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Casing & Tubing Mechanical Design, API TR 5C3 / ISO 10400 Biaxial Collapse Ellipse

API 5C3 Casing Biaxial Tension Collapse Derating Formula

Calculate Casing Diameter-to-Thickness Ratio (D/t), Hencky-von Mises Biaxial Yield Reduction Factor, Effective Axial-Derated Yield Ypa (psi), and Biaxial Collapse Rating Pca (psi).

Hanging 52,000 psi of buoyant string weight on L-80 casing slashes its API 5C3 external collapse rating in HALF—crushing evacuated pipe flat during swabbing or DST evacuation!

Catalog **Zero-Tension Collapse Ratings `P_{c0}`** (`psi`, e.g. `3,810` psi for `9-5/8"` `40.0` lb/ft `L-80` casing at `D / t = 24.37`) apply ONLY at the very bottom joint where axial hanging weight is zero! Higher up a deep intermediate string, buoyant hanging tension **`sigma_a = F_{axial} / A_{steel}`** (`psi` positive in tension) combines with external mud-minus-internal-fluid hoop compression (`-sigma_theta`) on the **Hencky-von Mises Distortion-Energy Yield Ellipse (`API TR 5C3` / `ISO 10400`)**: axial tension pre-consumes octahedral shear capacity, degrading **Effective Circumferential Yield Strength to `Y_{pa} = Y_p * (sqrt(1 - 0.75 * (sigma_a / Y_p)^2) - 0.5 * (sigma_a / Y_p))`** (`psi`)! Across yield- and plastic-collapse regimes, **Biaxial Collapse Resistance `P_{ca} ~= P_{c0} * (Y_{pa} / Y_p)`** (`psi`, exact for yield collapse and conservative first-order design check across plastic transition)—explaining why upper-middle mixed-grade joints collapse inward when drill-stem tests evacuate internal hydrostatic back-pressure!

Verify on `9.625`-in, `40.0` lb/ft (`t = 0.395` in) `L-80` (`Y_p = 80,000` psi) Intermediate Casing—Outside_Diameter `D` = 9.625 in (B2), Wall_Thickness `t` = 0.395 in (B3), Minimum_Yield `Y_p` = 80,000 psi (B4), Buoyant_Axial_Stress `sigma_a` = 18,000 psi (B5), and Nominal_Collapse `P_{c0}` = 3,810 psi (B6): Slenderness `D / t` equals `24.37` (E2), Hencky-von Mises Factor equals `0.8683` (E3), Effective Biaxial Yield `Y_{pa}` drops to `69,467` psi (E4), and Derated Collapse Rating `P_{ca}` equals **`3,308` psi** (`-13.2%` below handbook `3,810` psi! E5)!

API 5C3 Biaxial Casing KPI (9.625" x 0.395" L-80, Yp=80,000 psi, Pc0=3,810 psi)FormulaVerified Output
Slenderness Ratio (D / t)Casing_OD_in / Wall_Thickness_t_in24.37 (plastic collapse regime)
Hencky-von Mises Biaxial FactorSQRT(1 - 0.75 * (sa / Yp)^2) - 0.5 * (sa / Yp)0.8683 (0.5015 @ 52,000 psi tension!)
Effective Hoop Yield Ypa (psi)Nominal_Yp_psi * Hencky_VonMises_Factor69,467 psi (40,121 psi under heavy hang)
Derated Collapse Rating Pca (psi)Zero_Tension_Pc0_psi * Hencky_Factor3,308 psi (1,911 psi = -50% LOSS!)

API TR 5C3 Hencky-von Mises Distortion-Energy Biaxial Collapse Formula

Validate `Casing_OD D` in `[2.375, 30.0]` in, `Wall_Thickness t` in `[0.15, 1.50]` in (`with D / t > 8`), `Yield_Strength Y_p` in `[40,000, 165,000]` psi, `Axial_Tension sigma_a` in `[0, 0.90 * Y_p]` psi, and `Catalog_Collapse P_{c0}` in `[500, 25,000]` psi!

=LET(od_i, B2, wt_i, B3, yp_p, B4, sa_p, B5, pc_z, B6, sr_x, sa_p / yp_p, hv_f, SQRT(1 - 0.75 * (sr_x ^ 2)) - 0.5 * sr_x, IF(OR(od_i < 2.375, od_i > 30, wt_i < 0.15, wt_i > 1.5, od_i / wt_i <= 8, yp_p < 40000, yp_p > 165000, sa_p < 0, sa_p > 0.9 * yp_p, pc_z < 500, pc_z > 25000), "Invalid Casing Input", ROUND(pc_z * hv_f, 0)))

Upper-String Heavy Hanging Tension (`sigma_a = 52,000` psi = `65%` of Yield) Collapse Halving Check

Evaluate a joint high up the `12,000`-ft string carrying `B5 = 52,000` psi axial tension (`65%` of `L-80` yield): Hencky-von Mises Factor E3 plunges to **`0.5015`** (`Y_{pa}` = `40,121` psi in E4), **chopping Collapse Resistance E5 nearly in half from `3,810` down to `1,911` psi**—demanding heavier `47.0` lb/ft `P-110` top-section Tapered Casing Design!

=IF(ISTEXT(E5), E5, ROUND(SQRT(1 - 0.75 * ((B5 / B4) ^ 2)) - 0.5 * (B5 / B4), 4))

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