30.15. Use of Spectral Acceleration in Performance-Based Design (PBD)

• Sa is used in pushover analysis and nonlinear time-history analysis to determine demand at different performance levels (IO, LS, CP).

In performance-based design (PBD), the use of spectral acceleration (Sa) goes beyond traditional linear elastic design approaches. Linear elastic design primarily considers structures' behavior under immediate or minimal load conditions, meaning they return to their original form after an earthquake. However, structures often experience more severe conditions during actual earthquakes, requiring a deeper understanding of their performance.
To address this, engineers utilize methods such as pushover analysis and nonlinear time-history analysis. Pushover analysis involves applying a gradually increasing load to the structure until it reaches its yield point, helping assess its capacity under various conditions. Nonlinear time-history analysis allows engineers to simulate the structure's response over time during an earthquake, providing a more realistic prediction of performance.

Imagine a bridge designed to hold 10 cars at once. A linear elastic design would assume that if the weight of cars exceeds this limit, the bridge would either hold or break. However, in real-life scenarios, a bridge might bend and flex under a more significant weight but not necessarily collapse immediately. Thus, engineers akin to bridge designers would investigate how much the bridge can safely bend under different scenarios, ensuring it's safe for use under inclement conditions, just like they analyze how buildings behave in an earthquake.

• Spectral acceleration is plotted against spectral displacement to form: – Demand spectrum (from hazard) – Capacity curve (from structure) • Their intersection gives performance point.

In performance-based design, two essential concepts are the demand spectrum and capacity curve. The demand spectrum represents the expected seismic demand on a structure during an earthquake, illustrated as a plot of spectral acceleration against spectral displacement. This shows the forces that might act on a building based on seismic hazard assessments. On the other hand, the capacity curve represents the building's ability to withstand those forces, illustrating how much displacement the structure can endure before failure.
By plotting both the demand spectrum and the capacity curve on the same graph, engineers can identify the intersection point. This point represents the 'performance point,' where the structure’s capacity meets the seismic demand. Understanding this intersection allows engineers to determine if a design meets safety standards during potential seismic events.

Consider a trampoline. The more weight you put on the trampoline (demand), the more it stretches downward (displacement). The trampoline's edges (capacity curve) show how much it can stretch before someone might fall off. The point where the weight you're applying meets the trampoline's maximum stretch illustrates its 'performance point.' Similar to how understanding this helps avoid accidents, engineers need to understand the performance point of buildings to prevent them from failing during earthquakes.

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