Seismic Response Spectrum Simulator: Earthquake Design Tool

simulator advanced ~12 min
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Sa = 0.72 g — T=0.5 s, ζ=5%, PGA=0.3 g

A structure with 0.5 s natural period and 5% damping on moderate soil (S=1.2) under 0.3 g PGA experiences a spectral acceleration of 0.72 g — 2.4 times the ground acceleration due to dynamic amplification.

Formula

Sa(T) = PGA · S · 2.5 · (Tc/T) for T > Tc
Sd = Sa · T² / (4π²)
η = √(10/(5+ζ)) ≥ 0.55 (damping correction)

Earthquakes & Dynamic Amplification

An earthquake shakes the ground, but the forces a building experiences depend on its own dynamic properties. A structure acts as a filter: it amplifies ground motion at frequencies near its natural frequency and attenuates others. This phenomenon — dynamic amplification — means a building can experience forces several times greater than the ground motion itself. The response spectrum captures this amplification across all possible natural periods, providing the essential design tool for earthquake engineering.

The Response Spectrum

A design response spectrum has three distinct regions. At very short periods (stiff structures), spectral acceleration equals the PGA. In the constant-acceleration plateau (typically 0.1-0.5 s), amplification reaches 2.5× PGA. At longer periods, spectral acceleration decreases inversely with period as structures become flexible enough to partially isolate themselves from ground shaking. This simulation draws the full spectrum and highlights where your structure sits on the curve.

Damping & Energy Dissipation

All real structures have some inherent damping — energy lost through material hysteresis, friction at connections, and interaction with non-structural elements. Typical values are 2% for steel frames, 5% for reinforced concrete, and 7% for masonry. Higher damping reduces the resonance peak dramatically. Modern seismic design often adds supplemental damping devices: viscous fluid dampers, friction dampers, or tuned mass dampers that can increase effective damping to 15-20%, cutting seismic forces nearly in half.

Soil Effects & Site Classification

The journey of seismic waves from bedrock to the surface fundamentally depends on soil conditions. Soft clay deposits can amplify bedrock motion by factors of 2-3, particularly at periods matching the soil's natural period. This site amplification effect is captured by the soil factor S in design codes. The 1985 Mexico City earthquake and 2011 Christchurch earthquake both demonstrated catastrophic soil amplification. Site classification (rock, stiff soil, soft soil) is therefore one of the first steps in any seismic design.

FAQ

What is a response spectrum?

A response spectrum is a plot of the maximum response (acceleration, velocity, or displacement) of single-degree-of-freedom oscillators as a function of their natural period, all subjected to the same ground motion. It distills a complex earthquake time history into a design tool that tells engineers what forces their structure will experience.

What is peak ground acceleration (PGA)?

PGA is the maximum acceleration recorded at the ground surface during an earthquake, expressed as a fraction of gravitational acceleration (g). A PGA of 0.3 g means the ground accelerated at about 3 m/s². Seismic hazard maps specify design PGA values based on location and return period.

How does damping reduce seismic response?

Damping dissipates vibration energy as heat, reducing the amplitude of oscillation at each cycle. Increasing damping from 2% to 5% typically reduces spectral acceleration by 25-30%. Supplemental damping devices — viscous dampers, friction dampers, or tuned mass dampers — can dramatically improve seismic performance.

Why does soil type affect seismic response?

Soft soils amplify ground motion, especially at longer periods. Seismic waves slow down in soft soil, increasing amplitude (conservation of energy). The 1985 Mexico City earthquake dramatically demonstrated this: buildings on the lake bed (soft clay) suffered far more damage than identical buildings on rock, because the soft soil amplified the 2-second period waves that matched the buildings' natural frequency.

Sources

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