Comparison of Bending in Beams

Aim: Compare the performance of three types of beams under bending load.

Introduction: A beam is a structural element that primarily resists loads applied laterally to the beam's axis. Its mode of deflection is primarily by bending. The loads applied to the beam result in reaction forces at the beam's support points. The total effect of all the forces acting on the beam is to produce shear forces and bending moments within the beam, that in turn induce internal stresses, strains and deflections of the beam. Beams are characterized by their manner of support, profile (shape of cross-section), equilibrium conditions, length, and material.

Beams are traditionally descriptions of buildings or civil engineering structural elements, but any structures such as automotive automobile frames, aircraft components, machine frames, and other mechanical or structural systems contain beam structures that are designed to carry lateral loads are analyzed in a similar fashion.

Problem Statement: The beams are extruded to 400mm from the faces having the dimensions given in the sketches. A load of 1500N is applied to the smaller faces of all the beams, that is, 40mm face of beam 2, and 45mm faces of beam 1 and beam 3. The results of the Strain Stress and Displacement plots are to be compared and then the best out of the three is to be given.

Procedure:

1. Create the models as per the given dimensions and extrude them to 400mm.
2. Now, go to Simulation and perform a static study for each beam.
3. Apply the material to the beams, that is, Alloy Steel.
4. Select the fixed geometry for each beam.
5. Apply a uniformly distributed load of 1500N on the smaller faces of each beam.
6. Create a fine mesh for each beam.
7. Run the study and now compare the results.

Beam Models:

Beam 1

Beam 3

Beam 2

Outputs:

The beams with fixed constraints, loads applied and meshes created along with the outputs for each case are shown below:

Beam 1

Beam 2

Beam 3

Comparison of Results:

Beam	Max.Von Mises Stress (MPa)	Max. Displacement (mm)	Max. Equivalent Strain	Factor of Safety
1	10.79	0.04376	3.55E-05	57.49
2	23.43	0.08606	8.32E-05	26.48
3	42.61	0.3124	1.52E-04	14.56

As shown in the table above, beam 1 shows minimum values for stress and displacement along with lesser strain compared to beam 2. If we do not consider the economic or weight criteria, beam 1 would be our obvious choice. If the material used is more and so is the cost, no one will really choose beam 1. However, beam 3 is the best option in economic and weight terms, but the value of stress and displacement is high which is not good. Beam 2 is good in terms of stress and displacement as well as strain. Beam 2 also uses less material, thereby reducing cost and weight.

Therefore, I-section beam or beam 2 is the best choice for the given conditions among the three beams.