Criteria for earthquake-resistant design of the structure, Part 4: Industrial structures including stack-like structures )

Scope of IS 1893 Part 4: Key Formulas, Tables & Specifications

IS 1893 Part 4 deals with seismic design of industrial structures, equipment, and piping.

Key Symbols (Clauses 5.1 & 5.2)

Important Table: Coefficients CT and Cv (Clause 14.1)

General Principles

• Structures in Category 2, 3, and 4 must be designed for Design Basis Earthquake (DBE).
• Use Equivalent Static Lateral Force Method for simplified seismic analysis.
• The seismic base shear ( V_b ) is calculated using:

[ V_b

IS 1893 Part 4: Key Symbols, Notations & Tables

1. Symbols and Notations (Clause 5.1 & 5.2)

2. Important Table: Coefficients CT and Cv (Clause 14.1)

*Note: (k =

Key Assumptions in Earthquake Resistant Design (IS 1893 Part 4, Clause 6.2):

• Impulse Nature of Earthquake: Earthquake ground motions are impulsive, irregular, and short-duration; steady-state resonance is unlikely.
• Non-coincidence of Maximum Loads: Earthquake does not coincide with maximum wind, flood, or sea waves.
• Elastic Modulus: Use static values of elastic modulus unless dynamic values are available (refer IS 456, IS 800, IS 1343).

Important Symbols (Clause 5.1)

Typical Formulas

• Seismic Base Shear:

[ V_b = A \times W = Z \times I \times R \times S_s \times W ]

Where:

• (V_b) = design base shear

• (W) = total seismic weight

• (Z) = zone factor

• (I) = importance factor

• (R) = response reduction factor

• (S_s) = spectral acceleration coefficient

• Natural Period (Approximate for RC Frame):

[ T = 0.075 \times h^{0.75} ]

where (h) = height of structure in meters.

Tables Summary

flowchart LR
    A[Earthquake Ground Motion]
    B[Irregular, Impulsive]
    C[No Steady Resonance]
    D[Design Assumptions]
    E[

Characteristics of Seismic Ground Motions (IS 1893 Part 4, Clause 6.1)

• Depend on:

  • Earthquake magnitude and depth of focus
  • Distance from epicenter
  • Seismic wave path characteristics
  • Soil strata at site

• Ground Motion Components:

  • Random vibrations resolved in 3 mutually perpendicular directions
  • Predominantly horizontal
  • Vertical inertia forces must be considered unless proven insignificant (important for large spans, prestressed/cantilevered members)

• Effects of Vertical Component:

  • Can reduce gravity forces detrimentally, especially in prestressed/cantilevered elements
  • Requires special attention in design

Key Symbols Relevant to Ground Motion

Horizontal Seismic Coefficient (Clause 8.3)

• ( A_h = \frac{Z I}{2 R} \frac{S_a}{g} )

Where:

Summary Diagram of Ground Motion Components

graph LR
    A[Seismic Ground Motion]
    A --> B[Horizontal Components (X, Y)]
    A --> C[Vertical Component (Z)]
    B --> D[Predominant Direction]
    C --> E[Consider for Large Spans & Stability]

Note: For detailed spectral acceleration values and soil effects, refer to IS 1893 Part 1 tables and soil classification criteria.

IS 1893 Part 4: Design Criteria for Industrial Structures

Key Assumptions (Clause 6.2)

• Earthquake ground motion is impulsive, irregular, and short-duration; steady-state resonance is unlikely.
• Earthquake does not coincide with max wind, flood, or sea waves.
• Elastic modulus for materials can be taken as static values unless otherwise specified (refer IS 456, IS 800, IS 1343).

Scope of Industrial Structures (Clause 1.3)

• Covers process industries, power plants, petrochemical, steel, pharmaceutical, cement, textile, off-shore, and many more.
• Includes stack-like structures such as cooling towers, chimneys, silos, transmission towers, pressure vessels.

Reference Codes for Design

• IS 456: Plain & Reinforced Concrete
• IS 800: Steel Construction
• IS 1343: Prestressed Concrete
• IS 1893 (Part 1): General Earthquake Design Provisions
• IS 4998: Reinforced Concrete Chimneys
• IS 6533: Steel Chimneys
• IS 13920: Ductile Detailing for RC Structures

Design Load Combinations (per IS 1893 Part 1 & Part 4)

Important Notes

• Use static elastic modulus for material stiffness.
• Stack-like structures require special dynamic considerations.
• Refer to IS 1893 Part 1 for response spectrum and seismic coefficients.

flowchart TD
    A[Industrial Structures] --> B[Process Industries]
    A --> C[Power Plants]
    A --> D[Petrochemical Plants]
    A --> E[Steel & Metal Plants]
    A --> F[Pharmaceutical & Cement]
    A --> G[Stack-like Structures]
    G --> H[Cooling Towers]
    G --> I[Chimneys]
    G --> J[Silos]
    G --> K[Transmission Towers]

For detailed seismic coefficients, ductility factors, and load combinations, refer to IS 1893 Part 1 and

IS 1893 Part 4: Design Spectrum & Seismic Coefficients

Key Formula for Seismic Coefficient (Clause 8.3.2)

[ A = \frac{Z \times I \times S}{g \times R} ]

Where:

• Z = Zone factor (Annex A / Table 2 of IS 1893 Part 1)
• I = Importance factor (Table 2)
• S/g = Spectral acceleration coefficient for site soil type (Annex B / Fig. 1 of IS 1893 Part 1)
• R = Response reduction factor (Table 3)

Note: For Category 1 structures, seismic force = 2 × force calculated by above formula.

Zone Factor (Annex A)

Design Spectrum (Annex B)

• Spectral acceleration coefficients (S/g) vary by soil type:
  • Type I: Rock or Hard Soil
  • Type II: Medium Soil
  • Type III: Soft Soil

The response spectrum curves (Sa/g vs. period T) are provided graphically in IS 1893 Part 1 Fig. 1 and Part 4 Fig. 2 for 5% damping.

Important Tables:

Summary

• Calculate seismic coefficient A using soil-specific spectral acceleration.
• Multiply by zone and importance factors.
• Divide by response reduction factor.
• Use design spectrum curves for dynamic analysis.

flowchart TD
    A[Start: Determine Site Parameters] --> B[Identify Seismic Zone (Z)]
    B --> C[Determine Soil Type → Get S/g from Design Spectrum]
    C --> D[Select Importance Factor (I)]
    D --> E[Select Response Reduction Factor (R)]
    E --> F[Calculate Seismic Coefficient: A = (Z × I × S/g)

IS 1893 Part 4: Key Formulas & Specifications for Analysis Procedures and Modal Combination

1. Modal Combination (Clause 10.2.5.2)

• Complete Quadratic Combination (CQC) Method:

[ R = \sqrt{\sum_{i=1}^r \sum_{j=1}^r R_i R_j P_{ij}} ]

Where:

• ( R ) = peak response quantity (displacement, force, etc.)
• ( R_i, R_j ) = response in mode (i) and (j) (with sign)
• ( P_{ij} ) = cross-modal correlation coefficient, calculated as:

[ P_{ij} = \frac{8 \zeta (1 + \beta) \beta^{1.5} + (1 - \beta)^2 (1 + \beta^2)}{(1 - \beta^2)^2 + 4 \zeta^2 \beta (1 + \beta)^2} ]

• ( \zeta ) = modal damping ratio (from Table 4, Clause 9.4)
• ( \beta = \frac{\omega_j}{\omega_i} ) (frequency ratio)
• ( \omega_i, \omega_j ) = circular frequencies of modes (i) and (j)
• ( r ) = number of modes considered

2. Alternative Modal Combination (for non-closely spaced modes):

[ R = \sum_{k=1}^r |R_k| ]

• Sum of absolute modal responses

3. Damping Ratios (Clause 9.4, Table 4)

4. Load Combination Note (Clause 7.3.2.1)

• Combine responses from different ground motion components at member force/stress level.
• Use appropriate load combinations as per Clause 7.3.

flowchart TD
    A[Modal Analysis] --> B[Calculate modal responses \(R

IS 1893 (Part 4) - Detailed Analysis Requirements (Clause 10.2)

Key Points from Clause 10.2:

• Detailed Analysis is mandatory for:

  • Structures of Category 2 and 3 in seismic zones III, IV, and V.
  • Complex structures where simplified methods are inadequate.

• Analysis Methods Allowed:

  • Response Spectrum Method
  • Time History Analysis
  • Other advanced dynamic analysis methods

Key Specifications:

Typical Formulas:

• Modal Mass Participation Factor:

  [ \Gamma_i = \frac{\sum m_j \phi_{ij}}{\sum m_j} ]

  Where:

  • (m_j) = Mass at jth degree of freedom
  • (\phi_{ij}) = Mode shape value at jth DOF for ith mode

• Equivalent Lateral Force (for simplified check):

  [ F = C_s W ]

  Where:

  • (C_s) = Seismic coefficient from response spectrum
  • (W) = Weight of the structure

Summary Diagram:

flowchart TD
    A[Start: Structure Category & Zone] --> B{Category 2 or 3?}
    B -- No --> C[Simplified Analysis (Clause 10.3)]
    B -- Yes --> D{Seismic Zone III, IV, V?}
    D -- No --> C
    D -- Yes --> E[Detailed Analysis (Clause 10.2)]
    E --> F[Use Response Spectrum or Time History]
    F --> G[Consider 90% Mass Participation]
    G --> H[Apply Load Combinations per IS 1893]

In brief: Use detailed dynamic analysis (

Time Period Estimation for Stack-like Structures (IS 1893 Part 4)

Key Formulae for Fundamental Time Period, T

1. More Accurate Formula (Clause 14.1):

[ T = C_r \times \frac{h^2}{\sqrt{W / E_s}} ]

• ( C_r ) = coefficient from slenderness ratio (Table 6)
• ( h ) = height of structure above base (m)
• ( W ) = total weight above base (kN)
• ( E_s ) = modulus of elasticity of structural material (kN/m²)

2. Rayleigh's Approximation (Clause 14.2):

[ T = 2 \pi \sqrt{\frac{\sum W_i \delta_i^2}{g \sum W_i \delta_i}} ]

• ( W_i ) = lumped weight at ith location (kN)
• ( \delta_i ) = lateral static deflection at ith location (m)
• ( g ) = acceleration due to gravity (9.81 m/s²)
• ( N ) = number of lumped weights

Use this when structure rests on frames or skirts (e.g., silos, cooling towers).

Important Notes:

• Use only one formula for design.
• If vibration test data exists for a similar structure and soil, it can be adopted.
• Damping factors (Table 7) vary by material and strain; use appropriate damping in spectral analysis.
• Calculate seismic coefficient ( A_h ) using IS 1893 Part 1 spectrum with:

[ A_h = \frac{Z I}{R} S_a / g ]

where ( Z ) = zone factor, ( I ) = importance factor, ( R ) = response reduction factor.

Typical Stack-like Structures (Category 2 mostly):

• Chimneys, silos, ventilation stacks, refinery vessels.
• Refer to Table 5 for categorization.

Summary Diagram

graph TD
    A[Stack-like Structure] --> B[Input Parameters: h, W, Es]
    B --> C{Choose Formula}
    C -->|Clause 14.1| D[Use \( T = C_r \frac{h^2}{\sqrt{W/E_s}} \)]
    C -->

Mathematical Modeling of Stack-like Structures (IS 1893 Part 4, Clause 17.2.1)

• Modeling Requirements:
  • Capture variation in stiffness (cross-section, shell thickness).
  • Include lining mass (lumped at corbel level for chimneys).
  • Model foundation stiffness and soil deformation.
  • Use minimum 10 beam elements for sufficient accuracy.
  • For axi-symmetric stacks, use axi-symmetric finite elements.

Key Tables and Formulas

Notes:

• For soil-structure interaction, use shear wave velocity (v_s) to compute (G).
• For fixed base or raft on hard soil, moment

IS 1893 (Part 4) - Special Design Considerations for Reinforced Concrete Stacks

1. Design Forces & Distribution

• Seismic Shear Force, V:

  [ V = C_s \times A \times W \times D_s ]

  Where:

  • (C_s) = Shear coefficient (from slenderness ratio (k), Table 6)
  • (A) = Design horizontal seismic coefficient (Clause 16)
  • (W) = Total weight including lining and contents
  • (D_s) = Distribution factor for shear at height (x) (Table 10 & 11)

• Bending Moment, (M), at distance (x) from top:

  [ M = C_m \times A \times W \times D_m ]

  • (C_m) = Moment coefficient (from slenderness ratio (k))
  • (D_m) = Moment distribution factor (Table 10 & 11)

2. Foundation Soil & Pile Group Stiffness (Table 12)

• Parameters:
  • (G = \rho v_s^2) (shear modulus)
  • (\nu) = Poisson's ratio
  • (r_0) = radius of raft
  • (n) = number of piles
  • (E, I, T, d) = pile material properties and dimensions

3. Damping Factors (Table 7)

| Material

Seismic Zone Factors (IS 1893 Part 4 - 2005)

Zone Factor (Z) for Maximum Considered Earthquake (MCE):

• Z values correspond to seismic zones defined in IS 1893 (Part 1).

Key Formula for Seismic Coefficient (Clause 8.3.2):

[ A_h = \frac{Z \times I \times S_a}{2 \times R} ]

Where:

Importance Factor (I) for Industrial Structures (Table 2):

Higher I may be assigned at project discretion.

Soil Type Classification (for spectral values):

• Type I: Rock or hard soil (well-graded gravel, N > 30)
• Type II: Medium soil (N between 10 and 30)
• Type III: Soft soil (N < 10)

Summary:

• Use Z from the seismic zone.
• Multiply by I (importance factor).
• Use spectral acceleration S_a/g from soil type.
• Divide by 2R (response reduction factor) to get seismic coefficient for design.

This forms the basis for seismic force calculations in industrial structures per IS 1893 Part 4.

flowchart LR
    A[Seismic Zone (Z)] --> B[Calculate Seismic Coefficient]
    C[Importance Factor (I)] --> B
    D[Spectral Acceleration (S_a/g

IS 1893 Part 4: Design Response Spectra for Rock and Soil Sites

Key Formula for Seismic Coefficient (Clause 8.3.2)

[ S_a = \frac{Z \times I \times S}{2 \times R} ]

Where:

• Z = Zone factor (Annex A / IS 1893 Part 1 Table 2)
• I = Importance factor (Table 2)
• S/g = Spectral acceleration coefficient for site type (Annex B)
• R = Response reduction factor (Table 3)

Note: For Category 1 structures, seismic force = 2 × force from above formula.

Zone Factor Z (Annex A)

Spectral Acceleration Coefficients (Annex B)

• Type I: Rock or Hard Soil
• Type II: Medium Soil
• Type III: Soft Soil

Spectral acceleration ( S_a/g ) varies with natural period ( T ) and soil type (refer to Fig. 2 in IS 1893 Part 4).

Important Tables

Summary Workflow for Response Spectrum Analysis (Clause 10.2.5)

1. Select Z from seismic zone.
2. Determine I based on structure importance.
3. Choose spectral acceleration ( S_a/g ) for site type.
4. Use R for ductility and redundancy.
5. Calculate seismic coefficient ( S_a ).
6. Perform response spectrum analysis using this design spectrum.

flowchart TD
    A[Select Seismic Zone (Z)] --> B[Determine Importance Factor (I)]
    B --> C[Choose Site Type & Get