SEISMIC

Response Spectrum

Plot of peak structural response vs. natural period for an earthquake. IS 1893 Fig. 2 gives design spectra for 5% damping.

Also calleddesign spectrumsa/g
Related on InfraLens
CODES
IS 1893
Definition

A response spectrum is a plot of the peak response (acceleration, velocity, or displacement) of a single-degree-of-freedom (SDOF) oscillator versus its natural period T, for a given earthquake ground motion and damping ratio (typically 5%). The spectrum encapsulates the earthquake's frequency content in a form directly usable for design — given any building's natural period, the spectrum gives the peak response without time-history simulation. IS 1893 Part 1:2016 Fig. 2 specifies the design response spectrum for India, providing Sa/g vs T for three soil types (rocky, medium soil, soft soil).

The characteristic shape of any response spectrum: a flat 'plateau' region of nearly constant Sa/g for short periods (T = 0.1-0.5s), a descending region following Sa/g ≈ K/T for medium periods (T = 0.5-2.5s), and a further descending region for long periods. The plateau corresponds to the period range where the structure resonates strongly with the ground motion's dominant frequency. IS 1893 Fig. 2 plateau values: 2.5 for rocky/hard soil, 2.5 for medium soil with shifted plateau, 2.5 for soft soil with longer plateau extending to T = 0.4 s. Soft-soil spectra are more critical for tall buildings (T > 1s); rocky-soil spectra for low-rise (T < 0.4s).

Response spectrum analysis (RSA) per IS 1893 Cl. 7.8 is mandatory for irregular buildings, tall buildings (>40 m), and buildings in Zone IV/V. The procedure: (1) eigenvalue analysis to find modes and periods, (2) for each mode, read Sa/g from spectrum and compute modal participation factor and modal base shear, (3) combine modal responses by SRSS (Square-Root-of-Sum-of-Squares) or CQC (Complete Quadratic Combination — for closely-spaced modes per Cl. 7.8.4.4), (4) scale to ≥ 85% of equivalent static base shear (Cl. 7.8.2). RSA captures higher-mode effects critical for tall buildings; equivalent-static method ignores them.

Typical values
Plateau Sa/g2.5 (5% damping, all soil types)
Plateau period range — rockyT = 0.10-0.40 s
Plateau period range — medium soilT = 0.10-0.55 s
Plateau period range — soft soilT = 0.10-0.67 s
Sa/g at T = 1.0 s (rocky)≈ 1.0
Sa/g at T = 1.0 s (soft soil)≈ 1.67
Where used
  • Equivalent static method — Sa/g read for fundamental period T
  • Response spectrum analysis (RSA) — input for dynamic modal analysis
  • Time history analysis — spectrum-compatible motions generated for non-linear analysis
  • Performance-based design — capacity spectrum compared against demand spectrum
  • Liquid-retaining structures — IS 1893 Part 2 spectrum for sloshing modes
Acceptance / threshold
Per IS 1893 Cl. 7.8: response spectrum analysis required for irregular or tall buildings; modal combination by SRSS or CQC; minimum 90% mass participation in considered modes; base shear scaled up to ≥ 85-90% of static method.
Site example
Site reality: a 28-storey Mumbai tower's first three modes (T₁ = 4.2s, T₂ = 3.8s, T₃ = 1.1s) accounted for only 65% mass participation. Engineer initially considered 3 modes adequate. Peer review correctly required including ≥ 14 modes to reach 90% mass participation per IS 1893 Cl. 7.8.4.2 — the higher modes contributed 25% of base shear and changed shear distribution dramatically. Reduced modal completeness causes real under-design in tall buildings; verify mass participation before signing off any RSA.
Frequently asked
What is design response spectrum?
A plot of peak structural acceleration (Sa/g) versus natural period (T) for an earthquake, used to determine the design force on a structure of any period. IS 1893 Part 1:2016 Fig. 2 provides three design spectra (rocky/medium/soft soil) for 5% damping in India. Multiply Sa/g by structure mass and zone-importance-reduction factors to get base shear.
How does soil type affect the response spectrum?
Soft soil amplifies low-frequency (long-period) ground motion through resonance with the soil column. Soft-soil spectrum has the same plateau Sa/g (= 2.5) but the plateau extends to longer periods (up to T = 0.67s vs 0.40s on rocky soil). For T ≥ 0.5s, soft-soil Sa/g is significantly higher than rocky — by 50-100% at T = 1-2s. This is why tall buildings on soft soil have higher seismic demand.
When is response spectrum analysis required?
Per IS 1893 Cl. 7.8.1, dynamic analysis (RSA or time history) is mandatory for: (a) regular buildings >40 m height in Zones III/IV/V, (b) any building >12 storeys, (c) any irregular building (vertical or plan irregularity per Table 5/6) in Zones IV/V, (d) all buildings >90 m height regardless of zone or regularity. For other buildings, the equivalent static method is permitted.
Related seismic terms
Earthquake / Seismic Zones (II-V)
Zone II (least)-V (most) per IS 1893
Ductile Detailing (Seismic)
Special seismic detailing per IS 13920
Base Shear
Horizontal seismic force at the base of a structure. Vb = Ah × W, where Ah = (Z/2)(I/R)(Sa/g). IS 1893 Cl. 7.5.
Importance Factor (I)
Multiplier on seismic force based on building criticality. Hospitals: 1.5. Schools: 1.5. Residential: 1.0.
Response Reduction Factor (R)
Reduces elastic seismic forces to design forces accounting for ductility. SMRF: 5.0. OMRF: 3.0. Shear wall: 4.0.
Special Moment Resisting Frame (SMRF)
Frame designed and detailed for high ductility per IS 13920. R = 5.0. Required in Zone IV/V for important buildings.
Soft Storey / Stilt Floor
Storey with stiffness <70% of the storey above — typical of stilt parking. IS 1893 Cl. 7.10 mandates 2.5× design force.
Soil-Structure Interaction (SSI)
Interaction between flexible soil and structure under earthquake. Considered for tall buildings on soft soils per IS 1893.