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Seismic analysis
Seismic analysis
Seismic analysis
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First and second modes of building seismic response

Seismic analysis is a subset of structural analysis and is the calculation of the response of a building (or nonbuilding) structure to earthquakes. It is part of the process of structural design, earthquake engineering or structural assessment and retrofit (see structural engineering) in regions where earthquakes are prevalent.

As seen in the figure, a building has the potential to 'wave' back and forth during an earthquake (or even a severe wind storm). This is called the 'fundamental mode', and is the lowest frequency of building response. Most buildings, however, have higher modes of response, which are uniquely activated during earthquakes. The figure just shows the second mode, but there are higher 'shimmy' (abnormal vibration) modes. Nevertheless, the first and second modes tend to cause the most damage in most cases.

The earliest provisions for seismic resistance were the requirement to design for a lateral force equal to a proportion of the building weight (applied at each floor level). This approach was adopted in the appendix of the 1927 Uniform Building Code (UBC), which was used on the west coast of the United States. It later became clear that the dynamic properties of the structure affected the loads generated during an earthquake. In the Los Angeles County Building Code of 1943 a provision to vary the load based on the number of floor levels was adopted (based on research carried out at Caltech in collaboration with Stanford University and the United States Coast and Geodetic Survey, which started in 1937). The concept of "response spectra" was developed in the 1930s, but it wasn't until 1952 that a joint committee of the San Francisco Section of the ASCE and the Structural Engineers Association of Northern California (SEAONC) proposed using the building period (the inverse of the frequency) to determine lateral forces.[1]

The University of California, Berkeley was an early base for computer-based seismic analysis of structures, led by Professor Ray Clough (who coined the term finite element.[2] Students included Ed Wilson, who went on to write the program SAP in 1970, an early "finite element analysis" program.[3]

Earthquake engineering has developed a lot since the early days, and some of the more complex designs now use special earthquake protective elements either just in the foundation (base isolation) or distributed throughout the structure. Analyzing these types of structures requires specialized explicit finite element computer code, which divides time into very small slices and models the actual physics, much like common video games often have "physics engines". Very large and complex buildings can be modeled in this way (such as the Osaka International Convention Center).

Structural analysis methods can be divided into the following five categories.

Equivalent static analysis

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This approach defines a series of forces acting on a building to represent the effect of earthquake ground motion, typically defined by a seismic design response spectrum. It assumes that the building responds in its fundamental mode. For this to be true, the building must be low-rise and must not twist significantly when the ground moves. The response is read from a design response spectrum, given the natural frequency of the building (either calculated or defined by the building code). The applicability of this method is extended in many building codes by applying factors to account for higher buildings with some higher modes, and for low levels of twisting. To account for effects due to "yielding" of the structure, many codes apply modification factors that reduce the design forces (e.g. force reduction factors).[4]

Response spectrum analysis

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See also: Response spectrum

This approach permits the multiple modes of response of a building to be taken into account (in the frequency domain). This is required in many building codes for all except very simple or very complex structures. The response of a structure can be defined as a combination of many special shapes (modes) that in a vibrating string correspond to the "harmonics". Computer analysis can be used to determine these modes for a structure. For each mode, a response is read from the design spectrum, based on the modal frequency and the modal mass, and they are then combined to provide an estimate of the total response of the structure. In this we have to calculate the magnitude of forces in all directions i.e. X, Y & Z and then see the effects on the building. Combination methods include the following:

  • absolute – peak values are added together
  • square root of the sum of the squares (SRSS)
  • complete quadratic combination (CQC) – a method that is an improvement on SRSS for closely spaced modes

The result of a response spectrum analysis using the response spectrum from a ground motion is typically different from that which would be calculated directly from a linear dynamic analysis using that ground motion directly, since phase information is lost in the process of generating the response spectrum.

In cases where structures are either too irregular, too tall or of significance to a community in disaster response, the response spectrum approach is no longer appropriate, and more complex analysis is often required, such as non-linear static analysis or dynamic analysis.

Linear dynamic analysis

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Static procedures are appropriate when higher mode effects are not significant. This is generally true for short, regular buildings. Therefore, for tall buildings, buildings with torsional irregularities, or non-orthogonal systems, a dynamic procedure is required. In the linear dynamic procedure, the building is modelled as a multi-degree-of-freedom (MDOF) system with a linear elastic stiffness matrix and an equivalent viscous damping matrix.

The seismic input is modelled using either modal spectral analysis or time history analysis but in both cases, the corresponding internal forces and displacements are determined using linear elastic analysis. The advantage of these linear dynamic procedures with respect to linear static procedures is that higher modes can be considered. However, they are based on linear elastic response and hence the applicability decreases with increasing nonlinear behaviour, which is approximated by global force reduction factors.

In linear dynamic analysis, the response of the structure to ground motion is calculated in the time domain, and all phase information is therefore maintained. Only linear properties are assumed. The analytical method can use modal decomposition as a means of reducing the degrees of freedom in the analysis.

Nonlinear static analysis

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In general, linear procedures are applicable when the structure is expected to remain nearly elastic for the level of ground motion or when the design results in nearly uniform distribution of nonlinear response throughout the structure. As the performance objective of the structure implies greater inelastic demands, the uncertainty with linear procedures increases to a point that requires a high level of conservatism in demand assumptions and acceptability criteria to avoid unintended performance. Therefore, procedures incorporating inelastic analysis can reduce the uncertainty and conservatism.

This approach is also known as "pushover" analysis. A pattern of forces is applied to a structural model that includes non-linear properties (such as steel yield), and the total force is plotted against a reference displacement to define a capacity curve. This can then be combined with a demand curve (typically in the form of an acceleration-displacement response spectrum (ADRS)). This essentially reduces the problem to a single degree of freedom (SDOF) system.

Nonlinear static procedures use equivalent SDOF structural models and represent seismic ground motion with response spectra. Story drifts and component actions are related subsequently to the global demand parameter by the pushover or capacity curves that are the basis of the non-linear static procedures.

Nonlinear dynamic analysis

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Nonlinear dynamic analysis utilizes the combination of ground motion records with a detailed structural model, therefore is capable of producing results with relatively low uncertainty. In nonlinear dynamic analyses, the detailed structural model subjected to a ground-motion record produces estimates of component deformations for each degree of freedom in the model and the modal responses are combined using schemes such as the square-root-sum-of-squares.

In non-linear dynamic analysis, the non-linear properties of the structure are considered as part of a time domain analysis. This approach is the most rigorous, and is required by some building codes for buildings of unusual configuration or of special importance. However, the calculated response can be very sensitive to the characteristics of the individual ground motion used as seismic input; therefore, several analyses are required using different ground motion records to achieve a reliable estimation of the probabilistic distribution of structural response. Since the properties of the seismic response depend on the intensity, or severity, of the seismic shaking, a comprehensive assessment calls for numerous nonlinear dynamic analyses at various levels of intensity to represent different possible earthquake scenarios. This has led to the emergence of methods like the incremental dynamic analysis.[5]

See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Seismic analysis

View on Grokipedia
from Grokipedia
Seismic analysis is the process of evaluating a structure's response to earthquake-induced ground motions, a critical subset of that calculates dynamic forces, deformations, and accelerations to ensure safety and performance during seismic events. It encompasses the assessment of how buildings, bridges, and other interact with seismic waves, focusing on preventing collapse and minimizing damage through precise modeling of material behavior and site-specific hazards. The primary goal of seismic analysis is to achieve life safety by limiting collapse risk to approximately 1% over a 50-year period for typical structures, while also supporting operational continuity for critical facilities like hospitals. Key principles include accounting for ground shaking intensity, which varies by , fault proximity, and return periods of 475 to 2,475 years for design earthquakes, as well as structural —the ability to undergo inelastic deformations without failure. Analysis also considers irregularities such as soft stories or torsional effects that amplify vulnerabilities, integrating geotechnical factors like to predict realistic responses. Common methods range from simplified equivalent lateral force procedures, which distribute static loads based on base shear (V = C_s W, where C_s is the seismic coefficient and W is the structure's weight), to advanced dynamic approaches. Linear methods assume elastic behavior for initial designs, while nonlinear techniques, including pushover and response history , capture damage progression using time-history ground motions scaled to site hazards, requiring a minimum of 11 sets of records for statistical reliability. These analyses adhere to standards like ASCE/SEI 7-22, which define performance levels such as immediate and prevention, enabling engineers to balance cost, risk, and resilience in seismic-prone regions.

Overview and Fundamentals

Definition and Objectives

Seismic analysis is a subset of in that evaluates the response of , bridges, and other to earthquake-induced ground motions, aiming to predict deformations, forces, and accelerations to prevent collapse and limit damage. This process involves modeling seismic loads and assessing how structures interact with dynamic forces, ensuring designs incorporate and to absorb energy without . The primary objectives of seismic analysis are to safeguard human life, maintain structural integrity during and after earthquakes, and support operational continuity for critical facilities, while complying with established building codes such as ASCE 7 in the United States and Eurocode 8 in . These codes outline performance levels, from life safety in moderate events to collapse prevention in severe ones, emphasizing risk reduction through engineered resilience. Seismic analysis plays a crucial role in mitigating the devastating impacts of earthquakes, which caused an estimated 1.87 million deaths worldwide in the alone, highlighting the need to minimize both loss of life and economic disruptions from structural failures. Key terminology includes seismic zones, which delineate regions of elevated risk based on historical and fault activity; design response spectra, graphical representations of maximum expected structural responses (such as ) across varying periods for a given site; and base shear, the total horizontal force applied at the structure's base to simulate seismic demands. These concepts underpin the evaluation of site-specific hazards and guide the proportioning of structural elements.

Historical Development

The , one of the most destructive events in European history, marked a pivotal moment in the scientific study of earthquakes and spurred early innovations in earthquake-resistant construction. The disaster prompted the reconstruction of the city with techniques like the pombaline cage, a wooden lattice framework designed to enhance structural flexibility and reduce collapse risk during shaking. Throughout the , post-earthquake observations in regions like and documented patterns of structural failure, laying groundwork for empirical design rules, though formal seismic provisions remained limited. The early 20th century saw the emergence of the first seismic building codes. In , the 1923 Great Kanto Earthquake, which killed over 140,000 people, led to the revision of the Urban Building Law, introducing the world's first national seismic design standard with a minimum horizontal seismic coefficient of 0.1 to ensure structural stability. In the United States, followed suit in the 1930s; the (magnitude 6.4), which caused widespread damage to unreinforced masonry schools and resulted in 120 deaths, prompted the Field Act of 1933. This legislation mandated equivalent static analysis methods for public school buildings, applying lateral forces based on building weight and height to simulate seismic loads, and extended seismic provisions to statewide building codes for the first time. Mid-century advancements focused on more refined analytical tools. Maurice A. Biot developed the method in and 1940s, first outlined in his 1932 doctoral dissertation and subsequent publications, providing a way to characterize ground motions and predict maximum structural responses across frequencies—a foundational milestone for later dynamic analyses. The 1960s and 1970s brought the rise of time-history dynamic analysis, enabled by early computers at institutions like the , allowing engineers to model nonlinear structural behavior under actual records. The (magnitude 6.7), which exposed limitations in linear models by causing unexpected damage to modern buildings, accelerated the adoption of nonlinear static and dynamic methods to better capture material yielding and . In the 21st century, seismic analysis evolved toward performance-based and probabilistic frameworks. The Federal Emergency Management Agency's FEMA 356 (2000) prest Standard established guidelines for performance-based seismic design and rehabilitation, defining objectives like life safety and collapse prevention under varying hazard levels to guide nonlinear evaluations. Probabilistic seismic hazard analysis, incorporating site-specific ground motion uncertainties, became integral to modern codes like ASCE 7. The 2011 Tohoku Earthquake (magnitude 9.0), while validating Japan's stringent codes by limiting structural collapses, influenced updates to address long-period motions in high-rise designs and enhanced tsunami-resistant provisions in building standards. Key figures in this progression include George W. Housner, whose work on seismic force distributions shaped code development; Nathan M. Newmark, who advanced methods for distributing seismic shears in multistory buildings; and Anil K. Chopra, whose textbooks on structural dynamics provided essential frameworks for earthquake response analysis.

Key Concepts in Structural Dynamics

Structural dynamics forms the foundational framework for understanding how buildings and other structures respond to seismic excitations, such as ground motions. At its core, this discipline models structures as systems that vibrate under dynamic loads, where the response depends on the system's , , and properties. These concepts are essential for seismic analysis, as they enable engineers to predict displacements, velocities, and accelerations that could lead to structural damage or collapse. A single-degree-of-freedom (SDOF) represents the simplest model in , idealizing a structure as a single connected to a fixed base by a spring and damper, with motion constrained to one direction. The equation of motion for an SDOF subjected to ground acceleration u¨g(t)\ddot{u}_g(t) is given by mu¨(t)+cu˙(t)+ku(t)=−mu¨g(t)m\ddot{u}(t) + c\dot{u}(t) + ku(t) = -m\ddot{u}_g(t), where mm is the , cc is the viscous , kk is the , u(t)u(t) is the relative displacement of the with to the ground, u˙(t)\dot{u}(t) is the relative velocity, and u¨(t)\ddot{u}(t) is the relative acceleration. This equation derives from Newton's second law applied to the free-body diagram of the , incorporating the inertial from ground motion as the external excitation. The natural of the undamped is ωn=k/m\omega_n = \sqrt{k/m}
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