Engineering guide
This module calculates pipe bends under internal pressure to TRD 301 Annex 2, part of the German Technical Rules for Steam Boilers (TRD). In a pipe bend, the stress distribution around the circumference is not constant: at the inside of the bend (intrados) the hoop stress exceeds that of a straight pipe, at the outside of the bend (extrados) it is lower. Starting from the required wall thickness of the straight pipe per TRD 301 Eq. (5), separate wall thickness requirements for the two sides of the bend are therefore derived via coefficients for the intrados and extrados.
The calculation is needed wherever boiler tubes and piping are bent: during bending, the wall thins at the outside of the bend and thickens at the inside, so the as-built wall thicknesses on both sides must be verified against their respective requirements. The module compares the existing wall thicknesses (net of allowances) with the required values, reports the mean stresses at the intrados and extrados, and states whether the verification is satisfied.
The TRD rules were withdrawn at the end of 2012. For recalculating existing plants, TRD 301 Annex 2 remains governing; for new designs, pipe bends are calculated to EN 12952-3 or, for piping, to EN 13480-3 with comparable intrados/extrados coefficients.
Scope
- Bends
Typical workflow
Define the design quantities of the straight pipe
The design pressure and design temperature are applied; the allowable stress follows from the material, its strength value, the safety factor and the joint efficiency. With these, the required wall thickness of the straight pipe is calculated per TRD 301 Eq. (5).
Record the bend geometry
The governing quantities are the inside diameter and the bend radius. The ratio of bend radius to pipe diameter determines how strongly the stresses at the intrados and extrados deviate from the straight pipe.
Determine the coefficients for the intrados and extrados
The coefficients for the inside and outside of the bend are calculated from the bend geometry. Multiplied by the wall thickness of the straight pipe and supplemented by the allowances for wall thickness undertolerance and corrosion, they yield the required wall thicknesses including allowances for both sides of the bend.
Verify the existing wall thicknesses
The as-built wall thicknesses at the intrados and extrados — after bending, i.e. with thickening at the intrados and thinning at the extrados — are corrected for the allowances and compared with the requirements. In addition, the mean stresses on both sides of the bend are compared with the allowable stress; the module reports whether the verification is satisfied.
Frequently asked questions
Why does the inside of the bend need a greater wall thickness than the straight pipe?
At the intrados, the load-carrying circumferential line is shorter than the area whose pressure load it must carry — the hoop stress therefore exceeds that of the straight pipe, and the more so the tighter the bend (small ratio of bend radius to diameter). At the extrados the ratio reverses, so less wall thickness is theoretically sufficient there. However, since the wall thins on the outside during bending, the extrados check is usually still the critical manufacturing verification.
What role does wall thinning play in pipe bending?
During cold or hot bending, the wall thickness at the outside of the bend typically decreases by several percent, depending on the bend radius and the process, while the inside thickens. The calculation therefore uses the actual as-built wall thicknesses on both sides. In fabrication practice, the mother pipe is selected such that the required extrados wall thickness is safely maintained after thinning.
Does the verification also apply to bends with a weld seam?
Yes, longitudinally welded pipes and bends are covered via the joint efficiency, which reduces the allowable stress. If the seam lies in the bend region, its position relative to the intrados and extrados must be considered — the seam is usually placed on the neutral axis, where the hoop stress corresponds to that of the straight pipe.
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