The ASCE 7-22 Standard [1], Sect. 12.9.1.6 specifies when P-delta effects should be considered when running a modal response spectrum analysis for seismic design. In the NBC 2020 [2], Sent. 4.1.8.3.8.c gives only a short requirement that sway effects due to the interaction of gravity loads with the deformed structure should be considered. Therefore, there may be situations where second-order effects, also known as P-delta, must be considered when carrying out a seismic analysis.
This article presents the basic concepts in structural dynamics and their role in the seismic design of structures. Great emphasis is given to explaining the technical aspects in an understandable way, so that readers without deep technical knowledge can gain an insight into the subject.
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.
This article will show you the Building Model add-on, which has been enhanced with one important advantage: calculating the center of mass and center of rigidity.
The “Modal Analysis” add-on in RFEM 6 allows you to perform modal analysis of structural systems, thus determining natural vibration values such as natural frequencies, mode shapes, modal masses, and effective modal mass factors. These results can be used for vibration design, as well as for further dynamic analyses (for example, loading by a response spectrum).
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).
Seismic Analysis in RFEM 6 is possible using the modal analysis and the response spectrum analysis add-ons. As a matter of fact, the general concept of the earthquake analysis in RFEM 6 is based on the creation of a load case for the modal analysis and the response spectrum analysis, respectively. The standard groups for these analyses are set in the Standards II tab of the model’s Base Data.
Building Model is one of the special solution add-ons in RFEM 6. It is an advantageous tool for modeling, with which building stories can be created and manipulated easily. Building Model can be activated at the beginning of the modeling process and afterwards.
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.
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").
The story drift of a building provides valuable information about its structural behavior under seismic loads. These could cause large horizontal deformations and even instabilities. Some standards, therefore, call for a check of the story drift in its center of gravity. It indicates, for example, if a second-order analysis (P-Δ effect) is necessary.
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.
As of the version 5.06.1103, masses of nodes, lines, members, and surfaces can be neglected in RF‑DYNAM Pro. The setting to activate this feature can be found in the Details dialog box; the neglected masses are valid for all defined mass cases.
In the DYNAM Pro add‑on module for RSTAB, you can now neglect masses that may have a negative effect on the equivalent mass factor when calculating eigenvalues. To do this, you can disable the masses under [Details]. These include primarily mass points located in the support of the structures.
In RF-/DYNAM Pro - Natural Vibrations, it is possible to transfer complete load cases/load combinations as masses. To do this, you can simply save the load case or the load combination to be considered as a mass case in the add‑on module.
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.