Bending of Beams

OBJECTIVE:

The aim of this project is to perform bending simulation in three beams with different geometry, compare the results of stress, displacement and strain for all three cases and suggest the best geometry.

SOLUTION:

The bending simulation on the beams are carried out, considering the structure as cantilever beams. A cantilever beam is a structural element which extends/overhangs horizontally and is supported at only one end. In this project three cantilever beams, with different geometries are subjected to bending, the results are compared and the best geometry is found out.

Step1: The first step in the analysis is to create a 3D model of the beams.

Case1:

The beam has a simple rectangular cross section with 45mm width, 80mm depth and 400mm length.

Case2:

The beam has an ‘I’ cross section and length of 400mm

Case3:

The beam has a ‘C’ cross section with a length of 400mm.

Step2: The second step is to assign material to the beams. For all the cases the material was assigned as Alloy Steel. The material properties are as given below:

Step3: The next step is to fix one end of the beam and application of the load on the top horizontal face, so that the beam exhibits the cantilever behaviour. This can be done by selecting the face and assigning it as a fixed under the fixture tab. The force can be assigned under the external load tab. For all the three cases a uniform load of 1500N was applied in the downward direction on the smallest top horizontal face. The smallest face for case1 and case3 is 45mm and 40mm for case2. The models are as shown:

Step4: The final step is to mesh the model. For all the three cases a mesh size of 6mm was used to discretize the models. The meshed models are as shown:

RESULTS:

The models were solved and the stress, strain and displacement were compared.

Case1:

Case2:

Case3:

	Mass (kg)	Max Von Mises Stress (MPa)	Strain (x 10^-5)	Max displacement (x 10^-2 mm)
Case 1	1.44	9.44	3.01	3.1
Case 2	0.307	23.3	7.654	8.55
Case 3	0.419	41.75	14.06	30.2

From the results, it can be observed that the simple rectangular cross section exhibits the minimum values for stress, strain and displacement. Hence, when only the geometries are considered, the best beam is the one with the rectangular cross section. But in most practical scenarios, mass plays a significant role in beams and it can be observed that the mass is least for the ‘I’ section beam (almost one fifth of the rectangular beam). The stress, strain and displacement values for the ‘I’ beam are intermediate and not as high as the ‘C’ section. Hence, in such a scenario ‘I’ section is the more preferred beam cross section.