Concept explainers
(a)
Find the value of
(a)
Answer to Problem 149P
The value of
Explanation of Solution
Given information:
The radius of the circular plate is
The width of the rectangular post is
The applied force is
Calculation:
Sketch the cross section of disk as shown in Figure 1.
Refer to Figure 1.
Calculate the moment along
Substitute
Calculate the moment along
Substitute
Sketch the cross section of the rectangular post as shown in Figure 2.
Refer to Figure 2.
Calculate the area
Substitute
Calculate the moment of inertia along
Substitute
Calculate the moment of inertia along
Substitute
The location of point D along
The location of point D along
Calculate the stress
Substitute
The stress
Calculate the stress at point D
Substitute
Calculate the value of
Differentiate both sides of the Equation with respect to
Substitute
Substitute
Therefore, the value of
(b)
Find the values of stress at A, B, C, and D.
(b)
Answer to Problem 149P
The stress at A is
The stress at B is
The stress at C is
The stress at D is
Explanation of Solution
Given information:
The radius of the circular plate is
The width of the rectangular post is
The applied force is
Calculation:
Refer to part (a).
The value of
The bending moment along x direction is
Substitute
The bending moment along z direction is
Substitute
Calculate the stress at A
Refer to Figure 2 in part (a).
The location of point A along
The location of point A along
Substitute
Hence, the stress at A is
Calculate the stress at B
Refer to Figure 2 in part (a).
The location of point B along
The location of point B along
Substitute
Hence, the stress at B is
Calculate the stress at C
Refer to Figure 2 in part (a).
The location of point C along
The location of point C along
Substitute
Hence, the stress at C is
Calculate the stress at D
Refer to Figure 2 in part (a).
The location of point D along
The location of point D along
Substitute
Therefore, the stress at D is
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Chapter 4 Solutions
Mechanics of Materials, 7th Edition
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