As you've already learned, the results of a Modal Analysis load case are displayed in the program after a successful calculation. You can thus immediately see the first mode shape graphically or as an animation. You can also easily adjust the representation of the mode shape standardization. Do that directly in the Results navigator, where you have one of four options for the visualization of the mode shapes available for the selection:
- Scaling the value of the mode shape vector uj to 1 (considers the translation components only)
- Selecting the maximum translational component of the eigenvector and setting it to 1
- Considering the entire eigenvector (including the rotation components), selecting the maximum, and setting it to 1
- Setting the modal mass mi for each mode shape to 1 kg
You can find a detailed explanation of the mode shape standardization in the OnlineManual here.
Is the calculation finished? The results of the modal analysis are then available both graphically and in tables. Display the result tables for the load case or the load cases of the modal analysis. Thus, you can see the eigenvalues, angular frequencies, natural frequencies, and natural periods of the structure at first glance. The effective modal masses, modal mass factors, and participation factors are also clearly displayed.
You can perform the calculation of the warping torsion on the entire system. Thus, you consider the additional 7th degree of freedom in the member calculation. The stiffnesses of the connected structural elements are automatically taken into account. It means, you don't need to define equivalent spring stiffnesses or support conditions for a detached system.
You can then use the internal forces from the calculation with warping torsion in the add-ons for the design. Consider the warping bimoment and the secondary torsional moment, depending on the material and the selected standard. A typical application is the stability analysis according to the second-order theory with imperfections in steel structures.
Did you know that The application is not limited to thin-walled steel cross-sections. Thus, it is possible for you, for example, to perform the calculation of the ideal overturning moment of beams with solid timber cross-sections.
- Response spectra in accordance with different standards
- The following standards are implemented:
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EN 1998-1:2010 + A1:2013 (European Union)
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DIN 4149:1981-04 (Germany)
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DIN 4149:2005-04 (Germany)
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IBC 2000 (USA)
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IBC 2009-ASCE/SEI 7-05 (USA)
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IBC 2012/15 - ASCE/SEI 7-10 (USA)
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IBC 2018 - ASCE/SEI 7-16 (USA)
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ÖNORM B 4015:2007-02 (Austria)
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NTC 2018 (Italy)
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NCSE-02 (Spain)
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SIA 261/1:2003 (Switzerland)
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SIA 261/1:2014 (Switzerland)
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SIA 261/1: 2020 (Switzerland)
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O.G. 23089 + OG 23390 (Turkey)
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SANS 10160-4 2010 (South Africa)
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SBC 301:2007 (Saudi Arabia)
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GB 50011 - 2001 (China)
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GB 50011 - 2010 (China)
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NBC 2015 (Canada)
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DTR BC 2-48 (Algeria)
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DTR RPA99 (Algeria)
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CFE Sismo 08 (Mexico)
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CIRSOC 103 (Argentina)
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NSR - 10 (Colombia)
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IS 1893:2002 (India)
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AS1170.4 (Australia)
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NCh 433 1996 (Chile)
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- The following National Annexes according to EN 1998‑1 are available:
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DIN EN 1998-1/NA:2011-01 (Germany)
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ÖNORM EN 1991-1-1:2011-09 (Austria)
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NBN - ENV 1998-1-1: 2002 NAD-E/N/F (Belgium)
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ČSN EN 1998-1/NA:2007 (Czech Republic)
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NF EN 1998-1-1/NA:2014-09 (France)
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UNI-EN 1991-1-1/NA:2007 (Italy)
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NP EN 1998-1/NA:2009 (Portugal)
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SR EN 1998-1/NA:2004 (Romania)
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STN EN 1998-1/NA:2008 (Slovakia)
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SIST EN 1998-1:2005/A101:2006 (Slovenia)
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CYS EN 1998-1/NA:2004 (Cyprus)
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NA to BS EN 1998-1:2004:2008 (United Kingdom)
- NS-EN 1998-1:2004 + A1:2013/NA:2014 (Norway)
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- User-defined response spectra
- Direction-relative response spectrum approach
- Relevant mode shapes for the response spectrum can be selected manually or automatically (5% rule from EC 8 can be applied)
- Generated equivalent static loads are exported to load cases, separately for each modal contribution and separately for each direction
- Result combinations by modal superposition (SRSS and CQC rule) and direction superposition (SRSS or 100% / 30% rule)
- Signed results based on the dominant eigenmode can be displayed
Is your goal to determine the number of mode shapes? The program offers you two methods for this. On the one hand, you can manually define the number of the smallest mode shapes to be calculated. In this case, the number of available mode shapes depends on the degrees of freedom (that is, the number of free mass points multiplied by the number of directions in which the masses act). However, it is limited to 9999. On the other hand, you can set the maximum natural frequency the way that the program determined the mode shapes automatically until reaching the natural frequency set.
- Consideration of 7 local deformation directions (ux, uy, uz, φx, φy, φz, ω) or 8 internal forces (N, Vu, Vv, Mt,pri, Mt,sec, Mu, Mv, Mω) when calculating member elements
- Usable in combination with a structural analysis according to linear static, second-order, and large deformation analysis (imperfections can also be taken into account)
- In combination with the Stability Analysis add-on, allows you to determine critical load factors and mode shapes of stability problems such as torsional buckling and lateral-torsional buckling
- Consideration of end plates and transverse stiffeners as warping springs when calculating I-sections with automatic determination and graphical display of the warping spring stiffness
- Graphical display of the cross-section warping of members in the deformation
- Full integration with RFEM and RSTAB
- Response spectra of numerous standards (ASCE 7-16, NBC 2015, etc.)
- User-defined response spectra or those generated from accelerograms
- Direction-relative response spectrum approach
- Manual or automatic selection of the relevant mode shapes of response spectra (5% rule of EC 8 applicable)
- Result combinations by modal superimposition (SRSS or CQC rule) and by direction superimposition (SRSS or 100% / 30% rule)
The results of warping torsion analysis are displayed in RF-/STEEL AISC and RF-/STEEL EC3 in the usual way. Among other results, the corresponding result windows include the critical warping and torsional values, internal forces, and design summary.
The graphical display of mode shapes (incl. warping) enables a realistic assessment of buckling behavior.
After the calculation, the eigenvalues, natural frequencies, and natural periods are listed. These result windows are integrated in the main program RFEM/RSTAB. The mode shapes of the structure are included in tables and can be displayed graphically or as an animation.
All result tables and graphics are part of the RFEM/RSTAB printout report. This way, clearly arranged documentation is ensured. Furthermore, it is possible to export the tables to MS Excel.
Input windows require all data necessary for determination of natural frequencies, such as mass shapes and eigenvalue solvers.
The RF-/DYNAM Pro - Natural Vibrations add-on module determines the lowest eigenvalues of the structure. The number of eigenvalues can be adjusted. Masses are directly imported from load cases or load combinations (with optional consideration of total masses or a load component in the direction of gravity).
Additional masses can be defined manually at nodes, lines, members, or surfaces. Furthermore, it is possible to control the stiffness matrix by importing normal forces or stiffness modifications of a load case or combination.
- You can activate or deactivate the use of torsional warping in the Add-ons tab of the model's Base Data.
- After activating the add-on, the user interface in RFEM is extended by some new entries in the navigator, tables, and dialog boxes.
- Combination of user-defined time diagrams with load cases or load combinations (nodal, member, and surface loads, as well as free and generated loads, can be combined with time-variable functions)
- Combination of several independent excitation functions
- Extensive library of seismic events (accelerograms)
- Linear implicit Newmark analysis or modal analysis in time history
- Structural damping using Rayleigh damping coefficients or Lehr's damping
- Direct import of initial deformations from a load case or combination
- Graphical display of results in a time history diagram
- Export of results in user-defined time steps or as an envelope
Calculation in RFEM
The nonlinear time history analysis is performed with the implicit Newmark analysis or the explicit analysis. Both are direct time integration methods. The implicit analysis requires small time steps to provide precise results. The explicit analysis determines the required time step automatically to provide the stability to the solution. The explicit analysis is suitable for the analysis of short excitations, such as impulse excitation, or an explosion.
Calculation in RSTAB
The nonlinear time history analysis is performed with the explicit analysis. This is a direct time integration method and determines the required time step automatically in order to provide the solution stability.
The equivalent load analysis calculation generates load cases and result combinations. The load cases include the generated equivalent loads, which are subsequently superimposed in result combinations. First, the modal contributions are superimposed with the SRSS or CQC rule. Signed results based on the dominant mode shape are possible.
Afterwards, the directional components of earthquake actions are combined with the SRSS or the 100% / 30% rule.
Did you know that Equivalent static loads are generated separately for each relevant eigenvalue and excitation direction. These loads are saved in a load case of the Response Spectrum Analysis type and RFEM/RSTAB performs a linear static analysis.
Have you already discovered the tabular and graphical output of masses in mesh points? That's right, this is also part of the modal analysis results in RFEM 6. This way, you can check the imported masses that depend on various settings of the modal analysis. They can be displayed in the Masses in Mesh Points tab of the Results table. The table provides you with an overview of the following results: Mass - Translational Direction (mX, mY, mZ), Mass - Rotational Direction (mφX, mφY, mφZ), and the Sum of Masses. Would it be best for you to have a graphical evaluation as quickly as possible? Then you can also graphically display the masses in mesh points.
Due to the integration of RF‑/DYNAM Pro in RFEM / RSTAB, you can incorporate numeric and graphic results from RF‑/DYNAM Pro – Forced Vibrations in the global printout report. Also, all RFEM options are available for a graphical visualization.
The results of the time history analysis are displayed in a time course monitor. All results are displayed as a function of time. You can export the numeric values to MS Excel.
In the case of a time history analysis, you can export results of the individual time steps or filter most unfavourable results of all time steps.
The response spectrum analysis generates result combinations. Internally, the modal contributions and the directional components of earthquake actions are combined.
It is necessary to enter the required response spectra, accelerations, or time diagrams. Dynamic load cases define the location and direction of response spectra effects as well as acceleration time, or force-time excitations.
Timing diagrams are combined with static load cases, which provides great flexibility. For the time history analysis, you can import the initial deformation from any load case or load combination.
The input parameters relevant for the selected standards are suggested by the program in accordance with the rules. Furthermore, it is possible to enter response spectra manually. Dynamic load cases define a direction of response spectra effects and the structure eigenvalues that are relevant for the analysis.
- User-defined time diagrams as a function of time, in tabular form, or as harmonic loads
- Combination of the time diagrams with RFEM/RSTAB load cases or combinations (enables definition of nodal, member, and surface loads, as well as free and generated loads varying over time)
- Combination of several independent excitation functions
- Nonlinear time history analysis with the implicit Newmark analysis (RFEM only) or the explicit analysis
- Structural damping using Rayleigh damping coefficients or Lehr's damping
- Direct import of initial deformations from a load case or combination (RFEM only)
- Stiffness modifications as initial conditions; for example, axial force effect, deactivated members (RSTAB only)
- Graphical display of results in a time history diagram
- Export of results in user-defined time steps or as an envelope
The RF-DYNAM Pro - Natural Vibrations module of RFEM provides four powerful eigenvalue solvers:*Root of characteristic polynomial
- Method by Lanczos
- Subspace Iteration
- ICG iteration method (Incomplete Conjugate Gradient)
The DYNAM Pro - Natural Vibrations module for RSTAB provides two eigenvalue solvers:
- Subspace Iteration
- Shifted inverse power method
The selection of the eigenvalue solver depends primarily on the size of the model.
Due to the integration of RF‑/DYNAM Pro in RFEM or RSTAB, you can incorporate numeric and graphic results from RF‑/DYNAM Pro - Nonlinear Time History to the global printout report. Also, all RFEM and RSTAB options are available for a graphical visualization. The results of the time history analysis are displayed in a time history diagram.
The results are displayed as a function of time and the numerical values can be exported to MS Excel. Result combinations can be exported, either as a result of a single time step or the most unfavorable results of all time steps are filtered out.
Equivalent static loads are generated separately for each relevant eigenvalue and excitation direction. They are exported to static load cases to perform the linear static analysis in RFEM/RSTAB.
The time history analysis is performed with the modal analysis or the linear implicit Newmark analysis. The time history analysis in this add‑on module is restricted to linear systems. Although the modal analysis represents a fast algorithm, it is necessary to use a certain number of eigenvalues to ensure the required accuracy of results.
The implicit Newmark analysis is a very precise method, independent of the number of eigenvalues used, but requires sufficient small time steps for calculation. For the response spectra analysis, equivalent static loads are calculated internally. A linear static analysis is performed subsequently.
- Nonlinear member types, such as tension and compression members or cables
- Member nonlinearities, such as failure, tearing, yielding under tension or compression
- Support nonlinearities, such as failure, friction, diagram, and partial activity
- Release nonlinearities, such as friction, partial activity, diagram, and fixed if positive or negative internal forces
Since RF-/STEEL Warping Torsion is fully integrated in RF-/STEEL AISC and RF‑/STEEL EC3, the data are entered in the same way as for the usual design in these modules. It is only necessary to select the option "Perform warping analysis" in the Details dialog box, tab Warping Torsion (see the figure on the right). You can also define the maximum number of iterations in this dialog box.
The warping torsion analysis is performed for sets of members in RF-/STEEL AISC and RF‑/STEEL EC3. You can define boundary conditions such as nodal supports or member end releases for them.
It is also possible to specify imperfections for the nonlinear calculation.
The load cases of the type Response Spectrum Analysis contain the generated equivalent loads. First, the modal contributions have to be superimposed with the SRSS or CQC rule. In this case, you can use the signed results based on the dominant mode shape.
Afterwards, the directional components of earthquake actions are combined with the SRSS or the 100% / 30% rule.
Did you know? You can easily define structural modifications in load cases of the Modal Analysis type. This allows you, for example, to individually adjust the stiffnesses of materials, cross-sections, members, surfaces, hinges, and supports. You can also modify stiffnesses for some design add-ons. Once you select the objects, their stiffness properties are adapted to the object type. In this way, you can define them in separate tabs.
Do you want to analyze the failure of an object (for example, a column) in the modal analysis? This is also possible without any problems. Simply switch to the Structure Modification window and deactivate the relevant objects.
- Automatic consideration of masses from self-weight
- Direct import of masses from load cases or load combinations
- Optional definition of additional masses (nodal, linear, surface masses, as well as inertia masses)
- Combination of masses in different mass cases and mass combinations
- Preset combination coefficients according to EC 8
- Optional import of normal force distributions (in order to consider prestress, for example)
- Stiffness modification (for example, deactivated members or stiffnesses can be imported from RF-/CONCRETE)
- Consideration of failed supports or members
- Definition of several natural vibration cases (for example, to analyze different masses or stiffness modifications)
- Results of eigenvalue, angular frequency, natural frequency, and period
- Determination of mode shapes and masses in nodes or FE mesh points
- Results of modal masses, effective modal masses, and modal mass factors
- Visualization and animation of mode shapes
- Various scaling options for mode shapes
- Documentation of numerical and graphical results in the printout report
- Applicable for members defined as sets of members
- Separate solver that considers 7 deformation directions (ux, uy, uz, φx, φy, φz, ω) or 8 internal forces (N, Vu, Vv, Mt,pri, Mt,sec, Mu, Mv, Mω)
- Nonlinear design according to second-order analysis
- Input of imperfections
- Calculation of critical load factors and buckling mode shapes as well as the visualization of them (incl. warping)
- Integration into member design in the RF-/STEEL AISC and RF‑/STEEL EC3 add‑on modules
- Available for all thin‑walled steel cross‑sections