Deformable Body Mechanics Question A steelwalled cylindrical

Deformable Body Mechanics Question

A steel-walled cylindrical pressure vessel is located at sea level, where standard atmospheric conditions exist (listed in picture):

The vessel is allowed to fill with air (at those conditions) and then is sealed off. (The initial internal gage pressure is therefore zero) Assume that the absolute pressure p, absolute temperature T, and desity rho are related by the equation of state p=R*rho*T , R=287.058 (gas constant for dry air)

If the allowable normal and shear stresses in the vessel wall are 110 MPa and 60 MPa respectively, find the max permissible increase in temperature, delta T max (in degrees Kelvin)

Solution

The eqns for the wall stress for a thin wall cylinder are: tangential (hoop) = pR/t

radial pR/2t

Taking the smaller of the given values ( 60MPa) = pR/t ( actually it is the other way around)-normal stress should be smaller

Depending on which value one takes,upper pressure p is 18 to 33 times the atmos pressure.

Using the eqn P/T = const, the temperature can go upto 18 to 33 times the old temp, assuming density is constant ( m/V constant). By then the cylinder would melt.