Challenge 2- Comparing the performance of three types of beams under bending load.

AIM: - COMPARING THE PERFORMANCE OF THREE TYPES OF BEAMS UNDER BENDING LOAD

In the given problem first, three beams of different cross-sectional areas are to be modeled 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.

The three cross-sections of the beam sketched in Solidworks are shown below:

1. RECTANGULAR CROSS-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:

The beam is a Cantilever Beam with one end of the beam being fixed and the other being free. This will be done through the following steps:

First activating the Solidworks 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.

The next step in the analysis is to assign the material to the beam. To do so right-click on ‘Week 2 beam 1’ (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:

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:

Now, click on the green check to finish.

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:

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:

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.

The same procedure is followed to create the other two beams which are as follows:

2. 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:

Now select the ‘Simulation’ option and click on ‘New Study’ and then similar to the previous beam analysis select the Static analysis option.

The next step in the analysis is to assign the material to the beam. To do so right-click on ‘Week 2 beam 2’ (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:

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:

Click on the green check to finish.

Next, the external load is added, in the same way as done for the rectangular beam. After applying the load, the beam will look like this:

After this the meshing is done, here also the ‘Global Size’ limit is kept as 6 mm.

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.

C-SECTION:

Cross-section sketch: The cross-section of the C-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:

Now select the ‘Simulation’ option and click on ‘New Study’ and then similar to the previous beam analysis select the Static analysis option.

The next step in the analysis is to assign the material to the beam. To do so right-click on ‘Week 2 beam 3’ (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:

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:

Next, the external load is added, in the same way as done for the rectangular beam. After applying the load, the beam will look like this:

After this the meshing is done, here also the ‘Global Size’ limit is kept as 7 mm.

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. Rectangular Cross-Section:

a) Stress:

The plot showing the stress distribution throughout the beam is shown below:

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 8.3587 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.

b) Strain:

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 2.4877 x 10^-5.

The strain values are seen to gradually decrease when moving from the fixed end toward the free end.

c) Displacement:

The plot for displacement is shown below:

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.

All the results combined are shown below:

2. I-SECTION:

a) Stress:

The maximum stress values are seen at the fixed end along the Flanges of the cross-section. The value of the maximum stress in this section is equal to 22.6052 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.

b) Strain:

Here also, the maximum strain is obtained at the flanges of the cross-section and its value is 7.6882 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) Displacement:

The displacement is maximum at the free end and its value at the location is 0.08557 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.

The combined view of the results is shown below:

3. C-SECTION:

a) Stress:

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 39.2258 MPa. This stress value is the maximum of all three beams.

b) Strain:

The strain is also maximum at the same location where the stress is maximum and its value is 1.381 x 10^-4 which is the maximum out of the three beams.

Displacement:

The displacement is seen to be maximum at the free end at the tip of the flange and the value of maximum displacement is 0.30331 mm.

A combined view of the result is mentioned below:

CONCLUSION:

	STRESS (MPa)	STRAIN (*10^-5)	DISPLACEMENT (mm)
Rectangular Section	8.3587	2.4877	0.03101
I-Section	22.6052	7.6882	0.08557
C-Section	39.2258	13.81	0.30331

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.

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.