Earthquake Engineering Terminology: Response Spectrum, Fragility Curve, Ground Motion Scaling, and Incremental Dynamic Analysis

 

 Earthquake Engineering Terminology

 What Does “Spectrum” Mean in Earthquake Engineering?

In earthquake engineering, a spectrum is a graph that shows how strongly an earthquake affects structures with different natural vibration periods.

In simple words:

An earthquake spectrum tells us how much a structure will shake depending on how flexible or stiff it is.

 

Why a Spectrum Is Needed

Different buildings respond differently to the same earthquake:

• Short, stiff buildings → shake fast
• Tall, flexible buildings → shake slowly

The spectrum captures all these possible responses in one graph.

 

What Is Plotted in an Earthquake Spectrum?

Horizontal Axis (X-axis)

• Natural period (T) in seconds
  (sometimes frequency instead)

Vertical Axis (Y-axis)

One of the following:

• Spectral acceleration (Sa) – most common
• Spectral velocity (Sv)
• Spectral displacement (Sd)

 

What Is Response Spectrum? (Most Important)

A response spectrum is created by:

1.   Taking one earthquake ground motion record

2.   Applying it to many single-degree-of-freedom (SDOF) systems

3.   Each system has a different natural period

4.   Recording the maximum response of each system

The plot of these maximum responses = response spectrum

 

Types of Earthquake Spectra

1. Acceleration Response Spectrum (Sa–T)

• Most widely used
• Used for:
• Design
• Base shear calculation
• Code spectra

2. Velocity Response Spectrum (Sv–T)

• Useful for energy-based analysis

3. Displacement Response Spectrum (Sd–T)

• Important for:
• Drift control
• Performance-based design

 

 

Role of Damping in Spectrum

Spectra depend on damping ratio:

• Standard value: 5%
• Higher damping → lower spectral values
• Lower damping → higher spectral values

That is why spectra are always written as:

“5% damped response spectrum”

 

Simple Definition

An earthquake spectrum is a graphical representation of the maximum response of single-degree-of-freedom systems with different natural periods subjected to the same ground motion.

 

What Is a Target Spectrum?

A target spectrum is a reference response spectrum that represents the expected earthquake demand at a site.

In simple terms:

Target spectrum = “How strong the earthquake shaking is expected to be for different vibration periods of a structure.”

It tells us:

• How much acceleration, velocity, or displacement a structure may experience
• At different natural periods (T)

Why Do We Need a Target Spectrum?

Target spectra are used to:

1.   Design structures (code-based seismic design)

2.   Scale earthquake records for:

o    Nonlinear time-history analysis

o    Performance-based design

3.   Compare structural demand vs capacity

In performance-based engineering:

Ground motions are scaled so their response spectra match the target spectrum.

Types of Target Spectra

1. Design Response Spectrum (Most Common)

Used in code-based design.

2. Uniform Hazard Spectrum (UHS)

• Same probability of exceedance at all periods
• Used in advanced performance-based design

3. Conditional Mean Spectrum (CMS)

• Conditioned at a specific period (very realistic)
• Used in modern nonlinear analysis

 

Simple Definition

A target spectrum is a site-specific response spectrum representing the expected seismic demand, used as a reference for structural design and scaling of ground motion records.

 

Fragility curve

In earthquake engineering, a fragility curve is a probabilistic relationship that quantifies how likely a structure is to reach or exceed a specified damage state when subjected to a given level of earthquake intensity.

Think of a fragility curve as answering this question:

“If an earthquake of this strength occurs, what is the probability that my building will suffer moderate damage, severe damage, or collapse?”

Axes of a Fragility Curve

Horizontal Axis (X-axis): Earthquake Intensity Measure (IM)

Common choices:

• Peak Ground Acceleration (PGA)
• Spectral Acceleration
• Peak Ground Velocity (PGV)
• Intensity measures from response spectra

Vertical Axis (Y-axis): Probability (0 to 1)

• 0 → No chance of damage
• 1 → Certain damage

 

what is scaling in Scaling Ground Motions

Scaling is the application of a scale factor to a ground-motion time history so that one or more of its intensity measures (IMs) match a prescribed target level required by seismic design codes or performance-based assessment procedures.

Mathematically:

Where,

• = ground acceleration time history
• = scale factor

 

Scaling of ground motions is the process of adjusting the amplitude of recorded earthquake accelerograms so that their intensity level is compatible with a target seismic demand, typically defined by a design or target response spectrum.

 

For each seismic hazard level you are analyzing, you must use at least 11 different earthquake records as a group.

 

The MCE_R response spectrum represents the maximum site-specific seismic demand with very low probability of exceedance, while the design response spectrum is obtained by reducing the MCE_R spectrum by two-thirds to account for inelastic structural behavior and is used for routine structural design.

 

Incremental Dynamic Analysis (IDA)

 

Incremental Dynamic Analysis (IDA) is a nonlinear dynamic analysis procedure in which a structural model is subjected to a suite of ground motion records, each scaled incrementally to increasing intensity levels, in order to trace the entire structural response from elastic behavior to collapse.

 

Purpose of IDA

IDA is used to:

• Quantify collapse capacity
• Develop fragility curves
• Evaluate performance-based seismic design
• Assess uncertainty and record-to-record variability