IS 1893 (Part 1): 2016 — Dynamic Analysis
Earthquake Resistant Design of Structures · Bureau of Indian Standards
Dynamic Analysis Methods
Response Spectrum vs Time History
A comprehensive technical explainer for mid-level engineers — covering every clause, formula, limitation, and workflow under IS 1893 (Part 1): 2016, with interactive calculators.
Overview & Applicability
Cl. 7.6IS 1893 (Part 1): 2016 mandates dynamic analysis for a wide range of structures. Unlike the simplified Equivalent Static Method (ESM), dynamic analysis accounts for the actual frequency content of earthquake ground motion and the structure’s own vibrational behaviour.
When is Dynamic Analysis Mandatory?
Under IS 1893:2016, dynamic analysis is compulsory for almost all buildings in Zones III, IV & V, and for buildings taller than 15 m in Zone II. Equivalent Static Analysis is only permitted for regular buildings ≤15 m height in Seismic Zone II (Cl. 7.6.1).
🔵 Response Spectrum Method (RSM)
Uses a smooth design spectrum (Sa/g vs T) to determine the maximum response in each mode, then combines modes statistically. Fast, code-standardised, and widely used in practice.
🟠 Time History Analysis (THA)
Uses actual or simulated acceleration time histories as input. Provides a step-by-step dynamic response. More accurate but complex — used for critical and irregular structures.
IS 1893:2016 Key Upgrade
The 2016 revision introduced separate response spectra for the Equivalent Static Method and the Response Spectrum Method (extended to 6 s), and modified cracked section properties (70% MI for columns, 35% MI for beams) for computing period of vibration.
Design Response Spectrum
Cl. 6.4The Design Horizontal Seismic Coefficient Ah is the fundamental parameter for seismic force calculation. It combines zone hazard, structural flexibility, importance, and ductility into one coefficient:
Spectral Acceleration Sa/g — Clause 6.4.2
IS 1893:2016 provides separate spectra for the Response Spectrum Method (5% damping, up to 6 s) for three soil types:
| Time Period T (s) | Soil Type I (Hard/Rock) | Soil Type II (Medium) | Soil Type III (Soft) |
|---|---|---|---|
| 0 – 0.10 | 1 + 15T | 1 + 15T | 1 + 15T |
| 0.10 – 0.40 | 2.50 | 2.50 | 2.50 |
| 0.40 – 0.55 | 1.00 / T | — | — |
| 0.40 – 0.75 | — | 1.36 / T ×(1/1.36) | — |
| 0.55 – 4.00 | 1.36 / T | — | — |
| 0.75 – 5.00 | — | 1.36 / T | 1.67 / T |
| 4.00 – 6.00 | 0.34 | 0.27 | 0.34 |
Zone Factor (Z) — Table 3
Zone II: 0.10
Zone III: 0.16
Zone IV: 0.24
Zone V: 0.36
Importance Factor (I) — Table 8
Residential/Office: 1.2
Critical facilities: 1.5
Emergency structures: 1.5
Industrial: 1.0
Response Reduction (R) — Table 9
Unreinforced masonry: 1.5
RC shear wall: 3 – 5
SMRF (ductile): 5
Steel braced: 4
Response Spectrum Method (RSM)
Cl. 7.7The RSM is the primary dynamic analysis method in IS 1893:2016 for regular and irregular buildings. It evaluates the response of a Multi-Degree-of-Freedom (MDOF) system by superimposing the responses of each mode of vibration, each treated as a separate Single-Degree-of-Freedom (SDOF) system.
RSM Step-by-Step Workflow
Determine Structural Properties
Calculate mass matrix [M] and stiffness matrix [K]. For IS 1893:2016, use cracked section properties: 70% of gross MI for columns and 35% of gross MI for beams.
Compute Natural Periods (Tₖ) by Eigenvalue Analysis
Solve [K – ω²M]{φ} = 0 to get natural frequencies ωₖ and mode shapes {φₖ}. The number of modes must capture ≥ 90% mass participation (Cl. 7.7.5.2).
Read Spectral Acceleration Aₖ from Design Spectrum
For each mode k with period Tₖ, read Sa/g from the IS 1893 design spectrum for the appropriate soil type. Then: Aₖ = (Z/2) × (I/R) × (Sa/g)
Compute Modal Participation Factor (Pₖ) — Cl. 7.7.5.4
Pₖ = [Σ Wᵢ φᵢₖ / g] / [Σ Wᵢ φ²ᵢₖ / g]
This quantifies how much each mode participates in the response.
Calculate Lateral Force at Each Floor (Qᵢₖ)
Qᵢₖ = Aₖ × Pₖ × φᵢₖ × Wᵢ (Cl. 7.7.5.4c)
This gives the lateral force at floor i in mode k.
Compute Storey Shear in Each Mode (Vᵢₖ)
Sum Qᵢₖ from top down: Vᵢₖ = Σ Qⱼₖ for j = i to n (Cl. 7.7.5.4d)
Combine Modes — SRSS or CQC (Cl. 7.7.5.4e)
Combine peak modal responses using SRSS (for well-separated modes) or CQC (for closely-spaced modes, recommended by IS 1893:2016).
Scale Base Shear (Cl. 7.7.3)
Compare RSM base shear VB_RS with empirical base shear VB_SS. If VB_RS < VB_SS, scale all response quantities by VB_SS / VB_RS.
Modal Combination Methods — Cl. 7.7.5.4(e)
SRSS — Square Root of Sum of Squares
r = √(Σ rₖ²)
When to use: Modes are well-separated (Tᵢ/Tⱼ < 0.9). Underestimates response when modes are close. Simple and conservative for most cases.
CQC — Complete Quadratic Combination ✓ Preferred
r = √(Σᵢ Σⱼ rᵢ ρᵢⱼ rⱼ)
When to use: Closely-spaced modes (recommended by IS 1893:2016 as default). Cross-correlation coefficient ρᵢⱼ accounts for mode interaction. More accurate than SRSS.
Base Shear Scaling — Cl. 7.7.3
This is a critical check! The RSM can sometimes give a lower base shear than the empirical formula (which uses an estimated fundamental period). IS 1893 requires scaling up in this case.
VB_SS = Ah × W (using empirical Tₐ)
VB_RS = base shear from RSM analysis
Vertical Direction (Cl. 7.7.3b)
For vertical seismic load, the design acceleration in the vertical direction = 2/3 × maximum horizontal design acceleration. The scale factor for vertical direction = max(scale factor in X, scale factor in Z).
Vik = Σj≥i Qjk
Time History Analysis (THA)
Cl. 7.9Time History Analysis (also called Response History Analysis) is the most rigorous dynamic analysis method. It directly integrates the equations of motion using actual or synthetic ground acceleration records as input, providing the full time-dependent structural response.
Equations of Motion
Ground Motion Record Selection — Cl. 7.9.2
📋 Minimum Records Required
IS 1893:2016 requires a minimum of 7 ground motion records for time history analysis when the mean response is used as the design basis. If fewer than 7 records are used, the maximum (envelope) response must be taken.
🎯 Record Sources
Records can be: (1) Recorded accelerograms from past earthquakes scaled to match design spectrum; (2) Simulated/artificial records generated to match site-specific spectrum; (3) Spectrum-compatible synthetic records.
| Requirement | IS 1893:2016 Provision |
|---|---|
| Number of records | Minimum 7 (mean governs); <7 → use maximum |
| Spectrum compatibility | Mean spectrum of records ≥ design spectrum in range 0.2Tₙ to 1.5Tₙ |
| Record duration | Appropriate to site seismicity and structure fundamental period |
| Scaling | Scale factor applied to match design spectrum amplitude |
| Damping | 5% for RC structures, 2% for steel structures |
| Direction | Analyze in two orthogonal horizontal directions simultaneously for 3D models |
THA Step-by-Step Workflow
Build 3D Structural Model
Include all mass, stiffness (cracked sections per IS 1893:2016), and damping (5% for RC). Define floor diaphragm rigidity as required.
Select & Scale Ground Motion Records
Choose ≥ 7 records from strong motion databases (PEER, CESMD). Scale each so the mean spectrum matches or exceeds the IS 1893 design spectrum in the critical period range (0.2Tₙ to 1.5Tₙ).
Perform Time Integration
Numerically integrate equations of motion using Newmark-β method (β = 0.25, γ = 0.5) or Wilson-θ method. Time step Δt ≤ 0.01 s (or Tₙ/10, whichever is smaller).
Extract Response Quantities
Record peak floor displacements, storey drifts, base shear, and member forces at each time step for each record.
Average Results (for ≥ 7 Records)
Take the mean of peak responses across all records as the design value. If < 7 records, use the maximum envelope across all records.
Integration Method: Newmark-β (Most Common)
With β = 0.25 and γ = 0.5 (constant average acceleration), the method is unconditionally stable for linear systems. For nonlinear THA, use smaller time steps (Δt ≤ 0.005 s) to ensure convergence.
RSM vs THA — Side-by-Side Comparison
Response Spectrum Method
- Uses smooth design spectrum (statistical representation)
- Evaluates maximum response in each mode separately
- Modes combined by CQC or SRSS (statistical)
- All results are positive (signs lost in combination)
- Fast computation — minutes for most buildings
- Suitable for linear elastic analysis only
- Standard IS 1893 method for regular & irregular structures
- Base shear must be scaled if RSM < ESM value
- 90% mass participation must be captured
- Torsion added per Cl. 7.8 (5% accidental eccentricity)
Time History Analysis
- Uses actual or simulated acceleration records
- Provides complete time-dependent response
- Modes implicitly captured — no combination needed
- Signs of forces are preserved throughout analysis
- Computationally intensive — hours for complex models
- Can handle nonlinear material & geometry (NLTHA)
- Required for base-isolated, damped, or critical structures
- Minimum 7 records; mean or maximum governs design
- Full frequency content automatically captured
- Record-to-record variability must be addressed
| Parameter | Response Spectrum Method | Time History Analysis |
|---|---|---|
| IS 1893 Clause | Cl. 7.7 | Cl. 7.9 |
| Structural Model | Linear elastic MDOF | Linear or Nonlinear MDOF |
| Input | Design spectrum (Sa/g vs T) | Acceleration time history üg(t) |
| Number of Records | N/A (single spectrum) | Minimum 7 records |
| Modal Combination | SRSS or CQC | Not needed (implicit) |
| Sign of Forces | Lost (always positive) | Preserved |
| Damping | Built into spectrum (5%) | Explicit Rayleigh damping |
| Story Drift Check | ≤ 0.004h (Cl. 7.11.1) | ≤ 0.004h (Cl. 7.11.1) |
| Applicability | Most buildings | Critical, base-isolated, irregular |
| Computational Effort | Low–Moderate | High–Very High |
Torsion & Drift Checks
Cl. 7.8 & 7.11🌀 Design Eccentricity — Cl. 7.8
The design eccentricity accounts for both static (eₛᵢ) and accidental eccentricity:
edᵢ = 1.5eₛᵢ + 0.05bᵢ (or)
edᵢ = eₛᵢ – 0.05bᵢ
where bᵢ = plan dimension in direction of force, eₛᵢ = static eccentricity (CM to CR distance).
📏 Storey Drift Limit — Cl. 7.11.1
Maximum inter-storey drift:
Δ ≤ 0.004 × h
where h = storey height. For buildings with brittle finishes, this is more critical. A warning is issued by analysis software if this limit is exceeded.
Torsion in RSM — Cl. 7.7.5.4
For RSM, torsional moment at each floor is calculated for each mode using the design eccentricity. The lateral nodal forces from torsion are algebraically added to the modal response quantities before CQC/SRSS combination.
Soft Storey Warning — Table 5
A soft storey exists when the lateral stiffness of a floor is less than 70% of the storey above, or less than 80% of the average of the three storeys above. Soft storey buildings require special detailing and analysis. IS 1893:2016 mandates a warning flag in such cases.
Interactive Seismic Calculator
IS 1893:2016IS 1893:2016 Dynamic Analysis Calculator
Response Spectrum Method · Base Shear · Floor Forces · Storey Shear
Enter the structural time period to look up the design spectral acceleration Sa/g from IS 1893:2016 Table/Fig. 2.
🎯 Key Takeaways for Engineers
CQC is the default in IS 1893:2016 for modal combination — use SRSS only when all mode periods are well-separated (Tᵢ/Tⱼ < 0.9).
Base shear scaling is mandatory (Cl. 7.7.3). If RSM base shear < empirical ESM value, all responses must be scaled up by VB_SS/VB_RS.
90% mass participation must be achieved in RSM (Cl. 7.7.5.2). Add more modes if needed — typically 3× storeys is a safe start.
Cracked sections (IS 1893:2016): Use 70% EI for columns and 35% EI for beams when computing period of vibration. This changes Tₙ significantly.
THA minimum 7 records: Use the mean response. Fewer than 7 → use the maximum (envelope). Scale records to match IS 1893 design spectrum in range 0.2T to 1.5T.
Drift limit = 0.004h (Cl. 7.11.1) for all buildings. Check at every storey. Torsion from 5% accidental eccentricity must be included in all cases.
