I need help with this problem Two cylinders are shrinkfitted

I need help with this problem.

Two cylinders are shrink-fitted together to form a composite open cylinder. Both cylinders are made of a steel having a yield stress of 700MPa. The inner cylinder has inner and outer diameters of 100 and 150+ mm (150+ means more than 150), respectively. The outer cylinder has inner and outer diameters of 150 and 300mm, respectively. Assume a=300/2=150mm, c=150/2=75mm, b=100/2=50mm

a. Determine the shrink pressure pc and maximum internal pressure pi that can be applied to the cylinder if it has been designed with a factor of safety of SF=1.85 for simultaneous initiation of yielding at the inner radii of the inner and outer cylinders. Use the maximum shear stress criterion of failure.

b. Determine the outer diameters of the inner cylinder required for the design. For the steel, Young’s modulus is 200GPa and Poisson’s ratio is 0.29.

Solution

The shrink pressure is 354 mpa , while the maximum internal pressure is 470mpa.

The outer dia for the inner cylinder is 170 mm