## Stress Analysis

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

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Areas

External area Internal area

Area of steel

Ai A

• D2 = fd2
• A0 - 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

0 0

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### Responses

• Cynthia
What is a stress analysis for casing?
8 years ago