Criteria for design of reinforced concrete chimneys, Part 1: Assessment of loads

Scope & Key Specifications from IS 4998 (Part 1): 1992

1. Scope Overview

• Applies to reinforced concrete chimneys.
• Covers dynamic behavior, wind loads, natural frequency, and vibration analysis.
• Correlation length ( L ) in diameters: 1.0 (if no field data).
• Wind pressure at height ( z ): [ P_z = 0.6 V_{10}^2 \quad \text{(N/m}^2\text{)} ]
• ( V_{10} ): hourly mean wind speed at 10 m height (from IS 875 Part 3).

2. Key Parameters

3. Modulus of Elasticity of Concrete for Natural Frequency (Clause 3.1)

Use these values for dynamic analysis.

4. Natural Frequency Calculation

IS 4998 (Part 1) - Symbols and Definitions (Key Extracts)

Modulus of Elasticity for Concrete Grades (Clause 3.1)

Important Formula

• Design Wind Pressure:

[ P_z = 0.6 \times V^2 ]

Where (V) = wind speed in m/s at height z.

Notes

• Use Strouhal number (Sn) = 0.2 for vortex shedding calculations.
• Structural damping (\xi) is typically taken as 0.016.

Natural Frequency of Chimney in Bending (IS 4998 Part 1)

Key Points from IS 4998:

• Modulus of Elasticity (E) for Concrete Grades:

• Use homogeneous material assumption with above E values for natural frequency calculation.
• Discretize chimney structure (e.g., as beam elements) and apply standard vibration analysis methods (e.g., Rayleigh’s method, finite element).
• Dynamic behavior accounted by chosen E values.

Simplified Formula (for tapered chimneys):

[ V_{cr} = \frac{f_i d Z_{ei}}{S_n} ]

Where:

• (V_{cr}) = Critical wind speed at height (Z_{ei})
• (f_i) = Frequency of ith mode
• (d) = Diameter at height (Z_{ei})
• (S_n) = Natural frequency parameter (depends on mode and structure)

Terrain Power Law Exponent (x) for wind profile (IS 875 Part 3):

Calculation Steps Summary:

1. Select appropriate E based on concrete grade.
2. Model chimney as discretized beam with uniform/homogeneous properties.
3. Calculate natural frequency using standard vibration analysis (e.g., Rayleigh’s method).
4. For tapered chimneys, use the formula for critical wind speed (V_{cr}) to assess across-wind effects.
5. Use terrain exponent (x) for wind speed profile.

Typical Rayleigh's Formula for First Mode Frequency

IS 4998 Part 1: Loads to be Considered for Chimney Design

Key Loads (Clause 5.1)

• Dead loads (self-weight + imposed loads)
• Wind loads (lateral & circumferential) per IS 875 (Part 3):1987
• Earthquake loads
• Temperature effects (vertical & circumferential)

Load Combinations (Clause 5.3)

• Across-wind and along-wind moments combined as root sum square:
  [ M_{total} = \sqrt{M_{along}^2 + M_{across}^2} ]

Notes:

• Use higher wind load from simplified (A-4.1) or random response (A-5.1) methods.
• Secondary effects due to deflection must be included.
• Local loads on shell should be considered if applicable.

flowchart TD
    A[Loads to Consider] --> B[Dead Loads]
    A --> C[Wind Loads (IS 875 Pt 3)]
    A --> D[Earthquake Loads]
    A --> E[Temperature Effects]
    F[Load Combinations] -->|b| B & C
    F -->|c| B & D
    F -->|d| B & E
    F -->|e| B & C & E
    F -->|f| B & D & E
    F -->|g| Circumferential Wind
    F -->|h| Circumferential Temperature
    F -->|j| Circumferential Wind + Temperature

This summary ensures design accounts for all critical load effects per IS 4998.

IS 4998 Part 1: Assessment of Loads on Chimneys

Key Points from Clause 5 & 4.3.2:

• Wind Loads are critical and must be assessed using methods in Annex A.
• For design, use the higher value between:
  • Simplified method (Clause A-4.1)
  • Random response method (Clause A-5.1)
• Thermal loads (Clause 4.5) depend on chimney specifics and must be considered separately.

Important Formulas & Tables for Wind Load (Annex A):

1. Basic Wind Pressure:

[ p = 0.6 \times V^2 \quad \text{(kN/m}^2\text{)} ] Where (V) = basic wind speed (m/s).

2. Along-wind Load (Simplified method):

[ F = C_d \times p \times A ]

• (C_d) = drag coefficient (depends on chimney shape)
• (A) = projected area normal to wind

3. Random Response Method:

• Accounts for dynamic effects, turbulence.
• Requires spectral analysis (details in Annex A-5.1).

Typical Drag Coefficients (C_d):

Summary:

• Use higher wind load from simplified or random response method.
• Include thermal effects as per chimney design.
• Refer to Annex A for detailed load calculations and dynamic factors.

flowchart LR
    A[Start: Determine Wind Speed V] --> B[Calculate Basic Wind Pressure p = 0.6 V²]
    B --> C{Choose Load Method}
    C -->|Simplified| D[Calculate F = Cd × p × A]
    C -->|Random Response| E[Spectral Analysis for Dynamic Load]
    D --> F[Select Higher Load]
    E --> F
    F --> G[Add Thermal Loads as per Clause 4.5]
    G --> H[Final Load for Design]

For detailed tables and dynamic factors, always consult **Ann

IS 4998 Part 1: Load to be Considered (Clauses 5.1, 5.3, and related)

Key Loads for Chimney Design:

• Dead Loads (including imposed loads)
• Wind Loads (lateral and circumferential)
• Earthquake Loads
• Temperature Effects (vertical and circumferential)

Load Combinations (Clause 5.3):

• Dead + Wind
• Dead + Earthquake
• Dead + Temperature
• Dead + Wind + Temperature
• Dead + Earthquake + Temperature
• Circumferential effects due to wind, temperature, and both combined

Important Notes:

• Use higher of along-wind loads from simplified (A-4.1) or random response method (A-5.1).
• Across-wind loads combined with along-wind loads via root sum square of moments.
• Secondary deflection effects considered for one cycle.
• Local loads on shell must be considered.

Design Wind Pressure:

[ P_z = 0.6 \times V_{10}^2 \quad (N/m^2) ] where (V_{10}) = hourly mean wind speed at 10 m height (m/s).

Parameters:

Moment Combination for Wind Loads:

[ M_{combined} = \sqrt{M_{along}^2 + M_{across}^2} ]

Summary Diagram (Load Combinations):

graph LR
    A[Dead Load] -->

Foundation Load Considerations - IS 4998 Part 1 (1992)

Key Points:

• Clause 5.2: Foundation must be checked for minimum weight of chimney shell alone combined with lateral loads (wind, seismic).
• Clause 5.1.1: Imposed loads are excluded in overall shell and foundation design but included for platforms/local strengthening.
• Clause 1.5: Factor of Safety (FoS) against overturning:
  • Shell alone: ≥ 1.5
  • Completed chimney: ≥ 2.0

Load Components for Foundation Design:

• Dead Load: Weight of shell and lining.
• Lateral Loads: Wind, seismic, etc.
• Imposed Loads: Only for platforms/local elements, not for shell/foundation.

Overturning Stability Check:

[ \text{FoS} = \frac{\text{Restoring moment (weight)}}{\text{Overturning moment (lateral loads)}} ]

Ensure:

• ( \text{FoS}_{shell} \geq 1.5 )
• ( \text{FoS}_{completed} \geq 2.0 )

Wind Load Calculation (Clause 4.3.2):

Wind pressure, ( p = 0.6 \times V^2 ) (kN/m²), where ( V ) = design wind speed (m/s).

Summary Table:

graph LR
A[Chimney Shell Weight] --> C[Foundation Stability]
B[Lateral Loads (Wind, Seismic)] --> C
D[Imposed Loads (Platforms)] --> E[Local Element Design]
C --> F[Check FoS ≥ 1.5 (Shell), 2.0 (Completed)]
E --> G[Check Local Strengthening]

References: IS 4998 Part 1 (1992), Clauses 1.5, 4.3.2, 5.1.1,

IS 4998 Part 1: Loading Conditions for Chimney Shell Design

Key Load Combinations (Clause 5.3)

• (b) Dead loads + wind loads
• (c) Dead loads + earthquake loads
• (d) Dead loads + temperature effect
• (e) Dead loads + wind loads + temperature effect
• (f) Dead loads + earthquake loads + temperature effect
• (g) Circumferential effect due to wind
• (h) Circumferential effect due to temperature
• (j) Circumferential effect due to wind + temperature (g + h)

Important Notes:

• Combine across-wind and along-wind moments using root sum square:

  [ M_{combined} = \sqrt{M_{along}^2 + M_{across}^2} ]

• Consider secondary effects due to deflection for one cycle.

• Use higher along-wind load from simplified (A-4.1) or random response method (A-5.1).

• Wind loads per IS 875 (Part 3): 1987.

• Dead + wind or dead + earthquake loads apply for shell alone.

Wind Pressure Formula:

[ P_z = 0.6 \times V_z^2 \quad \text{(N/m}^2) ]

where (V_z) = design wind speed at height (z).

Parameters:

• (L): Correlation length = 1 diameter (if no data)
• (m_e, m_{ei}): Equivalent mass/unit length in modes
• (M_{oe}, M_{oi}): Ring moments due to circumferential wind (N-m/m)
• (t_s): Shell thickness (m)
• (r): Twice turbulence intensity
• (I_m): Mean shell radius (m)
• (V_{10}): Wind speed at 10 m height
• (x_{\beta} = 0.016): Structural damping fraction

Summary Table: Load Combinations

Circumferential Wind Moments (IS 4998 Part 1, Clause 5.4)

Formula:

[ M_{oe} \text{ or } M_{oi} = 0.33 \times P_z \times r_m \quad \text{(N-m per meter height)} ]

• (M_{oe}), (M_{oi}): External and internal ring moments
• (P_z): Design wind pressure at height (z) (N/m²), from IS 875 (Part 3) treating chimney as Class A structure
• (r_m): Mean radius of the shell at section considered (m)

Key Notes:

• Hoop force and shear due to ovaling are not considered.
• (P_z) is obtained from hourly mean wind pressure, typically (P_z = 0.6 V^2) (N/m²), where (V) is wind speed in m/s.
• Mean radius (r_m) is the average radius at the section under consideration.

Moment Due to Corbel Loads (Clause 5.5)

[ M_k = W \times e ]

• (M_k): Moment due to corbel (N-m)
• (W): Load on corbel (N)
• (e): Distance between shell centerline and load CG (m)

Effect of (M_k) is distributed over length = max(depth of corbel, (0.76 \times \sqrt{r_m t_s})) where (t_s) = shell thickness (m).

Summary Table

Moment Due to Corbel Loads (IS 4998 Part 1, Clause 5.5)

Key Formula:

[ M_k = W \times e ]

• Mk = Moment due to corbel load (N-m)
• W = Load on corbel (N)
• e = Distance from shell centerline to load centroid (m)

Sign Convention:

• (+W \times e) for tension on the inner face of shell (above corbel)
• (-W \times e) for tension on the outer face of shell (below corbel)

Distribution Length for Moment Effect

The moment effect is distributed over a length (L_d), where:

[ L_d = \max \left( \text{depth of corbel at shell junction}, \quad 0.76 \times V \times t_s \right) ]

• (V) = shell radius (m)
• (t_s) = shell thickness at section (m)

Additional Relevant Parameters from IS 4998:

Summary:

• Calculate moment (M_k) using load and eccentricity.
• Apply sign based on corbel position relative to shell.
• Distribute moment over length (L_d) for structural analysis.
• Use wind pressure and ring moments for combined load effects.

flowchart LR
    W[Load on Corbel (W)]
    e[Distance e]
    Mk[Moment Mk = W × e]
    Position{Corbel Position}
   

Wind Effect on Chimneys (IS 4998 Part 1)

Key Parameters:

• L = Correlation length in diameters (take as 1.0 if unknown)
• ka = Aerodynamic damping coefficient (0.0 to 0.5)
• Taper:
  [ \text{Taper} = \frac{2(d_{av} - d_{top})}{H} ]
  • (d_{av}) = average diameter over top half
  • (d_{top}) = diameter at top
  • (H) = chimney height

Power Law Exponent (x) for Wind Velocity Profile (IS 875 Part 3):

Critical Wind Speed at height (z_{ei}):

[ V_{er} = f_i \frac{d_{zei}}{S_n} ]

• (f_i) = frequency of ith mode
• (d_{zei}) = diameter at height (z_{ei})
• (S_n) = natural damping

Modal Response for Tapered Chimneys (Taper > 1 in 50):

[ \text{Modal response} = \text{complex function involving } z_{ei}, L, t, H, k_a, d ] (Refer to Clause 1.0 for detailed formula)

Load Calculations:

• Shear force (F_{zo}) and Bending moment (M_{zo}) at height (z_o) per Clause A-4.2
• Across-wind load calculated from peak response amplitude at critical wind speed

Summary Workflow:

1. Determine taper.
2. Select power law exponent (x) for terrain.
3. Calculate critical wind speed (V_{er}) for each mode.
4. Calculate modal response using formulas for tapered or non-tapered chimneys.
5. Compute shear force and bending moment.

flowchart TD
    A

Key Formulas & Specifications for Estimation of Wind Loads on Chimneys (IS 4998 Part 1)

1. Design Wind Pressure at height z: [ P_z = 0.6 \times V_{22}^2 \quad \text{(N/m}^2\text{)} ] where (V_{22}) = hourly mean wind speed at height z (m/s).

2. Hourly Mean Wind Speed at 10 m: [ V_{10} = V_b \times k_2 ] (V_b), (k_2) as per IS 875 (Part 3):1987.

3. Equivalent Mass per Unit Length: [ m_e, m_{ei} \quad \text{(kg/m) for 1st and ith vibration modes} ]

4. Correlation Length: [ L = 1.0 \times \text{diameter (if no field data)} ]

5. Turbulence Intensity: [ r = 2 \times \text{turbulence intensity} ]

6. Critical Wind Speed for ith Mode: [ V_{cri} \quad \text{(m/s)} ]

7. Structural Damping: [ \beta = 0.016 \quad \text{(fraction of critical damping)} ]

8. Shell Thickness & Radius:

   • (t_s) = shell thickness (m)
   • (r_m) = mean radius of shell (m)

9. Strouhal Number: [ S_n = 0.2 ]

10. Load on Corbel: [ k = \text{moment due to corbel load (N-m)} ]

Design Guidance

• Use higher of along-wind loads from:

  • Simplified method (Annex A-4.1)
  • Random response method (Annex A-5.1)

• Wind loads must conform to IS 875 (Part 3):1987.

Summary Table of Key Parameters

| Parameter | Symbol | Typical Value / Note | |------------------------

IS 4998 Part 1: Natural Frequency Calculation Key Points

1. Modulus of Elasticity for Concrete (Clause 3.1, Table A-3)

2. Natural Frequency Calculation (Clause 4.2.1)

• For the i-th mode of vibration, natural frequency is ( f_i ) (Hz).
• Mass per unit length at height ( z ): ( m_z ) (kg/m).

Shear Force ( F_{z0i} ) and Bending Moment ( M_{z0i} ) at height ( z_0 ):

[ F_{z0i} = 4 m_z^2 f_i^2 \int_{0}^{z_0} m_z , dz ]

[ M_{z0i} = 4.72 f_i^2 \int_{0}^{z_0} m_z (z - z_0) , dz ]

3. Critical Wind Speed for Vortex Shedding (Clause 4.3)

[ V_{cr} = f_i \times d \times S_n ]

• ( V_{cr} ): critical wind speed (m/s)
• ( f_i ): natural frequency (Hz)
• ( d ): characteristic dimension (m)
• ( S_n ): Strouhal number (dimensionless)

4. Mass Damping Parameter ( \xi ) (Clause 4.2.2)

[ \xi_i = \frac{\delta}{2\pi} = B = 0.016 ]

• ( \delta ): logarithmic decrement of damping
• ( B ): structural damping fraction of critical damping
• Equivalent mass per unit length ( m_{ei} ) defined in Clause A-4.2

IS 4998 Part 1: Simplified Wind Load Calculation for RC Chimneys

Key Formulas & Parameters:

• Design Wind Pressure at height z:

  [ P_z = 0.6 \times V^2 ]

  where ( V ) = wind speed at height ( z ) (m/s), ( P_z ) in N/m².

• Hourly mean wind speed at 10 m height:

  [ V_{10} = V_b \times k_2 ]

  per IS 875 (Part 3).

• Equivalent mass per unit length in ith mode:

  [ m_{ei} \quad \text{(kg/m)} ]

• Correlation length:

  [ L = 1.0 \times \text{diameter (if no data)} ]

• Turbulence intensity factor:

  [ r = 2 \times \text{turbulence intensity} ]

• Strouhal number:

  [ S_n = 0.2 ]

• Structural damping:

  [ \beta = 0.016, \quad \delta = 2\pi \beta ]

• Design wind pressure at height z:

  [ P_z = 0.6 \times V^2 ]

Important Notes:

• Use higher value of wind load from simplified method (A-4.1) or random response method (A-5.1).
• Wind loads must conform to IS 875 (Part 3): 1987.
• Parameters like shell thickness ( t_s ), mean radius ( I_m ), and height ( W_z ) are essential for sectional calculations.
• Critical wind speed ( V_{cri} ) for mode ( i ) is used in dynamic analysis.

Simplified Wind Load Calculation Flow:

flowchart TD
    A[Start] --> B[Obtain hourly mean wind speed V_10]
    B --> C[Calculate design wind pressure P_z = 0.6 * V^2]
    C --> D[Determine equivalent mass m_ei and mode shapes]
    D --> E[Calculate wind load using simplified method (A-4

IS 4998 Part 1: Across-Wind and Along-Wind Load Responses

1. Along-Wind Load (Clause 4.1)

• Use higher of:
  • Simplified method (A-4.1)
  • Random response method (A-5.1)

2. Across-Wind Load on Chimney (Clause 1.0, A-5.3)

• Parameters:
  • ( L ) = Correlation length in diameters (take as 1.0 if unknown)
  • ( k_a ) = Aerodynamic damping coefficient (0.0 to 0.5)
  • ( x ) = Power law exponent (terrain-dependent, IS 875 Part 3)

• Critical wind speed for mode ( i ): [ V_{cr} = f_i \frac{d Z_{ei}}{S_n} ] where:
  • ( f_i ) = natural frequency of mode ( i )
  • ( d ) = diameter at height ( Z_{ei} )
  • ( S_n ) = Strouhal number (0.2)

3. Across-Wind Oscillation Amplitude (Clause A-4.2)

[ n_{oi} = \frac{C_L H}{2 \pi f_i m_i} \sqrt{\frac{K_{s1}}{S_n}} ]

• ( n_{oi} ) = peak tip deflection (m)
• ( C_L ) = peak oscillatory lift coefficient (0.16)
• ( H ) = chimney height (m)
• ( K_{s1} ) = mass damping parameter for mode ( i )
• ( m_i ) = modal mass

If ( n_{oi} > 0.04 d ), adjust amplitude:

[ n_{oi} = \left(\frac{n_{oi}}{0.04 d}\right)^3 \