Design stress

EN 10253 Tees

Check Crotch Tee Reinforcement

A welding tee is a prefabricated, crotch-shaped tee — a crotched tee with the crotch machined or formed with the crotch left at the full tee thickness. Calculated to EN 10253 (welded steel butt-welding pipe fittings).

The EN 13480 branch calculator has a dedicated welding tee mode for exactly this situation. Instead of the rectangular area ratio method used for a standard opening, it builds the reinforcement and pressure areas from the actual crotch geometry of the tee, following the interpretation from EN 10253 for calculating the exact areas. You can run it in the EN 13480 Branch (Opening) Reinforcement Calculator by switching to welding tee mode.

Because the crotch shape of a manufactured tee is not fully defined by the standard, the calculation introduces a crotch radius factor that lets the engineer state the size of the crotch. In short: the larger the credited crotch radius, the larger the pressurised area it must support, so the result becomes generally conservative with a larger crotch size.

The Method in One Picture

The method works on a longitudinal slice through the tee, exactly like the standard area ratio method — only the geometry is taken from the tee crotch instead of a rectangle:

  • The straight wall of the header and the branch, up to the crotch, still contributes reinforcement as before (A_fs, A_fb)
  • The crotch is calculated seperately as reinforcement (A_fsc, A_fbc), with a thickness that is the same as the header thickness
  • The projected pressure area A_p is built from the square and shaped geometries, the crotch pressure areas (A_psc, A_pbc) and the total reinforcement area similar to the normal branch.

The evaluation is the same as the standard method: the opening is compliant when the available reinforcement force is greater than or equal to the required reinforcement force.

Tee Outlet Lengths

The geometry of the calculation is driven by the two outlet lengths of the tee:

  • F — the outlet length of the run (header side)
  • G — the outlet length of the branch

These are not user inputs. The calculator looks them up from the standard tee dimensions table (the T-table, covering header outer diameters from 21.3 mm to 610 mm), indexed by the header outer diameter and the branch outer diameter. If the exact size combination is not in the table, the closest available size is used, and if a specific branch size is not available for that header, the default outlet length for the header size is used.

Example values from the table:

Header OD (mm)Branch OD (mm)F — run (mm)G — branch (mm)
88.942.28670
114.360.310589
114.388.910598
219.1141.3178162

Maximum and Credited Crotch Radius

The crotch of the tee can at most reach the space available between the branch and the header. The calculator first determines the maximum radius the crotch could have on each side:

r_{\text{max, b}} = G - \frac{D_{h}}{2} r_{\text{max, s}} = F - \frac{D_{b}}{2}

where D_h and D_b are the outer diameters of the header and the branch. The usable maximum radius is the smaller of the two:

r_{\text{max}} = \min\left(r_{\text{max, b}}, \; r_{\text{max, s}}\right)

The credited crotch radius r_c is then the maximum radius scaled by the crotch radius factor k, capped at 1.0:

r_{c} = r_{\text{max}} \times \min\left(k, 1\right)
  • k = 1.0 — the full available crotch space is credited (crotch-supported tee, full crotch)
  • k = 0.5 — the default; half of the available crotch space is credited
  • k → 0 — no crotch reinforcement is credited (behaves like a normal branch)

In addition, the calculation uses an effective crotch thickness e_c, taken as the average of the two analysis thicknesses:

e_{c} = \frac{e_{bana} + e_{hana}}{2}

Reinforcement Lengths

For a standard opening the reinforcement length is simply sqrt(D_eq × e_ana). For a welding tee it is the same but limited by the tee dimension, it cannot be past the weld end of the Tee:

l_{b} = \min\left(\sqrt{D_{eqb} \times e_{bana}}, \; G - \frac{D_{h}}{2} - \left(1 - \frac{\pi}{4}\right) \times r_{c}\right) l_{s} = \min\left(\sqrt{D_{eqh} \times e_{hana}}, \; F - \frac{D_{b}}{2} - \left(1 - \frac{\pi}{4}\right) \times r_{c}\right)

The term (1 − π/4) × r_c accounts for the curved crotch: the reinforcement zone on the crotch side runs along the crotch arc, not in a straight line, so a portion of the reinforcement length is “consumed” by the curve.

Crotch Angles

The reinforcement zones that fall on the crotch are bounded by an angle measured from the centre of the crotch. The angle is 0° when the reinforcement length is shorter than the crotch arc (π/4 × r_c) — the reinforcement is then fully on the crotch — and it grows towards 45° as the reinforcement length exceeds the crotch arc:

\alpha_{s} = 45 \times \max\left(1 - \frac{l_{s}}{\frac{\pi}{4} \times r_{c}}, 0\right) \alpha_{b} = 45 \times \max\left(1 - \frac{l_{b}}{\frac{\pi}{4} \times r_{c}}, 0\right)

Compensated Lengths

The reinforcement lengths l_s and l_b are measured along the surface (straight part plus crotch arc). The area formulas below work in the tangent plane of the crotch, so the lengths are converted to their tangent-equivalent:

l_{s,i} = r_{c} - r_{c} \times \sin(\alpha_{s}) + \max\left(l_{s} - r_{c} \times \frac{\pi}{4}, 0\right) l_{b,i} = r_{c} - r_{c} \times \sin(\alpha_{b}) + \max\left(l_{b} - r_{c} \times \frac{\pi}{4}, 0\right)

These compensated lengths define the rectangular bounding box of the whole opening + reinforcement zone that is used in the projected area.

Interpolated Crotch Thickness

The effective thickness within the crotch transitions from the pipe analysis thickness to the crotch thickness e_c over the 45° crotch sector. The interpolation is based on the crotch angles from the previous section:

e_{sc} = \frac{45 - \alpha_{s}}{45} \times e_{hana} + \frac{\alpha_{s}}{45} \times e_{c} e_{bc} = \frac{45 - \alpha_{b}}{45} \times e_{bana} + \frac{\alpha_{b}}{45} \times e_{c}

When the angle is 0° the full pipe thickness applies (no crotch involved); at 45° the full crotch thickness applies.

Reinforcement Areas

Four areas contribute to the available reinforcement:

Straight header and branch wall (only the part of the reinforcement zone that lies outside the crotch):

A_{fs} = \max(l_{s,i} - r_{c}, 0) \times e_{hana} A_{fb} = \max(l_{b,i} - r_{c}, 0) \times e_{bana}

Crotch sectors — an annular sector over the (45° − α) crotch angle, plus the triangular wedge at the transition:

A_{fsc} = \left[\left(r_{c} + \frac{e_{sc} + e_{c}}{2}\right)^{2} - r_{c}^{2}\right] \times \pi \times \frac{45 - \alpha_{s}}{360} + e_{sc}^{2} \times \frac{\tan(\alpha_{s})}{2} A_{fbc} = \left[\left(r_{c} + \frac{e_{bc} + e_{c}}{2}\right)^{2} - r_{c}^{2}\right] \times \pi \times \frac{45 - \alpha_{b}}{360} + e_{bc}^{2} \times \frac{\tan(\alpha_{b})}{2}

The total reinforcement area is the sum:

A_{f} = A_{fs} + A_{fsc} + A_{fb} + A_{fbc}

Projected Pressure Areas

The shape of the crotch also increases the pressure areas in size that must be carried by the reinforcement. For each side the crotch pressure area is:

A_{psc} = r_{c}^{2} \times \left[\frac{1}{2}\left(1 - \sin(\alpha_{s})\right)^{2} - \pi \times \frac{45 - \alpha_{s}}{360} + \frac{1}{2}\sin(\alpha_{s})\left(\cos(\alpha_{s}) - \sin(\alpha_{s})\right)\right] A_{pbc} = r_{c}^{2} \times \left[\frac{1}{2}\left(1 - \sin(\alpha_{b})\right)^{2} - \pi \times \frac{45 - \alpha_{b}}{360} + \frac{1}{2}\sin(\alpha_{b})\left(\cos(\alpha_{b}) - \sin(\alpha_{b})\right)\right]

The total projected area is the bounding rectangle built from the compensated lengths, plus the crotch pressure areas, minus the reinforcement area already accounted for inside that rectangle:

A_{p} = \left(\frac{D_{b}}{2} + l_{s,i}\right) \times \left(\frac{D_{h}}{2} + l_{b,i}\right) - l_{s,i} \times l_{b,i} + A_{psc} + A_{pbc} - A_{f}

Required and Available Force

The balance is identical in form to the standard area ratio method:

A_{avail} = \left(S_{header} - \frac{P}{2}\right) \times \left(A_{fs} + A_{fsc}\right) + \left(S_{branch} - \frac{P}{2}\right) \times \left(A_{fb} + A_{fbc}\right) A_{req} = P \times A_{p}

where S_header and S_branch are the design stresses (the branch is limited to the header design stress if it would be higher) and P is the design pressure.

Code Compliance and Utilisation

A_{req} \leq A_{avail} A_{req} > A_{avail} Utilisation = \left( \frac{A_{req}}{A_{avail}} \right) \times 100\%

A utilisation of 80% means the tee opening uses 80% of its available reinforcement capacity. Values above 100% mean the connection does not meet the code requirement.

Step-by-Step Calculation Process

The calculator performs the following steps for each tee branch and each pressure/temperature case:

  1. Verify the header and branch straight pipes — Both the header and the branch are checked against the internal pressure requirement first. If either fails, the branch calculation cannot be completed.
  2. Determine analysis thicknesses — Manufacturing tolerance, corrosion allowance, and thread allowance (if applicable) are subtracted from the nominal wall thickness of each pipe.
  3. Determine design stresses — The header and branch allowable stresses are looked up at the design temperature; the branch stress is limited to the header value if it would be higher.
  4. Check validity limits — The branch must not be larger than the header, and the thickness/diameter ratio must fall within the limits of EN 13480 Figure 8.3.1-1.
  5. Get tee outlet lengths — F (run) and G (branch) are looked up from the tee dimensions table for the header and branch outer diameters.
  6. Calculate maximum and credited crotch radius — r_max from the outlet geometry, then r_c from the crotch radius factor, plus the crotch thickness e_c.
  7. Calculate reinforcement lengths — l_b and l_s, limited by the crotch geometry.
  8. Calculate crotch angles — α_s and α_b.
  9. Calculate compensated lengths — l_s,i and l_b,i in the tangent plane.
  10. Calculate interpolated crotch thickness — e_sc and e_bc.
  11. Calculate reinforcement areas — A_fs, A_fb, A_fsc, A_fbc and the total A_f.
  12. Calculate projected area — A_psc, A_pbc and the total A_p.
  13. Evaluate compliance — Required force against available force, and the utilisation percentage.

Each step is documented in the calculation report with formulas, intermediate values, and units for full traceability.

Key Inputs

InputDescriptionDefault
Welding TeeSwitch that enables the welding tee calculation modeNo
Crotch Radius FactorScale (0–1) applied to the maximum available crotch radius0.5

Frequently Asked Questions

Where do the outlet lengths F and G come from?

They are the standard outlet lengths of the tee — F for the run (header side) and G for the branch — looked up from the tee dimensions table (the T-table) by header and branch outer diameter. The table covers header sizes from 21.3 mm to 610 mm; the closest size is used for combinations that are not in the table.

How is this different from the standard branch calculation?

The standard calculation assumes a rectangular reinforcement zone around a plain opening. The welding tee mode replaces that rectangle with the actual crotch geometry: the reinforcement and pressure areas are built from the crotch radius, the crotch angles, and the interpolated crotch thickness, while the force balance (required vs. available) stays the same.

Does the welding tee mode still check the straight pipes?

Yes. Before the tee calculation runs, both the header and the branch are verified against the internal pressure requirement for the straight pipe, and the EN 13480 thickness ratio limits still apply. Only the reinforcement check itself changes.

Can I use this for a crotch-supported tee?

Yes. Use a high crotch radius factor (up to 1.0) to credit the full crotch space. Generally the larger crotch radius gives a more conservative result, because the pressurised crotch area grows with the radius faster than the extra reinforcement.

By Yasin Mohamed 28 August 2026