9.2 Annular Plate Evaluation, Stress Criteria & Critical Zones

Structural Mechanics of the Shell-to-Bottom Joint

In an aboveground flat-bottom storage tank, the intersection between the cylindrical vertical shell and the horizontal bottom plate is the most structurally complex and highly stressed location in the entire vessel. When the tank is filled with liquid, the hydrostatic pressure pushes the lowest shell course radially outward. Because the bottom plate is anchored by friction against the foundation pad and restrained by the weight of the liquid column, the shell cannot expand freely at its base.

+-------------------------------------------------------------------------+
|                   SHELL-TO-BOTTOM ROTATIONAL MOMENTS                    |
|                                                                         |
|                     |   |                                               |
|                     |   |  Lowest Shell Course                          |
|                     |   |  (Expands radially under hydrostatic load)    |
|                     |   |                                               |
|                     |   v                                               |
|                     |   |   Hydrostatic Bulging                         |
|                     |  /                                                |
|                     | /  <-- Rotational Bending Moment (M_0)            |
|                     |/                                                  |
|   ==================+================================================   |
|   Outer Projection  | Inner Annular Ring (Absorbs cyclic bending)       |
|   (>= 2 in.)        | [CRITICAL ZONE: Inner 3 inches from shell]        |
+---------------------+---------------------------------------------------+

This physical restraint generates severe localized edge forces:

• A horizontal radial shear force ($Q_0$) acting inward at the bottom corner.
• A heavy rotational bending moment ($M_0$) that produces high secondary bending stresses and plastic hinge action in the bottom plate immediately adjacent to the corner weld.

Annular Plate Ring vs. Sketch Plate Bottom

To safely accommodate these localized bending stresses, modern tank engineering differentiates between two distinct plate bottom arrangements:

1. Annular Plate Ring: A continuous ring of thick, trapezoidal or segmented steel plates butt-welded together with complete penetration and fusion (typically using temporary backing strips). The annular ring is situated directly beneath the shell, absorbing the heavy secondary bending moments and distributing shell compressive loads into the foundation.
2. Sketch Plates and Center Plates: The interior floor plates located radially inward from the annular ring. Sketch plates are typically thinner (nominal $1/4\text{ in.}$ or $0.250\text{ in.}$) and are joined using simple three-lap or two-lap fillet-welded joints.

Per API Standard 650 Section 5.5.1, a butt-welded annular plate ring is mandatory when the first shell course nominal thickness exceeds certain design thresholds (e.g., thicker than $1.0\text{ in.}$), when high-strength steels are utilized, or when operating stresses in the bottom shell course exceed specific limits.

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Product Stress Calculation in the First Shell Course

Under API 653, the integrity and required thickness of an annular plate ring are not assessed against arbitrary static values; rather, they depend directly on the tensile hoop stress in the lowest shell course ($t_1$).

The stress in the first shell course is calculated with the same one-foot design point used everywhere else in API 653 and API 650 — note the $(H-1)$ term, which is dropped surprisingly often:

US Customary Units:

$S_{\text{design}} = \frac{2.6 \cdot D \cdot (H - 1) \cdot G}{t} \qquad S_{\text{hydro test}} = \frac{2.6 \cdot D \cdot (H - 1)}{t}$

Where:

• $S$: Product hoop stress in the first shell course (in pounds per square inch, $\text{lbf/in.}^2$ or $\text{psi}$).
• $D$: Nominal tank diameter (in feet, $\text{ft}$).
• $H$: Maximum design liquid level measured from the bottom of the first shell course (in feet, $\text{ft}$); the $(H-1)$ term places the design point 1 ft above the bottom girth seam.
• $G$: Specific gravity of the stored liquid (dimensionless; water = 1.0).
• $t$: Nominal thickness of the lowest (first) shell course, excluding corrosion allowance (in inches, $\text{in.}$).

SI Metric Units:

$S_{\text{design}} = \frac{4.9 \cdot D \cdot (H - 0.3) \cdot G}{t}$

Where:

• $S$: Product hoop stress (in megapascals, $\text{MPa}$).
• $D$: Nominal tank diameter (in meters, $\text{m}$).
• $H$: Maximum design liquid level (in meters, $\text{m}$); the SI design point is 0.3 m above the bottom girth seam.
• $G$: Specific gravity of the stored liquid.
• $t$: Nominal thickness of first shell course (in millimeters, $\text{mm}$).

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API 653 Table 4.5: Minimum Annular Plate Ring Thickness

Table 4.4 or Table 4.5? API 653 Table 4.4 is Bottom Plate Minimum Thickness — the 0.10 in. / 0.05 in. MRT thresholds for the general floor. API 653 Table 4.5 is Annular Bottom Plate Thicknesses (in.). The annular ring is read from Table 4.5, and confusing the two tables is a guaranteed wrong answer in the open-book section.

Once the stress in the first shell course and the nominal thickness of that course, $t_1$, are determined, the Authorized Inspector enters API 653 Table 4.5 to obtain the minimum acceptable annular plate thickness. The table is published for product specific gravity less than 1.0; for $G \ge 1.0$ the annular thickness comes from the corresponding API 650 annular-plate table instead, plus any specified corrosion allowance.

Table 4.5 is indexed by four stress bands — not three — and the bands are not round numbers:

API 653 Table 4.5 — Annular Bottom Plate Thicknesses (in.), Product Specific Gravity < 1.0

Table notes that matter:

• The thicknesses assume the foundation provides uniform support under the full width of the annular plate. Where the foundation is not properly compacted — particularly on the inside of a concrete ringwall — settlement produces additional stresses in the annular plate that the table does not cover.
• "Plate thickness" refers to the tank shell as constructed, not the corroded shell.
• The tabulated value is the thickness required at the end of the operating interval; anticipated metal loss over the run must be added to it when checking present compliance.
• Table 4.5 values must be taken plus any specified corrosion allowance when applied to a tank in service.

[!NOTE] Because of strength requirements, the minimum thickness of an annular plate ring is usually greater than 0.10 in. — the annular ring is not governed by the general bottom-plate MRT of Table 4.4. Isolated pitting will not appreciably affect the strength of the plate.

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The Critical Zone: Definition, Mechanics and Repair Prohibitions

API 653 Section 9.10.1 defines one of the most critical structural boundaries in storage tank engineering: the Critical Zone.

Outside Tank                                              Inside Tank
      |                                                        |
      |                   Tank Shell Course                    |
      |                        |    |                          |
      |<----- >= 2 in. ------->| t  |<-------- 3 in. --------->|<------ >= 21 in. ----->|
------+========================+====+==========================+=========================+---
Outer | Outer Shell Fillet     |    | Inner Corner Fillet      | Inner Annular Ring     | Lap Joint
Edge  | Weld                   |    | Weld                     |                        | to Sketch
      |                        |    |                          |                        | Plates
      |                        |    |<----- CRITICAL ZONE ---->|                        |
      |                        |    |   (No Lap Patches!)      |                        |

Formal Code Definition

The Critical Zone is defined as the annular plate or sketch plate bottom within 3 inches (75 mm) measured radially inward from the inside surface of the tank shell, starting from the toe of the inside shell-to-bottom corner fillet weld.

Engineering Significance

Because the corner fillet weld acts as a rotational clamp against the bulging shell, bending stresses peak within this 3-inch radial band. The steel is subjected to complex triaxial stress states, cyclical mechanical fatigue during tank filling and emptying cycles, and high susceptibility to environmental cracking (e.g., caustic embrittlement or wet $H_2S$ blistering).

Severe Repair Restrictions in the Critical Zone (Section 9.10.1.2)

Due to the concentration of bending fatigue stresses, API 653 imposes strict prohibitions within the Critical Zone:

1. Lap-Welded Patch Plates Prohibited: Installing lapped patch plates across the shell-to-bottom corner weld or within the 3-inch Critical Zone is strictly prohibited, except under specialized engineered provisions (e.g., when installing an entirely new bottom, or with explicit engineering calculations and specific weld spacing per API 653 Section 9.10.1.2).
2. Mandatory Insert Plate Repair: When severe thinning, pitting, or crack defects are discovered within the Critical Zone, the damaged annular plate section must be cut out and replaced with a full-penetration, butt-welded insert plate that reproduces the original joint geometry, complete with full radiographic (RT) or ultrasonic (UT) examination.
3. Lap Patches Outside the Critical Zone: Welded patch plates placed on bottom sketch plates must terminate at least 3 inches (75 mm) radially away from the shell-to-bottom corner weld. They can never encroach into the Critical Zone.
4. Weld Seam Clearances: Welded patch plates outside the Critical Zone must maintain a minimum clearance of 2 inches (50 mm) or $5t$ (whichever is greater) from existing bottom plate seams, or cross the seam at an angle $\ge 45^\circ$ and extend at least $6\text{ in.}$ past the seam.

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Annular Plate Dimensional Criteria

During out-of-service inspection, the Authorized Inspector must verify two fundamental geometric parameters that govern the annular plate ring:

1. Minimum External Projection (API 650 5.5.2 & API 653 Section 4.4)

API 650 5.5.2 requires the annular plate to project at least 2 in. (50 mm) outside the shell. API 653 adds a separate in-service criterion for the projection measured at the outside toe of the shell-to-bottom weld: at least 3/8 in. (10 mm) of projection, with a projection thickness of not less than 0.1 in. (2.5 mm).

• Rationale: An external projection of less than 2 inches allows soil moisture, rainwater runoff, and atmospheric debris to corrode the plate edge immediately adjacent to the shell weld, accelerating corner-joint deterioration and making non-destructive ultrasonic verification impossible from the outside.

2. Minimum Radial Width (API 650 5.5.2)

The annular plate ring must maintain a minimum internal radial width of 24 inches (600 mm) measured between the inside surface of the tank shell and the inner circumferential lap or butt joint connecting to the bottom sketch plates.

API 650 establishes that the radial width ($L$) must satisfy the elastic foundation bending formula:

$L \ge 2\sqrt{R \cdot t_a} \ge 24\text{ in.} \quad (600\text{ mm})$

Where $R$ is the nominal tank radius and $t_a$ is the nominal annular plate thickness. This ensures the secondary rotational moment $M_0$ has completely attenuated before reaching the first lap-welded joint on the sketch plates.

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Step-by-Step Worked Numerical Example

Engineering Problem:

A refined gasoline storage tank ($G = 0.75$) has a nominal diameter of $D = 140\text{ ft}$ and a maximum design liquid level of $H = 48\text{ ft}$.

• The lowest shell course has a nominal thickness of $t_1 = 0.875\text{ in.}$
• The tank is equipped with an annular plate ring.
• Ultrasonic thickness scanning during an out-of-service inspection reveals that the minimum thickness of the annular plate within the Critical Zone has corroded down to $0.220\text{ in.}$
• Anticipated corrosion rate over the next 10-year operating interval is $0.006\text{ in./year}$.

Step 1: Calculate the design stress in the first shell course $S = \frac{2.6 \cdot D \cdot (H - 1) \cdot G}{t_1} = \frac{2.6 \cdot 140 \cdot 47 \cdot 0.75}{0.875}$ $S = \frac{12,831}{0.875} = 14,664\text{ psi}$

Step 2: Determine the applicable stress band in API 653 Table 4.5 Since $S = 14,664\text{ psi} < 24,300\text{ psi}$, the tank falls in the first stress column. The nominal thickness of the first shell course is $t_1 = 0.875\text{ in.}$, which falls in the row $0.75 < t_1 \le 1.00\text{ in.}$

From Table 4.5, the minimum required thickness at the end of the next operating interval is: $t_{\text{Table }4.5} = 0.17\text{ in.} \quad (4.3\text{ mm})$

Watch the row-and-column interaction: had the stress landed one band higher (< 27,000 psi), the same $t_1$ row would demand 0.22 in. — a 29 % jump for a stress change of well under 3,000 psi.

Step 3: Calculate projected annular thickness at the end of the 10-year interval $t_{projected} = t_{actual} - (O_r \times \text{Rate}) = 0.220 - (10 \times 0.006) = 0.220 - 0.060 = 0.160\text{ in.}$

Step 4: Evaluate Code Compliance $t_{projected} = 0.160\text{ in.} < t_{\text{Table }4.5} = 0.170\text{ in.}$ Conclusion: The projected thickness ($0.160\text{ in.}$) fails to meet the minimum required Table 4.5 thickness ($0.170\text{ in.}$). The annular ring cannot remain in service for 10 years without repair. The maximum allowable run time is: $O_{r\_max} = \frac{0.220 - 0.170}{0.006} = \frac{0.050}{0.006} \approx 8.33\text{ years}$