r4.05.01 Seismic response by transient analysis

Summary

The most frequently used methods for the seismic analysis of structures are spectral methods and transient methods.

Transient methods (direct linear or not, by modal synthesis) make it possible to calculate the response of structures under the effect of imposed earthquakes: single excitation (identical at each of the anchor points of the structure) or multiple and to take into account their possible non-linear behavior.

As far as spectral methods are concerned, the maximum response, for each vibration mode, of each anchor point is calculated. The maximum response of the whole structure, on average, in a statistical sense, is then determined by combining the maximum responses of the modes. This type of analysis is explained in the reference documentation [R4.05.03].

Table of Contents

• 1. Seismic behavior of a structure
  • 1.1. Definitions
• 2. Seismic response of a system to one degree of freedom
• 3. Seismic response of a system with several degrees of freedom
  • 3.1. Equations of motion in the absolute coordinate system
  • 3.2. Equations of motion in the relative coordinate system
  • 3.3. Calculation of seismic loading
  • 3.4. Incident wave charging
• 4. Transient seismic response by modal synthesis
  • 4.1. Description of the method
  • 4.2. Choosing the modal base
  • 4.3. Taking into account non-linear forces in the dynamic response of the structure studied by modal synthesis
  • 4.4. Calculation of the dynamic response of the studied structure by modal synthesis
  • 4.5. Taking into account neglected modes by static correction
  • 4.6. Taking into account the multi-supported nature of a structure
  • 4.7. Post-treatments
• 5. Direct transient seismic response
  • 5.1. Taking into account depreciation equivalent to modal depreciation
  • 5.2. Taking into account a multi-support request with the restoration of relative and absolute fields
• 6. Soil-structure interaction
  • 6.1. Impedance of a foundation
  • 6.2. Taking into account modal depreciation calculated according to the RCC -G rule
  • 6.3. Stiffness distribution and ground damping
  • 6.4. Taking into account an absorbent border
• 7. Bibliography
• 8. Description of document versions