In order to perform a stress analysis of casing or tubing, we need to understand how the stresses and displacements in a tube are affected by internal and external pressure, axial forces and temperature.
In particular we need to know how stresses and displacements change as we change internal or external pressure, temperature or apply an axial force to the end.1
Areas
External area Internal area
Area of steel
Ai A
A0 Ai A
If the outside diameter, D, and the inside diameter, d, are in inches, then the area is in square inches (in2).
Moments of Inertia
Polar moment of inertia J = 21 (5)
1Note: Triaxial Coordinates
I is used in bending equations and J is used in torsion equations.
Stresses
Lame's equations for stresses in a tube, given an internal pressure, Pi, and an external pressure, P0> are
Radial stress Sr = P^) (1- £)2) - P (-r2) (1- ({¥)
The variable 'b' ranges from d at the inside wall to D at the outside wall. It is useful to note that the sum
This fact will be used in determining the axial stress Sz or the axial strain ez. The stresses Sr and St do not depend on Sz.
Axial stress
If the tension T is in pounds and the area A is in in2, then Sz is in psi. Bending stress
The bending equation developed by Lubinski is
The pure beam bending equation is fbeam = 17'135 * D * C * (D2-d2)
The bending stress is
or beam which ever is larger lub or beam
LUBINSKI TUBE Hooke's law for stress-strain relations
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