Advanced Strength of Materials
Problem Set 4
1. A thick-walled steel cylinder with an inside diameter of 6 in. was designed with a minimum wall thickness to withstand an internal pressure of 15,000 psi while developing a maximum tensile stress of 25,000 psi. If the internal pressure must be doubled, what is the minimum thickness for a shrink-fitted jacket that will prevent the maximum tensile stress in the assembly from exceeding 25,000 psi?
2. A steel cylinder with an internal diameter of 3.00 in. and an external diameter of 4.80 in. is wound with a single layer of 0.050-in. diameter high-strength steel wire under a tensile stress of 50,000 psi. Determine the maximum allowable internal pressure if the tensile stress in the cylinder is not to exceed 40,000 psi. What will be the stress in the wire when the cylinder is under this pressure?
3. A laminated cylinder consists of a jacket with an inside diameter of 10 in. and an outside diameter of 12 in. shrunk onto a tube with an inside diameter of 6 in. The initial shrinkage pressure is 4,000 psi. The cylinder is then subjected to an internal pressure of 30,000 psi. Determine:
a. The initial interference if the cylinder is made of steel (E = 30,000,000 psi and µ = 0.30).
b. The maximum tensile stresses in the jacket and in the tube.
4. A steel (E = 30,000,000 psi and µ = 0.30) cylinder having an internal diameter of 6 in. and an external diameter of 8 in. is shrunk over a tube having an internal diameter of 4 in. If the laminated cylinder is designed so that the maximum tensile stress in the tube will equal the maximum tensile stress in the jacket after an internal pressure of 24,000 psi is applied to the assembly, determine:
a. The initial shrinkage pressure between the tube and the jacket.
b. The interference required to produce this shrinkage pressure.
5. What is the maximum speed at which a steel (E = 30,000,000 psi, µ = 0.30, and ɣ = 490 lb/ft3 or = 0.2836 lb/in3) disk with an outside diameter of 20 in. may be rotated if the maximum tensile stress is not to exceed 25,000 psi?
6. What is the maximum tensile stress developed in a steel (see problem 5) disk having an outside diameter of 18 in. and an inside diameter of 3 in. when it is rotating at 8000 rpm?
7. A steel (see problem 5) disk having an outside diameter of 8 in. and an inside diameter of 0.998 in. is shrunk on a steel shaft having an outside diameter of 1.000 in. Determine the maximum tensile stress in the disk when it is rotating at 10,000 rpm.

Advanced Strength of Materials Problem Set 4 1. A thick-walled st...