Concept explainers
For the curved bar shown, determine the stress at point A when (a) h = 50 mm, (b) h = 60 mm.
Fig. P4.161 and P4.162
(a)
The stress at point A.
Answer to Problem 161P
The stress at A is
Explanation of Solution
Given information:
The value of h is
The inner
The width and depth of the bar are
The moment (M) is
Calculation:
Calculate the cross-section area (A) of the bar as follows:
Calculate the radius (R) of the neutral surface using the relation:
Substitute
Calculate the mean radius
Substitute
The distance (e) between the neutral axis and the centroid of the cross-section using the relation:
Substitute
Calculate the value of
The distance
Calculate the stress at point A using the relation:
Substitute
Thus, the stress at point A is
(b)
The stress at point A.
Answer to Problem 161P
The stress at A is
Explanation of Solution
Given information:
The value of h is
The inner
The width and depth of the bar are
The moment (M) is
Calculation:
Calculate the cross-section area (A) of the bar as follows:
Calculate the radius (R) of the neutral surface using the relation:
Substitute
Calculate the mean radius
Substitute
The distance (e) between the neutral axis and the centroid of the cross-section using the relation:
Substitute
Calculate the value of
The distance
Calculate the stress at point A using the relation:
Substitute
Thus, the stress at point A is
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Chapter 4 Solutions
EBK MECHANICS OF MATERIALS
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