In order to understand the concept of pressure thrust, we can take a hydraulic cylinder, with a spring inside, as a reference for a simple bellows, designed for axial movement. The force on the pipe fittings or anchors “F” = (effective bellows area) x (operating pressure). The hydraulic piston represents the effect of the pressure thrust that the expansion joint can exert on the pipe anchors or pressure thrust limiters (hinges, gimbals, turnbuckles) that may form part of the expansion joint structure. The area of the hydraulic cylinder would be the effective area of the bellows.
Any flexible element mounted in a piping system, be it a bellows, a spheroidal rubber body or an airtight fabric, subjected to internal pressure, tends to stretch, generating a force known as pressure reaction force. This is nothing more than Pascal’s principle.
This force is equivalent to the product of the pressure times the average area of the flexible element:
Frp = P x A
This force must be contained, in a piping system, by fixed supports with zero degrees of freedom or fixed points. When an expansion joint has an external structure, such as tensioners, hinges or gimbals, these are responsible for containing this force.
The effect produced by internal pressure corresponds to a thrust called pressure reaction force (PRF) that is created by installing a flexible element in a pipe line, such as an expansion joint, in a rigid piping system that is under pressure. The pressure thrust force is a function of the system pressure and the average diameter of the bellows. In cases of internal or positive pressure, the bellows are forced to extend in length while the opposite is observed in cases of external or negative pressure. This force is transmitted from the ends of the expansion joint along the pipe.
The force is transmitted with equal intensity in all directions.
Just as pressure acts internally in a cylindrical container, with its ends closed, a tension will appear in the longitudinal walls of the container produced by the pressure reaction force (PRF) as shown in the figure. As in any cylindrical body with a mobile element, it does not have longitudinal resistance. The FRP longitudinal force will tend to move the parts apart until they separate, as occurs for example in a plunger. A similar situation occurs if we join the moving parts with a welded bellows.
The FRP pressure reaction force is given by the following equation:
FRP = p * A f
FRP = p * π/4 * (d + h)^2
Where: FRP = Pressure reaction force
p = Internal pressure
A= Internal area of the cross section
d=External diameter of the pipe
h=Wave height
*** (d+h) Average diameter of the bellows
There are several ways to contain the transmission of pressure reaction force or prevent the joint from expanding. The measures can be:
- Place fixed supports on the pipe sections on both sides of the joint. The FRP must be taken into account when sizing the supports, since in some cases this force can be very high.
- Use expansion joints with a structure that can resist force. In this case the FRP is contained by the structure itself, freeing the fixed points and/or equipment from that load. It is in this case that the joint will not work axially, but can deform mainly laterally.
- Using self-compensated expansion joints allows you to avoid the effect of FRP, through the use of a compensating bellows.
