Calculate the component stresses set-up in the vessel material at point A` (bottom of vessel at mid-span) indicated on the figure due to the loading conditions.

Coursework: 2D Stress and Strain Analysis

The pressurised cylinder vessel shown in the figure is simply-supported over a span of 10 m.

It has an inner diameter of 2100 mm and a wall thickness of 15 mm, and the total mass of the vessel is 15500 kg. During a production process, the vessel operates with an internal pressure of 0.50 MN/m2, and is also subjected to a pure axial force of 600 kN and a torque of 1000 kNm as shown. For the vessel plate material, Young`s modulus of Elasticity is 201 GN/m2, the modulus of rigidity is 83 GN/m2 and Poisson`s ratio is 0.29.

i) Calculate the component stresses set-up in the vessel material at point  A` (bottom of vessel at mid-span) indicated on the figure due to the loading conditions.

ii) Evaluate the 2D complex stress system for the vessel.

iii) Determine the magnitude of the principal stresses and their nature, and the maximum shear stress analytically and graphically, and the angle of the planes on which the major principal stresses act.

iv) Evaluate the minimum factor of safety for the vessel if the vessel plate material has a maximum yield stress of 235 MN/m2 and a maximum allowable shear stress of 110 MN/m2, and compare with the required factor of safety of 3.