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.

Calculadora con inteligencia artificial (IA) para Concrete Tank Calculation

Download TXT
Desarrollado con IA: este chat puede contener errores. Por favor, verifique la información importante.
  • 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