Comparison of Bending Beams
Aim: The main objective is to analyze and compare the bending of beams with different cross-sections (Rectangular, I- section, C-section) based on their stress, strain, and displacement curve respectively.
Software Used: All the models prepared, simulation performed using Solidworks only.
Theory: The bending of a beam is a crucial part of structural analysis and comes under finite element analysis.
Let us understand the Finite element analysis (FEA) first.
FEA: It is an analysis that is done using a finite element method in which dividing the body into the smaller part which we called mesh and perform that study on that after that combine the results and provide an approximate solution to a large variety of problems.
Stress: It is a state in which internal resisting force is generated when the body is subjected to an external load and the resistance offered by the body to deformation is called the stress.
Strain: When the body is subjected to the load conditions it undergoes deformation which causes the dimensions of the body to change. Hence it is defined as the change in length by original length as longitudinal strain. Similarly, the volumetric strain is defined as a change in volume by original volume.
Bending of Beam: Bending is a type of normal stress (a combination of compression and tension) when applied on a body causes to generate the bending stresses along the neutral axis.
Bending can be caused by applying an external load perpendicular to the longitudinal axis of the body.
Sketch
case 1
Rectangular beam
case 2
I section beam
case 3
C section beam
Modeling: The length of each beam is 400mm in each case.
case 1
Rectangular beam
case 2
I section beam
case 3
C section beam
Material Used: In all the cases, the material is defined as Alloy Steel.
Boundary Conditions: One side of the extruded beam is fixed parallel to the cross-section and the load is applied on the top face of 1500N as shown below.
Case 1
Case 2
Case 3
Meshing: Mesh was set to fine to get more accurate results.
case 1
Rectangular beam
case 2
I section beam
case 3
C section beam
Results:
case 1
Rectangular beam
Stress
Normal behavior was observed that stress is maximum at the fixed end for the given conditions.
Strain
The strain will be also maximum at the fixed end as upper end is in tension and lower end in compression due to bending.
Displacement
Combined
case 2
I section beam
Stress
For this cross-section, stress is also maximum at the fixed end.
Strain
The strain is said to be maximum at the fixed end too, the upper edge is in tension while the lower edge is in compression.
Displacement
Combined
case 3
C section beam
Stress
Here Torsion comes into the picture and plays an important role in deciding the stress, strain, and displacement.
As we can see that stress-induced are higher in amount.
Strain
Displacement
Combined
It helps us to observe the system closely and corresponding to the stress condition there will be a particular strain and displacement.
Observation & Comparison: 1. The yield strength of all the beams is the same.
2. The maximum stress developed is less for a rectangular section as compared to the I and C section.
3. Based on Strain Plot, it can be seen that it is maximum for the C section, then I section and least for the Rectangular section.
4. Similar results were obtained for displacement as in the case of strain.
5. In the case of the C section, there will be torsion which can be seen in the above plots due to its shape and the load conditions, for this reason, it will be least preferred.
6. Based upon considering weight, it would be higher for a rectangular beam compared to the I section.
7. All these comparisons and observations landed on 1 thing that the I SECTION BEAM will be most preferred from all aspects.