1 · Design inputs

NPS 8 Sch 40 run (8.625 × 0.322) with an NPS 4 Sch 40 branch (4.5 × 0.237) at 90°, no pad, no allowance credit. Required walls: th = 0.147 in, tb = 0.077 in.

2 · Method

With β the branch angle, allowances c deducted, and d₁ the effective opening length:

d₁ = [ D_b − 2(T_b − c) ] / sin β

A₁ = t_h · d₁ · (2 − sin β)  (required)

A₂ = (2·d₂ − d₁) · (T_h − t_h − c)  (excess run wall)

A₃ = 2·L₄ · (T_b − t_b − c) / sin β  (excess branch wall)

A₂ + A₃ + A₄ ≥ A₁ → PASS

where d₂ is the reinforcement-zone half-width, L₄ the height limit measured along the branch, and A₄ pad and weld areas. Required thicknesses t_h, t_b come from Eq. (3a) for run and branch.

3 · Calculation

1. Opening: d₁ = 4.5 − 2·0.237 = 4.026 in; zone half-width d₂ = d₁ = 4.026 in.
2. Height limit: L₄ = min(2.5·(T_h−c), 2.5·(T_b−c)+T_r) = min(0.805, 0.5925) = 0.5925 in.
3. Required: A₁ = 0.147·4.026·(2−1) = 0.5918 in².
4. Run excess: A₂ = (2·4.026−4.026)·(0.322−0.147) = 4.026·0.175 = 0.7046 in².
5. Branch excess: A₃ = 2·0.5925·(0.237−0.077) = 0.1896 in².
6. Balance: 0.7046 + 0.1896 = 0.8942 ≥ 0.5918 → PASS, excess 0.3023 in².

4 · Results PASS

5 · Verification statement

The result values above are locked as fixture branch-reinforcement.json, case “8x4 sch40 90-degree unreinforced -> pass”, tolerance 0.0001, in the calc-core continuous verification gate (see https://pipingtoolset.com/trust/validation.html). Allowable-stress and factor data are user-supplied inputs; citations: ASME B31.3, Process Piping — ¶304.3.3, reinforcement of welded branch connections; Fig. 304.3.3 nomenclature. · ASME B31.1 ¶104.3.1 uses the same area-replacement principle for the Power line card.