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r₁ (hoop) r₂(axial) r₂ Figure 7.1a- Figure 7.2a Figure 7.1b- Figure 7.2b Problem 7.1 The two pressure vessels shown in Figure 7.1 has thickness t=5 mm and radius r=100 mm. The internal pressure is specified to p=25 bar. Assuming the state of stress plane, a) Calculate the stresses in the directions r₁ and r2, b) Calculate the maximum in-plane shear stress in the wall of the pressure vessel, c) Calculate the principal stresses, d) Construct Mohr's circle for the stress state. Assumining the stress state three dimensional, e) calculate the maximum out-of- plane stress in the pressure vessel Ans: Cylindrical case: a) 0₁-50 N/mm², 0₁-25 N/mm², b) Tmax-in-plane-12.5 N/mm², c) -, d) Tmax-out-of-plane=25 N/mm², e) - Spherical case: a) 0₁-25 N/mm², 0₁-25 N/mm², b) Tmax-in-plane-0, c)-, d) Tmax-out-of-plane=12.5 N/mm², e) - r₁ P