Branch Reinforcement Calculator

Formula overview

SI: P and S in MPa; diameters, thicknesses, and zone dimensions in mm; areas in mm². β in degrees.

ASME B31.3 para 304.3.3 — area replacement:

  A_available = A2 + A3 + A4  ≥  A1

  th = P·Dh / [2(Sh·Eh·Wh + P·Yh)]      header pressure thickness
  tb = P·Db / [2(Sb·Eb·Wb + P·Yb)]      branch pressure thickness

  d1 = opening / sin β
  A1 = th · d1 · (2 − sin β)
  A2 = (2·d2 − d1) · (Th − th − c)
  A3 = 2·L4·(Tb − tb − c) / sin β
  A4 = weld metal ( + pad area when a pad is fitted )

Worked example

2" Sch 40 branch on a 6" Sch 40 header, β = 90°, P = 2 MPa,
S = 138 MPa, E = W = 1.0, Y = 0.4, c = 1.6 mm
Th = 7.11 mm, Tb = 3.91 mm, opening d1 = 52.5 mm

th = 2 × 168.3 / [2 × (138 + 0.8)] = 1.21 mm
tb = 2 × 60.3  / [2 × (138 + 0.8)] = 0.43 mm

A1 = 1.21 × 52.5 × (2 − 1)         = 64 mm²   required
A2 = (2 × 52.5 − 52.5) × (7.11 − 1.21 − 1.6) = 226 mm²

Excess header wall alone provides 3.5× the required area,
before A3 and A4 are counted — no pad needed on this connection.

Common mistakes

• Forgetting to deduct the corrosion allowance from the excess wall. A2 and A3 credit only metal above the pressure requirement and above c — counting corroded metal as reinforcement is the classic non-conservative error here.
• Specifying a pad reflexively. On a thick header with a small branch the excess wall usually satisfies A1 on its own, and a pad adds cost, a crevice, and an inspection point for no structural benefit.
• Using the branch OD as the opening. The opening d1 is the finished hole in the header, corrected for the branch angle by dividing by sin β — an angled take-off makes an elliptical, larger opening and needs more reinforcement.

FAQ