Criteria for the structural design of reinforced concrete natural draught cooling towers

IS 11504: Scope - Key Symbols, Proportions & Construction Checks

1. Scope & Symbols (Clause 3.1)

• Geometry & Dimensions:

  • ( D ): Base diameter at basin sill level
  • ( R_o ): Horizontal radius
  • ( H ): Total tower height above basin sill
  • ( H_b ): Vertical distance from throat to basin sill
  • ( r_t ): Top radius
  • ( t ): Thickness of shell
  • ( T_{th} ): Throat radius

• Material Properties:

  • ( E ): Short-term modulus of elasticity of concrete
  • ( \nu ): Poisson’s ratio of concrete

• Stress Resultants:

  • ( M_m, M_c, M_t ): Meridional, circumferential, twisting moments/unit length
  • ( N_m, N_c ): Meridional, circumferential stress resultants/unit length
  • ( Q_m, Q_c ): Transverse shear stress resultants/unit length

• Loads & Pressures:

  • ( p' ): Design wind pressure coefficient
  • ( P_{cr} ): Critical buckling pressure
  • ( P_+, P_0, P_z ): Load components/unit area

2. Recommended Shell Proportions (Clause 6.1.1)

• Designs should adhere to commonly adopted hyperbolic shell proportions used in cooling towers.
• Deviations require careful structural study.

3. Constructional Geometry Checks (Clause 7.4)

• Horizontal radius readings every 6 m height or weekly during construction.
• Ground stations arranged at ≤ 10° plan angle apart for absolute position checks.

Summary Diagram: Shell Geometry & Stress Resultants

graph TD
    A[Shell Geometry] -->|Dimensions| B(Base Diameter D)
    A --> C(Height H)
    A --> D(

IS 11504 - Key Definitions, Symbols & Wind Pressure Distribution

1. Key Definitions & Symbols (Clause 2.0 & 3.1)

2. Wind Pressure Coefficient Distribution (Clause 2.2 & Appendix A)

The wind pressure coefficient around the shell is:

[ p'(\theta) = \sum_{n=0}^7 F_n \cos(n \theta) ]

• (p') = design wind pressure coefficient
• (F_n) = Fourier coefficients (Table below)
• (\theta) = angular position from wind direction (degrees)

This series is accurate up to 7 terms.

IS 11504 - Symbols, Notations & Key Formulas

Key Symbols (Clause 3.1)

Wind Pressure Coefficient (Clause 2.2)

[ p'(\theta) = \sum_{n=0}^{7} F_n \cos(n\theta) ]

• (p'): design wind pressure coefficient
• (\theta): angular position from wind direction (degrees)
• (F_n): Fourier coefficients (Table below)

Use with basic wind pressure from IS 875.

Geometry of Hyperboloid (Clause B-2)

[ \frac{r^2}{a^2} - \frac{y^2}{b^2} = 1 ]

• Radii of curvature:

[ R_m = r \csc \phi = \frac{r(1 + (dr/dy)^

IS 11504: Key Formulas, Tables & Specifications for Materials

1. Concrete Materials (Clause 4.1)

• Concrete shall conform to IS 456:1978 (Code of Practice for Plain and Reinforced Concrete).
• Key properties include:
  • Modulus of Elasticity (E): Short-term modulus used in design.
  • Poisson's Ratio (ν): Typically ~0.2 for concrete.
• Unit weights and dead loads per IS 1911:1967.

2. Steel Reinforcement (Clause 4.2)

• Steel types allowed for reinforcement:
  • Mild steel & medium tensile bars: IS 432 (Part 1 & 2)-1982
  • Hot-rolled mild & medium tensile deformed bars: IS 1139-1966
  • Hard-drawn steel wire fabric: IS 1566-1982
  • Cold-worked high strength deformed bars: IS 1786-1979

3. Key Symbols (Clause 3.1)

4. Typical Dead Load Calculation (IS 1911)

[ \text{Dead Load} = \text{Unit weight} \times \text{Volume} ]

• Unit weights (approximate):
  • Concrete: 24 kN/m³
  • Steel: 78.5 kN/m³

5. Steel Reinforcement Grades (IS 1786)

flowchart TD
    A[Materials] --> B[Concrete

IS 11504: Loads and Load Combinations

Key Loads to Consider (Clause 5.1)

• Dead Load (DL): As per IS 1911-1967; includes self-weight and permanent fixtures.
• Earthquake Forces (EL): As specified.
• Thermal Restraint Loads: Due to temperature variations.
• Construction Loads: Temporary loads during construction.
• Other Loads: Snow, foundation settlement, etc.

Load Combinations (Clause 5.2)

• Follow IS 875 (Part 5) - 1964 for load combinations.
• Typical load combination formula:

Important Notes

• Dead loads must be carefully assessed (Clause 5.1.1).
• Secondary stresses from permanent fixtures should be investigated.
• Wind pressure distribution is detailed in Appendix A (Clauses 5.1.3 and 6.2).

Summary Diagram: Load Combination Concept

flowchart LR
    DL[Dead Load] --> LC[Load Combination]
    LL[Live Load] --> LC
    EL[Earthquake Load] --> LC
    TRL[Thermal Restraint Load] --> LC
    CL[Construction Load] --> LC
    OL[Other Loads] --> LC
    LC --> Design[Design Load for Analysis]

For detailed values and factors, refer to IS 875 (Part 5) and IS 1911 for dead load assessment.

IS 11504 - Tower Design Considerations: Key Points

1. Permissible Stresses

• Follow IS 456-1978 for permissible stresses in concrete and steel.
• Typical permissible stresses:
  • Concrete compression: ~0.45 fck
  • Steel tension: ~0.87 fy

2. Vibration Characteristics (Clause 6.3.4)

• Natural frequency ( f \propto \frac{1}{\sqrt{m} \cdot h} )
• Taller towers have lower natural frequencies → higher susceptibility to wind-induced vibrations.
• Design must ensure damping or stiffness to avoid resonance with wind vortex shedding.

3. Foundation Specifications (Clause 6.5.2)

4. General Design Notes

• Wind load design per IS 875 (Part 3).
• Structural stability against overturning and sliding must be checked.
• Reinforced concrete detailing as per IS 456.

graph TD
A[Tower Height] -->|> 75 m| B[Continuous Foundation]
A -->|≤ 75 m| C[Isolated Foundation]
D[Vibration Frequency] -->|Inversely proportional| E[Tower Height & Mass]
E --> F[Design for Wind-Induced Vibrations]

Summary: Use IS 456 for stresses, design foundations based on height, and carefully assess vibration for tall towers to ensure structural safety.

IS 11504: Constructional Aspects - Key Formulas, Tables & Specifications

1. Dimensional Tolerances (Clause 7.3)

2. Shell Geometry Checking (Clause 7.4)

• Ground stations spaced ≤ 10° plan angle apart.
• Horizontal radius readings every 6 m height or weekly.

3. Shell Formwork (Clause 7.2)

• Must be rigid, shape-preserving, tight-fitting.
• Recommended: Steel formwork.
• Should prevent deflection/movement during concreting.
• Follow IS 456-1978 for general formwork provisions.

4. Recommended Shell Proportions (Clause 6.1.1)

• Designs limited to well-studied hyperbolic shell proportions commonly used in cooling towers.
• Other shapes require detailed study.

Summary Diagram: Tolerances & Checks

graph TD
A[Shell Construction] --> B[Dimensional Tolerances]
B --> C[Horizontal Centre Line ±15 mm]
B --> D[Meridional Centre Line ±10 mm]
B --> E[Thickness +10/-5 mm]
B --> F[Horizontal Radius ±40 to 50 mm]
A --> G[Geometry Checks]
G --> H[Ground Stations ≤10° apart]
G --> I[Height-based survey inaccuracies]
I --> J[≤30m: ±15 mm]
I --> K[30-60m: ±40 mm]
I --> L[60-120m: ±

Wind Pressure Distribution on Cooling Tower Shell (IS 11504 - Appendix A)

• Applicable for towers ≤ 120 m height and ≤ 100 m base diameter.

1. Wind Pressure Coefficient (p') Formula:

[ p'(\theta) = \sum_{n=0}^{7} F_n \cos(n \theta) ]

• (\theta) = Angular position around shell (degrees from wind direction)
• (F_n) = Fourier coefficients (see table below)

2. Fourier Coefficients (F_n):

Series up to 7 terms provides sufficient accuracy.

3. Design Wind Pressure on Shell:

[ p_{design}(\theta) = p_{basic} \times p'(\theta) ]

• (p_{basic}) = Basic wind pressure from IS 875 (Part 3)
• Multiply (p'(\theta)) by (p_{basic}) to get local pressure.

4. Additional Notes:

• Pressure distribution is symmetrical about wind centerline.
• Increase values by 10% to account for geometric imperfections.

graph LR
A[Basic Wind Pressure (IS 875)] --> B[Multiply by p'(\u03B8)]
B --> C[Design Wind Pressure Distribution]
C --> D[Shell Surface Load]

This method ensures accurate circumferential wind load modeling for cooling tower shell design.

IS 11504 - Analysis of Shell (Clause 6.3.1 & Appendix B)

Key Points:

• Analysis basis: Use elasticity theory for thin shells of revolution; concrete assumed uncracked, homogeneous, isotropic.
• Recommended method: Bending analysis preferred over membrane analysis for stress resultants.
• Boundary conditions:
  • Upper edge: Free edge with smooth thickness transition to ring beam.
  • Lower edge: Elastically supported by columns; smooth thickness transition to thickened lower ring beam.

Important Symbols:

Typical Governing Equations (Membrane & Bending):

• Membrane equilibrium:

[ \frac{dN_\theta}{d\theta} + (N_\phi - N_\theta) \cot \theta + q R = 0 ]

• Bending moments and compatibility involve differential equations relating (M_\theta, M_\phi) and shell curvature.

Design Recommendations:

• Smooth thickness transitions to avoid stress concentrations.
• Consider elastic support at the base.
• Account for wind loads (design wind pressure coefficient (p')) though vibration effects are not fully covered.

graph LR
A[Shell of Revolution] --> B[Membrane Analysis]
A --> C[Bending Analysis (Recommended)]
B --> D[Stress Resultants Nθ, Nφ]
C --> E[Moments Mθ, Mφ and Shear Qθ, Qφ]
F[Boundary Conditions] --> G[Upper Edge: Free, Smooth Transition]
F --> H[Lower Edge: Elastic Support, Thickened Ring Beam]

For detailed formulas and equilibrium equations, refer to Appendix B of IS 11504.