion, and Figure 2.11 shows that at that time the actual world population growth rate was about 1% per year. The figure also shows an anticipated roughly linear decrease in growth rate that extrapolates to zero growth in about the year 2080. Assuming an average growth rate of 0.5% between 2012 and 2080, what would the world population be in 2080? How does this compare with estimates discussed in the text for limits to human population?
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A composite beam is fabricated by bolting two 3.1-in.-wide by 14-in.-deep timber planks to the sides of a 0.4-in. by 14-in. steel plate.
The moduli of elasticity of the timber and the steel are 1940 ksi and 30300 ksi, respectively. The simply supported beam spans a
distance of 21 ft and carries two concentrated loads P, which are applied as shown. Assume LAB = LCD = 5 ft, Lgc = 11 ft, b = 3.1 in., d = 14
in. and t = 0.4 in.
(a) Determine the maximum bending stresses σ,, σ, produced in the timber planks and the steel plate if P = 2.1 kips.
(b) Assume that the allowable bending stresses of the timber and the steel are 830 psi and 24900 psi, respectively. Determine the
largest acceptable magnitude for concentrated loads P. (You may neglect the weight of the beam in your calculations.)
LAB
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Answers:
LCD
LBC
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D
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i
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i
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The internal shear force at a certain section of a steel beam is V = 107 kips. If the beam has the cross section shown, determine the
shear stress at point H, which is located 2 in. below the top surface of the flanged shape. The centroid is 5.283 in. above the bottom
surface of the beam, and the moment of inertia about the z axis is 465.8 in.4.
5 in.
2 in.
H
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1 in.
1 in.
12 in.
8 in.
1 in.
11.51 ksi
O 9.72 ksi
8.34 ksi
6.03 ksi
○ 7.73 ksi
The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 33.6 ksi. Assume P = 70 kips.
L₁ = 2.2 ft, and L2 = 6.6 ft.
(a) Determine the minimum section modulus required for this beam.
(b) From the table below, select the lightest W shape that can be used for this beam.
(c) What is the total weight of the steel beam itself (ie, not including the loads that are carried by the beam)?
Lu
B
D
L2
L₁
Wide-Flange Sections or W Shapes-U.S. Customary Units
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x
be
Web
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Flange
width
Flange
thickness
Designation
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d
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W24 x 94
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0.515
9.07
0.875
2700
222
9.87
109
24.0
1.98
24 x 76
22.4
23.9
0.440
8.99
0.680
2100
176
9.69
82.5
18.4
1.92
24 x 68
20.1
23.7
0.415
8.97
0.585
1830
154
9.55
70.4
15.7
1.87
24 x 55
16.2
23.6
0.395
7.01
0.505
1350
114
9.11
29.1
8.30
1.34
W21 x 68
20.0
21.1
0.430
8.27
0.685
1480
140
8.60
64.7
15.7
1.80
21 x 62
18.3
21.0
0.400
8.24
0.615
1330
127…
Chapter 2 Solutions
Sustainable Energy
Ch. 2 - A quantity has a doubling time of 110 years....Ch. 2 - The population of a particular country has a...Ch. 2 - Prob. 4PCh. 2 - Prob. 5PCh. 2 - The total world population in 2012 was about 7...Ch. 2 - The population of a state is 25,600 in the year...Ch. 2 - The population of a country as a function of time...Ch. 2 - Prob. 9PCh. 2 - Prob. 10PCh. 2 - Prob. 11P
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