Comparison of bending in beams

AIM: To find the best structure by the results so obtained on the analysis of the beams of different cross sections under bending load.

Implementation:

There are 3 cases that are to be considered here to be analyzed and find the best cross section that withstands the load of 1500N with permissible range values of mechanical properties like stress, strain and displacement.

The following are the cross sections that are considered.

These are modelled using the solidworks software where the beams of this cross section is made with a length of 400mm and analyzed respectively for the stress, strain and displacement.

Case 1:
Rectangular cross section beam of 400 mm length where one end is fixed and a load of 1500N is applied on the face of 45mm dimension. Here the material is considered to be an alloy steel and the load and constraints are given respectively. Here the mesh is generated wth default settings or can be changed to refine the mesh with smaller element size if needed. Later on completing the simulation, we can compare the results of the this beam of stress, strain and displacement in a single window as follows.

The above is the results obtained for the rectangular beam and it is observed that there is a max stress of 9.452e+06 which is less than the yield strength, stating that the factor of safety is above 1 and the beam is safe, we can also conclude that the max stress is found at the top face near the fixed end as it is subjected to bending (tension). Then the displacement of 3.1e-02 mm and a strain of 2.98e-05 are observed from the above results.

Case 2:
I cross section beam of 400 mm length where one end is fixed and a load of 1500N is applied on the face of 40mm top face dimension. Here the material is considered to be an alloy steel, then load and constraints are given respectively. Here the mesh is generated wth default settings or can be changed to refine the mesh with smaller element size, if needed. Later on completing the simulation, we can compare the results of the this beam of stress, strain and displacement in a single window as follows.

From the above results, it is observed that there is a max stress of 2.494e+07 which is less than the yield strength, stating that the factor of safety is above 1 and the beam is safe, we can also conclude that the max stress is found at the top face near the fixed end as it is subjected to bending (tension). Then the displacement of 8.56e-02 mm and a strain of 7.968e-05 are observed from the above results.

Case 3:
U cross section beam of 400 mm length where one end is fixed and a load of 1500N is applied on the face of 45mm dimension. Here the material is considered to be an alloy steel, then load and constraints are given respectively. Here the mesh is generated wth default settings or can be changed to refine the mesh with smaller element size, if needed. Later on completing the simulation, we can compare the results of the this beam of stress, strain and displacement in a single window as follows.

From the above results, it is observed that there is a max stress of 4.108e+07 which is less than the yield strength, stating that the factor of safety is above 1 and the beam is safe, we can also conclude that the max stress is found at the bottom face near the fixed end as it is subjected to twisting moment. Then the displacement of 3.025e-01 mm and a strain of 1.421e-04 are observed from the above results.

Conclusion:

On the application of the same load on the 3 cases and to decide the best combination we also need to verify the strength-to-weight ratio in order to improve the performance not only in a mechanical aspect but also economically. Here in the 3 cases, case 2 i.e. the I section is best as on comparision with other cases in weight it is in the fashion of rectangular c/s< I section < U section, and in the efficiency of mechanical properties rectangular c/s> I section> U section, as an compromise, it concluded that the I section is better of the 3 cases as it has less wight and also can withstand the load with lesser stress, strain and displacement stating that it can withstand the load.