Παράδειγμα Επισκόπηση
In this example you will learn the basic steps of beam model creation, meshing, υλικά, boundary conditions and loads input. An analysis will be performed using linear static and linear buckling analysis.
The example shown in this tutorial is the beam with a total length 1700 mm και βάθος 500 χιλ. The web has thickness 2 mm και υπάρχουν δύο ανοίγματα ιστού (κυκλικό σχήμα) με διαμέτρους 400 mm και 350 χιλ. Οι επάνω και κάτω φλάντζες έχουν πλάτος 100 mm και πάχος 8 χιλ. Ο ιστός της δοκού σκληρύνεται και από τις δύο πλευρές με κατακόρυφα ενισχυτικά και διαμήκη ενισχυτικά (στα άκρα). Τα κατακόρυφα ενισχυτικά δημιουργούν δύο κύρια φύλλα μήκους 750 χιλ. Όλα τα ενισχυτικά έχουν πλάτος 50 mm και πάχος 12 χιλ. The beam is loaded by a concentrated vertical force located at the top of the vertical stiffeners in the middle, and the beam has two supports below the second and the fourth vertical stiffeners.
The beam is made of steel with yielding stress 230 MPa for the web, και 245 MPa for other elements.
The current example represents the experimental test from the paper “Ultimate Behavior of Perforated Steel Plate Girders Subjected to Shear Loading. Alireza Bahrami, Mahdi Najarnasab. The Open Construction and Building Technology Journal”.
Βήμα 1. Ιστός
In the Web panel define the web with length (μεγάλο) 1700 χιλ, βάθος (Η) 500 mm και πάχος (τ) 2 χιλ.
Βήμα 2. Πέλματα
In the Flange panel define top and bottom flanges the full length of the web (μεγάλο) 1700 χιλ, with starting and ending width (σι) 100 mm και πάχος (τ) 8 χιλ
Βήμα 3. Κάθετα ενισχυτικά
In the Vertical Stiffener panel define stiffeners with spans (SL) 100, 750, 750 και 100 mm from the left side of the beam. Define them all with the width (σι) 50 mm και πάχος (τ) 12 χιλ.
Βήμα 4. Διαμήκεις ενισχυτές
In the Longitudinal Stiffener panel define 6 ενισχυτικά. At the beginning of the beam (SL: 0 χιλ) define 3 stiffeners with length (μεγάλο) 100 mm and position from top (ST1, ST2) 125, 250, και 375 χιλ. The other three stiffeners start from the distance (SL) 1600 χιλ. Πλάτος (σι) και πάχος (τ) είναι τα ίδια με τα κατακόρυφα ενισχυτικά.
Βήμα 5. Ανοίγματα Ιστού
In the Web Openings panel define two openings. Και τα δύο έχουν σχήματα CIR (κυκλικό σχήμα) με ακτίνα (Ρ1) 200 και 175 χιλ. Ένα άνοιγμα είναι διευθετημένο στο (SL) 475 mm από τα αριστερά, και το δεύτερο στο 750 χιλ. The opening center is shifted from the top (ST) επί 250 χιλ.
Βήμα 6. Πλέγμα
In the Mesh panel define mesh element sizes on the side length as 25 χιλ, and on the opening length as 15 χιλ. ο 25 Το μήκος πλευράς mm θα εφαρμοστεί για τον ιστό, πέλματα, και ενισχυτικά άκρα. ο 15 mm opening length will be applied for the opening edges. Click the Preview button to see the potential FE nodes distribution. Click the Generate button to create the FE mesh for analysis.
Βήμα 7. Όρια
In the Boundary Stiffeners panel define constrains for the beam. Here one pin and one roller supports are at the bottom of stiffener 2 and stiffener 4. Define the first two rows in the table as the left and right parts of the stiffener 2 (Ονομα: V2L, V2R). Define the side of the stiffeners to be constrained (σι). Follow the global axis to define restrictions for the nodes (pinned support has only one release for rotation about z-axis). The other two rows in the table corresponded to the roller support, below the parts of the vertical stiffener 4 (Ονομα: V4L, V4R). The beam has no lateral translations. Define next 4 rows in the table for right side of the stiffener V2R, V3R, V4R, select ET and EB, and define restrictions only along axis Z. Click on the Preview button to see the nodes with constrains.
Βήμα 8. Φορτία
In the Stiffener Loads panel define the concentrated load at the middle of the beam. The load has value 40 kN and will be applied on top of two vertical stiffeners. In the table define two rows, select left and right parts of the stiffener 3 (V3L, V3R). Apply half of the load (Fz: 20 ΚΝ) to the top side (Τ) of each part of the stiffener. Click Preview to see how the load is distributed in FE nodes.
Βήμα 9. Ανάλυση
Select Linear Static in the Analysis Type panel and click the Analysis button.
Βήμα 10. Displacements Results
In the Results panel select result type from dropdown list. Display a deformed view of the model with its deformation scaling.
Βήμα 11. Αποτελέσματα άγχους
Select Result type ‘S, stress’ to check the stress distribution contour. Select different stress components and display the contour. The normal stress (ΧΧ) value is 308 MPa and exceeds the yielding stress of the web 230 MPa. This indicates on the occurrence of plastic strain zones in the web. In the next Tutorial this plasticity will be investigated in more detail for this beam.
Βήμα 12. Linear Buckling Analysis
Now investigate the linear buckling shapes and critical buckling forces of the beam. Select ‘Linear Buckling’ in the Analysis Type panel. Select the necessary number of buckling shapes, or ‘Eigen Modes’. Τυπικά, for the current type of beam analysis, 3-5 modes is enough. Κάντε κλικ στο κουμπί Ανάλυση.
Βήμα 13. Buckling Results
In the Linear buckling results panel you can select the result mode. Here are the 3 modes with their corresponding buckling load factors. If multiply the factor by the applied load value you will receive the critical linear buckling force. Για παράδειγμα, with our applied force of 40 kN the critical buckling load will be Fcr = 0.965 Χ 40 = 38.6 ΚΝ. Στην πράξη, this means that if apply this critical load to the structure, then the structure becomes unstable in terms of linear buckling stability. The buckling shapes can be seen after clicking on the Display button. Potential buckling shapes are mainly located around the web. This kind of buckling is called as local buckling. Using these results can be confirmed that the structure does not have enough capacity for this applied load. This is also proven by the experimental test results. From the experiment the critical force is below 40 ΚΝ.
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