Solid Mechanics Course No. ME213

Thick walled pressure vessels Considerations σl σr r z ro ri σr σt pi po Applications pi = 0 Submarine Vacuum chamber Shrink fit Buried pipe po = 0 Gun barrel Liquid- or gas-carrying pipe Hydraulic cylinder Gas storage tank ME213 Solid Mechanics

Thick walled pressure vessels Applications pi = 0 Submarine Vacuum chamber Shrink fit Buried pipe po = 0 Gun barrel Liquid- or gas-carrying pipe Hydraulic cylinder Gas storage tank ME213 Solid Mechanics

Thick walled pressure vessels Stresses in thick cylinder In general the stress equations of equilibrium without body forces can be given as ...(1) ME213 Solid Mechanics

Thick walled pressure vessels Stresses in thick cylinder In general the stress equations of equilibrium without body forces can be given as ...(2) ME213 Solid Mechanics

Thick walled pressure vessels Stresses in thick cylinder In a plane stress situation if the cylinder ends are free to expand and due to uniform radial deformation and symmetry The equation of equilibrium reduces to σz = 0 τrz = τθz = τrθ = 0 This can be written in the following form: ...(3) ME213 Solid Mechanics

Thick walled pressure vessels Stresses in thick cylinder If we consider a general case with body forces such as centrifugal forces in the case of a rotating cylinder or disc then the equations reduce to which may be written as ...(4) It is convenient to solve the general equation so that a variety of problems may be solved. ME213 Solid Mechanics

Thick walled pressure vessels Strains in thick cylinder Representation of radial and circumferential strain. The strains εr and εθ may be given by ...(5) ...(6) ME213 Solid Mechanics

Thick walled pressure vessels Strains in thick cylinder Combining above equations we have ...(7) Now from equation (4) we may write and combining this with equation (7) we may arrive at ...(8) For a non-rotating thick cylinder with internal and external pressures pi and po we substitute ω = 0 in equation (8) and this gives ...(9) ME213 Solid Mechanics

Thick walled pressure vessels Strains in thick cylinder A standard solution for equation (9) is σr = c rn where c and n are constants. Substituting this in equation (9) and also combining with equation (3) we have ...(10) where c1 and c2 are constants ME213 Solid Mechanics