Pipe Bend Thickness Calculator
Minimum wall thickness at the intrados and extrados of a pipe bend per ASME B31.3 para 304.2.1, using the bend radius correction factor I.
When to use this calculator
Use when a bend or elbow has to be checked separately from the straight pipe it connects. A bend is not uniformly stressed: the inside of the curve, the intrados, carries more hoop stress than straight pipe of the same size and needs a thicker wall, while the outside, the extrados, needs less. The correction factor I captures this from the bend radius ratio, and the difference is large enough that a wall thickness passing on the straight run can fail at the intrados of a tight bend.
Required inputs
- Design pressure P and outside diameter D
- Bend radius R1, or the R1/D ratio
- Allowable stress S, joint quality factor E, weld strength reduction factor W
- Temperature coefficient Y, corrosion allowance c
Expected outputs
- Correction factor I at intrados and extrados
- Required thickness at each, and the governing value
- Minimum thickness tm = t + c
Formula overview
SI: P and S in MPa, D and t in mm. R1/D is dimensionless — 1.5 for a long-radius elbow, 1.0 for a short-radius one.
ASME B31.3 para 304.2.1:
t = P·D / [ 2·(S·E·W/I + P·Y) ]
I_intrados = (4(R1/D) − 1) / (4(R1/D) − 2) > 1, thickens the wall
I_extrados = (4(R1/D) + 1) / (4(R1/D) + 2) < 1, thins the wall
tm = t + c the intrados normally governsWorked example
6" long-radius elbow, R1/D = 1.5, P = 2 MPa, D = 168.3 mm,
S = 138 MPa, E = W = 1.0, Y = 0.4, c = 1.6 mm
I_intrados = (6 − 1)/(6 − 2) = 1.250
I_extrados = (6 + 1)/(6 + 2) = 0.875
t_intrados = 336.6 / [2 × (138/1.250 + 0.8)] = 1.51 mm
t_extrados = 336.6 / [2 × (138/0.875 + 0.8)] = 1.06 mm
straight pipe, for comparison = 1.21 mm
The intrados needs 25% more wall than the straight run.
tm = 1.51 + 1.6 = 3.11 mm.Common mistakes
- Checking only the straight pipe. A bend on the same line and the same schedule can fail at the intrados even when the straight run passes, particularly on short-radius elbows where R1/D = 1.0 pushes I to 1.5.
- Ignoring forming thinning. A bend pulled from straight pipe loses wall at the extrados during forming, so the as-formed thickness there may be well below the parent pipe even though the code requirement is lower.
- Assuming a fitting is exempt. A standard elbow bought to ASME B16.9 is qualified by the fitting standard, but a field-formed or mitred bend has to be shown adequate by this calculation.
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