Design response spectra are crucial tools in earthquake engineering. They graphically represent how structures respond to seismic ground motion, helping engineers determine design forces and displacements. By plotting spectral acceleration against vibration period, these spectra guide structural system selection and analysis.

Seismic coefficients play a key role in translating spectral data into design parameters. Factors like short-period and 1-second spectral accelerations, site coefficients, and importance factors are combined to calculate design forces. These coefficients help engineers tailor designs to specific site conditions and building importance.

Design Response Spectra Fundamentals

Interpretation of design response spectra

• Design response spectrum graphically represents maximum structural response to earthquake ground motion plots spectral acceleration against vibration period
• Short-period region reflects stiff structures' response (buildings)
• Constant acceleration region shows moderate-period structures' behavior
• Constant velocity region represents flexible structures' response (bridges)
• Constant displacement region indicates very flexible or isolated structures
• Seismic hazard level determines overall spectrum amplitude (PGA, 2% in 50 years)
• Site classification affects spectrum shape (soil vs rock)
• Importance factor scales spectrum based on structure criticality (hospitals vs residential)
• Used to determine design base shear, guide structural system selection, estimate max displacements

Calculation of seismic coefficients

• $S_s$ spectral response acceleration at short periods reflects high-frequency ground motion
• $S_1$ spectral response acceleration at 1-second period represents long-period motion
• $F_a$ short-period site coefficient amplifies or de-amplifies $S_s$ based on soil conditions
• $F_v$ long-period site coefficient modifies $S_1$ for site-specific effects
• Design spectral acceleration parameters:
  1. Calculate $S_{DS} = \frac{2}{3} F_a S_s$ for short-period design
  2. Compute $S_{D1} = \frac{2}{3} F_v S_1$ for 1-second period design
• Seismic design category determined using $S_{DS}$, $S_{D1}$, occupancy category (A to F)
• Seismic response coefficient $C_s = \frac{S_{DS}}{R/I_e}$
  • $R$ response modification factor accounts for ductility, overstrength (1.5 to 8)
  • $I_e$ importance factor prioritizes essential facilities (1.0 to 1.5)

Application of Seismic Coefficients and Site-Specific Factors

Application of seismic forces

• Seismic base shear $V = C_s W$ where $W$ effective seismic weight includes dead load, percentage of live load
• Vertical distribution of seismic forces $F_x = C_{vx} V$
  • $C_{vx}$ vertical distribution factor considers higher mode effects
• Story shears summed from top down, overturning moments calculated
• Accidental torsion accounts for mass eccentricity (typically 5% of building dimension)
• Orthogonal effects combine responses in principal directions (100-30 rule)
• Load combinations consider seismic forces with gravity, wind loads

Influence of soil on response spectra

• Site classes A (hard rock) to F (very poor soil) based on shear wave velocity, SPT, undrained shear strength
• Soft soils amplify ground motions, especially at long periods
• Stiff soils, rock generally have less amplification, may deamplify high frequencies
• Site-specific geotechnical investigations required for complex sites, tall structures
• Near-fault effects:
  1. Directivity pulses in fault-normal direction
  2. Fling step permanent ground displacement
• Basin effects prolong shaking duration, amplify long-period motions
• Topographic effects amplify motions at ridge tops, reduce in valleys
• Liquefaction potential assessed, may require special design considerations
• Site-specific spectra developed using:
  1. Probabilistic Seismic Hazard Analysis (PSHA) for risk-based design
  2. Deterministic Seismic Hazard Analysis (DSHA) for maximum considered scenarios