Comparison of stress, deformation and strains produced in beams having different cross sections under similar loading condition and suggesting the best out of three cases.

Aim:- Comparison of stress, deformation and strains produced in beams having different cross sections under similar loading condition and suggesting the best out of three cases.

Introduction:-

Bending in a beam :- it is a phenomenon in which after application of forces on a beam, the bending stresses are generated in the particular body.In our case all beams are of cantilever type.

Cantilever beams:- The beam's one end is fixed and the other end is free. After application of force at the free end , reaction forces has been developed at fixed end.Major stresses generated in these types of beams are bending stresses.

Bending stress:- When load is applied perpendicular to the beam, then the stress produced due to these forces are bending stresses.

Linear Static structural simulation (3D):-

1. This type of simulation mainly carried out to evaluate the displacements, stresses and strains produced in the structures. Stress and strain varies linearly in this type of analysis.
2. We can perform this type of analysis in 1D/2D/3D, according to the problems complexity to optimize the computation time.
3. I have performed static structural simulation in solidworks to evaluate the effect of loading conditions on results of beams having different cross section.

There are three stages in simulation

1.) Pre-processing:- In this stage we have to set-up the boundary conditions according to required case.

• Geometry Creation:-•Following models are constructed in solidworks using the dimensions provided in the assignment.
• Meshing:- Following mesh attributes are used for all of the three cases

Mesh type:- Solid mesh

Element size:- 5 mm

Mesh Quality- High

- Applying Boundary conditions:- These are used as per given in the problem. Beams one end is fixed and 1500 N load is applied on the portions of the model as given in the problem.

Material Application:- Used standard Alloy steel available in the material library to all 3 cases.

Applied Load:- Uniformly distributed Normal force 1500 N

Fixed geometry:- One of the end of beam is fixed.

2. Solution:- After applying all necessary boundary conditions according to our problem statement, this problem has been solved by the software to give results for stress, deformation and strains developed in the given model.

3. Post processing :- In this step we get various contour plots for our required results. We can interpret the behavior of the model under applied loading conditions.

In this case we got deformation, stress and strains plots for each case and we can compare the cases on the basis of plots that we are having.

I have compared the results with the help of following table. Detail images and plots are attached in the presentation.

	Case-1	Case-2	Case-3
Total maximum Von-mises stress (MPa)	9.397	23.576	46.475
Total maximum Deformation (MM)	0.031	0.086	0.37
Total Equivalent strain	3.148 x 10-5	8.284 x 10-5	1.652 x 10-4
Mass (Kg)	11.08	2.365	2.922

Result and Conclusion:-

1. We have assigned Alloy steel as a material, which is having yield strength of 620.422 MPa.
2. If we see our results, stress produced in each and every case is within the limit of the material, so we can say that for the applied load of 1500 N , stress produced in every case is within limit. i.e our design is safe according to the linear static considerations. (Non linearity may give different results).
3. After seeing above results, we can easily say that Case-1 is the safest one among three, because the maximum possible stress, deformation and strain is less than other two cases, which is ultimately good, but we have to also consider the other factors affecting the results.
4. Almost all three are having same cross sectional extreme dimensions i.e breadth and height. Only case -2 is having breadth equal to 40 mm instead of 45 mm. Therefore the cross section plays very important role while deciding the optimum case.
5. Case-1 is the safest, but the material required is highest in case 1. We have to select the best out of three according to our problem statement.
6. The best case out of three cases is Case-2, because the stress produced is within materials yield limit, deformations produced are moderate when compared with the other two cases, strains produced are also moderate and most important thing is material requirement i.e mass is 2.365 Kg which is least among other cases.