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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.
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.
Long-span glued-laminated beams are usually supported by a reinforced concrete column with torsional restraints.
In the case of tension connections with cleats subjected to unilateral loading, the external members (side timber) are loaded by an additional bending moment due to the eccentric load distribution. However, this fact is not mentioned in EN 1995‑1‑1 and is considered in the National Annex to DIN EN 1995‑1‑1 by the reduction of the tensile strength. This reduction depends on the pull-off strength of the fasteners.
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.
The new RFEM software generation provides the option to perform stability design of tapered timber members in line with the equivalent member method. According to this method, the design can be performed if the guidelines of DIN 1052, Section E8.4.2 for variable cross-sections are met. In various technical literature, this method is also adopted for Eurocode 5. This article demonstrates how to use the equivalent member method for a tapered roof girder.
As an alternative to the equivalent member method, this article describes the possibility to determine the internal forces of a wall at risk of buckling according to the second-order analysis, taking imperfections into account, and to subsequently perform the cross-section design for bending and compression.
The following article describes a design using the equivalent member method according to [1] Section 6.3.2, performed on an example of a cross-laminated timber wall susceptible to buckling described in Part 1 of this article series. The buckling analysis will be performed as a compressive stress analysis with reduced compressive strength. For this, the instability factor kc is determined, which depends primarily on the component slenderness and the support type.
Basically, you can design the structural components made of cross-laminated timber in the RF-LAMINATE add-on module. Since the design is a pure elastic stress analysis, it is necessary to additionally consider the stability issues (flexural buckling and lateral-torsional buckling).
In the RF-/TIMBER Pro, RF-/TIMBER AWC, and RF-/TIMBER CSA add-on modules, you can consider the resulting deformation of a member or set of members. In addition to the local directions y and z, you have the option "R." This allows you to compare the total deflection of a girder to the limit values given in the standards.
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 current literature, the formulas used to determine internal forces and deformations manually are usually specified without considering the shear deformation. The deformations resulting from shear force are often underestimated in timber construction in particular.
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 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.
The RX‑TIMBER stand-alone program offers you the option to optimize the lateral-torsional bracing. With this selection, the program iteratively determines the required minimum length of the lateral-torsional bracing.
There are several options for calculating a semi-rigid composite beam. They differ primarily in the type of modeling. Whereas the Gamma method ensures simple modeling, additional efforts are required when using other methods (for example, shear analogy) for the modeling which are, however, offset by the much more flexible application compared to the Gamma method.
The same structures are often needed in several projects, such as the purlin with columns and braces in this example. The dimensions can be changed directly in RFEM or RSTAB by shifting the nodes.
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 the default setting, the cross-section class for each member and load case is determined automatically in the design modules. In the input window of the cross sections, however, the user can also specify the cross-section class manually; for example, if local buckling is excluded by the design.
- 001555
- Modeling | Loading
- RFEM 5
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- RSTAB 8
- RF-TIMBER AWC 5
- TIMBER AWC 8
- RF-TIMBER CSA 5
- TIMBER CSA 8
- RF-TIMBER Pro 5
- TIMBER Pro 8
- RF-JOINTS Timber | Timber to Timber 5
- JOINTS Timber | Timber to Timber 8
- RF-JOINTS Timber | Steel to Timber 5
- JOINTS Timber | Steel to Timber 8
- RF-LIMITS 5
- LIMITS 8
- RF-LAMINATE 5
- Timber Structures
- Laminate and Sandwich Structures
- Structural Analysis & Design
- Finite Element Analysis
- Steel Connections
- Eurocode 0
- Eurocode 5
- ANSI/AISC 360
- SIA 260
- SIA 265
In addition to determining loads, some particularities concerning the load combinatorics in timber design have to be considered. Contrary to steel structures, where the largest loading results from all unfavorable actions, in timber construction, the strength values depend on the load duration and timber humidity. Special characteristics have to be considered as well for the serviceability limit state design. The following article discusses the effects on the design of wooden elements and how this is possible with RSTAB and RFEM.
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.
Slender bending beams that have a large h/w ratio and are loaded parallel to the minor axis tend to have stability issues. This is due to the deflection of the compression chord.
The previous article, titled Lateral-Torsional Buckling in Timber Construction | Examples 1, explains the practical application for determining the critical bending moment Mcrit or the critical bending stress σcrit for a bending beam's lateral buckling using simple examples. In this article, the critical bending moment is determined by considering an elastic foundation resulting from a stiffening bracing.
The article titled Lateral-Torsional Buckling in Timber Construction | Theory explains the theoretical background for the analytical determination of the critical bending moment Mcrit or the critical bending stress σcrit for the lateral buckling of a bending beam. This article uses examples to verify the analytical solution with the result from the eigenvalue analysis.
The joint type "Main member only" in RF‑/JOINTS Timber - Steel to Timber can also be applied for more than one connected member.
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.
The fundamental requirements of a structural system are (according to the basis of structural design) sufficient ultimate limit state, serviceability, and resistance. Structures must be designed in such a way that no damage occurs due to events such as the impact of a vehicle.
RF-/JOINTS Timber – Timber to Timber allows you to design main-connected beam joints. This article explains the determination of forces in screws of a beam connected to a torsionally rigid main beam.
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.
RF-CONCRETE Members for RFEM or CONCRETE for RSTAB propose an automatically created reinforcement to the user if the "Design the provided reinforcement" option is selected in Window 1.6 "Reinforcement".