How can you compare static and dynamic earthquake-resistant structures?

1 Static analysis

Static analysis is a method of evaluating the seismic response of a structure by applying a simplified equivalent lateral force to each floor or mass point. The equivalent lateral force is proportional to the seismic weight of the structure and the seismic coefficient, which depends on the site conditions, the importance of the structure, and the ductility of the system. Static analysis is relatively easy and fast to perform, but it has some limitations. It assumes that the structure behaves linearly and elastically, and that the earthquake loading is uniform and constant. It also neglects the effects of higher modes of vibration, damping, and soil-structure interaction.

2 Dynamic analysis

Dynamic analysis is a method of evaluating the seismic response of a structure by solving the equations of motion for each degree of freedom. The equations of motion account for the inertia, stiffness, and damping of the structure, as well as the external forces from the ground motion. Dynamic analysis can be linear or nonlinear, depending on whether the structure remains elastic or experiences inelastic deformations. Dynamic analysis can also be modal or direct, depending on whether the structure is decomposed into its natural modes of vibration or solved as a whole. Dynamic analysis is more accurate and realistic than static analysis, but it requires more computational resources and data.

3 Response spectrum analysis

Response spectrum analysis is a type of linear dynamic analysis that uses a response spectrum curve to represent the peak response of a structure to a given ground motion. A response spectrum curve shows the maximum displacement, velocity, or acceleration of a single-degree-of-freedom system with different natural periods and damping ratios. Response spectrum analysis is based on the assumption that the response of a structure is dominated by its fundamental mode of vibration, and that the responses of different modes are uncoupled and can be superimposed. Response spectrum analysis is simpler and faster than direct dynamic analysis, but it does not capture the effects of mode shapes, mode coupling, and higher modes.

4 Time history analysis

Time history analysis is a type of direct dynamic analysis that uses a time history record to represent the ground motion. A time history record shows the variation of ground displacement, velocity, or acceleration with time at a specific location. Time history analysis can be linear or nonlinear, depending on the behavior of the structure. Time history analysis is the most comprehensive and realistic method of dynamic analysis, but it requires a large amount of data and computation. It also depends on the selection and scaling of the time history record, which may not reflect the actual or probable ground motion at the site.

5 Performance-based design

Performance-based design is a modern approach to earthquake-resistant design that aims to achieve specific performance objectives for a structure under different levels of seismic hazard. Performance objectives can be expressed in terms of structural damage, nonstructural damage, functionality, or safety. Performance-based design requires the use of nonlinear dynamic analysis to assess the capacity and demand of the structure, as well as the use of probabilistic methods to quantify the seismic hazard and the performance criteria. Performance-based design is more flexible and rational than conventional design based on prescriptive codes, but it also involves more uncertainty and complexity.

6 Comparison criteria

When comparing static and dynamic earthquake-resistant structures, there are several criteria to consider, such as cost, safety, and functionality. Generally, dynamic structures are more expensive than static ones; however, they may also have lower repair costs and higher resilience in the event of an earthquake. In terms of safety, dynamic structures are typically safer than static ones; however, they may require more complex analysis and testing. Regarding functionality, dynamic structures are usually more functional than static ones; however, they may have more complex and sensitive systems that need to be restored.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?