Concept explainers
4.127 through 4.134 The couple M is applied to a beam of the cross section shown in a plane forming an angle β with the vertical. Determine the stress at (a) point A, (b) point B, (c) point D.
Flg. P4.129
(a)
Find the stress at point A.
Answer to Problem 129P
The stress at point A is
Explanation of Solution
Given information:
The couple acts in a vertical plane
The angle is
Calculation:
Sketch the beam cross section as shown in Figure 1.
Refer to Figure 1.
Calculate the moment along
Substitute
Calculate the moment along
Substitute
Calculate the moment of inertia along y axis
Calculate the moment of inertia along z axis
Calculate the stress
The location of point A along z axis
The location of point A along y axis
Calculate the stress at point A
Substitute
Therefore, the stress at point A is
(b)
The stress at point B.
Answer to Problem 129P
The stress at point B is
Explanation of Solution
Given information:
The couple acts in a vertical plane
The angle is
Calculation:
Refer to part (a).
The moment along y axis
The moment along z axis
The moment of inertia along y axis
The moment of inertia along z axis
Refer to Figure 1 in part (a).
The location of point B along z axis
The location of point B along y axis
Calculate the stress at point B
Substitute
Therefore, the stress at point B is
(c)
The stress at point D.
Answer to Problem 129P
The stress at point D is
Explanation of Solution
Given information:
The couple acts in a vertical plane
The angle is
Calculation:
Refer to part (a).
The moment along y axis is
The moment along z axis is
The moment of inertia along y axis is
The moment of inertia along z axis is
Refer to Figure 1 in part (a).
The location of point D along z axis
The location of point D along y axis
Calculate the stress at point D
Substitute
Therefore, the stress at point D is
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Chapter 4 Solutions
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