Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
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Textbook Question
Chapter 4, Problem 4.5.36P
A simple beam AB supports two connected wheel loads 3P and 2P that are a distance d apart (see figure). The wheels may be placed at any distance x from the left-hand support of the beam. (Assume P = 12 kN, d = 2 m, and 1 = 15 m.)
(a)
Determine the distance .y that will produce the maximum shear force in the beam, and also determine the maximum shear force Vmax.
(b)
Determine the distance v that will produce the maximum bending moment in the beam, and also draw the corresponding bending-moment diagram.
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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
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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 4 Solutions
Mechanics of Materials (MindTap Course List)
Ch. 4 - Calculate the shear force V and bending moment...Ch. 4 - Determine the shear force V and bending moment M...Ch. 4 - Determine the shear force V and bending moment M...Ch. 4 - Calculate the shear force V and bending moment M...Ch. 4 - Consider the beam with an overhang shown in the...Ch. 4 - The beam ABC shown in the figure is simply...Ch. 4 - The beam ABCD shown in the figure has overhangs at...Ch. 4 - At a full d raw, an archer applies a pull of 130 N...Ch. 4 - A curved bar ABC is subjected to loads in the form...Ch. 4 - Under cruising conditions, the distributed load...
Ch. 4 - A beam ABCD with a vertical arm CE is supported as...Ch. 4 - A simply supported beam AB supports a trapezoid...Ch. 4 - Beam ABCD represents a reinforced-concrete...Ch. 4 - Find shear (V) and moment (M) at x = 3L/4 for the...Ch. 4 - Find expressions for shear force V and moment M at...Ch. 4 - Find expressions for shear force V and moment Mat...Ch. 4 - Find expressions for shear force V and moment Mat...Ch. 4 - Find expressions for shear force V and moment M at...Ch. 4 - Find expressions for shear force V and moment M at...Ch. 4 - Find expressions for shear force V and moment M at...Ch. 4 - A cable with force P is attached to a frame at A...Ch. 4 - Find expressions for shear force V and moment M at...Ch. 4 - A cable with force P is attached to a frame at D...Ch. 4 - Frame ABCD carries two concentrated loads (2P at T...Ch. 4 - Frame ABC has a moment release just left of joint...Ch. 4 - The simply supported beam ABCD is loaded by a...Ch. 4 - The centrifuge shown in the figure rotates in a...Ch. 4 - Draw the shear-Force and bending-moment diagrams...Ch. 4 - A simple beam AB is subjected to a counter...Ch. 4 - Draw the shear-force and bending-moment diagrams...Ch. 4 - The cantilever beam AB shown in the figure is...Ch. 4 - Cantilever beam AB carries an upward uniform load...Ch. 4 - The simple beam AB shown in the figure is...Ch. 4 - A simple beam AB subjected to couples M1and 3M2...Ch. 4 - A simply supported beam ABC is loaded by a...Ch. 4 - A simply supported beam ABC is loaded at the end...Ch. 4 - A beam ABC is simply supported at A and B and has...Ch. 4 - Beam ABCD is simply supported at B and C and has...Ch. 4 - Draw the shear-force and bending-moment diagrams...Ch. 4 - The simple beam AB supports a triangular load of...Ch. 4 - The beam AB shown in the figure supports a uniform...Ch. 4 - A cantilever beam AB supports a couple and a...Ch. 4 - The cantilever beam A B shown in the figure is...Ch. 4 - Beam ABC has simple supports at .A and B. an...Ch. 4 - Beam ABC with an overhang at one end supports a...Ch. 4 - Consider the two beams shown in the figures. Which...Ch. 4 - The three beams in the figure have the same...Ch. 4 - The beam ABC shown in the figure is simply...Ch. 4 - A simple beam AB is loaded by two segments of...Ch. 4 - Two beams (see figure) are loaded the same and...Ch. 4 - The beam A BCD shown in the figure has overhangs...Ch. 4 - A beam ABCD with a vertical arm CE is supported as...Ch. 4 - Beams ABC and CD are supported at A,C, and D and...Ch. 4 - The simple beam ACE shown in the figure is...Ch. 4 - A beam with simple supports is subjected to a...Ch. 4 - A beam of length L is designed to support a...Ch. 4 - The compound beam ABCDE shown in the figure...Ch. 4 - Draw the shear-force and bending-moment diagrams...Ch. 4 - The shear-force diagram for a simple beam is shown...Ch. 4 - The shear-force diagram for a beam is shown in the...Ch. 4 - A compound beam (see figure) has an internal...Ch. 4 - A compound beam (see figure) has an shear release...Ch. 4 - A simple beam AB supports two connected wheel...Ch. 4 - The inclined beam represents a ladder with the...Ch. 4 - Beam ABC is supported by a tie rod CD as shown....Ch. 4 - A plane frame (see figure) consists of column AB...Ch. 4 - The plane frame shown in the figure is part of an...
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