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.
The three types of moment frames (Ordinary, Intermediate, Special) are available in the Steel Design add-on of RFEM 6. The seismic design result according to AISC 341-22 is categorized into two sections: member requirements and connection requirements.
The National Building Code of Canada (NBC) 2020 Article 4.1.8.7 provides a clear procedure for earthquake methods of analysis. The more advanced method, the Dynamic Analysis Procedure in Article 4.1.8.12, should be used for all structure types except those that meet the criteria set forth in 4.1.8.7. The more simplistic method, the Equivalent Static Force Procedure (ESFP) in Article 4.1.8.11, can be used for all other structures.
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. The coefficient θ is calculated as follows:$$\mathrm\theta\;=\;\frac{\displaystyle{\mathrm P}_\mathrm{tot}\;\cdot\;{\mathrm d}_\mathrm r}{{\mathrm V}_\mathrm{tot}\;\cdot\;\mathrm h}\;$$
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.
The Steel Design add-on in RFEM 6 now offers the ability to perform seismic design according to AISC 341-16 and AISC 341-22. Five types of seismic force-resisting systems (SFRS) are currently available.
The three types of moment frames (Ordinary, Intermediate, Special) are available in the Steel Design add-on of RFEM 6. The seismic design result according to AISC 341-16 is categorized into two sections: member requirements and connection requirements.
Moment frame design according to AISC 341-16 is now possible in the Steel Design add-on of RFEM 6. The seismic design result is categorized into two sections: member requirements and connection requirements. This article covers the required strength of the connection. An example comparison of the results between RFEM and the AISC Seismic Design Manual [2] is presented.
The design of an Ordinary Concentrically Braced Frame (OCBF) and a Special Concentrically Braced Frame (SCBF) can be carried out in the Steel Design add-on of RFEM 6. The seismic design result according to AISC 341-16 and 341-22 is categorized into two sections: Member Requirements and Connection Requirements.
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.
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 earthquakes so far that the 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 moderate this disadvantage is to use the equivalent linear combination when combining the modal responses. This article explains this option by describing an example.
The events of recent years remind us of the importance of earthquake engineering in seismic regions. For you as an engineer, the design of structures in earthquake-prone areas is a constant trade-off between economic efficiency – the financial possibilities – and structural safety. If a collapse is inevitable, engineers must estimate how it will affect the structure. This article aims to provide you with an option on how to perform this estimation.
The goal of using the RFEM 6 and Blender with the Bullet Constraints Builder add-on is to obtain a graphical representation of the collapse of a model based on real data of physical properties. RFEM 6 serves as the source of geometry and data for the simulation. This is another example of why it is important to maintain our programs as so-called BIM Open, in order to achieve collaboration across software domains.
Plastic hinges are imperative for the Pushover Analysis (POA) as a nonlinear static method for the seismic analysis of structures. In RFEM 6, plastic hinges can be defined as member hinges. This article will show you how to define plastic hinges with bilinear properties.
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).
In RFEM 6, seismic analysis can be done by using the Modal Analysis and the Response Spectrum Analysis add-ons. Once the spectral analysis has been performed, it is possible to use the Building Model add-on to display story actions, interstory drifts, and forces in shear walls.
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.
Blast loads from high-energy explosives, either accidental or intentional, are rare but may be a structural design requirement. These dynamic loads differ from standard static loads due to their large magnitude and very short duration. A blast scenario can be carried out directly in an FEA program as a time history analysis to minimize loss of life and evaluate varying levels of structural damage.
With the RF-/TIMBER Pro add-on module, you can perform the vibration design known from DIN 1052 for the design according to EN 1995-1-1. In this design, the deflection under permanent and quasi-permanent action at the ideal one‑span beam may not exceed the limit value (6 mm according to DIN 1052). If you consider the relation between the natural frequency and the deflection for a hinged single-span beam subjected to a constant distributed load, the 6 mm limit value results in a minimum natural frequency of about 7.2 Hz.
In RFEM, you can modify stiffnesses for materials, cross-sections, members, load cases, and load combinations in many places. There are two options in RF‑DYNAM Pro for considering these modifications when determining the natural frequencies.
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 National Building Code of Canada (NBC) 2015 Article 4.1.8.7 provides a clear procedure for earthquake methods of analysis. The more advanced method, the Dynamic Analysis Procedure in Article 4.1.8.12, should be used for all structure types except those that meet the criteria set forth in 4.1.8.7. The more simplistic method, the Equivalent Static Force Procedure (ESFP) in Article 4.1.8.11, can be used for all other structures.
In this article, representations of a blast scenario of a remote detonation performed in RF-DYNAM Pro - Forced Vibrations are shown, and the effects are compared in the linear time history analysis.
The steady state for periodically excited structures can be determined by means of the modal analysis in the DYNAM Pro - Forced Vibrations add-on module. This is an advantage if only the structure's steady state is of interest. Instead of a complete solution of the equation of motion, only a special solution is displayed.
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.