Calculate pipe stretch from temperature change or axial load using length, material, diameter, wall thickness, and force inputs for thermal and load cases.

Free thermal movement or uniform, small-strain axial elasticity. Presets are approximate material assumptions; use manufacturer properties at operating temperature. Restraint, pressure effects, creep, yield and buckling are not modeled.

Final minus initial temperature; a temperature difference has no 32° offset.

Pipe Stretch Formula

For a uniform pipe in small-strain linear axial elasticity, use the following formula. The separate free thermal mode uses ΔL = αLΔT with a constant assumed expansion coefficient. Preset properties are approximate; restraint, pressure effects, creep, yield and buckling are not modeled.  PVC and CPVC thermal examples use 54 and 61.2 µm/(m·K); the PE4xxx HDPE example uses 144 and the PEX example 140. HDPE and PEX axial modes require a user-supplied modulus appropriate to temperature and load duration.

PS = F × L × 12 / (A × E)

Variables:

  • PS is the Pipe Stretch (inches)
  • F is the force (lbf) 
  • L is the length (ft) 
  • A is the cross-sectional area (in^2) 
  • E is the material’s elastic modulus (psi); use a value appropriate to the alloy, grade, temperature and duration. The carbon-steel preset assumes 29 × 10^6 psi, not a universal value for all metals.

How to Calculate Pipe Stretch?

The following steps outline how to calculate the Pipe Stretch.

  1. First, determine the force (lbf).
  2. Next, determine the length (ft). 
  3. Next, determine the pipe wall cross-sectional area A = πt(OD − t), in square inches when OD and wall thickness t are in inches. Choose the applicable elastic modulus E; require 0 < t < OD/2. 
  4. Next, gather the formula from above = PS = F*L*12 / (A*E).
  5. Finally, calculate the Pipe Stretch.
  6. After inserting the variables and calculating the result, check your answer with the calculator above. 

Example Problem:

Use the following variables as an example problem to test your knowledge.

force (lbf) = 500

length (ft) = 3

cross-sectional area (in^2) = 20

For an assumed E = 29,000,000 psi, PS = 500 × 3 × 12 / (20 × 29,000,000) = 0.0000310345 in (about 0.000788276 mm). The supplied area is the pipe wall area. This is elastic displacement, not an allowable-load assessment.