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The response spectrum analysis is one of the most frequently used design methods in the case of earthquakes. This method has many advantages. The most important is the simplification: It simplifies the complexity of an earthquake to such an extent that a design can be performed with reasonable effort. The disadvantage of this method is that a lot of information is lost due to this simplification. One way to mitigate this disadvantage is to use the equivalent linear combination when combining the modal responses. This article explains this option by describing an example.
In order to consider inaccuracies regarding the position of masses in a response spectrum analysis, standards for seismic design specify rules that have to be applied in both the simplified and multi-modal response spectrum analyses. These rules describe the following general procedure: The story mass must be shifted by a certain eccentricity, which results in a torsional moment.
![Reduction of Building to Cantilever Structure: The individual mass points represent the floors. The deflection due to the normal compression forces shown in (a) is (b) converted into equivalent moments of displacement or shear forces [2].](/en/webimage/009762/2420261/01-en-png-12-png.png?mw=512&hash=8189361dbff525c2ff39c36a72a1ca91810208f6)
For the ultimate limit state design, EN 1998-1 Section 2.2.2 and 4.4.2.2 [1] requires the calculation considering the second-order theory (P-Δ effect). This effect may be neglected only if the interstory drift sensitivity coefficient θ is less than 0.1.
This article* explores the role of the Design Response Spectrum across different seismic analysis methods, demonstrating its significance from simplified static approaches up to advanced dynamic simulations.
- Response spectra of numerous standards (ASCE 7-16, NBC 2015, etc.)
- User-defined response spectra or those generated from accelerograms
- Direction-relative response spectrum approach
- Manual or automatic selection of the relevant mode shapes of response spectra (5% rule of EC 8 applicable)
- Result combinations by modal superimposition (SRSS or CQC rule) and by direction superimposition (SRSS or 100% / 30% rule)
The time history analysis is performed with the modal analysis or the linear implicit Newmark analysis. The time history analysis in this add‑on module is restricted to linear systems. Although the modal analysis represents a fast algorithm, it is necessary to use a certain number of eigenvalues to ensure the required accuracy of results.
The implicit Newmark analysis is a very precise method, independent of the number of eigenvalues used, but requires sufficient small time steps for calculation. For the response spectra analysis, equivalent static loads are calculated internally. A linear static analysis is performed subsequently.
It is necessary to enter the required response spectra, accelerations, or time diagrams. Dynamic load cases define the location and direction of response spectra effects as well as acceleration time, or force-time excitations.
Timing diagrams are combined with static load cases, which provides great flexibility. For the time history analysis, you can import the initial deformation from any load case or load combination.
- Combination of user-defined time diagrams with load cases or load combinations (nodal, member, and surface loads, as well as free and generated loads, can be combined with time-variable functions)
- Combination of several independent excitation functions
- Extensive library of seismic events (accelerograms)
- Linear implicit Newmark analysis or modal analysis in time history
- Structural damping using Rayleigh damping coefficients or Lehr's damping
- Direct import of initial deformations from a load case or combination
- Graphical display of results in a time history diagram
- Export of results in user-defined time steps or as an envelope
RF‑/DYNAM Pro – Forced Vibrations and RF‑/DYNAM Pro – Equivalent Loads perform the multi-modal response spectrum analysis. What are the differences?
I have used the RF‑/DYNAM Pro add-on module to generate the governing result combinations of seismic loads. What is the subsequent procedure to carry out the design of the individual structural components?
Warum bekomme ich bei einer Berechnung mit RF-/DYNAM Pro nur Erdbebenlasten in eine Richtung berechnet?
How can I enter or read out a response spectrum via the COM interface in DYNAM Pro?
How many mode shapes do I need to consider in the dynamic analysis?
Is there any option to generate a "response spectrum according to the standard" with user-defined parameters in the RF‑DYNAM Pro add-on module?
