Metody seizmické analýzy jsou základními nástroji v seizmickém inženýrství, které umožňují inženýrům vyhodnotit odezvu budov a infrastruktury na seizmické síly. Each method varies in complexity, accuracy, and computational demands, catering to different design scenarios, structural complexities, and seismic zones.
This article provides a comprehensive overview of essential seismic analysis methods, explaining their principles and applications, as well as the scenarios in which they are most effective. Once you understand these concepts, you can explore our next KB article, which illustrates how these methods can be implemented using the appropriate add-ons for RFEM 6/RSTAB 9.
Statická analýza
Equivalent Lateral Force Method
This method is one of the simplest approaches for estimating seismic forces. It is widely used for structures with a regular, symmetric configuration and relatively limited height. For such structures, the contribution of the first mode is typically dominant, with the modal participating mass ratio of the first mode shape often exceeding 70-80%, making it acceptable to consider only the first mode shape of the structure. Hence, the loading values are determined by distributing the base shear across each floor based on the first mode shape. This is achieved by defining a static force derived from the properties of the first mode.
Applications:
- Suitable for buildings with regular geometry and uniform mass distribution.
- Commonly used for (initial) design or code compliance checks.
Limitations:
- Ignores higher vibration modes and their contributions.
- Limited applicability to irregular or high-rise buildings.
Pushover Analysis Method
The pushover analysis method is another static method, but also a nonlinear one since it involves applying a static load combined with non-linear analysis. The structure is subjected to unit forces in the shape of the first mode, and the locations of plastic hinges are determined iteratively. This analysis provides the capacity spectrum, which, when compared with the selected response spectrum, reflects the structure's actual performance level. If the structure is irregular or tall—meaning that higher modes play a significant role—the modal pushover analysis should be used. In this case, both the first mode shape and higher modes are considered (like modal analysis).
Applications:
- The primary purpose of the push-over analysis is to assess the seismic performance of existing structures, making it especially valuable for retrofitting. It can be used to evaluate the effectiveness of proposed modifications.
- It is also useful for simplifying the structural behavior under horizontal loads. The resulting force-deformation curve (capacity curve) provides engineers with an intuitive way to interpret and understand the structure's behavior.
Limitations:
- Ignores higher vibration modes and their contributions.
- Commonly used in performance-based seismic design where the goal is to ensure that the structure performs adequately during a seismic event, rather than just meeting code-prescribed forces.
Dynamická analýza
Spektrální analýza
In response spectrum analysis, the eigenmodes of the structure are combined with the corresponding accelerations from the response spectrum. By weighting the mode shapes with their effective modal masses and applying the accelerations, a structural state—including resulting deformations and internal forces—can be derived without the need to create equivalent loads. The results from the individual modes are then combined using standardized combination techniques, with the most common being the SRSS (Square Root of the Sum of the Squares) rule.
Structures possess multiple degrees of freedom, leading to several mode shapes. The contribution of each mode shape is typically defined by the modal participating mass ratio, which represents the mass associated with each mode shape divided by the total mass of the structure. Since calculating for every mode is generally impractical, design codes allow the total participating modal mass ratio to exceed a certain percentage, though the exact threshold may vary depending on the specific code or annex being applied.
Applications:
- Applicable to buildings with no significant nonlinear behavior, where elastic analysis provides an adequate level of safety, or where the structural nonlinearity can be simplified using a behavior factor that accounts for inelastic behavior in the response spectrum analysis. This factor may be referred to by different names depending on the specific standard or code being used.
- For situations where the computational simplicity of RSA outweighs the need for detailed, time-dependent results.
Limitations:
- Assumes linear elastic behavior, making it unsuitable for structures expected to undergo significant nonlinear behavior that cannot be adequately handled using the behavior factor.
- Simplified representation of seismic Input: The design response spectrum used in RSA is typically derived from a simplified, idealized representation of ground motion.
Time-History Analysis
This method involves applying time-dependent ground motion records (accelerograms) to a structural model to simulate its response over time. It provides detailed results, including displacements, accelerations, and internal forces at each time step. The analysis can be either linear or nonlinear, depending on the way the material behavior and structural response are accounted for during the loading process. In the linear case, the structure is modeled assuming linear elastic behavior, while in the nonlinear case, the analysis accounts for both material and geometric nonlinearities. Therefore, nonlinear time history analysis is the most advanced approach, capturing the full range of material and geometric nonlinearity under time-dependent seismic loads.
Applications:
- Commonly used in detailed design stages or for structures in zones with high seismic activity.
- Essential for complex, irregular, or highly sensitive structures.
Limitations:
- Computationally intensive and time-consuming.
- Requires expertise in modeling and interpretation.
Závěr a výhled
Seismic analysis methods range from simple static approaches to highly detailed dynamic simulations, each serving specific design needs and structural complexities. Table 1 provides an overview of the trade-offs between complexity, accuracy, and the practical applications of each method. While the Equivalent Lateral Force Method suffices for regular low-rise buildings, advanced methods like Nonlinear Time History Analysis are indispensable for complex structures in zones with high seismic activity. The choice of method should balance accuracy, computational demands, and project requirements, ensuring resilient designs that protect lives and infrastructure during earthquakes.
| Metoda | Complexity | Accuracy | Main Use Cases |
|---|---|---|---|
| Equivalent Lateral Force (ELF) | Slabé | Low to Moderate | Used for preliminary seismic design, primarily in regular low- to mid-rise buildings where dynamic effects are not dominant. |
| Response Spectrum Analysis (RSA) | Mírné | Moderate to High | RSA is ideal for general seismic design and dynamic analysis of important structures where a time history analysis is impractical. |
| Pushover analýza | Moderate to High | Moderate to High (for nonlinear static cases) | Used for performance-based seismic design and for assessing progressive collapse in buildings. |
| Linear Time History Analysis (LTHA) | Vysoká | High (for linear behavior) | Applied in structures such as high-rise buildings and critical infrastructure which require detailed dynamic response evaluation when subjected to specific ground motions. |
| Nonlinear Time History Analysis (NLTHA) | Very High | Highest | Essential for structures with complex seismic demands, including base-isolated buildings, bridges, and structures with significant nonlinear behavior. |