Casing Collapse Pressure Calculator: Yield Strength Collapse via the Lame Thick-Wall Solution

Solve the yield strength collapse pressure of thick-wall oilfield casing and tubing: find the collapse rating from outside diameter, wall thickness, and minimum yield strength, compare collapse pressure across steel grades, or solve the yield strength needed to hit a target collapse rating. Everything updates live.

Yield Strength Collapse and the Lame Thick-Wall Solution

Casing and tubing collapse when external pressure exceeds the pipe’s ability to resist it. API Bulletin 5C3 defines four collapse regimes depending on the diameter-to-wall-thickness ratio (D/t) and yield strength: yield strength collapse, plastic collapse, transition collapse, and elastic collapse. This tool covers yield strength collapse, the regime that applies to thick-wall pipe, generally D/t below about 15, where the tangential (hoop) stress at the inner wall reaches the material’s yield strength before any buckling instability can occur.

Unlike the plastic, transition, and elastic collapse regimes, which use empirical curve-fit coefficients calibrated against test data for specific steel grades, yield strength collapse is derived directly from the Lame thick-wall elastic solution for a cylinder loaded only by external pressure. Solving that classical elasticity result for the pressure at which inner-wall tangential stress equals yield strength gives Py = 2 x Yp x [(D/t) – 1] / (D/t)^2, where Yp is minimum yield strength, D is outside diameter, and t is nominal wall thickness.

Why This Regime Is Fully Derivable

The general Lame tangential stress at the inner wall of a thick cylinder under external pressure alone is sigma_theta = 2 x Po x ro^2 / (ro^2 – ri^2), where ro and ri are the outer and inner radii and Po is the external pressure. Setting this equal to yield strength Yp and solving for Po, then rewriting ro and ri in terms of outside diameter and wall thickness, produces the D/t form of the equation used above exactly, with no empirical fitting involved. The quick solve tab reports a tangential stress check alongside the collapse pressure so you can confirm this consistency directly: the check value always equals the yield strength entered.

Because this regime is only valid for thick-wall pipe, the calculator flags a warning whenever the D/t ratio rises above about 15, since thinner-wall pipe collapses at a lower pressure than this formula predicts, governed instead by plastic or elastic buckling instability rather than pure material yield.

Comparing Collapse Pressure Across Steel Grades

Because the yield strength collapse equation is linear in Yp, moving to a higher-strength grade raises collapse pressure in direct proportion, exactly as it does for burst pressure under Barlow’s equation. The grade comparison tab holds OD and wall thickness fixed and varies only minimum yield strength across rows, isolating exactly how much grade selection alone changes the collapse rating of a given thick-wall pipe body.

Solving for Required Yield Strength

Casing design sometimes works backward from a required collapse rating, set by expected evacuation or trapped-pressure scenarios, to the minimum yield strength a given pipe size must carry. Rearranging the equation makes that solve direct: Yp = Py x (D/t)^2 / [2 x ((D/t) – 1)]. The reverse tab defaults to a 5.0in OD, 0.5in wall example, confirming the required yield strength lands exactly on N-80 grade steel.

Common Mistakes

Applying the yield strength collapse formula to thin-wall pipe with D/t well above 15, which overstates true collapse resistance since real failure shifts to plastic or elastic buckling at lower pressure.

Treating collapse pressure as independent of axial load, when in practice tension or compression in the string reduces the effective collapse resistance and must be checked separately in a full casing design.

Assuming the same steel grade gives identical burst and collapse ratings, when in fact burst pressure scales differently with pipe geometry than collapse pressure, so a pipe favorable for one failure mode is not automatically favorable for the other.

Ignoring the difference between nominal and actual (as-manufactured) wall thickness, since API manufacturing tolerances affect collapse resistance just as they affect burst rating.

Who Uses This

Drilling and completion engineers checking collapse resistance for casing and tubing strings.

Well control specialists evaluating fully evacuated or gas-filled annulus scenarios.

Petroleum and mechanical engineering students studying thick-wall cylinder theory and its application to tubular design.

Tubular design engineers cross-checking published API collapse ratings for thick-wall pipe sizes.

Try It Above

Use the quick solve tab to convert outside diameter, wall thickness, and minimum yield strength directly into yield strength collapse pressure, move to the grade comparison tab to see how much steel grade alone changes the rating, or use the solve tab when you need the yield strength required to reach a target collapse pressure.

Related Calculators and References

Continue building your workflow with the Casing Burst Pressure Calculator. For background on the full set of API collapse regimes, see DrillingFormulas.com: Collapse Pressure Property for Oilfield Tubular.