Concrete Tank Calculation

Concrete Tank Calculation: Precision Engineering for Durable Storage Solutions

Concrete tank calculation is the process of determining structural and hydraulic parameters for safe tank design. This article covers formulas, variables, and real-world applications.

Learn how to calculate volume, thickness, reinforcement, and pressure resistance for concrete tanks. Detailed tables and examples included.

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  • Calculate volume and wall thickness for a cylindrical concrete tank with 10m diameter and 5m height.
  • Determine reinforcement requirements for a rectangular concrete tank holding 50,000 liters.
  • Estimate hydrostatic pressure and base slab thickness for a 20m³ concrete water tank.
  • Compute concrete volume and steel area for a circular tank with 8m radius and 4m height.

Common Parameters and Values in Concrete Tank Calculation

ParameterSymbolTypical RangeUnitsDescription
Tank Diameter (cylindrical)D2 – 30mDiameter of circular tank
Tank HeightH1 – 15mHeight of tank wall
Wall Thicknesst0.15 – 0.5mThickness of concrete wall
Concrete Compressive Strengthf’c20 – 50MPaConcrete strength at 28 days
Steel Yield Strengthfy415 – 500MPaYield strength of reinforcement steel
Hydrostatic PressureP0 – 150kPaPressure exerted by stored liquid
Concrete Densityρc2300 – 2500kg/m³Density of concrete
Water Densityρw1000kg/m³Density of water (reference liquid)
Modulus of Elasticity (Concrete)Ec20,000 – 40,000MPaElastic modulus of concrete
Reinforcement Ratioρ0.001 – 0.03–Ratio of steel area to concrete cross-section

Fundamental Formulas for Concrete Tank Calculation

1. Volume of Cylindrical Tank

The volume V of a cylindrical tank is calculated by:

V = π × (D / 2)2 × H
  • V: Volume (m³)
  • D: Diameter of tank (m)
  • H: Height of tank (m)

This formula assumes a perfect cylinder filled to height H.

2. Hydrostatic Pressure on Tank Wall

Pressure P at depth h is:

P = ρw × g × h
  • P: Pressure (Pa or N/m²)
  • ρw: Density of liquid (kg/m³)
  • g: Acceleration due to gravity (9.81 m/s²)
  • h: Depth below liquid surface (m)

Maximum pressure occurs at tank base (h = H).

3. Minimum Wall Thickness for Cylindrical Tank

Using thin-wall pressure vessel theory, wall thickness t is:

t = (P × D) / (2 × fc × φ)
  • t: Wall thickness (m)
  • P: Maximum hydrostatic pressure (Pa)
  • D: Tank diameter (m)
  • fc: Allowable concrete stress (Pa)
  • φ: Strength reduction factor (typically 0.65 – 0.75)

Note: Concrete tensile strength is low; reinforcement is required to resist tension.

4. Reinforcement Area Calculation

Required steel area As to resist tensile stress:

As = (P × D × H) / (2 × fy)
  • As: Steel reinforcement area (m²)
  • P: Hydrostatic pressure (Pa)
  • D: Diameter (m)
  • H: Height (m)
  • fy: Yield strength of steel (Pa)

This formula assumes uniform tensile stress distribution.

5. Base Slab Thickness Calculation

Base slab thickness tbase can be estimated by:

tbase = √( (P × D) / (4 × fc) )
  • tbase: Base slab thickness (m)
  • P: Hydrostatic pressure (Pa)
  • D: Tank diameter (m)
  • fc: Allowable concrete stress (Pa)

Ensures slab resists bending and punching shear.

Detailed Explanation of Variables and Typical Values

  • Diameter (D): Common tank diameters range from 2m for small tanks to over 30m for industrial storage.
  • Height (H): Heights vary widely; typical water tanks are 3-10m tall.
  • Wall Thickness (t): Usually between 0.15m and 0.5m depending on pressure and reinforcement.
  • Concrete Strength (f’c): Normal structural concrete ranges from 20 MPa to 50 MPa; higher strength concrete reduces thickness.
  • Steel Yield Strength (fy): Common reinforcement steel grades yield between 415 MPa and 500 MPa.
  • Hydrostatic Pressure (P): Calculated from liquid density and height; water exerts 9.81 kPa per meter depth.
  • Strength Reduction Factor (φ): Accounts for uncertainties; typically 0.65 to 0.75 per design codes like ACI 318.

Real-World Application Examples

Example 1: Cylindrical Water Storage Tank Design

A municipal water tank is designed with a diameter of 10 meters and a height of 5 meters. The tank stores potable water (density 1000 kg/m³). Concrete compressive strength is 30 MPa, and steel reinforcement yield strength is 500 MPa. Calculate the tank volume, maximum hydrostatic pressure, minimum wall thickness, and required steel reinforcement area.

Step 1: Calculate Volume

V = π × (10 / 2)2 × 5 = π × 52 × 5 = π × 25 × 5 = 392.7 m³

The tank holds approximately 392,700 liters of water.

Step 2: Calculate Maximum Hydrostatic Pressure

P = 1000 × 9.81 × 5 = 49,050 Pa = 49.05 kPa

Step 3: Calculate Minimum Wall Thickness

Assuming allowable concrete tensile stress fc = 0.33 × f’c = 0.33 × 30 MPa = 9.9 MPa = 9,900,000 Pa, and φ = 0.7:

t = (P × D) / (2 × fc × φ) = (49,050 × 10) / (2 × 9,900,000 × 0.7) = 490,500 / 13,860,000 ≈ 0.0354 m

This thickness (3.54 cm) is very thin; practical minimum thickness is 0.15 m to accommodate reinforcement and durability.

Step 4: Calculate Required Steel Reinforcement Area

As = (P × D × H) / (2 × fy) = (49,050 × 10 × 5) / (2 × 500,000,000) = 2,452,500 / 1,000,000,000 = 0.00245 m²

Steel area required is 2,450 mm², which can be provided by several rebars depending on diameter.

Example 2: Rectangular Concrete Tank for Chemical Storage

A rectangular concrete tank measures 6m length, 4m width, and 3m height. It stores a chemical with density 1200 kg/m³. Concrete strength is 40 MPa, steel yield strength 415 MPa. Calculate volume, hydrostatic pressure at base, and estimate wall thickness assuming uniform pressure.

Step 1: Calculate Volume

V = Length × Width × Height = 6 × 4 × 3 = 72 m³

Step 2: Calculate Hydrostatic Pressure at Base

P = 1200 × 9.81 × 3 = 35,316 Pa = 35.3 kPa

Step 3: Estimate Wall Thickness

For rectangular tanks, wall thickness is often governed by bending moments. Using a simplified approach:

t = √( (P × Width) / (2 × fc) )

Allowable concrete tensile stress fc = 0.33 × 40 MPa = 13.2 MPa = 13,200,000 Pa

t = √( (35,316 × 4) / (2 × 13,200,000) ) = √(141,264 / 26,400,000) = √0.00535 = 0.073 m

Minimum wall thickness is approximately 7.3 cm; practical design would increase to 0.15 m for safety and reinforcement.

Additional Considerations in Concrete Tank Design

  • Seismic Loads: Tanks in seismic zones require additional reinforcement and design checks per codes like ACI 350 or Eurocode 8.
  • Thermal Effects: Temperature gradients can induce stresses; expansion joints or flexible connections may be necessary.
  • Durability: Chemical exposure, freeze-thaw cycles, and abrasion affect concrete mix design and protective coatings.
  • Waterproofing: Integral waterproofing admixtures or membranes prevent leakage and corrosion of reinforcement.
  • Code Compliance: Follow standards such as ACI 350, AWWA D110, or EN 1992-3 for design and construction.

References and Further Reading