Comparison of bending in beams

Abstract: -

For this project, there will be three different types of beams (Rectangular beam, I- section beam and C- section beam). These beams will be extruded by a length of 400mm. From there, the beams will be simulated using the Finite Element Analysis techniques. A fixed fixture and a force of 1500N will be acting upon the on the smaller face of the beam. Following the simulation, there will be a comparison of the results of stress, displacement, strain and Factor of Safety for all three cases. After analysing all the results, the best beam for bending will be chosen.

Introduction

The beam, or flexural member, is a part exposed to loads applied transverse to the long measurement, making the part bend. There are different parts of beams, one of them is known as a cantilever beam. A cantilever beam is one in which one end is built into a wall or other support so that the built-in end cannot move or rotate. The end is said to be fixed if no rotation occurs.

1. Stress is the amount of internal force per unit area, the formula of stress can be shown below:

Stress can be tensile (positive) or compressive (negative).

2. Displacement happens as a result of the external actions, these actions make the materials deform. This deformation manifests itself in small movements or displacements of material points. In the case of a beam where the displacement is perpendicular to the structure, it is known as deflection. Displacement/Deflection has units of length (m or mm)

3. A strain is defined as the change in length over the initial length, a strain happens due to when the materials deform when subjected to external actions such as loads or temperature changes. Strain is dimensionless. It is often given as a percentage. The formula for strain as shown below:

Procedure

For sketching the model in SOLIDWORKS

1. Sketch the given three 2D drawings with the correct dimensions
2. Extrude each one of the sketches by 400mm

For FEA Analysis

1. Select Static study
2. Apply the material to the beam (Alloy Steel was chosen for all beams)
3. Apply fixed geometry and Loads
4. Mesh the body and Run the study
5. Compare the end results of each beam

Model 1

Figure 1 shows the provided drawing and its dimensions for model 1 is provided below:

Figure 1: drawing and dimensions for model 1

Figure 2 shows the model created by SOLIDWORKS

Figure 2: 3D model of the rectangular beam

Model 2

Figure 3 shows the provided drawing and its dimensions for model 2 is provided below:

Figure 3: drawing and dimensions for model 2

Figure 4 shows the model created by SOLIDWORKS:

Figure 4: 3D model of the I-section beam

Model 3

Figure 5 shows the provided drawing and its dimensions for model 3 is provided below:

Figure 5: drawing and dimensions for model 3

Figure 6 shows the model created by SOLIDWORKS:

Figure 6: 3D model of the C-section beam

The material used for this project is Alloy Steel, here are some of its properties shown below:

Figure 7: Alloy steel properties

Fixtures and Loads applied:-

To run a simulation, a fixed geometry and a load has to be added on the model. For the fixed geometry, the beam will be fixed at one end, this will enable the beam to be treated as a cantilever beam. As for the applied load, a downward force of 1500N will be applied onto the smaller face of each beam

For Model 1, the force was applied on the 45mm face as displayed below

Figure 8: fixture and load applied to the rectangular beam

For Model 2, the force applied was on the 40mm face as displayed below

Figure 9: fixture and load applied to the I-section beam

For Model 3, the force applied was on the 45mm face as displayed below

Figure 10: fixture and load applied to the C-section beam

Meshing:-

The mesh was done using the systems below for all models:

Figure 11: Mesh settings used for the project

The meshed model for model 1i s shown below:

Figure 12: The meshed model for the rectangular beam

The meshed model for model 2 is shown below:

Figure 13: The meshed model for the I-section beam

The meshed model for model 3 is shown below:

Figure 14: The meshed model for the C-section beam

Results:-

Results of the simulation are shown below:

Model 1: Rectangular beam

Figure 15: Von Mises Stresses for the rectangular beam

Figure 16: Displacement Plot for the rectangular beam

Figure 17: Strain plot for the rectangular beam

Model 2: I-section beam

Figure 18: Von Mises Stresses for the I-section beam

Figure 19: Displacement Plot for the I-section beam

Figure 20: Strain plot for the I-section beam

Model 3: C-section beam

Figure 21: Von Mises Stresses for the C-section beam

Figure 22: Displacement Plot for the C-section beam

Figure 23: Strain plot for the C-section beam

Comparison of the Results:-

Table 1: Summary of the results

Model	Maximum Von Mises Stress (MPa)	Maximum Displacement(mm)	Maximum Equivalent Strain	Factor of safety
1	9.407	0.031	3.239e-05	65.96
2	31.780	0.085	9.643e-05	19.52
3	46.460	0.333	1.547e-04	13.335

Observation and Conclusion:-

Table 1 shows that model 1 has the lowest values when it comes to maximum Von Mises stress and maximum displacement, but due to the relatively high Factor of Safety, the components would be much more expensive resulting in a higher cost of the design. As for model 3, its low Factor of safety means it is the optimum choice when considering only the economical aspect of the three models. However, Table 1 entails that the maximum stress values and displacement are very high compared to the other 2 beams, therefore it does not have a high value when it comes to the structural integrity of the beam. The values of model 2 indicate that the Factor of Safety in model 2 is not that much higher than beam 3, this means the material cost of model 2 will be reasonable unlike in model 1. Model 2 also exhibits similar values of maximum displacement and strain to beam 1. In conclusion, when considering all the economical, commercial and structural aspects of all the three models, Model 2( I-section beam) is the optimum model out of the three models.