- 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)
RF-/DYNAM Pro - Forced Vibrations | Features of Multi-Modal Response Spectrum Analysis
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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 an analysis can be carried out 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, Sections 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. The coefficient θ is defined as follows:
$$\mathrm\theta\;=\;\frac{\displaystyle{\mathrm P}_\mathrm{tot}\;\cdot\;{\mathrm d}_\mathrm r }{{\mathrm V}_\mathrm{tot}\;\cdot\;\mathrm h}\;(1)$$
where
θ is the interstory drift sensitivity coefficient,
Ptot is the total gravity load at and above the story considered in the seismic design situation (see Expression 2),
dr is the design interstory drift, evaluated as the difference of the average lateral displacements dS at the top and bottom of the story under consideration; for this, the displacement is determined using the linear design response spectrum with q = 1.0,
Vtot is the total seismic story shear determined using the linear design response spectrum,
h is the interstory height.
$$\mathrm\theta\;=\;\frac{\displaystyle{\mathrm P}_\mathrm{tot}\;\cdot\;{\mathrm d}_\mathrm r }{{\mathrm V}_\mathrm{tot}\;\cdot\;\mathrm h}\;(1)$$
where
θ is the interstory drift sensitivity coefficient,
Ptot is the total gravity load at and above the story considered in the seismic design situation (see Expression 2),
dr is the design interstory drift, evaluated as the difference of the average lateral displacements dS at the top and bottom of the story under consideration; for this, the displacement is determined using the linear design response spectrum with q = 1.0,
Vtot is the total seismic story shear determined using the linear design response spectrum,
h is the interstory height.
In this article, you will learn how to model and design cable structures in RFEM 6 or RSTAB 9.
![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=350&hash=dd36dc43123116724231958668ad6cdcb13a0169)
- 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)
Due to the integration of RF‑/DYNAM Pro in RFEM / RSTAB, you can incorporate numeric and graphic results from RF‑/DYNAM Pro – Forced Vibrations in the global printout report. Also, all RFEM options are available for a graphical visualization.
The results of the time history analysis are displayed in a time course monitor. All results are displayed as a function of time. You can export the numeric values to MS Excel.
In the case of a time history analysis, you can export results of the individual time steps or filter most unfavourable results of all time steps.
The response spectrum analysis generates result combinations. Internally, the modal contributions and the directional components of earthquake actions are combined.
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.
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 next procedure to perform the design of the individual structural components?
Why can I only calculate seismic loads in one direction when using RF‑/DYNAM Pro?
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?
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