2. A carbon steel alloy column of 2 m external diameter operates under vacuum with an absolute internal pressure of 100 mbar. a. Assuming a safety factor of 3, calculate the minimum thickness of the column. [5 marks] b. Stiffening rings are available to improve the buckling resistance of the column. i. Calculate the critical distance between the stiffening rings. [4 marks] Calculate the buckling pressure if stiffening rings with a spacing of 1/10 of the critical spacing distance are mounted on the column (use Figure 2.1). [9 marks] c. X-ray analysis of the column has shown that edge cracks of 1 mm diameter are present in the vessel wall. ii. i. Calculate the critical stress of fracture. ii. [4 marks] Determine if the column is more likely to yield or to fail by fast fracture. [3 marks] Useful data: Elastic module of carbon steel alloy equal to 123 GPa Fracture toughness of carbon steel alloy equal to 50 MPa m.5 1 mbar = 100 Pa~ 10 atm Yield stress of the carbon steel alloy equal to 800 MPa