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Frequently Asked Questions (FAQ)
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In a dynamic analysis, you can only calculate as many mode shapes as the structural system has degrees of freedom. The degrees of freedom mean the number of mass points multiplied by the number of the directions in which the masses act.
A cantilever that is not split by the FE mesh has a mass point at the end. The action direction of the masses in RF‑/DYNAM Pro is limited to the X and Y direction. Thus, the system has 2 degrees of freedom, thus 2 mode shapes can only be calculated.
Please note: In this case, the selection of the method for solving eigenvalue problem is very important. In contrast to the "Root of the characteristic polynomial" method, the Lanczos method cannot calculate all eigenvalues of the system, but only n -1, which means only 1 eigenvalue in this example.
AnswerFor the design using Equivalent Member Method and General Method, there are four degrees of freedom considered in the eigenvalue solver. These are as follows:
If the RF‑/STEEL Warping Torsion add-on module is activated, there are seven degrees of freedom available:
- uY' (displacement from the plane)
- φX' (rotation about the X'-axis)
- φZ' (rotation about the Z'-axis)
- ω (warping)
- ux (displacement in x)
- uy (displacement in y)
- uz (displacement in z)
- φx (rotation about the x-axis)
- φy (rotation about the y-axis)
- φz (rotation about the z-axis)
- ω (warping)
AnswerThe defined stiffness modifications are only considered in the stability analysis in RF‑STABILITY if the "Activate Stiffness Modifications from RFEM" option under the "Options" section in Window "1.1 General Data" is selected.
AnswerYou can change the cross-section, generally adjust the model and its loads, or activate stabilization measures in STEEL EC3.The settings of rotational restraint and shear panel defined in window 1.12 Parameters - Members or 1.13 Parameters - Sets of Members, which are then considered in the module-internal eigenvalue solver to determine the critical load, are particularly suitable for this.
To display the mode shape, the calculation must be successfully performed. If this is not possible, there are either invalid boundary conditions or no stability problem was found (convergence not reached). No critical buckling shape can be considered then.
The modules perform the eigenvalue analysis for the entire model with a certain axial force state. Depending on the number of eigenvalues required, the programs provide results of crictical load factors with the corresponding buckling shapes for an eigenvalue, and effective length about the major and minor axis for each member per mode shape.
Since each load case LC and each load combination CO often has a different axial force state in the elements available, there is a separate respective effective length result for each load situation of the frame column concerned. The effective length, which causes the column in the frame plane buckles sideway in the buckling shape, is the correct length to be used for the analysis of the load situation.
However, this result may be different because of various load situation in each analysis, the longest effective length of all analyses performed applies in the design on the safe side equally for all load situations.
The so-called Sturm sequence check tests whether all eigenvalues were found in a certain interval. It uses the diagonal matrix from the Gauss decomposition whose number of negative diagonal elements, corresponds to the number of eigenvalues below the respective interval limit.
Therefore, the Sturm sequence check is used for the given interval limits and calculates the difference from them.
It can be determined as many eigenvalues as there are degrees of freedom in the structure to which a mass is assigned. In order to determine the number of degrees of freedom, the number of nodal points of FE nodes must be multiplied by the active mass directions. The masses in fixed supports are not considered for this as they cannot freely oscillate.
If the "Divison for straight members" (RFEM) / "internal member division" (RSTAB) is not activated, it may happen, for example in the case of single-span beams, that the masses only exist in the supports and thus no eigenvalue can be determined. In such cases, activate the member division as shown in the figures.
Since the Lanczos solver in RF-DYNAM Pro cannot determine all existing eigenvalues, the "root of the characteristic polynomial" solving method can also provide remedy.
RSBUCK uses a momentary representation of the axial force distribution in the respective load state. The axial forces are increased iteratively until the critical load case occurs. In the numerical analysis, the stability load is indicated by the fact that the determinant of the stiffness matrix becomes zero.
If the effective length factor is known, the buckling load and buckling mode are determined based on this. For the lowest buckling load, all effective lengths and effective length factirs are determined.
Example: Hinged column with a length of 20 m, cross-section HE‑B 500, self-weight load
For the first buckling mode, you obtain the effective length factor of kcr,y = 2.92 for the buckling about the major axis. For the buckling about the minor axis with a buckling load of 651.3 kN, you obtain an effective length factor of 1.00.
If you set the expression for determining the buckling load Ncr = π² * E * I / Lcr² to Lcr and apply Ncr = 651.3 kN and Iy = 107,200 cm4, you obtain the Lcr,y of 58.4 m, which results in the effective length factor kcr,y of 2.92.
In RSBUCK, there are two effective length factors determined for each buckling mode and buckling load.
In order to obtain the correct effective length factor for the deflection perpendicular to the y-axis (buckling about the major axis), it is necessary to calculate several buckling modes (mode shapes). The correct value is displayed in Window 2.1. In the example, it is the third buckling mode with a buckling load of 5485.5 kN. For this load, the effective lengths and effective length factors are determined as follows: kcr,y = 1.0 and kcr,z = 0.345.
In the case of a quadratic cross-section, two equal effective lengths result as the stiffnesses in both directions are the same.
Check if the settings for considering the favorable effect by tension forces are the same in RSTAB and RSBUCK.
RSTAB determines the critical load factor according to the nonlinear calculation method: The loading is increased gradually by the value of the load factor increment Δk until the system becomes unstable. On the other hand, RSBUCK performs a linear eigenvalue analysis. Therefore, the elements acting nonlinearly, such as failing members or supports, may have different effects in RSTAB and RSBUCK.
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Wind Simulation & Wind Load Generation
With the stand-alone program RWIND Simulation, wind flows around simple or complex structures can be simulated by means of a digital wind tunnel.
The generated wind loads acting on these objects can be imported to RFEM or RSTAB.
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