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Stojan Petkovic Stojan Petkovic

CT Strength Limits

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Mechanics

CT Strength Limits

Stresses, burst, collapse and tension limits of coiled tubing for the load you enter, with the von Mises check against the yield factor. Oilfield or metric units.

Before you use the tools

The tools and calculators on this site are personal, informational aids made from public formulas and stated assumptions.

  • Results are approximate. They are not a design, a procedure or professional advice.
  • Do not use them as the only basis for work on wells, work under pressure, work with nitrogen or any other safety-critical action. Follow your company's procedures, the manufacturer's data and the instruction of the responsible person.
  • This is a personal, independent site. It does not represent any employer or company and uses none of their data. You are responsible for the data you enter and for your decisions.
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Tubing
in
in

(ODmax − ODmin) / OD; about 0.005 for new tubing

Material
psi

Minimum yield strength of the steel

%

Design factor on the yield strength

psi

Steel: about 30 million psi

Steel: 0.33

Loads
psi
psi
lbf

Positive in tension, negative in compression

ft

Radius the tubing is bent over; 0 for straight tubing

Safety factor of the API 5C7 collapse correction for tension, at least 1

Inputs

Result

Share of yield strength

– %

–

Stresses at the inside wall

Axial stress (worst side)
–
Hoop stress
–
Radial stress
–
Von Mises stress
–

Burst

API 5C3 internal yield
–
Capped-end yield
–
True burst
–

Collapse

Timoshenko, round
–
API 5C3, round
–
API 5C7, oval
–
Timoshenko, oval
–
API 5C7, oval, with tension
–

Tension limits

Maximum tension
–
Maximum tension at this pressure
–

Differential pressure (external − internal) –

Method

The tubing is checked as a thick-walled steel tube under internal and external pressure, axial force and an optional bend.

  1. Axial stress is the axial force over the steel area. A bend of radius R adds the bending stress E·OD/(2R) on the convex side and subtracts it on the concave side; the larger absolute value is used.
  2. Hoop and radial stress at the inside wall come from the Lamé equations for a thick cylinder; the radial stress there equals minus the internal pressure. The von Mises stress combines the three: √(σa² + σh² + σr² − σa·σh − σa·σr − σh·σr). Torque is not included.
  3. Burst: API 5C3 internal yield 0.875 · 2Y·t/D; capped-end yield (4Y/√3)·(t/D)·(1 − t/D), where the von Mises stress at the inside wall reaches Y; true burst (2Y/√3)·ln(OD/ID), where the whole wall yields.
  4. Collapse: Timoshenko, Pc = [Py·R + Pe·(1 + 3·ov·D/2t) − √((Py·R + Pe·(1 + 3·ov·D/2t))² − 4·Py·Pe·R)] / 2, with Py = 2Y·t/D, Pe = 2E/(1 − ν²)·(t/D)³ and R the reduction for axial stress; round tubing has ov = 0. API 5C3 uses the yield, plastic, transition or elastic range of D/t, with the yield strength reduced for axial stress. API RP 5C7 gives the collapse of oval tubing from the round collapse and the ovality, and in tension reduces it by Kcf = ((1/SF)^(4/3) − (L/Ly)^(4/3))^0.75.
  5. Tension limits: Ly = yield factor · Y · steel area, and the largest axial force that keeps the von Mises stress at the yield factor with the hoop and radial stress of the entered pressures.

Assumptions

  • A seamless steel tube with uniform wall and the nominal dimensions entered, without corrosion, wear or fatigue.
  • Pressures are uniform along the tubing; the stresses are those at the inside wall, the worst case.
  • Torque and shear stresses are not included.
  • The API collapse equations are valid for the D/t range of the standards; check results outside it.

Based on the API 5C3 and API RP 5C7 equations, Timoshenko collapse, the Lamé equations and the von Mises criterion. The calculation reproduces a reference worksheet for its example case. Check the standards before you rely on a result; fatigue life is not covered.

The tools are aids for engineers. Check the inputs and the results: responsibility for any decision stays with the user.