Concept explainers
Two brass rods AB and BC, each of uniform diameter, will be brazed together at B to form a nonuniform rod of total length 100 m that will be suspended from a support at A as shown. Knowing that the density of brass is 8470 kg/m3, determine (a) the length of rod AB for which the maximum normal stress in ABC is minimum, (b) the corresponding value of the maximum normal stress.
Fig. P1.6
(a)
The length of brass rod AB such that the maximum normal stress in ABC is minimum.
Answer to Problem 6P
The length of brass rod AB such that the maximum normal stress in ABC is minimum as
Explanation of Solution
Given information:
The total length of the rod is
The length of rod AB is a.
The length of rod BC is
The density of the brass is
The diameter of the rod AB is
The diameter of the rod BC is
Calculation:
Calculate the area
Here,
Substitute
Calculate the area
Here,
Substitute
Calculate the weights
Here,
Substitute
Calculate the weights
Here,
Substitute
Find the force
Here,
Substitute
Find the normal stress acting at point A using the formula:
Here,
Substitute
Find the normal stress acting at point B using the formula:
Here,
Consider
Substitute
Find the length of brass rod AB for the maximum stress in ABC as minimum:
Here,
Substitute
Thus, the length of brass rod AB is
(b)
The value of maximum normal stress of brass rods.
Answer to Problem 6P
The maximum normal stress of brass rods is
Explanation of Solution
Calculation:
Find the maximum normal stress of brass rod using the relation:
Substitute
Substitute
Thus, the maximum normal stress of brass rods is
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