Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Chapter 6, Problem 6.9.2P
Calculate the distance e from the centerline of the web of a C 310 × 45 channel section to the shear center E (see figure). Note: For put poses of analysis, consider the flanges to be rectangles with thickness îrequal to the average flange thickness given in Table F-3(b) in Appendix F.
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A 15 cm-OD pipe is buried with its centerline 1.25 m below the surface of the ground
[k of soil is 0.35 W/(m K)]. An oil having a density of 800 kg/m³ and a specific heat of 2.1 kJ/(kg
K) flows in the pipe at 5.6 L/s. Assuming a ground surface temperature of 5°C and a pipe wall
temperature of 95°C, estimate the length of pipe in which the oil temperature decreases by
5.5°C.
+
Tε = 5ºC
Z= 1.25 m
D= 15 cm
7p=95°C
Find the solution of the following Differential Equations
1) 4y+y=0,
y(0)=2,
y'(0) = 0.
2) y+y=0,
y(0) = A,
y'(0) = B.
3) "+2y'-8y=0,
y(0)=1,
y'(0)=8.
4) y"-2y-3y=0,
y(0)=1,
y'(0)=7.
5) y"-ky' =0,
y(0)=2,
y'(0) =k.
6) y+ky'-2k2y=0,
y(0)=2,
y'(0) = 2k.
7) y'+4y=0,
y(0)=2.8
y+y-17sin(21)
y(0)=-1.
9) y-y'-6y=0,
y(0)=6.
y'(0)=13.
10) y-y=0,
11) y"-4y+4y=0,
y(0)=4,
y'(0) = 0.
y(0) = 2.1,
y'(0)=3.9
12) y+2y+2y=0,
y(0)=1,
y'(0)=-3.
13)
"+7y+12y=21e",
y(0)=3.5,
y'(0)=-10.
14) "+9y=10e",
y(0)=0.
y'(0) = 0.
15) y+3y+2.25y=91³ +64.
y(0)=1,
y'(0) = 31.5
16) "-6y+5y= 29 cos(21),
y(0)=3.2,
y'(0) = 6.2
17) y+2y+2y=0,
y(0)=0,
y'(0)=1.
18) y+2y+17y=0,
y(0)=0,
y'(0)=12.
19) y-4y+5y=0,
y(0)-1,
y'(0) 2.
20) 9y-6y+y=0.
y(0)=3,
y'(0)=1.
21) -2y+10y=0,
y(0)=3,
y'(0)=3.
22) 4y-4y+37y=0,
(0) 3.
y(0) 1.5
23) 4y-8y+5y=0,
(0)-0,
y(0) 1.
24) y+y+1.25y=0,
y(0) 1.
y'(0) -0.5
25) y+y=2 cos(1).
y(0) 2.
y'(0) = 0.
26) -4y+3y=0,
(0)-3,
y'(0) = 7.
27) y+2y+y=e",
y(0)-0.
y'(0) = 0.
29)
28) y+2y-3y-10sinh(2),…
Chapter 6 Solutions
Mechanics of Materials (MindTap Course List)
Ch. 6 - A composite beam is constructed using a steel...Ch. 6 - A wood beam is strengthened using two steel plates...Ch. 6 - A composite beam consisting of fiberglass faces...Ch. 6 - A wood beam with cross-sectional dimensions 200 mm...Ch. 6 - A hollow box beam is constructed with webs of...Ch. 6 - A r o lukI f/frm f «m t ub e of ou t sid e d ia...Ch. 6 - A beam with a guided support and 10-ft span...Ch. 6 - A plastic-lined steel pipe has the cross-sectional...Ch. 6 - The cross section of a sand wie h beam consisting...Ch. 6 - The cross section of a sandwich beam consisting of...
Ch. 6 - A bimetallic beam used in a temperature-control...Ch. 6 - A simply supported composite beam 3 m long carries...Ch. 6 - A simply supported wooden I-beam with a 12-ft span...Ch. 6 - -14 A simply supported composite beam with a 3.6 m...Ch. 6 - -15 A composite beam is constructed froma wood...Ch. 6 - A wood beam in a historic theater is reinforced...Ch. 6 - Repeat Problem 6.2-1 but now assume that the steel...Ch. 6 - Repeat Problem 6.2-17 but now use a...Ch. 6 - A sandwich beam having steel faces enclosing a...Ch. 6 - A wood beam 8 in. wide and 12 in. deep (nominal...Ch. 6 - A simple beam of span length 3.2 m carries a...Ch. 6 - A simple beam that is 18 ft long supports a...Ch. 6 - The composite beam shown in the figure is simply...Ch. 6 - The cross section of a beam made of thin strips of...Ch. 6 - Consider the preceding problem if the beam has...Ch. 6 - A simple beam thai is IS ft long supports a...Ch. 6 - The cross section of a composite beam made of...Ch. 6 - A beam is constructed of two angle sections, each...Ch. 6 - The cross section of a bimetallic strip is shown...Ch. 6 - A W 12 x 50 steel wide-flange beam and a segment...Ch. 6 - A reinforced concrete beam (see figure) is acted...Ch. 6 - A reinforced concrete T-beam (see figure) is acted...Ch. 6 - A reinforced concrete slab (see figure) is...Ch. 6 - A wood beam reinforced using two channels is...Ch. 6 - A wood beam reinforced by an aluminum channel...Ch. 6 - A beam with a rectangular cross section supports...Ch. 6 - A wood beam with a rectangular cross section (see...Ch. 6 - Solve the preceding problem for the following...Ch. 6 - A simply supported wide-flange beam of span length...Ch. 6 - Solve the preceding problem using the fol...Ch. 6 - A wood cantilever beam with a rectangular cross...Ch. 6 - Solve the preceding problem for a cantilever beam...Ch. 6 - A 2-m-long cantilever beam is constructed using a...Ch. 6 - A wood beam AB with a rectangular cross section (4...Ch. 6 - A steel beam of I-section (see figure) is simply...Ch. 6 - A cantilever beam with a wide-flange cross section...Ch. 6 - Solve the preceding problem using a W 310 x 129...Ch. 6 - A cantilever beam of W 12 × 14 section and length...Ch. 6 - A cantilever beam built up from two channel...Ch. 6 - A built-Lip I-section steel beam with channels...Ch. 6 - Repeat Problem 6.4-14 but use the configuration of...Ch. 6 - A beam with a channel section is subjected to a...Ch. 6 - A beam with a channel section is subjected to a...Ch. 6 - An angle section with equal legs is subjected to a...Ch. 6 - An angle section with equal legs is subjected to a...Ch. 6 - A beam made up all woun equal leg angles is...Ch. 6 - The Z-section of Example D-7 is subjected to M = 5...Ch. 6 - The cross section of a steel beam is constructed...Ch. 6 - The cross section of a steel beam is shown in the...Ch. 6 - A beam with a semicircular cross section of radius...Ch. 6 - .10 A built-up bourn supporting a condominium...Ch. 6 - Asteelpost (E = 30 × 106 psi) having thickness t =...Ch. 6 - A C 200 x 17.1 channel section has an angle with...Ch. 6 - A cold-formed steel section is made by folding a...Ch. 6 - A simple beam with a W 10 x 30 wide-flange cross...Ch. 6 - Solve the preceding problem for a W 250 × 44.8...Ch. 6 - A beam of wide-flange shape, W 8 x 28, has the...Ch. 6 - Solve the preceding problem for a W 200 × 41,7...Ch. 6 - Calculate the distance e from the cent crime of...Ch. 6 - Calculate the distance e from the centerline of...Ch. 6 - The cross section of an unbalanced wide-flange...Ch. 6 - The cross section of an unbalanced wide-flange...Ch. 6 - The cross section of a channel beam with double...Ch. 6 - The cross section of a slit circular tube of...Ch. 6 - The cross section of a slit square tube of...Ch. 6 - The cross section of a slit rectangular tube of...Ch. 6 - A U-shaped cross section of constant thickness is...Ch. 6 - Derive the following formula for the distance e...Ch. 6 - Derive the following formula for the distance e...Ch. 6 - The cross section of a sign post of constant...Ch. 6 - A cross section in the shape of a circular arc of...Ch. 6 - Determine the shape factor f for a cross section...Ch. 6 - (a) Determine the shape factor/for a hollow...Ch. 6 - A propped cantilever beam of length L = 54 in....Ch. 6 - A steel beam of rectangular cross section is 40 mm...Ch. 6 - .5 Calculate the shape factor j for the...Ch. 6 - Solve the preceding problem for a wide-flange beam...Ch. 6 - Determine the plastic modulus Z and shape...Ch. 6 - Prob. 6.10.8PCh. 6 - Prob. 6.10.9PCh. 6 - Prob. 6.10.10PCh. 6 - A hollow box beam with height h = 16 in,, width h...Ch. 6 - Solve the preceding problem for a box beam with...Ch. 6 - A hollow box beam with height h = 9.5 in., inside...Ch. 6 - Solve the preceding problem for a box beam with...Ch. 6 - The hollow box beam shown in the figure is...Ch. 6 - Prob. 6.10.16PCh. 6 - Prob. 6.10.17PCh. 6 - A singly symmetric beam with a T-section (see...Ch. 6 - A wide-flange beam with an unbalanced cross...Ch. 6 - .20 Determine the plastic moment Mpfor beam having...
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