7. Results of analysis (part 1)
A. Display of results
The INSTANT steel suite provides a separate module to display and post-process the analysis results. This module also enables spectral analysis and the definition of various loading cases combinations as specified by the norms, as well as the calculation of envelopes and stresses. To open this module use the INSTANT steel – Linear 3D menu Analysis → Results. The following descriptions refer to the module INSTANT steel – Results.
When the “Results” module opens, it immediately displays the current structure and reads the node displacements from the first loading case solution and draws the deformed shape of the structure.
To display the results of a different loading case, select it either from the menu Loading → Static that will bring up the static loading cases dialog, or from the combo-box control.
Selecting the “Displacements” icon will allow access to the node displacement results. While this icon is selected, a click on any structure node will bring up a window that displays the displacements and rotations of that node under the current loading, as can be seen in the following image. In a similar way, the reactions can be displayed by selecting the “Reactions” icon and clicking on any support node.
Selecting the “Internal forces” icon will enable the display of beam internal forces diagrams. The beam can either be selected individually, as in the default mode, shown by the activation status of the “Select beams” icon, or as a collinear group, by activating the “Select collinear beams” icon. In the dialog that appears after beam selection, select the internal forces and moments that you want displayed (Fx, Fy, Fz, Mx, My, Mz). The results along the selected beams will be drawn in a diagram for each force and/or moment. By clicking at any point along the diagram, the exact results will be displayed in the right side fields. The following image shows the Mz diagram for the rafter of an inner frame.
Another method of displaying results is in tabular form by using the commands List → Displacement, List → Reactions and List → Forces from the program menu. In the dialog that appears, the results can be sorted by minimum – maximum by selecting a cell in the desired result column and pressing the “Min…Max” button.
To display the structure Eigenvectors use the command Loading → Free vibrations. The program provides information about every computed Eigenvector (period, frequency, modal mass participation factors). To enhance the visualization of the Eigenvector shape, an animated deformed structure can be displayed by selecting the “Animation” icon.
The seismic loading is defined using the Loading → Spectral command. The program allows definition of seismic loading conforming to norms EAK, Eurocode 8 and the Romanian P100-1/2004 specification. In this example the EC8 norm will be used. After selecting it, press the Modes button to select the modes that will be used in the spectral analysis.
In the dialog “Spectral data – Modes”, the periods of the free vibration modes and the modal masses are displayed in separate lists for each axis. In the lower part of the dialog are the lists of modes that will be used in the spectral analysis to determine the forces and displacements along the X, Y and Z directions. Modes can be selected individually from the upper lists and copied to the lower ones, or the “Assign” button can be used to automatically add all modes which have at least 1% of the total modal mass participation for each axis. In this example, the vertical component of the seismic action will be ignored; as a result the option will be left unchecked. In general, it is necessary to include as many Eigenmodes as possible to achieve a sum of minimum 90 % of the total modal mass participation in every direction. In this example this criterion has been met for both X and Z direction. After defining the modes, close the dialog by pressing the OK button and return to the “Spectral Analysis Data” dialog.
Press the “Spectrum” button to bring up the “Seismic spectral data EC8” dialog. The various parameters required to perform a spectral analysis conforming to the EC8 norm can be specified here. For the steel structure of this example, a ground acceleration of 0.16g, soil category B, structure importance II and a seismic factor q = 1.5 have been selected.
Press the OK button to return to the “Spectral Analysis Data” dialog. Since all required data has been entered the “Calculate” button has been activated and when you press it, the program will run the spectral analysis and generate a new loading case called “EC8”. This loading case can be used in the generation of various load combination required by the norm.
B. Load combinations
The Post-processing menu contains various tools to create and manage the load combinations. The most direct method of creating combinations is to use the Post-processing → Create command. The dialog that appears lists three types of load combinations that can be created with this tool.
- Combination creates a linear combination of loads that include the static and the spectral loading cases. The spectral response of the structure to seismic loads is calculated using the Complete Quadratic Combination (CQC) method. The superposition in space is based on the Newmark formulas which give the response S of a structure as the maximum of the following combinations:
- 1,0 Sx + 0,3 Sy + 0,3 Sz
- 0,3 Sx + 1,0 Sy + 0,3 Sz
- 0,3 Sx + 0,3 Sy + 1,0 Sz
Where Sx, Sy, Sz are the partial responses in the X, Y and Z directions. The program calculates the maximum values of the 6 (or 3 in a single plane model) components of the beam forces. Since the sign of the forces cannot be known, all possible combinations of directions with varying signs are created (8 in a single plane, 64 for a spatial model).
- Envelope creates an envelope of the loading cases and combinations selected by the user. Usually an envelope is defined to include the ULS and ULA combinations since the total number of combinations created automatically can be very great for a manual evaluation.
In this example, we are going to create automatic combinations using the Post Processing → Automatic combinations. The window “Automatic combinations” will appear. Select all the “Combination groups” and press “Create – Delete”. The automatic combinations are created taking into account the Eurocode criteria.
Then a dialog window will open “Processing…”. Press “Start”.
After the definition and verification of combinations and envelopes, the actual calculations of their results is performed using the command Post-processing → Calculation.
After the calculation is completed, the results of combinations and envelopes will be accessible for visualization using the methods described at the beginning of the current chapter.