General Engineering · Applied Mechanics · 2 marks · Numerical answer
A metal cylindrical air vessel has mean radius 1 m and wall thickness 4 mm. Allowable normal and shear stresses in its cylindrical portion are 100 and 40 MPa respectively. Using only these data, find maximum internal gauge pressure (two decimal MPa).
Thin-wall hoop stress is $\sigma_\theta=pr/t=250p$ when p is MPa. Axial stress is 125p, and radial stress is negligible. Normal-stress limit gives p ≤ 100/250 = 0.40 MPa. Maximum 3D shear is $(\sigma_\theta-0)/2=125p$, giving p ≤ 40/125 = 0.32 MPa. The governing value is **0.32 MPa**.
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