
(a)
Find the error in the computation of maximum stress by assuming the bar as straight.
(a)

Answer to Problem 166P
The error in the computation of maximum stress by assuming the bar as straight 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:
Substitute
Calculate the moment of inertia (I) of the cross-section of the bar using the relation:
Substitute
Calculate the distance (c) between the neutral axis and the extreme fiber using the relation:
Substitute
Calculate the stress
Substitute
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 actual stress using the relation:
Substitute
Calculate the error in the computation of maximum stress by assuming the bar as straight using the relation:
Substitute
Thus, the in the computation of maximum stress by assuming the bar as straight is
(b)
Find the error in the computation of maximum stress by assuming the bar as straight.
(b)

Answer to Problem 166P
The error in the computation of maximum stress by assuming the bar as straight 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 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 actual stress using the relation:
Substitute
Calculate the error in the computation of maximum stress by assuming the bar as straight using the relation:
Substitute
Thus, the in the computation of maximum stress by assuming the bar as straight is
(c)
Find the error in the computation of maximum stress by assuming the bar as straight.
(c)

Answer to Problem 166P
The error in the computation of maximum stress by assuming the bar as straight is
Explanation of Solution
Given information:
The value of h is
The inner radius
Show the unit conversion of inner radius as follows:
The inner
The width and depth of the bar are
The moment (M) is
Calculation:
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 actual stress using the relation:
Substitute
Calculate the error in the computation of maximum stress by assuming the bar as straight using the relation:
Substitute
Thus, the in the computation of maximum stress by assuming the bar as straight is
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Chapter 4 Solutions
Mechanics of Materials, 7th Edition
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