8.1 Shell Minimum Thickness Calculations (tmin for Hydrostatic & Operating Levels)

API 653 Aboveground Storage Tank Inspector Exam

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1 Chapter 1: API 653 Scope, Inspector Certification & Roles

1.1 Scope of API 653, Tank Types & Construction Standards 1.2 Inspector Roles, Responsibilities & Certification Requirements 1.3 Inspection Planning, Safety, Confined Space Entry & Preparation

2 Chapter 2: Tank Shell & Roof Components Inspection

2.1 Fixed Roof Types, Structural Supports & Inspection Practices 2.2 Floating Roofs, Seals, Drainage & Operational Issues 2.3 Shell Courses, Welds, Attachments & Wind Girders 2.4 Tank Appurtenances, Nozzles, Manways & Piping Connections

3 Chapter 3: Tank Bottom & Foundation Inspection

3.1 Tank Bottom Types, Annular Plates & Internal Bottom Inspection 3.2 Foundation Types (Concrete Ringwall, Earth, Asphalt) & Inspection 3.3 Leak Detection Systems, Secondary Containment & Under-Tank Monitoring

4 Chapter 4: Corrosion & Damage Mechanisms in Storage Tanks

4.1 Atmospheric Corrosion, Condensation & External Deterioration 4.2 Corrosion Under Insulation (CUI) & Piping/Nozzle Interfaces 4.3 Soil-Side Corrosion, Under-Bottom Pitting & Microbiologically Induced Corrosion (MIC) 4.4 Product-Side Deterioration: Chemical Attack, Ethanol SCC, Concentration Cell & Sulfuric Acid Corrosion

5 Chapter 5: Materials, Toughness & Brittle Fracture Prevention

5.1 Tank Steels, Material Specifications & Historic Standards 5.2 Brittle Fracture Assessment: Figure 5.1 Decision Tree & Exemption Curves (API 653 Section 5) 5.3 Charpy V-Notch Impact Testing & Minimum Design Metal Temperature (MDMT)

6 Chapter 6: Cathodic Protection & Interior Linings

6.1 Cathodic Protection Principles & Systems for Tank Bottoms (API RP 651) 6.2 CP Criteria, Surveys, Potential Measurements & Interference (API RP 651) 6.3 Tank Bottom Interior Linings, Surface Prep & Inspection (API RP 652)

7 Chapter 7: Corrosion Rates, Remaining Life & Inspection Intervals

7.1 Determining Corrosion Rates (Short-Term vs. Long-Term) 7.2 Remaining Life Calculations & Limiting Components 7.3 Establishing In-Service & Out-of-Service Inspection Intervals (API 653 Section 6)

8 Chapter 8: Tank Shell Minimum Thickness Evaluation

8.1 Shell Minimum Thickness Calculations (tmin for Hydrostatic & Operating Levels) 8.2 One-Foot Method, Variable Design Point & Reconstructed-Tank Shell Thickness 8.3 Joint Efficiency (E) Selection, Missing Data & Radiography Factors 8.4 Evaluation of Pitting, Localized Thin Areas (LTA) & Critical Length (L)

9 Chapter 9: Bottom Plate & Annular Ring Thickness Evaluation

9.1 Minimum Bottom Thickness Formulations (MRT, MRTbottom, MRTlinear) 9.2 Annular Plate Evaluation, Stress Criteria & Critical Zones 9.3 Bottom Pitting Evaluation & Remaining Thickness Before Next Inspection

10 Chapter 10: Tank Repairs & Alterations Standards

10.1 Classification: Repair vs. Alteration vs. Reconstruction (API 653 Section 9) 10.2 Shell Plate Replacement, Lapped Patch Plates & Insert Plates 10.3 Shell Penetrations, Door Sheets & Nozzle Additions 10.4 Hot Tapping Requirements, Limitations & Pre-Engineering (API 653 Section 9.15 & API Publ 2201)

11 Chapter 11: Welding Procedures, Qualifications & Quality Control

11.1 Welding Procedure Specification (WPS) & Procedure Qualification Record (PQR) per ASME IX 11.2 Welder Performance Qualification (WPQ) & Continuity per ASME IX 11.3 Essential, Non-Essential & Supplementary Essential Variables 11.4 Preheating, Post-Weld Heat Treatment (PWHT) & Weld Flaw Remediation

12 Chapter 12: Nondestructive Examination (NDE) Methods

12.1 Visual Examination (VT) & Magnetic Particle Testing (MT) per ASME V 12.2 Liquid Penetrant (PT) & Ultrasonic Thickness Measurement (ASME V Article 6 & SE-797) 12.3 Radiographic Testing (RT): Acceptance Criteria, Film Interpretation & ASME V/API 650

13 Chapter 13: Hydrostatic Testing & Post-Repair Examination

13.1 Hydrostatic Test Triggers, Exemption Criteria & Major Alterations (API 653 Section 12.3) 13.2 Leak Testing: Vacuum Box, Tracer Gas, Diesel & Air Pressure Tests 13.3 NDE Examination Requirements for Shell, Bottom, Roof & Nozzle Welds (API 653 Section 12.1)

14 Chapter 14: Relief Devices, Tank Settlement & Nameplate Records

14.1 Pressure & Vacuum Relief Devices, Venting Principles (API RP 576 & API 2000) 14.2 Tank Settlement Types: Uniform, Tilt, Out-of-Plane & Edge Settlement (API 653 Annex B) 14.3 Evaluating Settlement Limits, Cosine Curve Analysis & Remedial Action 14.4 Tank Marking, Nameplates, Inspection Reports & Recordkeeping (API 653 Section 13)

8.1 Shell Minimum Thickness Calculations (tmin for Hydrostatic & Operating Levels)

Key Takeaways Explain This Topic AI

API 653 Section 4.3.3 establishes governing equations for minimum acceptable shell thickness (t_min) under both product storage service and hydrostatic proof test conditions, evaluating hoop membrane stress at the One-Foot design point.

The governing formula for product service is t_min = [2.6 * D * (H - 1) * G] / (S * E), and for hydrostatic test service is t_min_t = [2.6 * D * (H_t - 1)] / (S_t * E), where D is tank diameter in feet and H is effective liquid head.

In-service allowable stress comes from API 653 Table 4.1 and is course-dependent: for the bottom and second courses S is the smaller of 0.80Y or 0.429T and S_t the smaller of 0.88Y or 0.472T, while for all other courses S is the smaller of 0.88Y or 0.472T and S_t the smaller of 0.90Y or 0.519T.

Unlike new construction design formulas in API 650, the API 653 t_min calculation contains zero corrosion allowance; t_min represents the absolute lower-bound structural retirement limit below which repair, replacement, or derating is mandatory.

When measured thickness falls below t_min the tank must be repaired or the allowable liquid level reduced by solving the minimum-thickness formula for height: H = (S E t_act)/(2.6 D G) + 1 for an entire shell course, and the same expression without the +1 for a locally thinned area, evaluated independently for every course.

Last updated: September 2026

8.1 Shell Minimum Thickness Calculations (tmin for Hydrostatic & Operating Levels)

API 653 Core Principle: The structural integrity of an aboveground storage tank shell depends on maintaining sufficient wall thickness to resist circumferential hoop tensile stresses generated by stored liquid. API 653 Section 4.3.3 establishes governing formulas to calculate the absolute minimum acceptable thickness ( t min t_{\text{min}} t min ​ ) below which the shell is deemed structurally deficient and must be repaired, replaced, or derated to a reduced maximum liquid height ( H max H_{\text{max}} H max ​ ).

When evaluating an in-service storage tank, the Authorized Inspector and storage tank engineer face an engineering problem distinct from initial tank design. During new construction under API Standard 650 , plates are sized with generous design safety factors, standardized plate roll thicknesses, and explicit corrosion allowances ( C A CA C A ) intended to provide a multi-decade operational service life. Conversely, API Standard 653 evaluates fitness-for-service: it determines the true lower-bound physical threshold required to prevent ductile rupture or plastic collapse under operating and hydrostatic loads.

1. Mechanics of Shell Hoop Stress & Derivation of the 2.6 Factor

A vertical cylindrical storage tank filled with liquid experiences internal hydrostatic pressure that increases linearly with depth. At any depth h h h (feet) below the liquid surface, the hydrostatic pressure P P P (pounds per square inch, psi) exerted on the shell wall is governed by fluid statics: P = ρ ⋅ g ⋅ h P = \rho \cdot g \cdot h P = ρ ⋅ g ⋅ h

Given that fresh water has a density of 62.43 lb/ft 3 62.43\text{ lb/ft}^3 62.43 lb/ft 3 and a 1-foot column of water over 1 square inch exerts a pressure of 62.43 / 144 = 0.4335 psi/ft 62.43 / 144 = 0.4335\text{ psi/ft} 62.43/144 = 0.4335 psi/ft : P = 0.4333 × G × h P = 0.4333 \times G \times h P = 0.4333 × G × h

where G G G is the specific gravity of the liquid relative to water ( G = 1.00 G = 1.00 G = 1.00 for water). HYDROSTATIC PRESSURE & HOOP STRESS

• Liquid Surface ============================== h = 0
• | |
• | Liquid Density: rho | P = 0.4333 * G * h
• | Specific Gravity: G |
• | |
• | | Increasing Hydrostatic
• | | Pressure Head
• | |
• | v
• Course 1 Base ============================== Maximum Pressure P_max
• <--- D --->

Hoop Tensile Stress: sigma_h = (P * D) / (2 * t)

In thin-walled cylindrical pressure vessel theory, circumferential membrane stress (hoop stress, σ h \sigma_h σ h ​ ) is expressed by Barlow's cylinder formula: σ h = P ⋅ r t = P ⋅ D in 2 ⋅ t \sigma_h = \frac{P \cdot r}{t} = \frac{P \cdot D_{\text{in}}}{2 \cdot t} σ h ​ = t P ⋅ r ​ = 2 ⋅ t P ⋅ D in ​ ​

where r r r is the tank radius in inches, D in D_{\text{in}} D in ​ is the inner diameter in inches ( D in = 12 × D ft D_{\text{in}} = 12 \times D_{\text{ft}} D in ​ = 12 × D ft ​ ), and t t t is the shell thickness in inches. Substituting the hydrostatic pressure equation into the hoop stress relation yields: σ h = ( 0.4333 ⋅ G ⋅ h ) ⋅ ( 12 ⋅ D ) 2 ⋅ t = 2.60 ⋅ D ⋅ h ⋅ G t \sigma_h = \frac{(0.4333 \cdot G \cdot h) \cdot (12 \cdot D)}{2 \cdot t} = \frac{2.60 \cdot D \cdot h \cdot G}{t} σ h ​ = 2 ⋅ t ( 0.4333 ⋅ G ⋅ h ) ⋅ ( 12 ⋅ D ) ​ = t 2.60 ⋅ D ⋅ h ⋅ G ​

The conversion factor 2.6 is precisely derived from basic physical units: Conversion Factor = 62.43 lb/ft 3 × 12 in./ft 144 in. 2 / ft 2 × 2 = 749.16 288 = 2.60125 ≈ 2.6 \text{Conversion Factor} = \frac{62.43\text{ lb/ft}^3 \times 12\text{ in./ft}}{144\text{ in.}^2/\text{ft}^2 \times 2} = \frac{749.16}{288} = 2.60125 \approx 2.6 Conversion Factor = 144 in. 2 / ft 2 × 2 62.43 lb/ft 3 × 12 in./ft ​ = 288 749.16 ​ = 2.60125 ≈ 2.6

To ensure structural integrity, the calculated hoop membrane stress must not exceed the maximum allowable stress of the material ( S S S ) multiplied by the joint efficiency ( E E E ) of the longitudinal/vertical weld seams: σ h ≤ S ⋅ E \sigma_h \le S \cdot E σ h ​ ≤ S ⋅ E .

2. API 653 Minimum Thickness Formulas

In accordance with API 653 Section 4.3.3.1 , minimum acceptable shell thicknesses are calculated using the One-Foot Method, evaluating hydrostatic head 12 inches (1.0 foot) above the bottom circumferential weld of the shell course under evaluation.

Product Storage Service ( t min t_{\text{min}} t min ​ )

For normal operational conditions storing product of specific gravity G G G : t min = 2.6 ⋅ D ⋅ ( H − 1 ) ⋅ G S ⋅ E t_{\text{min}} = \frac{2.6 \cdot D \cdot (H - 1) \cdot G}{S \cdot E} t min ​ = S ⋅ E 2.6 ⋅ D ⋅ ( H − 1 ) ⋅ G ​

Hydrostatic Proof Test Service ( t min,t t_{\text{min,t}} t min,t ​ )

For hydrostatic testing with water ( G = 1.00 G = 1.00 G = 1.00 ): t min,t = 2.6 ⋅ D ⋅ ( H t − 1 ) S t ⋅ E t_{\text{min,t}} = \frac{2.6 \cdot D \cdot (H_t - 1)}{S_t \cdot E} t min,t ​ = S t ​ ⋅ E 2.6 ⋅ D ⋅ ( H t ​ − 1 ) ​

Detailed Variable Definitions

Parameter Unit Definition & Code Criteria

t min t_{\text{min}} t min ​ inches Minimum acceptable thickness for product service exclusive of any operational corrosion allowance.

t min,t t_{\text{min,t}} t min,t ​ inches Minimum acceptable thickness for hydrostatic test conditions.

D D D feet Nominal tank diameter in feet.

H H H feet Height from the bottom of the shell course under consideration to the maximum design liquid level in feet. For Course 1, H H H is the total maximum design liquid height.

H t H_t H t ​ feet Height from the bottom of the shell course under consideration to the hydrostatic test liquid level in feet.

G G G dimensionless Stored liquid specific gravity. Shall not be taken as less than 1.0 if the tank is evaluated for water or if the stored product specific gravity is unspecified.

S S S lbf/in. 2 \text{lbf/in.}^2 lbf/in. 2 (psi) Maximum allowable stress for product service from API 653 Table 4.1 (different column for the bottom/second courses than for the upper courses).

S t S_t S t ​ lbf/in. 2 \text{lbf/in.}^2 lbf/in. 2 (psi) Maximum allowable hydrostatic test stress from API 653 Table 4.1 .

E E E dimensionless Original joint efficiency for the vertical weld seam in the shell course under consideration ( 0.35 ≤ E ≤ 1.00 0.35 \le E \le 1.00 0.35 ≤ E ≤ 1.00 ).

Course-by-Course Evaluation Rule: When evaluating courses above the lowest course (Course 2, Course 3, etc.), the liquid height H H H is measured from the bottom circumferential horizontal weld of that specific course up to the maximum liquid level. The term ( H − 1 ) (H - 1) ( H − 1 ) subtracts 12 inches from the liquid head acting on the bottom of that individual course.

3. In-Service Allowable Stress Philosophy (API 653 Table 4.1)

A core concept tested on the API 653 certification exam is the distinction in allowable stress levels between new construction ( API 650 ) and in-service evaluation ( API 653 Table 4.1, Maximum Allowable Shell Stresses ).

Table 4.1 or Table 4.2? API 653 Table 4.1 lists the maximum allowable shell stresses S S S and S t S_t S t ​ . API 653 Table 4.2 lists joint efficiencies E E E for welded joints, and Table 4.3 lists joint efficiencies for riveted joints. Reaching for the wrong table is one of the fastest ways to lose an open-book calculation question.

API 653 splits the allowable stress by course. The bottom and second courses are held to a tighter stress basis than the courses above them, because the lower courses carry the combined effect of maximum hydrostatic head and the shell-to-bottom rotational restraint: +-------------------------------------------------------------------------+

• | ALLOWABLE STRESS DESIGN COMPARISON |
• | |
• | API 650 (New Design - High Conservative Factor of Safety) |
• | - Product: S_d = min( 0.667 * Y , 0.400 * T ) |
• | - Hydrotest: S_t = min( 0.750 * Y , 0.429 * T ) |
• | |
• | API 653 (In-Service Fitness - per 4.3.3.1) |
• | BOTTOM AND SECOND COURSES: |
• | - Product: S = smaller of 0.80 * Y or 0.429 * T |
• | - Hydrotest: S_t = smaller of 0.88 * Y or 0.472 * T |
• | ALL OTHER (UPPER) COURSES: |
• | - Product: S = smaller of 0.88 * Y or 0.472 * T |
• | - Hydrotest: S_t = smaller of 0.90 * Y or 0.519 * T |
• +-------------------------------------------------------------------------+
• Mandatory Input Limits on Y and T

API 653 places explicit bounds on the two material inputs before they enter the stress equations:

Y Y Y = specified minimum yield strength of the plate; use 30,000 psi if not known .

T T T = the smaller of the specified minimum tensile strength of the plate or 80,000 psi ; use 55,000 psi if not known .

Table 4.1 values are the calculated stresses rounded to the nearest 100 lbf/in.²

For reconstructed tanks, Table 4.1 does not apply — S S S and S t S_t S t ​ come from the current applicable standard (API 650 Tables 5.2a/5.2b) or are calculated per API 653 Section 8.4.

Why API 653 Allows Higher Membrane Stresses

API 653 permits higher allowable stresses in service ( 0.80 × Y 0.80 \times Y 0.80 × Y vs. 0.667 × Y 0.667 \times Y 0.667 × Y ) for several well-founded engineering reasons:

Proven Fabrication & Material Proof: The existing tank has already survived fabrication residual stresses, full hydrostatic proof testing, and years of operational load cycles without brittle fracture or weld tear-out.

Elimination of Compounded Margins: New tank design incorporates standardized plate thickness round-ups, conservative corrosion allowances, and low design stresses. Compounding all these factors during in-service inspection would result in premature condemnation and wasteful scrapping of safe storage capacity.

Plastic Collapse Safety Margin: Setting S = 0.80 × Y S = 0.80 \times Y S = 0.80 × Y on the bottom and second courses retains a minimum 20% margin below the material yield point under maximum design fluid load, preventing permanent plastic strain or shell bulging.

Zero Corrosion Allowance in t min t_{\text{min}} t min ​

In API 650, design thickness includes nominal plate thickness plus specified corrosion allowance ( t d = t calc + C A t_d = t_{\text{calc}} + CA t d ​ = t calc ​ + C A ). In stark contrast, the API 653 t min t_{\text{min}} t min ​ formula includes ZERO corrosion allowance ( C A = 0 CA = 0 C A = 0 ).

t min t_{\text{min}} t min ​ represents the retirement thickness (lower-bound structural capacity).

The operational corrosion reserve is the difference between actual measured thickness ( t act t_{\text{act}} t act ​ ) and t min t_{\text{min}} t min ​ : Remaining Corrosion Allowance ( R C A ) = t act − t min \text{Remaining Corrosion Allowance } (RCA) = t_{\text{act}} - t_{\text{min}} Remaining Corrosion Allowance ( RC A ) = t act ​ − t min ​ Remaining Life ( R L ) = t act − t min Corrosion Rate ( C R ) \text{Remaining Life } (RL) = \frac{t_{\text{act}} - t_{\text{min}}}{\text{Corrosion Rate } (CR)} Remaining Life ( R L ) = Corrosion Rate ( CR ) t act ​ − t min ​ ​

API 653 Table 4.1 Allowable Shell Stresses for Common Steels

All four columns come straight out of Table 4.1; the exam expects you to read them, not to re-derive them.

Steel Specification Min. Yield Y Y Y (psi) Min. Tensile T T T (psi) S S S — Lower Two Courses (psi) S S S — Upper Courses (psi) S t S_t S t ​ — Lower Two Courses (psi) S t S_t S t ​ — Upper Courses (psi)

• ASTM A283 Grade C 30,000 55,000 23,600 26,000 26,000 27,000
• ASTM A285 Grade C 30,000 55,000 23,600 26,000 26,000 27,000
• ASTM A36 36,000 58,000 24,900 27,400 27,400 30,100
• ASTM A573 Grade 58 32,000 58,000 24,900 27,400 27,400 28,800
• ASTM A516 Grade 55 30,000 55,000 23,600 26,000 26,000 27,000
• ASTM A516 Grade 70 38,000 70,000 30,000 33,000 33,000 34,200
• ASTM A537 Class 1 50,000 70,000 30,000 33,000 33,000 36,300
• Unknown (welded) 30,000 55,000 23,600 26,000 26,000 27,000
• Riveted, unknown grade — — 21,000 21,000 21,000 21,000

Spot-check the pattern: for A283 Grade C, the lower-two-course product stress is the smaller of 0.80 × 30,000 = 24,000 0.80 \times 30{,}000 = 24{,}000 0.80 × 30 , 000 = 24 , 000 and 0.429 × 55,000 = 23,595 0.429 \times 55{,}000 = 23{,}595 0.429 × 55 , 000 = 23 , 595 , which rounds to 23,600 psi — exactly the tabulated value.

The Absolute Floor on t min t_{\text{min}} t min ​

Whatever the arithmetic produces, API 653 4.3.3.1 states that t min t_{\text{min}} t min ​ shall not be less than 0.1 in. (2.5 mm) for any tank course. On small-diameter or lightly loaded tanks the formula can return a number below 0.1 in.; the 0.1 in. floor governs instead.

4. Derating: Calculating Maximum Allowable Liquid Level ( H max H_{\text{max}} H max ​ )

When ultrasonic thickness (UT) inspection reveals that actual measured shell thickness t act t_{\text{act}} t act ​ has corroded below t min t_{\text{min}} t min ​ for the design liquid level, the facility owner-user must immediately take corrective action. If physical repairs (such as shell plate replacement or lap patch installation) are deferred, API 653 4.3.1.5 permits establishing a reduced allowable liquid level by taking the 4.3.3.1 minimum-thickness formula and solving for the height H H H . (API 653 4.3.3.2 is the companion rule that limits the hydrostatic test height H t H_t H t ​ — do not confuse the two.)

Mathematical Formulation for H max H_{\text{max}} H max ​

By setting t min = t act t_{\text{min}} = t_{\text{act}} t min ​ = t act ​ and algebraically rearranging the product service equation: t act = 2.6 ⋅ D ⋅ ( H max − 1 ) ⋅ G S ⋅ E t_{\text{act}} = \frac{2.6 \cdot D \cdot (H_{\text{max}} - 1) \cdot G}{S \cdot E} t act ​ = S ⋅ E 2.6 ⋅ D ⋅ ( H max ​ − 1 ) ⋅ G ​ 2.6 ⋅ D ⋅ ( H max − 1 ) ⋅ G = S ⋅ E ⋅ t act 2.6 \cdot D \cdot (H_{\text{max}} - 1) \cdot G = S \cdot E \cdot t_{\text{act}} 2.6 ⋅ D ⋅ ( H max ​ − 1 ) ⋅ G = S ⋅ E ⋅ t act ​ H max − 1 = S ⋅ E ⋅ t act 2.6 ⋅ D ⋅ G H_{\text{max}} - 1 = \frac{S \cdot E \cdot t_{\text{act}}}{2.6 \cdot D \cdot G} H max ​ − 1 = 2.6 ⋅ D ⋅ G S ⋅ E ⋅ t act ​ ​ H max = S ⋅ E ⋅ t act 2.6 ⋅ D ⋅ G + 1 H_{\text{max}} = \frac{S \cdot E \cdot t_{\text{act}}}{2.6 \cdot D \cdot G} + 1 H max ​ = 2.6 ⋅ D ⋅ G S ⋅ E ⋅ t act ​ ​ + 1

For hydrostatic testing of an altered or repaired tank with thinned shell plates: H t , max = S t ⋅ E ⋅ t act 2.6 ⋅ D + 1 H_{t,\text{max}} = \frac{S_t \cdot E \cdot t_{\text{act}}}{2.6 \cdot D} + 1 H t , max ​ = 2.6 ⋅ D S t ​ ⋅ E ⋅ t act ​ ​ + 1 MULTI-COURSE FILL HEIGHT EVALUATION

• +-----------------------------------------+ Top of Tank
• | Course 3: t_act = 0.220 in. | ---> H_total_3 = H_max_3 + Y_2
• +-----------------------------------------+ Elevation Y_2
• | Course 2: t_act = 0.380 in. | ---> H_total_2 = H_max_2 + Y_1
• +-----------------------------------------+ Elevation Y_1
• | Course 1: t_act = 0.490 in. | ---> H_total_1 = H_max_1
• +=========================================+ Datum (Floor: Y = 0)

GOVERNING FILL HEIGHT: H_allowable = min( H_total_1, H_total_2, H_total_3 )

Critical Engineering Rule: Derating must be evaluated independently for every shell course. For upper courses, H max , i H_{\text{max},i} H max , i ​ represents the allowable head above the bottom of course i i i . The absolute maximum permissible liquid level relative to the tank bottom datum is H total , i = H max , i + Y i H_{\text{total},i} = H_{\text{max},i} + Y_i H total , i ​ = H max , i ​ + Y i ​ , where Y i Y_i Y i ​ is the elevation of the lower girth weld of course i i i above the bottom. The lowest calculated value of H total H_{\text{total}} H total ​ among all courses governs the entire tank.

• 5. Step-by-Step Worked Numerical Examples
• Example 1: Multi-Course t min t_{\text{min}} t min ​ Determination

A refinery crude oil storage tank has the following parameters:

• Nominal diameter D = 120 ft D = 120\text{ ft} D = 120 ft
• Total design liquid height H = 48 ft H = 48\text{ ft} H = 48 ft
• Composed of 6 shell courses, each 8 ft 8\text{ ft} 8 ft tall
• Stored crude oil specific gravity G = 0.85 G = 0.85 G = 0.85

Shell material: ASTM A283 Grade C. From API 653 Table 4.1, the bottom and second courses use S = 23 , 600 psi S = 23,600\text{ psi} S = 23 , 600 psi and S t = 26 , 000 psi S_t = 26,000\text{ psi} S t ​ = 26 , 000 psi (the upper courses would use S = 26 , 000 psi S = 26,000\text{ psi} S = 26 , 000 psi and S t = 27 , 000 psi S_t = 27,000\text{ psi} S t ​ = 27 , 000 psi )

Longitudinal weld seams: Fully radiographed ( E = 1.00 E = 1.00 E = 1.00 )

Calculate t min t_{\text{min}} t min ​ for Course 1 and Course 2 under product service and hydrostatic test:

Course 1 Evaluation ( H 1 = 48 ft H_1 = 48\text{ ft} H 1 ​ = 48 ft from bottom of course to liquid level):

Product service ( t min , 1 t_{\text{min},1} t min , 1 ​ ): t min , 1 = 2.6 × 120 × ( 48 − 1 ) × 0.85 23 , 600 × 1.00 = 312 × 47 × 0.85 23 , 600 = 12 , 464.4 23 , 600 = 0.5281 in. ≈ 0.528 in. t_{\text{min},1} = \frac{2.6 \times 120 \times (48 - 1) \times 0.85}{23,600 \times 1.00} = \frac{312 \times 47 \times 0.85}{23,600} = \frac{12,464.4}{23,600} = 0.5281\text{ in. } \approx 0.528\text{ in.} t min , 1 ​ = 23 , 600 × 1.00 2.6 × 120 × ( 48 − 1 ) × 0.85 ​ = 23 , 600 312 × 47 × 0.85 ​ = 23 , 600 12 , 464.4 ​ = 0.5281 in. ≈ 0.528 in.

Hydrostatic test service ( t min,t , 1 t_{\text{min,t},1} t min,t , 1 ​ ): t min,t , 1 = 2.6 × 120 × ( 48 − 1 ) 26 , 000 × 1.00 = 312 × 47 26 , 000 = 14 , 664 26 , 000 = 0.5640 in. ≈ 0.564 in. t_{\text{min,t},1} = \frac{2.6 \times 120 \times (48 - 1)}{26,000 \times 1.00} = \frac{312 \times 47}{26,000} = \frac{14,664}{26,000} = 0.5640\text{ in. } \approx 0.564\text{ in.} t min,t , 1 ​ = 26 , 000 × 1.00 2.6 × 120 × ( 48 − 1 ) ​ = 26 , 000 312 × 47 ​ = 26 , 000 14 , 664 ​ = 0.5640 in. ≈ 0.564 in. Note: The hydrotest thickness ( 0.564 in. 0.564\text{ in.} 0.564 in. ) exceeds the product thickness ( 0.528 in. 0.528\text{ in.} 0.528 in. ). If a full hydrostatic test to 48 ft is required after a repair, the shell must satisfy 0.564 in. 0.564\text{ in.} 0.564 in.

Course 2 Evaluation ( H 2 = 48 − 8 = 40 ft H_2 = 48 - 8 = 40\text{ ft} H 2 ​ = 48 − 8 = 40 ft ):

Product service ( t min , 2 t_{\text{min},2} t min , 2 ​ ): t min , 2 = 2.6 × 120 × ( 40 − 1 ) × 0.85 23 , 600 × 1.00 = 312 × 39 × 0.85 23 , 600 = 10 , 342.8 23 , 600 = 0.4383 in. ≈ 0.438 in. t_{\text{min},2} = \frac{2.6 \times 120 \times (40 - 1) \times 0.85}{23,600 \times 1.00} = \frac{312 \times 39 \times 0.85}{23,600} = \frac{10,342.8}{23,600} = 0.4383\text{ in. } \approx 0.438\text{ in.} t min , 2 ​ = 23 , 600 × 1.00 2.6 × 120 × ( 40 − 1 ) × 0.85 ​ = 23 , 600 312 × 39 × 0.85 ​ = 23 , 600 10 , 342.8 ​ = 0.4383 in. ≈ 0.438 in.

Hydrostatic test service ( t min,t , 2 t_{\text{min,t},2} t min,t , 2 ​ ): t min,t , 2 = 2.6 × 120 × ( 40 − 1 ) 26 , 000 × 1.00 = 312 × 39 26 , 000 = 12 , 168 26 , 000 = 0.4680 in. ≈ 0.468 in. t_{\text{min,t},2} = \frac{2.6 \times 120 \times (40 - 1)}{26,000 \times 1.00} = \frac{312 \times 39}{26,000} = \frac{12,168}{26,000} = 0.4680\text{ in. } \approx 0.468\text{ in.} t min,t , 2 ​ = 26 , 000 × 1.00 2.6 × 120 × ( 40 − 1 ) ​ = 26 , 000 312 × 39 ​ = 26 , 000 12 , 168 ​ = 0.4680 in. ≈ 0.468 in.

Example 2: Derating Calculation ( H max H_{\text{max}} H max ​ )

During an out-of-service inspection of the tank in Example 1, ultrasonic thickness gauging of Course 1 reveals uniform internal corrosion. The actual measured thickness is found to be t act = 0.465 in. t_{\text{act}} = 0.465\text{ in.} t act ​ = 0.465 in. , which is less than t min , 1 = 0.528 in. t_{\text{min},1} = 0.528\text{ in.} t min , 1 ​ = 0.528 in.

Calculate the maximum safe liquid level ( H max H_{\text{max}} H max ​ ) for crude oil storage ( G = 0.85 G = 0.85 G = 0.85 ): H max = S ⋅ E ⋅ t act 2.6 ⋅ D ⋅ G + 1 H_{\text{max}} = \frac{S \cdot E \cdot t_{\text{act}}}{2.6 \cdot D \cdot G} + 1 H max ​ = 2.6 ⋅ D ⋅ G S ⋅ E ⋅ t act ​ ​ + 1 H max = 23 , 600 × 1.00 × 0.465 2.6 × 120 × 0.85 + 1 = 10 , 974 265.2 + 1 = 41.38 + 1 = 42.38 ft H_{\text{max}} = \frac{23,600 \times 1.00 \times 0.465}{2.6 \times 120 \times 0.85} + 1 = \frac{10,974}{265.2} + 1 = 41.38 + 1 = 42.38\text{ ft} H max ​ = 2.6 × 120 × 0.85 23 , 600 × 1.00 × 0.465 ​ + 1 = 265.2 10 , 974 ​ + 1 = 41.38 + 1 = 42.38 ft

Conclusion: The tank cannot operate at its original 48.0-foot design level. The liquid level must be administratively and mechanically derated to a maximum fill height of 42.3 feet (or the shell must be repaired).

6. Maximum Fill Height: Two Formulas, One Difference

The BOK asks the inspector to determine the maximum liquid height for a tank, and API 653 supplies two rearranged forms of the minimum-thickness equation. The exam will provide the formulas; it will not ask you to derive them by transposition. What it does test is knowing which one to use. H = S × E × t min ⁡ 2.6 × D × G (localized corroded area — NO +1) \boxed{H = \frac{S \times E \times t_{\min}}{2.6 \times D \times G}} \qquad \text{(localized corroded area — NO +1)} H = 2.6 × D × G S × E × t m i n ​ ​ ​ (localized corroded area — NO +1) H = S × E × t min ⁡ 2.6 × D × G + 1 (entire shell course — WITH +1) \boxed{H = \frac{S \times E \times t_{\min}}{2.6 \times D \times G} + 1} \qquad \text{(entire shell course — WITH +1)} H = 2.6 × D × G S × E × t m i n ​ ​ + 1 ​ (entire shell course — WITH +1)

Situation Formula Where H H H is measured from

Evaluating an entire shell course (4.3.3.1a) Include the + 1 The bottom of the shell course under consideration

Evaluating a locally thinned area or any other single location of interest (4.3.3.1b) Omit the + 1 The bottom of the length L L L of the thinned area — i.e., from the lowest point of the bottom of L L L

Why the difference? The one-foot method places the design point 12 in. above the bottom girth seam of a whole course, so the effective head is ( H − 1 ) (H-1) ( H − 1 ) and the rearranged form gains a + 1 +1 + 1 . When you evaluate a discrete corroded patch partway up a course, the head is already measured to that patch, so there is no foot to add back.

For the hydrostatic test height, substitute S t S_t S t ​ for S S S and take G = 1.0 G = 1.0 G = 1.0 (API 653, 4.3.3.2): H t = S t × E × t min ⁡ 2.6 × D + 1 (entire course) H t = S t × E × t min ⁡ 2.6 × D (locally thinned area) H_t = \frac{S_t \times E \times t_{\min}}{2.6 \times D} + 1 \quad \text{(entire course)} \qquad H_t = \frac{S_t \times E \times t_{\min}}{2.6 \times D} \quad \text{(locally thinned area)} H t ​ = 2.6 × D S t ​ × E × t m i n ​ ​ + 1 (entire course) H t ​ = 2.6 × D S t ​ × E × t m i n ​ ​ (locally thinned area)

Consequence check (API 653, 4.3.3.2 Notes): depending on the specific gravity used to determine t min ⁡ t_{\min} t m i n ​ , H t H_t H t ​ may come out lower than the design liquid level H H H . When it does, the owner/operator must determine the consequence and acceptability of operating the tank to H H H , and repairs to shell sections above H t H_t H t ​ must comply with the hydrostatic testing requirements of Section 12.3.