General Engineering · Applied Mechanics · 2 marks · Numerical answer
A thick cylinder has inner/outer diameters 20/40 mm and internal pressure 100 MPa. Taking tensile stress positive, find radial plus hoop stress at radius 15 mm, to two decimals MPa.
Lamé stresses are $\sigma_r=A-B/r^2$, $\sigma_\theta=A+B/r^2$. For zero external pressure, $A=p_i r_i^2/(r_o^2-r_i^2)=100(10^2)/(20^2-10^2)=100/3$ MPa. Their sum is radius-independent: 2A = **66.67 MPa**.
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