Beginner — Seismology Fundamentals
Start here if you are new to earthquake engineering.
Earthquake Causes and Seismic Waves
Earthquakes are caused by sudden release of energy along geological faults in the Earth's crust due to tectonic plate movements. The elastic rebound theory explains how strain energy accumulates over decades to centuries, then is released instantaneously during fault rupture. The location of initial rupture is the hypocenter (focus), and the point directly above on the surface is the epicenter. Fault types include strike-slip (San Andreas), normal (extensional regions), and thrust/reverse (subduction zones and collision boundaries).
Seismic waves radiate from the rupture in two forms: body waves (P-waves and S-waves) and surface waves (Love and Rayleigh waves). P-waves (primary, compressional) travel fastest at 5-7 km/s in crustal rock, alternating compression and dilation. S-waves (secondary, shear) travel at 3-4 km/s and cause perpendicular ground motion — they do not propagate through fluids. Surface waves travel slower but cause the largest ground displacements and most structural damage. The Richter scale measured local magnitude ML from seismograph amplitude, while the moment magnitude scale Mw is now preferred for its physical basis relating to seismic moment M₀ = μ·A·D.
Seismic Hazard Analysis and Ground Motion
Probabilistic Seismic Hazard Analysis (PSHA) quantifies the probability of exceeding various ground motion levels at a site from all possible earthquake sources. The Cornell-McGuire methodology integrates: earthquake source characterization (fault locations, magnitudes, recurrence rates), ground motion prediction equations (GMPEs, formerly attenuation relations), and uncertainty propagation through the total probability theorem. The USGS National Seismic Hazard Maps provide spectral acceleration values for 2% and 10% probability of exceedance in 50 years (2475-year and 475-year return periods).
Ground motion parameters include peak ground acceleration (PGA), peak ground velocity (PGV), and spectral acceleration (Sa) at various periods. The design earthquake in ASCE 7-22 uses risk-targeted ground motions with the Maximum Considered Earthquake (MCE_R) having a 1% probability of collapse in 50 years. Soil site effects amplify ground motion at specific periods depending on the site class (A through F, per ASCE 7 Table 20.3-1). Soft soils amplify long-period motions, which can be critical for tall buildings. Site-specific ground motion response analysis using programs like SHAKE or DEEPSOIL may be required for Site Classes E and F.
Response Spectra and Design Spectrum
A response spectrum plots the maximum response (acceleration, velocity, or displacement) of single-degree-of-freedom (SDOF) oscillators with varying natural periods subjected to a given ground motion record. The elastic response spectrum is the envelope of maximum responses across all periods, providing a practical design tool. For a given ground acceleration, the spectral acceleration Sa(T) = max(|ü(t) + üg(t)|) — the maximum absolute acceleration of the oscillator mass.
The ASCE 7 design response spectrum is constructed using the mapped MCE_R spectral response accelerations at short periods (Ss for T = 0.2 s) and 1-second period (S1). Site coefficients Fa and Fv adjust for site class effects. The design spectral acceleration parameters SDS = (2/3)·Fa·Ss and SD1 = (2/3)·Fv·S1 define the spectrum shape: Sa = SDS·(0.4 + 0.6T/T0) for T < T0, Sa = SDS for T0 ≤ T ≤ Ts, and Sa = SD1/T for T > Ts, where T0 = 0.2·SD1/SDS and Ts = SD1/SDS. Eurocode 8 uses Type 1 and Type 2 spectra with ground type factors S for different soil conditions.
Intermediate — Seismic Analysis Methods
Build on fundamentals with analysis methods.
Equivalent Lateral Force Procedure
The equivalent lateral force (ELF) procedure is the primary method for seismic design of regular buildings per ASCE 7 Chapter 12. The total base shear V = Cs·W, where the seismic response coefficient Cs = SDS/(R/Ie) but need not exceed SD1/(T·R/Ie) and must not be less than 0.044·SDS·Ie or 0.01W. R is the response modification factor (3 for ordinary moment frames, 8 for special moment frames), Ie is the importance factor (1.0 for Risk Category II, 1.5 for essential facilities), and W is the effective seismic weight (dead load + 25% of floor live load for storage + snow load where applicable).
The fundamental period T is estimated empirically: Ta = Ct·hn^x (Ct = 0.0466 for steel moment frames, 0.016 for concrete moment frames, hn in meters). Forces are distributed vertically: Fx = Cvx·V, where Cvx = wx·hx^k/Σ(w i·hi^k). The exponent k = 1 for T ≤ 0.5 s, k = 2 for T ≥ 2.5 s, and linear interpolation for intermediate periods. Story drift is checked under the design level forces with allowable drift limits of Δa = 0.025hsx for Risk Category II (ASCE 7 Table 12.12-1). P-delta effects are included when the stability coefficient θ = Px·Δ·Ie/(Vx·hsx·Cd) exceeds 0.10.
Modal Response Spectrum Analysis
Modal response spectrum analysis (RSA) provides a more accurate dynamic analysis for irregular or taller buildings. The method uses the natural mode shapes and periods from eigenvalue analysis to compute modal responses, then combines them using the Complete Quadratic Combination (CQC) for closely spaced modes or the Square Root of Sum of Squares (SRSS) for well-separated modes. The effective modal mass must capture at least 90% of the total mass, or a minimum of 3 modes per principal direction in three dimensions.
The number of modes required depends on structural regularity: regular buildings typically need 1-3 modes per direction; irregular buildings may require many more. The design force for element i in mode n is f_in = ρ·Wn·φin·Sa(Tn)/gn, where ρ is the redundancy factor, Wn is the modal effective weight, and φin is the mode shape component. Scaling of RSA results is required per ASCE 7: the base shear from RSA at the fundamental period must not be less than 85% of the ELF base shear (100% for structures with irregularity Type 1a, 1b, or 2). Use the Seismic Load Calculator to compute base shear.
Nonlinear Analysis and Pushover Method
Nonlinear static pushover analysis evaluates structural performance under increasing lateral loads (monotonic loading) up to target displacement, revealing inelastic behavior, plastic hinge formation, and failure sequence. The capacity spectrum method plots the pushover curve (base shear vs. roof displacement) transformed into spectral acceleration vs. spectral displacement (ADRS format). Performance levels per ASCE 41 include Immediate Occupancy (IO), Life Safety (LS), and Collapse Prevention (CP) based on plastic rotation limits, strength loss criteria, and residual drifts.
Nonlinear dynamic response history analysis (RHA) using earthquake ground motion records is the most rigorous method, required for seismically isolated structures, damping systems, and structures exceeding height limits. At least 7 ground motion records are scaled to match the target spectrum (mean spectrum not less than design spectrum over period range 0.2T to 1.5T). When 7+ records are used, the maximum response parameter is used; with 3-6 records, the maximum is used. Incremental dynamic analysis (IDA) subjects the structure to progressively scaled records to assess collapse capacity and the seismic fragility curve.
Advanced — Ductile Detailing and Earthquake-Resistant Design
For senior students and practicing engineers.
Ductile Detailing of RC Structures (ACI 318 and IS 13920)
Ductile detailing ensures that reinforced concrete structures can undergo large inelastic deformations without significant strength degradation during earthquakes. The strong-column-weak-beam concept requires the sum of column flexural strengths at a joint to exceed the sum of beam flexural strengths by at least 20% (ΣMnc ≥ 1.2ΣMnb per ACI 318 Section 18.7.3.2). This ensures plastic hinges form in beams rather than columns, creating a more ductile and stable mechanism that distributes energy dissipation across multiple locations.
Special moment frames require closely spaced hoops in potential plastic hinge zones: at columns, hoop spacing ≤ min(8db of longitudinal bar, 24db of hoop bar, half the minimum column dimension, 300 mm) over a length lo = max(h, H/6, 450 mm) from each joint face. In beams, hoops are required over length 2h from the column face with spacing ≤ min(d/4, 8db, 24db, 300 mm). The transverse reinforcement volumetric ratio ρs for spiral columns is ρs = 0.12·f'c/fyt in plastic hinge regions. Diagonal reinforcement is required for beam-column joints with high shear demand. Special structural walls require boundary elements where the neutral axis depth exceeds lw/(600·δu/hw).
Seismic Design of Steel Structures
Steel structures provide excellent ductility for seismic resistance when properly detailed. Special Moment Frames (SMF) with R = 8 require prequalified connections per AISC 358 (reduced beam section, bolted unstiffened/stiffened end plate, welded unreinforced flange with bolted web). The beam-to-column connection must develop at least 0.80Mp of the beam through the connection, and the beam must achieve a plastic rotation of 0.04 rad for SMF and 0.02 rad for Intermediate Moment Frames (IMF). Panel zone shear is checked and may require doubler plates or continuity plates.
Concentrically Braced Frames (CBF) use diagonal braces that carry axial forces. Special CBF (SCBF, R = 6) requires braces to be designed for 1.5 times the nominal strength of the gusset plate connection, ensuring ductile brace buckling precedes brittle connection failure. The brace slenderness ratio KL/r is limited to 200 for SCBF. Eccentrically Braced Frames (EBF, R = 8) use a link beam segment designed to yield in shear or flexure, acting as a ductile fuse. Link length determines behavior: short links yield in shear (e ≤ 1.6Mp/Vp), long links yield in flexure (e ≥ 2.6Mp/Vp), and intermediate links experience combined yielding.
Base Isolation and Energy Dissipation Systems
Base isolation decouples the structure from ground motion by introducing flexible bearings at the foundation level, shifting the fundamental period to 2-4 seconds where spectral accelerations are substantially reduced. Lead rubber bearings (LRB) combine rubber layers for flexibility with a lead core for damping and wind resistance. High-damping rubber bearings use specially compounded rubber with 10-20% inherent damping. Friction pendulum bearings use a concave sliding surface with self-centering capability. The design displacement D_M = (g·S_D1·T_M)/(4·π²·B_M) where B_M is the damping reduction factor from ASCE 7 Chapter 17.
Energy dissipation devices (dampers) absorb seismic energy through various mechanisms. Viscous fluid dampers generate force proportional to velocity (F = C·v^α), reducing response without adding stiffness. Metallic yielding dampers (ADAS, TADAS, Buckling-Restrained Braces) dissipate energy through stable yielding in tension and compression. BRBs have a steel core that yields axially within a concrete-filled steel tube that prevents buckling — providing symmetrical hysteretic behavior with high energy dissipation. Friction dampers use clamped sliding surfaces with predetermined slip load to dissipate energy through Coulomb friction. The capacity design method ensures that all elements outside the intended energy dissipation zones have sufficient over-strength to remain elastic during the design earthquake.
Practice Exercises
Exercise 1: Design Spectrum Construction
Given Ss = 1.2g, S1 = 0.5g, Site Class D (Fa = 1.1, Fv = 1.7), Risk Category II, construct the ASCE 7-22 design response spectrum. Determine SDS, SD1, T0, Ts, and the spectral acceleration at T = 0.8 s.
Exercise 2: Base Shear Calculation
A 10-story steel special moment frame building (R = 8, Ie = 1.0) has SDS = 0.8g and SD1 = 0.4g. The building height is 40 m and the seismic weight per floor is 8000 kN (including roof). Using the ELF procedure, calculate the total base shear, period using the approximate formula, and the lateral force distribution. Verify with the Seismic Load Calculator.
Exercise 3: Story Drift Check
For the building in Exercise 2, the calculated story displacements at the 5th floor are: δxe = 25 mm from the ELF analysis. The story height is 3.8 m. The deflection amplification factor Cd = 5.5 for SMF. Compute the design story drift, check against the allowable drift limit for Risk Category II (Δa = 0.025hsx), and determine the stability coefficient θ for P-delta effects. The cumulative gravity load above the 5th floor is 48,000 kN.
Exercise 4: Ductile Detailing Requirements
A special moment frame column is 500 mm × 500 mm with 8-25 mm diameter longitudinal bars and 10 mm diameter hoops. f'c = 35 MPa, fy = 420 MPa. The clear height is 3.5 m. Determine the plastic hinge length lo, maximum hoop spacing in the hinge zone, and the minimum transverse reinforcement volumetric ratio per ACI 318-19. The design axial load Pu = 1800 kN.
Related Calculators
Seismic Load Calculator
Calculate base shear and lateral forces per ASCE 7 and Eurocode 8.
Wind Load Calculator
Compute wind loads per ASCE 7 for comparison with seismic loads.
Live and Dead Load Calculator
Estimate gravity loads for earthquake weight calculation.
RC Column Design Calculator
Design columns with interaction diagrams for seismic combinations.
RC Beam Design Calculator
Design beams for capacity-based seismic design.
Moment of Inertia Calculator
Compute section properties for stiffness and period calculation.
References
- ASCE/SEI 7-22. Minimum Design Loads and Associated Criteria for Buildings and Other Structures. American Society of Civil Engineers, 2022.
- EN 1998-1. Eurocode 8: Design of Structures for Earthquake Resistance. European Committee for Standardization, 2004.
- Chopra, A.K. Dynamics of Structures: Theory and Applications to Earthquake Engineering. 5th ed., Pearson, 2017.
- Clough, R.W. and Penzien, J. Dynamics of Structures. 3rd ed., CSI, 2003.
- Paulay, T. and Priestley, M.J.N. Seismic Design of Reinforced Concrete and Masonry Buildings. Wiley, 1992.
- FEMA P-749. Earthquake-Resistant Design Concepts. FEMA, 2010.
- Civil Engineering Handbook — Seismic Design chapter.
- Engineering Formula Library — Seismic design formulas.
- Engineering Standards Reference — ASCE 7, Eurocode 8 provisions.
- Engineering Glossary — Definitions of earthquake engineering terms.