Comparision of Bending of Beams
AIM
Analyzing and comparing three beams of different cross section in terms of stress, displacement, and strain experienced during bending load conditions.
THEORY
Beam is a structural component which resists all the loads applied along the plane transverse to its axis. Bending plays a vital role. Bending phenomenoa is oserved when an external load applied is applied perpendicular to its longitudinal axis. There are different typer of beams
- Cantilever Beam- When the beam is fixed at one end and its other end is free.
- SIMPLY SUPPORTED BEAM- When one end is hinged and other end is supported by roller.
Basically, on loading, the beam experiences stresses, strains, and deflections. The bending also depends upon the support, cross-section, length, and material. The study of these stresses, strains, and deflections is used to determine the best possible beam
OBJECTIVE
the comparison of beams of different cross-section for cantilevers.
Cross sections
- Rectangular
- I-section
- C-section
PROCEDURE
1. Create the 3D model as per the dimensions provided.
The beams are extruded to 400 mm
A load of 1500 N is applied to the smaller faces of all the beams i.e 40mm face of beam 2 and 45 mm faces of beam 1 and beam 3.
The results in terms of Strain, Stress, and Displacement are to be compared and the suggestion of the best of the three is to be given.
2. Click on static study option
3. Select the material for the beams
4. Apply the required constraints
5. Apply the load
6. Meshing
7. Run the study
8. Compare the results.
Case 1: Rectangular C/S Beam
Case 2: I-SECTION BEAM
Case 3: C-SECTION BEAM
MATERIAL- ALLOY STEEL
The material is same for all 3 beams and the properties are listed below
CONTRAINS AND LOAD APPLYING
- One end of the material is fixed and othe end is left free.
- Load is applied at transvere face as shown in the figure
Rectangular C/S Beam
I-SECTION BEAM
C-SECTION BEAM
MESHING
size- 3.7mm
tolerence- 2.5mm
Rectangular C/S Beam
I-SECTION BEAM
C-SECTION BEAM
RESULTS
After completiong the analysis, the results are obtained as shown below
The calculations are done on the basis of Von Mises Theory
Rectangular C/S Beam
1. Stress Distribution
2. Displacement
Strain Distribution
I-SECTION BEAM
1. Stress Distribution
2. Displacement
Strain Distribution
C-SECTION BEAM
1. Stress Distribution
2. Displacement
Strain Distribution
COMPARISION OF RESULTS
|
BEAM (C/S) |
MAX VON MISES STRESS (in MPa) |
MAX DISPLACEMENT (in mm) |
MAX EQUIVALENT STRAIN |
| Rectangle | 7.256 | 0.031 | 7.545e-05 |
| I-section | 19.986 | 0.086 | 7.545e-05 |
| C-Section | 38.746 | 0.302 | 0.000128 |
CONCLUSIONS
- The rectangular C/S beam shows the minimum values of stress and displacement compared to other beams as the area of crosssection is high.
- The rectangular beam will be the best choice if we don't consider the economic and weight criteria.
- But I-section is mostly preffered since it is economical and the stress and displacement experienced are in between the values of rectangular section and C-section.
- The C — section beam is the best option for of economic point of view. But, the value of stress and displacement are high. So, we will not use it in practial senario.
- Hence, I — section beam is good in terms of stress and displacement as well as equivalent strain.
- The I-section beam uses less material,which is economical and also bear the high stress value.