Tank Weight and Load Calculation

Understanding Tank Weight and Load Calculation: Precision in Engineering

Tank weight and load calculation is essential for safe, efficient tank design and operation. It determines structural integrity and operational limits.

This article covers detailed formulas, common values, and real-world applications for accurate tank weight and load assessment.

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  • Calculate the total weight of a cylindrical storage tank with 10m diameter and 5m height.
  • Determine the load on tank supports for a 20,000-liter water tank.
  • Estimate the shell thickness required for a tank holding 15,000 kg of liquid.
  • Compute the combined weight of tank structure and liquid load for a vertical steel tank.

Comprehensive Tables of Common Values for Tank Weight and Load Calculation

ParameterTypical RangeUnitsDescription
Tank Diameter (D)1 – 30meters (m)Diameter of cylindrical tank shell
Tank Height (H)1 – 40meters (m)Height of tank shell excluding roof and bottom
Shell Thickness (t)5 – 25millimeters (mm)Thickness of tank shell plate
Roof Thickness (troof)5 – 20millimeters (mm)Thickness of tank roof plate
Bottom Thickness (tbottom)6 – 30millimeters (mm)Thickness of tank bottom plate
Material Density (ρmaterial)7,850 – 8,050kg/m³Density of steel or tank material
Liquid Density (ρliquid)500 – 1,200kg/m³Density of stored liquid (water, oil, chemicals)
Corrosion Allowance (c)1 – 3millimeters (mm)Additional thickness for corrosion protection
Load Factor (LF)1.1 – 1.5dimensionlessSafety factor applied to loads
Support Reaction Load (R)VarieskNLoad transmitted to tank supports

Fundamental Formulas for Tank Weight and Load Calculation

1. Shell Plate Weight Calculation

The weight of the cylindrical shell is calculated by multiplying the surface area of the shell by the thickness and material density.

Shell Weight (Wshell) = π × D × H × t × ρmaterial

  • D: Tank diameter (m)
  • H: Tank height (m)
  • t: Shell thickness (m)
  • ρmaterial: Material density (kg/m³)

Note: Thickness must be converted from millimeters to meters for calculation.

2. Roof Plate Weight Calculation

Assuming a flat or conical roof, the roof weight is calculated by the roof surface area times thickness and material density.

Roof Weight (Wroof) = Aroof × troof × ρmaterial

  • Aroof: Roof surface area (m²), typically π × (D/2)2
  • troof: Roof thickness (m)

3. Bottom Plate Weight Calculation

The bottom plate weight is similarly calculated by the bottom surface area times thickness and material density.

Bottom Weight (Wbottom) = Abottom × tbottom × ρmaterial

  • Abottom: Bottom surface area (m²), usually π × (D/2)2
  • tbottom: Bottom thickness (m)

4. Liquid Load Calculation

The load due to the liquid inside the tank is the volume of liquid multiplied by its density and gravity.

Liquid Load (L) = V × ρliquid × g

  • V: Volume of liquid (m³), calculated as π × (D/2)2 × Hliquid
  • ρliquid: Liquid density (kg/m³)
  • g: Acceleration due to gravity (9.81 m/s²)
  • Hliquid: Height of liquid inside tank (m)

5. Total Tank Weight

The total tank weight includes the shell, roof, bottom, and any additional components.

Total Weight (Wtotal) = Wshell + Wroof + Wbottom + Wadditional

  • Wadditional: Weight of nozzles, stiffeners, ladders, etc. (kg)

6. Load on Supports

The load transmitted to the tank supports is the sum of the tank weight and liquid load, multiplied by a load factor for safety.

Support Load (R) = (Wtotal + L) × LF

  • LF: Load factor (typically 1.1 to 1.5)

Detailed Explanation of Variables and Common Values

  • Diameter (D): The diameter directly affects surface area and volume. Common diameters range from 1m for small tanks to over 30m for industrial storage.
  • Height (H): Height influences volume and shell surface area. Heights vary widely depending on application.
  • Thickness (t, troof, tbottom): Thickness depends on design pressure, material strength, and corrosion allowance. Typical steel thickness ranges from 5mm to 25mm.
  • Material Density (ρmaterial): Steel density is approximately 7,850 kg/m³; stainless steel slightly higher.
  • Liquid Density (ρliquid): Water is 1,000 kg/m³; crude oil ranges 800-900 kg/m³; chemicals vary widely.
  • Corrosion Allowance (c): Added thickness to compensate for material loss over time, typically 1-3 mm.
  • Load Factor (LF): Safety factor to account for dynamic loads, wind, seismic activity, and uncertainties.

Real-World Application Examples of Tank Weight and Load Calculation

Example 1: Cylindrical Water Storage Tank Weight and Load

A vertical cylindrical steel tank stores potable water. The tank has a diameter of 8 meters, height of 6 meters, shell thickness of 10 mm, roof thickness of 8 mm, and bottom thickness of 12 mm. The steel density is 7,850 kg/m³, and water density is 1,000 kg/m³. Calculate the total tank weight, liquid load, and support load assuming a load factor of 1.2.

Step 1: Convert thickness to meters

  • t = 10 mm = 0.01 m
  • troof = 8 mm = 0.008 m
  • tbottom = 12 mm = 0.012 m

Step 2: Calculate shell weight

Wshell = π × D × H × t × ρmaterial

Wshell = 3.1416 × 8 × 6 × 0.01 × 7,850 = 11,832 kg

Step 3: Calculate roof weight

Roof area = π × (D/2)2 = 3.1416 × (4)2 = 50.27 m²

Wroof = 50.27 × 0.008 × 7,850 = 3,156 kg

Step 4: Calculate bottom weight

Wbottom = 50.27 × 0.012 × 7,850 = 4,734 kg

Step 5: Calculate total tank weight

Wtotal = 11,832 + 3,156 + 4,734 = 19,722 kg

Step 6: Calculate liquid load

Volume of liquid = π × (4)2 × 6 = 301.59 m³

Liquid weight = 301.59 × 1,000 = 301,590 kg

Liquid load (force) = 301,590 × 9.81 = 2,959,615 N ≈ 2,960 kN

Step 7: Calculate support load

Tank weight force = 19,722 × 9.81 = 193,434 N ≈ 193 kN

Total load = (193 + 2,960) × 1.2 = 3,371 kN

Result: The tank supports must be designed to carry approximately 3,371 kN.

Example 2: Load Calculation for a Chemical Storage Tank with Corrosion Allowance

A chemical storage tank has a diameter of 5 meters, height of 4 meters, shell thickness of 12 mm plus 2 mm corrosion allowance, roof thickness of 10 mm, and bottom thickness of 15 mm. The tank stores a chemical with density 1,100 kg/m³. Steel density is 7,850 kg/m³. Calculate the total weight and support load with a load factor of 1.3.

Step 1: Adjust shell thickness for corrosion

  • t = 12 + 2 = 14 mm = 0.014 m
  • troof = 10 mm = 0.01 m
  • tbottom = 15 mm = 0.015 m

Step 2: Calculate shell weight

Wshell = π × 5 × 4 × 0.014 × 7,850 = 3,448 kg

Step 3: Calculate roof weight

Roof area = π × (2.5)2 = 19.63 m²

Wroof = 19.63 × 0.01 × 7,850 = 1,540 kg

Step 4: Calculate bottom weight

Wbottom = 19.63 × 0.015 × 7,850 = 2,310 kg

Step 5: Calculate total tank weight

Wtotal = 3,448 + 1,540 + 2,310 = 7,298 kg

Step 6: Calculate liquid load

Volume = π × (2.5)2 × 4 = 78.54 m³

Liquid weight = 78.54 × 1,100 = 86,394 kg

Liquid load (force) = 86,394 × 9.81 = 847,597 N ≈ 848 kN

Step 7: Calculate support load

Tank weight force = 7,298 × 9.81 = 71,590 N ≈ 72 kN

Total load = (72 + 848) × 1.3 = 1,202 kN

Result: Supports must be designed for a load of approximately 1,202 kN.

Additional Considerations in Tank Weight and Load Calculations

  • Wind and Seismic Loads: Tanks in seismic zones or exposed to high winds require additional load factors and dynamic analysis per API 650 or ASCE 7 standards.
  • Thermal Expansion: Temperature variations cause expansion/contraction affecting stresses and load distribution.
  • Corrosion and Wear: Regular inspection and corrosion allowance ensure long-term structural integrity.
  • Material Selection: Different materials (carbon steel, stainless steel, composites) affect density and thickness requirements.
  • Code Compliance: Calculations must comply with standards such as API 650, API 620, ASME Section VIII, and local regulations.