# Pipestra Wall 0.1.0-beta - formulas, clauses and limits

Pipestra Wall calculates the **pressure design wall thickness** of straight pipe, bends/elbows, concentric reducers
and branch tees for internal pressure to **EN 13480-3** or **ASME B31.3**. It is Pipestra's own implementation of the
published code equations. All calculations run locally in the browser (Python in a web worker); nothing is uploaded.

> Beta software. Check every library allowable against your licensed code edition. Results must be verified by a
> qualified engineer. No liability.

Units: lengths mm, pressure bar(g) input (p [MPa] = p [bar] / 10), stresses MPa, temperatures °C.

## 1. Allowable stress

| Code | Symbol | Source |
|---|---|---|
| EN 13480-3 | f | Pipestra EN library (EN 10216-2/-5, EN 10217), time-independent design stress per 5.2: ferritic min(ReH(T)/1.5, Rm,20/2.4); austenitic A ≥ 30 % min(Rp1.0(T)/1.5, Rm,20/2.4) (the optional A ≥ 35 % rule is not used) |
| ASME B31.3 | S | Pipestra ASME library (Table A-1 values as transcribed, linear interpolation in temperature) |

Values are interpolated at the design temperature and clamped (with a warning) above the tabulated range. Creep
(time-dependent) design is **not** evaluated. A custom allowable can be entered instead.

## 2. Allowances and nominal wall

* c0 corrosion / erosion allowance, c2 other allowance (e.g. thinning, grooving), c1 mill under-tolerance.
* Minimum required thickness: `t_min = e + c0 + c2`.
* Required nominal (ordered) thickness:
  * tolerance in %: `t_req = (e + c0 + c2) / (1 − tol/100)`
  * tolerance in mm: `t_req = e + c0 + c2 + c1`
* Check of a nominal wall tn: available thickness `t_a = tn·(1 − tol/100) − c0 − c2` (or `tn − c1 − c0 − c2`),
  utilisation = required pressure thickness / t_a. The maximum allowable pressure is found by solving utilisation = 1.
* Recommended wall: next standard wall ≥ t_req.
  * EN: EN 10220 preferred thickness series (1.6 … 65 mm), limited to t ≤ OD/4. Which walls a mill supplies for a
    given OD depends on the producer and product standard.
  * ASME: ASME B36.10M / B36.19M schedules (5S … XXS) for NPS ½ – 24, 30, 36 (transcribed; verify).

## 3. Straight pipe

**EN 13480-3 6.1, eq. (6.1-1)**, valid for Do/Di ≤ 1.7:

    e = p·Do / (2·f·z + p)

z = weld joint factor (1.0 / 0.85 / 0.7 per 4.5). Do/Di > 1.7 is flagged "not valid".

**ASME B31.3 304.1.2, eq. (3a)**, valid for t < D/6:

    t = P·D / (2·(S·E·W + P·Y))

E = quality factor (Ej, Table A-1A/A-1B), W = weld strength reduction factor (302.3.5(e), Table 302.3.5; user input,
default 1.0, a warning is shown for welded pipe above 427 °C), Y from Table 304.1.1: ferritic steels 0.4 up to 482 °C,
0.5 at 510 °C, 0.7 from 538 °C; austenitic 0.4 up to 566 °C, 0.5 at 593 °C, 0.7 from 621 °C (linear in between).
t ≥ D/6 or P/(S·E) > 0.385 is flagged "not valid" (304.1.2(b), special consideration).

## 4. Bends and elbows

**EN 13480-3 6.2.3**, eqs. (6.2.3-1) and (6.2.3-2), with e from (6.1-1) and R the centreline radius:

    e_int = e·(R/Do − 1/4) / (R/Do − 1/2)      (intrados)
    e_ext = e·(R/Do + 1/4) / (R/Do + 1/2)      (extrados)

**ASME B31.3 304.2.1**, eqs. (3c), (3d), (3e):

    t = P·D / (2·(S·E·W/I + P·Y)),  I_i = (4·R1/D − 1)/(4·R1/D − 2),  I_e = (4·R1/D + 1)/(4·R1/D + 2),  I_sidewall = 1

Bend types:
* **Elbow** (uniform wall, e.g. a fitting): the intrados governs; `t_req` from e_int.
* **Pipe bend** (bent from straight pipe): the extrados thins. Ordered wall
  `max( t_req(e_int), t_req(e_ext) / (1 − thinning) )`. The thinning is the user's value or the geometric estimate
  `Do / (2R + Do)` (conservative, flagged). Use the bending supplier's guaranteed value.

Radius presets: 1.0·DN (2D), 1.5·DN (3D / long radius; NPS × 38.1 mm for ASME), 2.5·DN (5D), 3·Do, 5·Do or custom.
Butt-welding elbows to ASME B16.9 are rated by their listed standard (304.2.2) - this check is for pipe bends and
unlisted elbows.

## 5. Concentric reducers

Half-angle α = atan((D_L − D_S) / (2·L)) or entered directly. The cone wall is checked at the large end (constant
thickness).

**EN 13480-3 6.4** (cone rules, as in EN 13445-3 7.6), limit α ≤ 60°:

    cone        e_con = p·D_L/(2·f·z + p) / cos α
    large end   e_j = p·Dc·β/(2·f·z),  β = ⅓·√(Dc/e_j)·tan α/(1 + 1/√cos α) − 0.15,   Dc = D_L − e_j
    small end   e_1 = p·Dc·β_H/(2·f·z),  β_H = 0.4·√(Dc/e_1)·tan α/τ + 0.5,  τ = 1 + √(1/cos α),  Dc = D_S − e_1
    governing   e = max(e_con, e_j, e_1)

Junction thicknesses are iterated. The small-end form assumes cone and cylinder have the same thickness (s = 1).
Knuckles, the lengths over which the junction thickness is needed, and junction weld factors are not evaluated
(z is applied conservatively).

**ASME B31.3 304.6 / 304.7.2**: concentric reducers to B16.9 are rated by their listed standard (304.6.2). For
unlisted / fabricated cones the cone wall uses the ASME BPVC VIII-1 cone equation in outside-diameter form, limit
α ≤ 30°:

    t = P·D_L / (2·cos α·(S·E·W + 0.4·P))

Junction reinforcement is **screened only** with the Appendix 1-5 Δ tables (large end Table 1-5.1, small end
Table 1-5.2, as a function of P/(S·E)): if α > Δ a warning says reinforcement is required. The ring is not sized.

## 6. Tees and branch connections

Run (header) and branch are checked as straight pipe first. Then:

**EN 13480-3 8.4 - pressure-area method**, radial (90°) set-on / set-in branch, no reinforcing pad, no weld credit:

    e_as, e_ab = analysis thicknesses (nominal − tolerance − c0 − c2)
    r_is = Do_s/2 − e_as,  r_ib = d_ob/2 − e_ab
    l_s = √((2·r_is + e_as)·e_as),  l_b = √((d_ob − e_ab)·e_ab)
    Ap_s = r_is·(l_s + d_ob/2),  Ap_b = r_ib·(l_b + e_as)
    Af_s = e_as·l_s,  Af_b = e_ab·(l_b + e_as)
    (Af_s)·(f·z − p/2) + (Af_b)·(f·z_b − p/2) ≥ p·(Ap_s + Ap_b)

**ASME B31.3 304.3.3 - area replacement**, branch angle 45° ≤ β ≤ 90°, no pad:

    T_h, T_b = nominal walls less mill tolerance;  t_h, t_b from (3a);  c = c0 + c2
    d1 = (D_b − 2·(T_b − c)) / sin β
    d2 = max(d1, (T_b − c) + (T_h − c) + d1/2) ≤ D_h
    A1 = t_h·d1·(2 − sin β)
    A2 = (2·d2 − d1)·(T_h − t_h − c)
    A3 = 2·L4·(T_b − t_b − c) / sin β,   L4 = min(2.5·(T_h − c), 2.5·(T_b − c))
    A4 = 2 · ½ · leg²  (optional fillet welds)
    A2 + A3 + A4 ≥ A1

Recommended walls: the thinnest standard run wall for which a branch wall not heavier than the run wall passes both
the straight-pipe and the reinforcement check (thinnest such branch). If none exists, the lightest passing pair.
A heavier branch can sometimes reduce the run wall - enter walls to check other combinations.

## 7. Not covered (check separately)

* External pressure / vacuum, external loads, thermal and sustained stresses, fatigue, creep, test pressure.
* Reinforcing pads, extruded outlets, olets, crosses, multiple / adjacent openings, openings in bends or near welds.
* Eccentric reducers (use the largest wall angle as α), knuckled cones, cone junction lengths and ring sizing.
* Thick-walled pipe (EN Do/Di > 1.7, B31.3 t ≥ D/6) - flagged, not calculated.
* Listed fittings (EN 10253, ASME B16.9) are designed by their product standards; manufacturer data governs.
* Material notes (library sources, edition caveats) are shown with each result; verify them for your edition.

## 8. Verification

The Python solver is covered by unit tests with hand-calculated worked examples (tests/test_wall.py; the hand
calculations are in the test docstrings).