Concept explainers
An aluminum cylinder (Ea = 70 MPa, va = 0.33) with an outer diameter of 150 mm and inner diameter of 100 mm is to be press-fitted over a stainless-steel cylinder (Es = 190 MPa, vs = 0.30) with an outer diameter of 100.20 mm and inner diameter of 50 mm. Determine (a) the interface pressure p and (b) the maximum tangential stresses in the cylinders.
(a)
The pressure at the interface.
Answer to Problem 19P
The pressure at the interface is
Explanation of Solution
Write the expression for the radial interface.
Here, the outer radius of steel cylinder is
Write the expression for the interface pressure.
Here, the inner radius of steel cylinder is
Conclusion:
Substitute
Substitute
Thus the pressure at the interface is
(b)
The maximum tangential stress in aluminum cylinder.
The maximum tangential stress in steel cylinder.
Answer to Problem 19P
The maximum tangential stress in aluminum cylinder is
The maximum tangential stress in steel cylinder is
Explanation of Solution
Write the expression for maximum stress in aluminum cylinder.
Here, the pressure at interface is
Write the expression for maximum stress in steel cylinder.
Here, the maximum stress in steel cylinder is
Conclusion:
Substitute
Thus, the maximum tangential stress in aluminum cylinder is
Substitute
Thus, the maximum tangential stress in steel cylinder is
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Chapter 19 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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