Challenge 2- Comparing the performance of three types of beams under bending load.
Aim: - Comparing the performance of three types of beams (i.e. - Rectangular, I-Section and C-section) under bending load of 1500 N.
Introduction:
When a bending load is applied to a beam, it experiences a bending moment which causes change in its shape and development of internal stresses. The material is in compression on the inside of the curve and in tension at the outside of the curve. The transverse planes in the material remain parallel to the radius during bending.
The three cross-sections of the beam sketched in Solid works are shown below:
In the given problem first, three beams of different cross-sectional areas are to be modelled in SolidWorks. Next, the beam models are to be supplied with necessary boundary conditions, the loading conditions, and the meshing conditions.
Finally performing the simulation for all the three beams and comparing the resulting Stress, Strain, and Displacement in all three beams and based on that selecting the best one.
#1 Creation of 3D model in Solid Works
Rectangular Section:
It is a rectangular cross-section with dimensions of 80 mm x 45 mm.
The beam will be created after extruding this for 400 mm length normal to the cross-section area. The beam will look like as shown below:
I – Section:
Cross-section sketch: A cross-section of the I-section beam after successful sketching is shown below:
The beam will be created after extruding this for 400 mm length normal to the cross-section area. The beam will look like as shown below:
C – Section:
Cross-section sketch: The cross-section of the C-section beam after successful sketching is shown below and The beam will be created after extruding this for 400 mm length normal to the cross-section area. :
#2 Solid works simulation:
First activating the Solid works Simulation Add-in. Next, click on ‘New Study’, it will bring the Property Manager asks the type of analysis that should be performed on the given geometry.
Here, the ‘Static’ analysis will be chosen since the loading condition is gradually applied load condition.
Select the ‘Static’ option and then click on the green check to move further.
#3 Assigning the material:
The next step in the analysis is to assign the material to the beam. To do so right-click on ‘Part Model’ (the name of the geometry). A pop-up window will emerge, select the first option ‘Apply/Edit Material’. This will open the window showing all the different materials stored in the SolidWorks database. Select the material ALLOY STEEL, press Apply, and then close. On successfully applying the material to the beam will look like this:
For all the 3 cases of simulation we have selected the 'Alloy Steel' as a material
#4 Fixing one end of beam - Cantilever Beam:
The next step is to turn this beam into a Cantilever Beam. This is done by right-clicking on ‘Fixtures’ and then selecting the ‘Fixed Geometry’ option. After doing this, the property manager will ask to select the face which is needed to be fixed. Then, after selecting the desired surface the beam will look like this:
Rectangular Section:
I – Section:
C – Section:
#5 Adding the Force Component in Beam:
The next step is to add the external load to the beam. This is done by right-clicking on the option ‘External Loads’ and selecting the option ‘Force’. After that, the Property Manager will ask to select the face or edge on which the force must act. Now select the Top Face of the beam by clicking on it. Now give the magnitude of the force, equal to 1500 N, then click on the green check to finish. Now the beam will look like this:
Rectangular Section: Force along the 45mm face
I – Section: Force along the 40mm face
C – Section: Force along the 45mm face
#6 Adding the Force Component in Beam:
Now, the beam is required to mesh. The meshing is done by right-clicking the option ‘Mesh’ and then selecting the option ‘Create Mesh’. This will open the Property Manager window, in there click on the option ‘Mesh Parameters’ and set the ‘Global Size’ limit equal to 9 mm. Click the green check and then the software will mesh the beam. The beam after successful meshing will look like this:
Rectangular Section:
I – Section:
C – Section:
With this the beam is now ready to undergo the analysis, thus hit the option ‘Run This Study’, and the software will run the simulation and give the results obtained.
Results:
#1 Stress Results:
Rectangular Section:
From the figure, it is seen that the stresses induced are quite less than the yield strength of the material.
The maximum stress is seen to be present at the corners of the beam at the fixed section and its value is equal to 8.353 MPa. This is because in a cantilever beam all the load is supported by the fixed end only.
Hence the corner points of the cantilever beam are the critical points.
I – Section:
The maximum stress values are seen at the fixed end along the I Section of the cross-section. The value of the maximum stress in this section is equal to 26.45 MPa. This is quite higher than the previous beam because in this beam the cross-section area is very less and thus the material bearing the load at a particular cross-section is less. So, the stress-induced is greater.
C – Section:
In this beam, the maximum stress is seen to be acting at the corner of the fixed section at the junction of the flange and web. The value of the maximum stress is seen to be 37.23 MPa. This stress value is the maximum of all three beams.
#2 Displacement Result:
Rectangular Section:
As it can be seen from the plot, the maximum displacement is seen at the free end of the beam which is equal to 0.03101 mm.
Moving from the free end towards the fixed end the displacement value tends to decrease and is equal to zero at the fixed end.
I – Section:
The displacement is maximum at the free end and its value at the location is 0.08565 mm. again this value is greater than the previous beam. This is because in this beam the material at a particular section supporting the load is less than the rectangular beam. As a result, these sections displace more than the rectangular beam.
C – Section:
The displacement is seen to be maximum at the free end at the tip of the flange and the value of maximum displacement is 0.2915 mm.
#3 Strain Results:
Rectangular Section:
The plot showing the strain distribution throughout the beam length is shown below:
It can be seen from the plot that the maximum strain values are also seen at the corner elements of the beam. This is because these points experience the maximum stress values. The strain values at the critical points are seen to be equal to 2.483 x 10-5.
The strain values are seen to gradually decrease when moving from the fixed end toward the free end.
I – Section:
Here also, the maximum strain is obtained at the flanges of the cross-section and its value is 8.625 x 10-5. It is greater than the maximum strain developed in the previous beam because the stress value in this beam is higher.
Strain at the free end is zero because it is unconstrained and displaces along with the force.
C – Section:
The strain is also maximum at the same location where the stress is maximum and its value is 1.178 x 10-4 which is the maximum out of the three beams.
Animation of simulation videos:
#1 Rectangular Section: (Stress, Strain & Displacement)
https://drive.google.com/drive/folders/1Qhn5nlnszEpnrXe6rs3UXVvlOS6va_KS?usp=sharing
#2 I - Section: (Stress, Strain & Displacement)
https://drive.google.com/drive/folders/1zUSi_plk-mNHbcHn5HOWhD2mNHF1wmOX?usp=sharing
#3 C - Section: (Stress, Strain & Displacement)
https://drive.google.com/drive/folders/1pd7BJk01icAnPlsqmZ7NBilUNb3pTkhX?usp=sharing
Conclusion:
The load acting on all the beams is the same (1500 N), but due to the different cross-sections of each beam, the stress-induced are different for different beams.
Comparison of Results:
The maximum stress is seen to be acting in the C-Section beam, also the strain and maximum displacement values are maximum for the C-Section beam. So it can be said that the C-Section Beam is worst loaded.
On the other hand, the rectangular beam is having all minimum values of stress, strain, and displacement out of the three.
From the results it appears that a rectangular beam is the most obvious choice, however, in general, the I-section beam is preferred. This is because both sections will bear the load but the I-section beam consumes lesser material and give satisfactory results. So, I-Section Beams are more economical to use.