Mechanics of Materials
9th Edition
ISBN: 9780133254426
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Textbook Question
Chapter 8.2, Problem 8.73P
Determine the state of stress at point B at section a–a. The cross section has a diameter of 0.5 in. Use the curved-beam formula to calculate the bending stress.
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Find the second moment of area, the location of the neutral axis, and the distances from the neutral axis to the top and
bottom surfaces. Consider that the section is transmitting a positive bending moment about the z axis, Mz, where M₂ = 10
kip-in if the dimensions of the section are given in ips units, or M₂ = 1.13 kN·m if the dimensions are in Sl units. Determine
the resulting stresses at the top and bottom surfaces and at every abrupt change in the cross section.
From the figure,
с
- 12.5
B
A
y
I
50
100
75
12.5-
12.5
25
D
100
The area is determined to be 3750 mm²
The distances from the neutral axis to the top and bottom surfaces are determined to be 57.292
The second moment of area is determined to be 4.293
x 106 mm4.
mm and 42.708 ✪ mm.
Find the second moment of area, the location of the neutral axis, and the distances from the neutral axis to the top and
bottom surfaces. Consider that the section is transmitting a positive bending moment about the z axis, Mz, where M₂ = 10
kip-in if the dimensions of the section are given in ips units, or M₂ = 1.13 kN·m if the dimensions are in Sl units. Determine
the resulting stresses at the top and bottom surfaces and at every abrupt change in the cross section.
From the figure
Z
1 in
112
in
y
in → ← ¹ in
12
in
D
C
B
A
++
in
The area is determined to be 2.0625 in².
The distances from the neutral axis to the top and bottom surfaces are determined to be 0.858 x in and
The second moment of area is determined to be 0.447 in 4.
1.017
xin.
Determine the moment M that must be applied to the beam in order to create amaximum stress of 90 MPa. Also sketch the stress distribution acting over the cross section.
Chapter 8 Solutions
Mechanics of Materials
Ch. 8.1 - If it is subjected to an internal pressure of p =...Ch. 8.1 - If it is subjected to an internal pressure of p =...Ch. 8.1 - The thin-walled cylinder can be supported in one...Ch. 8.1 - If the inner diameter of the tank is 22 in., and...Ch. 8.1 - Prob. 8.5PCh. 8.1 - 8–6. If the flow of water within the pipe in Prob....Ch. 8.1 - A boiler is constructed of 8-mm-thick steel plates...Ch. 8.1 - 88. The steel water pipe has an inner diameter of...Ch. 8.1 - The steel water pipe has an inner diameter of 12...Ch. 8.1 - The A-36-steel band is 2 in. wide and is secured...
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Ch. 8.2 - Determine the stress components at point A. Sketch...Ch. 8.2 - for the stress components at point B.Ch. 8.2 - Determine the state of stress at point A at...Ch. 8.2 - Determine the state of stress at point B at...Ch. 8 - If it supports a cable loading of 800 lb,...Ch. 8 - Determine the state of stress at point E on the...Ch. 8 - Determine the state of stress at point F on the...Ch. 8 - If it has a mass of 5 kg/m, determine the largest...Ch. 8 - 8–78. Solve Prob. 8–77 if the bar has a circular...Ch. 8 - The suspender arm AE has a square cross-sectional...Ch. 8 - Prob. 8.80RPCh. 8 - 8–81. The hydraulic cylinder has an inner diameter...Ch. 8 - If the cross section of the femur at section aa...Ch. 8 - 8-83. Air pressure in the cylinder is increased by...Ch. 8 - *8-84. Determine the maximum force P that can be...Ch. 8 - and is used to support the vertical reactions of...Ch. 8 - and is used to support the vertical reactions of...
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