Engineers' Guide to Pressure Equipment - Index of

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Engineers’ Guide to Pressure Equipment
Fig. 3.4 Stresses in vessel heads
Fig. 3.5 Vessel head stresses – the derivation
normal, AC being the instantaneous radius of curvature of the meridian, r φ.
The components of the pressure and stress resultants along the outward
normal are:
• pressure: p dA = p (r dθ) r φ dφ;
• meridional stress: -2 S φ (t rdθ) sin (dφ/2);
• circumferential stress: -2 S θ (t r φ dφ) sin (dθ/2).sin φ.
Taking limits and replacing r = r θ sin φ, then equilibrium of the element
requires that
S θ / r θ + S φ / r φ = p / t i.e. the so-called membrane equation
and for vertical equilibrium of the dish area above the hoop
pr 2 p = 2 p r t S φ sin φ