Concept explainers
A rigid circular plate of 125-mm radius is attached to a solid 150 × 200-mm rectangular post, with the center of the plate directly above the center of the post. If a 4-kN force P is applied at E with θ = 30°, determine (a) the stress at point A, (b) the stress at point B, (c) the point where the neutral axis intersects line ABD.
Fig. P4.148
(a)
Find the value of stress at point A.
Answer to Problem 148P
The stress at point A 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:
Sketch the cross section of disk as shown in Figure 1.
Refer to Figure 1.
Consider the value of angle
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
Calculate the stress
Refer to Figure 2.
The location of point A along
The location of point A along
Calculate the stress at A
Substitute
Hence, the stress at A is
(b)
The values of stress at B.
Answer to Problem 148P
The stress at B is
Explanation of Solution
Given information:
Calculation:
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
(c)
The point where the neutral axis intersect ABD.
Answer to Problem 148P
The point where the neutral axis intersect ABD is
Explanation of Solution
Given information:
Calculation:
The stress at G
Refer to Figure 2 in part (a).
The location of point G along
The location of point G along
Substitute
Show the distance (d) between the point A and the point G as follows:
Thus, The point where the neutral axis intersect ABD is
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Chapter 4 Solutions
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