Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
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Textbook Question
Chapter 8.2, Problem 8.72P
Determine the state of stress at point A at section a–a. The cross section is circular and 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 (10th Edition)
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