Longitudinal Stress in Thin-Wall Pressure Vessels

[jamothedumbmechengstudent]

Bit confused on this - I get that the thin-wall equation for longitudinal stress in a thin wall cylinder is approximated as PD/4t, but why is it not just the pneumatic force acting on the vessel endcap / head over the CS area of the cylinder?

 

[rb1957]

because it is !

what is the pressure force on the end cap ? P*pi*D^2/4
what is the longitudinal area of the cylinder ? pi*D*t
force/area = (P*pi*D^2/4)/(pi*D*t) = PD/4t ... QED

 

[btrueblood]

Bit confused on this - I get that the thin-wall equation for longitudinal stress in a thin wall cylinder is approximated as PD/4t, but why is it not just the pneumatic force acting on the vessel endcap / head over the CS area of the cylinder?

It is. You could write the CS area of the cylinder as pi*D*t which is a good approximation for t<<D.

then sigma= pressure x cap area / CSarea

sigma =[P*D^2*pi/4] / [pi*D*t]

cancel the pi's and one D to get the equation you gave.