A cylindrical submersible's steel hull has mean radius and wall thickness
PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Fluid statics and the continuum picture · Solid continuum mechanics and complex fluids
Bending, Ringing, Breaking and Flowing, Ch Strain and stress in a deformed solid
Problem
A cylindrical submersible's steel hull has mean radius r=1.2m and wall thickness h=20mm, and dives to depth H=300m in seawater of density ρ=1025kgm−3. Treat the hull as an idealised thin cylinder, stiffened by internal frames, and find only its membrane stresses: this is not a check that the hull is safe, and whether it could buckle is a separate question not asked here.
((a)) Using the hydrostatic pressure law p=ρgH, held from the first fluids course (the solution of the equilibrium equation for a fluid at rest), find the external gauge pressure on the hull, taking g=9.8ms−2.
((b)) The hull is thin enough that free-body cuts across the hoop and along the axis give the compressive principal stresses σhoop=−pr/h and σaxial=−pr/(2h) (the radial stress being of order −p, much smaller than these and neglected). Evaluate these two stresses, draw Mohr's circle for them (state its centre and radius) and find the maximum in-plane shear stress in the hull wall and the angle, to the hoop direction, of the plane it acts on.
((c)) At the inner surface of the hull the radial stress is zero. Find the largest shear stress there on any plane through the point, and say which planes carry it.