Comparison of bending in beam

AIM:

To do a comparison between three types of beams in terms of stress, displacement, and strain generated during the bending load conditions by doing FEA in SOLIDWORKS

OBJECTIVE:

1. Draw the below provided sketches in solidworks.
2. You need to extrude the sketches to a length of 400mm
3. Apply a load of 1500N on the smaller face(i.e. 45mm face for case 1, 40mm face for case 2 and 45 mm face for case 3)
4. and compare the results of stress, displacement and strain for all the three cases and suggest the best out of the three.

Case 1:

Case 2:

Case 3:

(All Dimensions are in mm)

THEORY:

A beam is a structural component. It normally resists all the loads applied laterally to its axis. The only mode by which it can be deflected is bending. Bending is the behavior of the element when an external load is applied perpendicular to its axis. When the beam is fixed with one end and its other end is free then the beam is known as a cantilever beam. When the load is applied to the face perpendicular to its axis, then bending is experienced by the beam. The bending depends upon the support, cross section, length and its material. The bending of the beam includes internal stresses, strains, and deflections, with the studies of these parameters a best possible beam cam be determined.

Stress is the amount of internal force per unit area developed in an object subjected to an external force. Stress can be tensile or compressive.

Strain is the change in length over the initial length, it happens when the material deforms when it is subjected to external actions such as loads or temperature change. It is dimensionless.

Displacement is a result of external action, the actions make the material 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.

A simulation is the re-creation of a real world process in a controlled environment. It uses something called modeling to figure out the result of the simulation. Simulation is based on the process of modelling a real phenomenon with a set of mathematical formulas. It essentially allows the user to observe an operation through simulation without actually performing that operation.

PROCEDURE:

• Create a 3D model of three types of beams i.e. rectangular beam, I-section beam, and C-section beam and save them separately.

• Now for doing the simulation, click on ‘Simulation’ and then select ‘New Study’ and then ‘Static’ for static study.
• Now apply a material to beam that is Alloy steel for all the beams by right clicking on the part name and then on ‘Apply/Edit Material’.

• Now for fixing the beam at one end, this will enable the beam to be treated as a cantilever beam, right click on ‘Fixtures’ option and then on ‘Fixed Geometry’ option, then select the face that is to be fixed.
• Now for providing load right click on external loads option and select ‘Force’ option now select the face for normal force and then set the force to be 1500 N.

• Now for creating a mesh, right click on ‘Mesh’ them on ‘Create Mesh’ now use the ‘Mesh Parameters’ option.

• Now click on ‘Run This Study’ on the top menu bar for running the simulation.

RESULTS:

• RECTANGULAR BEAM

Displacement Strain Stress

• C – SECTION BEAM

Displacement Strain Stress

• I – SECTION BEAM

Displacement Strain Stress

COMPARISON OF RESULTS:

Beam	Max. Von Mises Stress (MPa)	Max. Equivalent Strain (MPa)	Max. Displacement (mm)
Rectangular	9.252	2.98e-005	0.031
C – Section	47.4	1.502e-004	0.2768
I – Section	26.81	8.499e-005	0.085

CONCLUSIONS:

• In rectangular beam we can see that the maximum Von Mises Stress is 9.252 MPa and maximum displacement is 0.031 mm that is smallest amongst all the three cases. This is the advantage of using a rectangular beam as it can bear a large amount of load and the deflection generated is also very less but the downside of rectangular beam is that it is the heaviest among all the three cases which makes it less useful as the material used is more and due to which the cost of using the beam also increases. Therefore this type of beam not used generally and is not the best beam type.
• In C – section beam we can see that the maximum Von Mises stress is 41.4 MPa and the maximum displacement is 0.2768 mm which is the highest amongst all the three cases. This states that it does not have a high value when it comes to the structural integrity of the beam. Therefore this type of beam is also not used as the stress induced is very high due to which the deflection is also high.
• In I – section beam we can see that the maximum Von Mises stress is 26.810 MPa and the maximum displacement of deflection is 0.085 mm which is in between the other two cases. This makes it the best beam configuration as in this type of beam the material used is also less and it still it can bear a high value of stress without much deflection. Due to less material used the overall cost of using this type of beam is also less as compared to rectangular beam.
• We can say that when considering all the economical, commercial and structural aspects of all the three types of beams, I – section beam is the best type of beam amongst all the three beams.