Earthquake engineering is a critical discipline that enables engineers to predict the forces acting on structures during seismic events and design safer buildings. Today, various analytical methods are used to evaluate the seismic performance of structures. These methods are generally classified into two main categories:
Linear analysis methods assume that structures behave within their elastic limits during earthquake loading. This approach provides engineers with a practical and reliable method during the design stage.
In Türkiye, seismic design calculations are governed by the Turkish Building Earthquake Code (TBEC 2018). Within the scope of linear seismic analysis, the two most widely used methods are:
These methods differ in the way earthquake effects are represented and calculated on structures.
Linear seismic analysis assumes that structural elements remain within their elastic behavior limits during an earthquake. In this approach, structural stiffness is considered constant and nonlinear material behavior such as plastic deformation is not explicitly modeled.
In reality, structures often experience inelastic deformations during strong earthquakes. However, instead of modeling this complex nonlinear behavior directly, seismic design codes represent it using a behavior factor (R factor) which reduces the elastic seismic forces.
The main advantages of this approach include:
In linear seismic analysis, earthquake effects can be represented in two different ways:
These approaches correspond to the Equivalent Seismic Load Method and the Response Spectrum Analysis respectively.
The Equivalent Seismic Load Method represents earthquake effects through equivalent static lateral forces applied to the structure.
In reality, earthquake motion is a dynamic and time-dependent phenomenon. However, this method simplifies seismic effects by representing them as statically applied lateral loads distributed along the height of the building.
The fundamental assumption of this method is:
The seismic behavior of the structure is dominated by the first vibration mode.
Based on this assumption, the total earthquake force is calculated as a base shear force, which is then distributed to the building floors according to predefined rules.
Calculation of Base Shear Force
The first step in the equivalent seismic load method is the calculation of the total seismic base shear force acting at the base of the structure.
This force depends on several parameters:
The calculated base shear force represents the total horizontal force expected to act on the structure during an earthquake.
Distribution of Seismic Forces Along the Building Height
Once the total base shear force is determined, it is distributed to each floor level of the structure.
The distribution is based on two primary parameters:
In general, upper floors experience larger seismic forces because they tend to undergo greater lateral displacements during seismic excitation.
This distribution approximates the first-mode vibration shape of the structure.
This method is widely used in engineering practice due to several important advantages.
Simplicity of calculations
The method follows a static analysis approach, making modeling and solution processes relatively straightforward.
Efficient for preliminary design
It is particularly useful during the early stages of design when different structural system alternatives are evaluated.
Reliable for regular structures
For low- and mid-rise regular buildings, the method provides sufficiently accurate results.
Limitations of the Method
Despite its practicality, the equivalent seismic load method may not provide sufficiently accurate results in certain situations.
The method may become inadequate in cases such as:
In such cases, representing the entire structural response with a single vibration mode becomes insufficient. Therefore, more advanced dynamic analysis methods such as Response Spectrum Analysis are required.
Response Spectrum Analysis is a linear dynamic analysis method that evaluates the seismic behavior of structures as a multi-degree-of-freedom dynamic system.
In this method, earthquake effects are not modeled directly in the time domain. Instead, the analysis uses a design acceleration response spectrum, which represents the maximum expected structural response to earthquake excitation.
The analysis procedure generally follows these steps:
For this reason, the method is commonly referred to as Modal Response Spectrum Analysis.
Every structure has a set of natural vibration modes determined by its mass and stiffness distribution.
These modes are typically defined as:
In many structures, the first mode dominates the overall seismic behavior. However, in taller or irregular structures, higher modes may contribute significantly to the structural response.
Therefore, a sufficient number of vibration modes must be included in the analysis.
Modal Mass Participation Ratio
The number of modes included in the analysis is determined based on specific criteria.
According to TBEC 2018:
This requirement ensures that the seismic response of the structure is adequately represented.
The structural responses obtained for each vibration mode represent independent maximum values. Therefore, they cannot be directly summed.
Instead, modal results are combined using statistical methods.
The most common modal combination techniques include:
SRSS (Square Root of the Sum of Squares)
A method based on the square root of the sum of the squared modal responses.
CQC (Complete Quadratic Combination)
A more advanced method that accounts for the correlation between closely spaced vibration modes.
When modal periods are close to each other, the CQC method is generally preferred.
Response spectrum analysis offers several important advantages compared to simplified static approaches.
More realistic representation of structural behavior
The dynamic characteristics of the structure are explicitly considered.
Inclusion of higher-mode effects
This is especially important for tall structures.
More reliable for irregular buildings
Torsional effects and structural irregularities can be captured more accurately.
The main difference between the equivalent seismic load method and response spectrum analysis lies in how earthquake forces are represented.
In the Equivalent Seismic Load Method, earthquake forces are modeled as a single static lateral load distribution applied to the structure.
In Response Spectrum Analysis, the structure is evaluated as a multi-modal dynamic system, and the contribution of each vibration mode is calculated separately.
For this reason, response spectrum analysis is generally considered a more comprehensive and advanced method.
Seismic analysis plays a critical role in ensuring structural safety during earthquake events. Linear analysis methods provide practical and reliable solutions during the design stage.
The Equivalent Seismic Load Method offers a fast and efficient approach for regular and relatively low-rise buildings. On the other hand, Response Spectrum Analysis provides a more advanced analytical framework capable of accurately modeling the dynamic behavior of complex structures.
In modern structural engineering practice, especially for tall and irregular buildings, Modal Response Spectrum Analysis has become one of the most widely used seismic analysis methods.
Advancements in seismic analysis techniques allow engineers to better evaluate structural performance and design safer structures capable of withstanding earthquake forces.