Expansion Joints - CAESAR II - Help

CAESAR II Users Guide

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CAESAR II
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CAESAR II Version
12

Checking the expansion joint box on the element enables definition of an expansion joint for that element. Expansion joints can be modeled as a single element across the flexible length of the joint or as a zero length element at the midpoint of the expansion joint. Expansion joints elements have a zero-length if the Delta fields on the Pipe Element spreadsheet are left blank or zero.

When an expansion joint has a defined length, CAESAR II builds the expansion joint as a beam element using the element length with the entered expansion joint stiffnesses.

Four stiffness values define the expansion joint:

  • Axial

  • Transverse

  • Torsion

  • Bending

Examples of the Stiffnesses

Define Finite Length Joints

For expansion joints where flexible length is defined, the bending stiffness is defined by the entered, flexible, length and the transverse stiffness of the joint. Some expansion joint catalogs list what would be called bending flexibility rather than the required bending stiffness used in CAESAR II. This bending flexibility is adequate for an expansion joint modeled by two rigid elements that are pinned at the joint midpoint (a zero-length expansion joint) but it is the wrong value for a flexible beam element. To address this ambiguity, CAESAR II calculates and applies a bending stiffness based on the entered expansion joint length and transverse stiffness. We suggest that you only enter the bending term from manufacturers' catalogs when using the zero-length expansion joint model or for rubber joint which do not follow beam bending definitions.

Typically, expansion joint manufacturers do not supply torsional stiffness data. If the manufacturer does not supply the data, enter a large torsional stiffness value, and verify that the resulting load on the bellows is not excessive. When the piping system is tight, and the diameter large, the magnitude of the large torsional stiffness can significantly affect the magnitude of the torsion carried by the joints. For example, a stiffness of 100,000 in.lb./deg. and 1E12 in.lb./deg. can produce considerably different torsional load results. Conservatively speaking, the tendency is to use the larger stiffness except that the torsional stiffness value is probably closer to the 100,000 in.lb./deg. In instances where a large torsional stiffness value is important, you can get a stiffness estimate from the manufacturer, or use the equation below to derive an estimate. Use this equation to conservatively estimate torsional loads on the bellows and surrounding equipment.

Where

p = 3.14159

Re = Expansion joint effective radius

t = Bellows thickness

E = Elastic Modulus

n = Poisson’s Ratio

L = Flexible bellows length

When the expansion joint has a zero length, none of the expansion joint stiffnesses are related. You must be sure that you enter a value in all of the Stiffness fields.

Calculate the Pressure Thrust

CAESAR II calculates the pressure thrust on the expansion joint if you type a value for the bellows Effective ID on the Expansion Joint auxiliary dialog box. If there is no Effective ID specified, then there is no pressure thrust calculated.

The mathematical model for pressure thrust indicates to apply a force equal to the pressure multiplied by the effective area of the bellows at the two nodes that define the expansion joint. The force can open the bellows if the pressure is positive and close the bellows if the pressure is negative.

This model does not correctly locate pressure load components in the vicinity of the expansion joint. In most cases, the misapplied load does not affect the solution.

There are two components of the pressure thrust to apply in practice rather than the one component applied in the model. The first component is equal to the pressure times the inside area of the pipe and acts at the first change in direction of the pipe on either side of the expansion joint. This load will tend to put the pipe wall between the change in direction and the expansion joint in tension. The second component is equal to the pressure times the difference between the bellows effective area and inside pipe area. This load acts at the end of the expansion joint and tends to open the bellows up putting the pipe between the expansion joint and the change in direction in compression.

In the mathematical model, the full component of the pressure thrust force is placed on the ends of the bellows instead of having a portion shifted out on either side of the expansion joint.