Question

A strain gauge affixed to the outside of a cylindrical pressure vessel at an angle of θ = 35° reads ε = 400 μm/m. The outside diameter of the vessel is 500mm and the wall thickness is 5 mm. If the veseel is constructed of A36 steel, determine the following:

a) The hoop and longitudinal stresses in the tank.

Hints: To solve you will need to consider the equations for strain transform and generalized Hooke’s Law. The hoop and longitudinal stresses correspond to the principal stresses. There is no shear stress at the orientation of the principal stresses.

b) The internal pressure in the tank.

c) The factor of safety with respect to maximum shear stress theory for the INSIDE of the tank.

d) The factor of safety with respect to Von Mises stress for the INSIDE of the tank.

Answer 1

Hook'Law stating that,

a law stating that the strain in a solid is proportional to the applied stress within the elastic limit of that solid.

Hoop stress is defined as

Circumferential stress or hoop stress, a normal stress in the tangential (azimuth) direction; Axial stress, a normal stress parallel to the axis of cylindrical symmetry; Radial stress, astress in directions coplanar with but perpendicular to the symmetry axis.

Radial and tangential stress in thick-walled cylinders or tubes with closed ends - with internal and external pressure. When a thick-walled tube or cylinder is subjected to internal and external pressure a hoop and longitudinal stress are produced in the wall.

Longitudinal Stresses is defined as

Longitudinal stress is the stress in a pipe wall, acting along the longitudinal axis of the pipe. And it is produced by the pressure of the fluid in the pipe. ... It is also called as Hoop stress. Radial stress is stress towards or away from the central axis of a component.