33.16. Use of Design Spectrum in Performance-Based Design

33.16.1 Performance Objectives

• Operational (minor damage)
• Life safety (moderate damage)
• Collapse prevention (major damage)

Design spectra are modified based on performance levels and hazard exceedance probabilities.

Performance objectives set the goals for how a structure should behave under seismic loads. They are categorized into three main levels:

1. Operational - This implies that the structure experiences minor damage that does not affect its functionality. An example could be a school where small cracks appear but students can continue classes.
2. Life Safety - At this level, moderate damage is acceptable, but the structure must protect the occupants from serious harm. For example, an office building may require minor repairs after an earthquake but is safe for occupancy.
3. Collapse Prevention - This is the most critical level, where the structure must remain standing during a severe earthquake to prevent loss of life, even if it becomes unusable afterward. Think of a hospital where ensuring that the building is still standing during an earthquake is vital for emergency services. The design spectrum is modified to ensure that these performance levels are met based on the probability of a certain earthquake happening in the area, indicating how often these performance levels should be able to withstand seismic events.

Imagine a children's playground designed for safety. The swings might be intended to be safe for everyday use (operational), the climbing frame should be resilient enough for children to play without risk (life safety), and structures like tall slides must be designed to tolerate extreme weather or seismic events without collapsing (collapse prevention). Just like the playground is designed with safety in mind at various usage levels, buildings are designed with different performance objectives depending on their use and the likelihood of earthquakes.

33.16.2 Demand-Capacity Ratios

• Spectrum used to estimate demand
• Compared against structural capacity curves (pushover analysis)

Demand-capacity ratios are crucial for assessing a structure's ability to handle seismic loads. This process involves two main concepts:

1. Demand - This refers to the seismic forces that the structure is expected to experience, represented by the design spectrum. Engineers use this spectrum to analyze how much load the building might endure during an earthquake.
2. Capacity - This represents the ability of the structure to resist these forces, determined through analysis methods like pushover analysis. This method involves subjecting the structure to increasing lateral forces until it reaches its limit, allowing engineers to see where it might fail. To ensure safety, the demand placed on the structure during an earthquake must not exceed its capacity. Engineers often express this relationship as a ratio: if the demand-capacity ratio is above 1, the structure may not withstand anticipated seismic events and require enhancements.

Think of a tightrope walker trying to perform acrobatics with a safety harness. The 'demand' is the stress experienced by the rope when the performer shifts their weight, while the 'capacity' is the weight limit of the harness. The tightrope walker aims to stay well within the limits of the harness to ensure safety. Similarly, in building design, engineers need to ensure that the forces expected during an earthquake do not exceed the structural limits to keep the building safe.

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