To evaluate whether it is also necessary to consider the second-order analysis in a dynamic calculation, the sensitivity coefficient of interstory drift θ is provided in EN 1998‑1, Sections 2.2.2 and 4.4.2.2. It can be calculated and analyzed using RFEM 6 and RSTAB 9.
For the ultimate limit state design, EN 1998‑1, Sections 2.2.2 and 4.4.2.2 require a 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.
Both the determination of natural vibrations and the response spectrum analysis are always performed on a linear system. If nonlinearities exist in the system, they are linearized and thus not taken into account. They are caused by, for example, tension members, nonlinear supports, or nonlinear hinges. This article shows how you can handle them in a dynamic analysis.
To be able to evaluate the influence of local stability phenomena of slender structural components, RFEM 6 and RSTAB 9 provide you with the option of performing a linear critical load analysis on the cross-section level. The following article explains the basics of the calculation and the result interpretation.
The design of cold-formed steel members according to the AISI S100-16 is now available in RFEM 6. Design can be accessed by selecting “AISC 360” as the standard in the Steel Design add-on. “AISI S100” is then automatically selected for the cold-formed design (Image 01).
The dynamic analysis in RFEM 6 and RSTAB 9 is divided into several add-ons. The Modal Analysis add-on is a prerequisite for all other dynamic add-ons, since it performs the natural vibration analysis for member, surface, and solid models.
Modal analysis is the starting point for the dynamic analysis of structural systems. You can use it to determine natural vibration values such as natural frequencies, mode shapes, modal masses, and effective modal mass factors. This outcome can be used for vibration design, and it can be used for further dynamic analyses (for example, loading by a response spectrum).
RF-/DYNAM Pro - Equivalent Loads allows you to determine the loads due to equivalent seismic loads according to the multi‑modal response spectrum method. In the example shown here, this was done for a multi‑mass oscillator.
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.
Both the determination of natural vibrations and the response spectrum analysis are always performed on a linear system. If nonlinearities exist in the system, they are linearized and thus not taken into account. Straight tension members are very often used in practice. This article will show how you can display them approximately correctly in a dynamic analysis.
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.
When introducing and transferring horizontal loads such as wind or seismic loads, increasing difficulties arise in 3D models. To avoid such issues, some standards (for example, ASCE 7, NBC) require the simplification of the model using diaphragms that distribute the horizontal loads to structural components transferring loads, but cannot transfer bending themselves (called "Diaphragm").
DIN EN 1998-1 with the National Annex DIN EN 1998-1/NA specifies how to determine seismic loads. The standard applies to structural engineering in seismic areas.
In RF-DYNAM Pro - Equivalent Loads, the equivalent seismic loads can be calculated according to different standards. By calculating the equivalent loads for each eigenmode, it is not directly possible to obtain the transversal shear for each story to perform an analysis afterwards. The following example describes the option to calculate the transversal shear quickly and efficiently.
In a multi-modal response spectrum analysis, it is important to determine a sufficient number of eigenvalues of the structure and to consider their dynamic responses. Regulations such as EN 1998‑1 [1] and other international standards require the activation of 90% of the structural mass. This means: to determine so many eigenvalues that the sum of the effective modal mass factors is greater than 0.9.
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.
The new RF‑/DYNAM Pro - Natural Vibrations module has been available since RFEM version 5.04.xx and RSTAB version 8.04.xx were released. Masses can now be imported directly from load cases and load combinations.