Contents
About this tool
The External Pressure calculator checks a flat-bottom tank for uniform external pressure (vacuum) to API 650 Annex V: the fixed roof under the total roof pressure, the roof-to-shell compression region, the shell by the transformed-shell method for wind plus external pressure and for external pressure alone, the number, spacing and size of intermediate stiffeners, the top and bottom end stiffeners, the stiffener welds, and the bottom under external pressure and flooding.
Scope
Annex V applies when the design external pressure is over 0.25 kPa (1 in. of water) and not over 6.9 kPa (1 lbf/in²). It does not apply to aluminum tanks. This is an indicative check, not a certified design; it follows API 650, 14th edition (August 2025), checked against the text and its V.10 example.
Quick start
Press Load illustrative sample: a 20 m × 12 m carbon steel tank for 1.5 kPa of vacuum (about 150 mm of water) with a 160 km/h wind, courses of 8, 6, 6, 6 and 6 mm, a butt-welded dome roof (R = 16 m, 10 mm), angle stiffeners and a 0.5 m flood. The shell needs 3 intermediate stiffeners; with 100 × 75 × 8 angles nothing fails.
- 1Section 1: diameter, Fy and E at the maximum operating temperature, and the courses from the bottom up. Tick V.5 if the Purchaser wants the corrosion allowance deducted.
- 2Section 2: Pe (without wind), Fpe, the wind speed (or PWV), Lr, the balanced snow load and the roof dead load.
- 3Section 3: the roof type with its angle or dish radius and plate thickness.
- 4Section 5: the stiffener sections and, if you want, their positions from the top; blank places them at equal transformed spacing.
- 5Section 6: the bottom plate, the product kept in the tank, and any flood.
- 6Tick the record items, then Calculate & Save and Print / PDF report.
Units and rule set
- The units choose the rule set. SI uses Annex V’s SI equations (m, mm, kPa, MPa, N/m, cm⁴, mm²); US customary uses its USC equations (ft, in., lbf/ft², lbf/in², lbf/in., in.⁴, in.²). The constants are rounded differently, so the two agree to within about 1 %.
- Shell courses are entered from the bottom, as in the other Tank Protocol tools; Annex V numbers them from the top, and the results use its numbering.
- Stiffener positions are measured from the top of the shell, as in V.10, in m or ft; switching units converts them.
Loads (section 2)
| Quantity | Rule | Sample |
|---|---|---|
| PWV | 1.48 (V/190)² kPa (31 (V/120)² lbf/ft²), V the 3-s gust | 1.050 kPa |
| Ps, shell | Greater of Pe and PWV + Fpe Pe | max(1.5, 1.050 + 0.6) = 1.650 kPa |
| Pr, roof (V.7) | Greater of DL + (Lr or S) + Fpe Pe and DL + Pe + 0.4 (Lr or S) | 0.770 + 1.5 + 0.4 = 2.670 kPa |
| ψ, condition 1 | 1.0 to 0.25 kPa; (Pe + 0.70)/0.95 to 0.70 kPa; Pe/0.48, at most 2.5 | 2.5 |
| ψ, condition 2 | Pe alone | 3.0 |
- DL defaults to the roof plate weight (77 kN/m³ × t); enter it to include framing. Lr is at least 1.0 kPa; Fpe at least 0.4 (5.2.2).
Fixed roof (section 3)
| Roof | Rule | Sample (dome, R 16 m) |
|---|---|---|
| Self-supporting dome or umbrella (V.7.3) | tdome = 141 R √(Pr/E); Areqd = 300 Pr R D / f; Xdome = 19.0 √(R t) | 8.26 mm ≤ 10 ✓; 1,709 mm²; 240 mm |
| Self-supporting cone (V.7.2) | tcone = 83 D / sin θ × √(Pr/1.72E); Areqd = 125 Pr D² / (f tan θ); Xcone = 13.4 √(D t / sin θ) | — |
| Top stiffener area (V.7.2.5, V.7.3.5) | Astiff = Areqd − ts1 Xshell − troof Xroof, Xshell = 13.4 √(D ts1) | 1,709 − 6 × 147 − 10 × 240 < 0: none needed |
| Column-supported cone (V.7.1) | Roof plate as beam, catenary or diaphragm by agreement; columns carry the added load (V.9.2) | record items |
- f is the smallest allowable tensile stress of roof, shell and stiffener; blank uses 0.6 Fy, as V.10 does.
- A required roof plate over 12.5 mm (0.5 in.) corroded is flagged: V.10 shows the answer, a dome with a smaller radius or a supported cone.
- The 5.10.5.1 / 5.10.6.1 minimums are checked in the Roof Design tool.
Shell buckling (section 4)
| Step | Rule | Sample |
|---|---|---|
| Transformed height (V.8.1.4) | HTS = Σ h (tsmin/t)2.5 | 4 × 2.4 + 2.4 × 0.752.5 = 10.769 m |
| Elastic buckling (V.8.1.1) | (D/tsmin)0.75 (HTS/D) (Fy/E)0.5 ≥ 0.00675 | 0.0471 ✓ |
| Unstiffened allowable (V.8.1.2) | E / (15,203 ψ (HTS/D)(D/tsmin)2.5) | 0.479 kPa (ψ 2.5) < 1.650; 0.399 kPa (ψ 3) < 1.5 |
| Safe height (V.8.2.1.2) | Hsafe = tsmin2.5 E / (15,203 D1.5 P ψ), the lesser of the two conditions | 3.13 / 2.87 → 2.868 m |
| Stiffeners (V.8.2.1.3) | Ns + 1 = HTS/Hsafe, rounded up | 3.76 → Ns = 3 |
- The shell is transformed to its thinnest course; when that is the top course, as usual, this is exactly V.8.1.4.
- The shell passes unstiffened when both conditions pass; otherwise it needs stiffeners at transformed spacing within Hsafe.
Stiffeners (section 5)
| Item | Rule | Sample (first stiffener) |
|---|---|---|
| Positions | Equal transformed spacing HTS/(Ns + 1), mapped back to the shell; or entered | 2.69, 5.38, 8.08 m from the top |
| Waves (V.8.2.2.1) | N² = 445 D³/(tsmin HTS²), 4 to 100 | 5,116 → 100 |
| Radial load (V.8.2.2.3) | Q = 1000 Ps Ls, Ls = (L1 + L2)/2 | 1000 × 1.650 × 2.69 = 4,441 N/m |
| Ireqd (V.8.2.2.5) | 37.5 Q D³ / (E (N² − 1)) cm⁴ | 67.6 cm⁴ |
| Areqd, Astiff (V.8.2.2.6) | Q D / 2fc; Areqd − 26.84 t √(D t), and at least ½ Areqd | 431 mm² (fc 103 MPa); at least 216 mm² |
| Iact | Stiffener + shell within wshell = 13.4 √(D t) each side, about the region’s centroid | angle 100 × 75 × 8: 523 cm⁴ ✓ |
| End stiffeners (V.8.2.3) | V1 = 250 Ps H; Ireqd as above with V1; Areqd = V1 D / 2f, less shell, roof (top) or bottom 16 tb (bottom) | 4,949 N/m; 75.4 cm⁴; 330 mm² |
| Welds (V.8.2.4) | Ww = √(Vs1² + Vs2²), Vs1 = 1000 Ps Ls, Vs2 = 100 vs qs/Iact; leg ≥ min(t, tstiff, 6 mm) | reported per stiffener |
- fc is 0.4 Fy for intermediate and bottom regions; carbon steel need not use less than 103 MPa (15,000 lbf/in²). Enter fc to use another value.
- An angle has its horizontal leg on the shell and its vertical leg at the outer end; a flat bar is a horizontal plate; or enter the area, own I and centroid.
- A flat bar wider than 16 times its thickness needs lateral bracing (V.8.2.5); an angle has an outer flange.
- Entered positions are checked: every transformed spacing, including to the top and bottom, must be within Hsafe.
Bottom (section 6)
| Condition | Rule | Sample |
|---|---|---|
| 1: external pressure (V.9.1) | Pe against the bottom plate weight plus the product required to remain; otherwise evaluate the bottom membrane (V.9.2) | 1.5 kPa ≤ 0.62 + 2.50 kPa (0.3 m of 850 kg/m³) ✓ |
| 2: flooding, Rule 1 (V.9.3.1) | Gin Hin + bottom ≥ Gout Hout | keep at least 0.51 m inside; 1.0 m ✓ |
| 2: flooding, Rule 2 | Otherwise anchorage, piping and sump, bottom and corner joint designed for the unbalanced pressure (up to +33 %) | record item |
The checks
| Check | Clause |
|---|---|
| Annex V applies | V.1 |
| Roof plate; roof-to-shell compression region | V.7.2, V.7.3 |
| Elastic buckling criterion | V.8.1.1 |
| Shell buckling (unstiffened, or stiffened within Hsafe) | V.8.1.2, V.8.2.1 |
| Intermediate stiffener spacing; intermediate stiffeners; lateral bracing | V.8.2.1 – V.8.2.2, V.8.2.5 |
| Top end stiffener; bottom end stiffener region | V.8.2.3 |
| Bottom under external pressure; flooding | V.9 |
| Fpe, Lr minimums | 5.2.2, 5.2.1 f |
| Design record | Annex V |
Design record (section 7)
- Tolerances of 7.5 (V.4); corrosion allowance decision (V.5); testing (V.6); load combinations (5.2.2).
- Supported cone roof plate and columns (V.7.1, V.9.2); stiffener welds and seams (V.8.2.4.5, V.8.2.2.2); flooding procedures (V.9.3); variables for Annexes M, S, SC, X (V.2).
How the numbers were checked
The test suite runs the V.10 example in US customary units and reproduces it: Pr 116.8 lbf/ft², tdome 0.529 in., Areqd 7.21 in.², Xdome 11.83 in., Xshell 7.12 in., the elastic criterion 1.23, HTS 43.54 ft, tsmin 0.698 in., Hsafe 5.84 ft and Ns = 7; for the uniform 0.395 in. shell, Q 69.1 lbf/in., Ireqd 6.36 in.⁴ and Areqd 2.16 in.²; for the end regions V1 86.4 lbf/in. and Areqd 1.8 in.²; and the bottom region’s 20.2 in.⁴.
- Where V.10 departs from the equations, the tool follows the equations: the end stiffener Ireqd uses 648 (V.10 writes 684, giving 8.39 in.⁴ instead of 7.95); and V.10 uses fc = 14,400 lbf/in² where carbon steel need not go below 15,000 (enter 14,400 to match it).
- V.8.2.2.1 prints N² with HTS; V.10 uses the stiffener spacing. The tool uses HTS, which gives a smaller N and so a larger, conservative Ireqd; in most tanks N² reaches the 100 cap either way.
- The SI sample is recomputed in this manual’s build; every check was made to fail in turn (small or unbraced stiffener, spacing, roof plate, cone over 12.5 mm, Pe outside the range, flooding).
Saving, reopening and reports
- Inputs are kept on this device and offered back; Calculate & Save stores the record in SI with its rule set; Show saved calculations lists and reopens them.
- Print / PDF report: summary, courses and transformed shell, loads, roof, shell with the graphic, stiffener table, bottom, record and inputs.
- The Annex L Data Sheet reads the design external pressure, Fpe and Annex V from the saved record.
Limits and interpretations
- Each rule set uses its printed equations; results are stored in SI.
- The shell is transformed to its thinnest course (Annex V transforms to the top course, which is normally the thinnest).
- One section is used for all intermediate stiffeners; a stiffener on a seam takes the course below it.
- Weld strength is reported as Ww; Annex V gives no weld allowable, so size the weld to the governing code.
- Supported cone roof plates, columns and the bottom membrane are design items outside this check.
- Wind girders for wind alone (5.9) are in the Wind Design tool; Annex V stiffeners may serve as wind girders when they meet both (5.9.6.9).
Glossary
| Pe | Specified design external pressure, without wind. |
| Ps, Pr | Total design external pressure for the shell and for the roof. |
| HTS | Height of the shell transformed to a uniform thickness. |
| Hsafe | Largest unstiffened height of the transformed shell. |
| ψ | Stability factor. |
| N | Number of buckling waves. |
| wshell | Shell acting with a stiffener on each side. |