# Converting Pipe Displacement into forces on a Bend

• Kevin-Newcastle
In summary: Gp = Maximum stress for your piping materialO.D. = Outside Diameter of your piping material pipe length = Length of piping material
Kevin-Newcastle
Hi there,

I am by no means a mathematician, I am currently working on a project to improve the safety of gas distribution systems in multi occupancy developments. I am hitting a bit of a wall regarding converting displacement onto force.

I am trying to calculate the stress applied to a point in a section of steel pipe work (point A on the sketch attached).

I can calculate the thermal expansion of the vertical 2” steel pipe and the total displacement (6.6mm).

Unless I’m wrong, the force on point A is dependent on the amount of displacement on the 2” steel (6.6mm 2” steel pipe), length of the off take (640mm of 3/4 steel pipe) and the flexibility of the material being used.

Any help would be greatly appreciated.

Kev

#### Attachments

• Steel pipe.jpg
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When designing the support system for a piping system, the goal is restrain the pipe as little as possible. The goal is to restrain only at connections, and just support the weight of the pipe in between. When a properly supported pipe expands/contracts, it floats to a configuration of minimum stress.

To find forces at constraints:
1) Determine the stress-free configuration at the first temperature.
2) Assume the entire line is floating in space. This is the stress-free configuration at the first temperature with all supports removed.
3) Change to the second temperature.
4) Calculate the forces (at the constraints) to move the constraint points back to their original position.
5) Done

Note that each pipe hanger is a constraint. If a hanger is free to move, then it is only supporting the weight of the pipe, and can be ignored.

anorlunda
I agree with @jrmichler. To rephrase his response slightly:

As you noted, that 2" pipe WILL grow in length with temperature. The simplest way to find the force at point "A" would be to ignore the 2" pipe and treat the 1/2" pipe as a simple cantilever beam. Then calculate the force needed to move the free end of the cantilever by your calculated 6.6mm displacement.

jrmichler
Your situation is complicated a bit by the fact that the 2" pipe is going to resist bending and exert a a stress at both ends of your 3/4" pipe, so it might be a good idea to use a cantilevered beam with the opposite end at the elbow being guided case for the calculation.

The equation to determine the maximum stress for your pipe at both ends of your 3/4" pipe based upon your deflection, assuming the 2" pipe is substantially more bend resistant than the 3/4" pipe, is:

Max Stress Gp = 3 x E Gp x (pipe O.D.) mm x (pipe end deflection) mm / (pipe length)^2 mm^2

where: E = Modulus of Elasticity for your piping material

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## What is pipe displacement and why is it important in understanding forces on a bend?

Pipe displacement refers to the amount of movement or change in position of a pipe when a force is applied to it. This is important in understanding forces on a bend because it helps us determine the amount of stress and strain that the pipe will experience, which can affect its structural integrity.

## How do you convert pipe displacement into forces on a bend?

To convert pipe displacement into forces on a bend, we use the principle of Hooke's Law, which states that the force applied to an object is directly proportional to the amount of displacement. By measuring the amount of displacement and applying the appropriate mathematical equations, we can calculate the forces on a bend.

## What factors can affect the accuracy of converting pipe displacement into forces on a bend?

There are several factors that can affect the accuracy of converting pipe displacement into forces on a bend. These include the material properties of the pipe, the type and magnitude of the applied force, the geometry of the bend, and any external factors such as temperature or corrosion.

## Are there any limitations to using pipe displacement to determine forces on a bend?

Yes, there are some limitations to using pipe displacement to determine forces on a bend. This method assumes that the pipe is a linear elastic material, which may not always be the case. It also does not take into account any non-uniformities or defects in the pipe, which can affect the accuracy of the calculations.

## How can understanding forces on a bend help in the design and maintenance of pipelines?

Understanding forces on a bend is crucial in the design and maintenance of pipelines as it allows engineers to determine the maximum load that a pipe can withstand before failure. This information can be used to design pipelines that can withstand the expected forces and to identify potential weak points in the pipeline that may require maintenance or repair.

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