Converting Pipe Displacement into forces on a Bend

[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

 

[jrmichler]

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.

 

[Tom.G]

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.

 

[JBA]

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