(a)
Find the tensile stress in the steel ring.
(a)
Answer to Problem 126P
The tensile stress in the steel ring is
Explanation of Solution
Given information:
Steel Ring:
The thickness
The Young’s modulus
The coefficient of thermal expansion
Brass Ring:
The thickness
The Young’s modulus
The coefficient of thermal expansion
Consider the strain in the steel ring and the brass ring due to tensile stress are denoted by
Consider the strain in the steel ring and the brass ring due to temperature stress are denoted by
Consider the total strain in the steel ring and the brass ring are denoted by
Consider the internal pressure in the steel ring is denoted by p.
Consider the external pressure in the steel ring is same as p.
The initial and final temperature of the ring are
Calculation:
Calculate the change in the temperature
Calculate the mean radius (r) of the ring as follows:
Substitute
Consider the tensile stress in the steel ring in the brass ring and the steel ring is denoted by
Calculate the total strain in the steel ring using the relation:
Calculate the change in length of circumference of the steel ring
Calculate the total strain in the steel ring using the relation:
Calculate the change in length of circumference of the steel ring
Equate Equation (1) and (2).
Substitute
Calculate the tensile stress in the steel ring using the relation:
Substitute
Thus, the tensile stress in the steel ring is
(b)
Find the pressure exerted by the brass ring on the steel ring.
(b)
Answer to Problem 126P
The pressure exerted by the brass ring on the steel ring is
Explanation of Solution
Refer part (a);
Get the value of the pressure exerted by the brass ring on the steel ring as
Thus, the external pressure on the brass ring is
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Mechanics of Materials - With Access
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