Pipe thermal expansion and restrained longitudinal stress
Free expansion of a section with a temperature change, and the longitudinal stress in a pipeline restrained by the soil, including the internal pressure (Poisson effect); the axial force.
ΔL = α · L · ΔT; σ_T = E · α · ΔTS_L = ν · P · D / (2 · t) − E · α · ΔTN = S_L · π · (D − t) · t; E = 206.8 GPa, ν = 0.3The expansion is for a section free to move axially (e.g. above ground between anchors). A buried line is held by the soil: on a straight run the expansion does not happen and the longitudinal stress S_L builds up. E = 206.8 GPa, ν = 0.3. Check the combined stress, upheaval buckling and expansion loops by the design code.
Source: ASME B31.4 (restrained longitudinal stress: S_L = E · α · (T₁ − T₂) + 0.3 · S_H); Hooke's law
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Operating temperature minus the tie-in (installation) temperature; positive when heated.
Carbon steel 1.2·10⁻⁵ 1/°C (ASME B31.4 gives 11.7·10⁻⁶); austenitic stainless 1.6–1.7·10⁻⁵.
Gauge; 0 to leave the pressure out.
Unit converter for this formulaLength · Temperature difference · Thermal expansion · Pressure · Force and load
- m1
- cm100
- mm1,000
- km0.001
- ft3.28084
- in39.3701
- 1/32 in1,259.84
- 1/64 in2,519.69
- mile0.000621371
- σ_T — Thermal stress when fully restrained–
- S_L — Restrained longitudinal stress (negative in compression)–
- N — Restrained axial force (negative in compression)–
More in Pipelines
Design wall thickness by Barlow's formula with the factors of ASME B31.4 (liquid pipelines) and B31.8 (gas pipelines), the corrosion allowance, and the allowable pressure of the selected pipe.
Weight per metre of steel pipe and of the whole section, the internal (line fill) volume and the mass of the product in the line.
Friction loss by Darcy-Weisbach (friction factor from Colebrook-White, 64/Re in laminar flow) plus the elevation change; the flow velocity and Reynolds number.
Gas flow rate from the inlet and outlet pressures — the general isothermal flow equation with the Colebrook-White friction factor; gas velocity, average pressure, Reynolds number.
Hoop stress and its percentage of SMYS at the test pressure — at the gauge and at the lowest point of the section, where the water column adds to the pressure.
Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.