Comparison of Bending in BEAMS

COMPARISON OF BEAMS

AIM : To compare the performance of three types of beams of different cross section under a bending load using Solidworks.

OBJECTIVE :

Compare the results of stress, displacement and strain for all the three cases i.e Rectangular, I and C section Beams and detect the best out of the three.

INTRODUCTION :

• A beam is a structural element that primarily resists loads applied laterally to the beam's axis. Its mode of deflection is primarily by bending. Bending characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element.
• When the length is considerably longer than the width and the thickness, the element is called a beam.

THEORY :

• Beam is geometrically a straight bar of an arbitrary cross-section, but it deforms only in directions perpendicular to its axis.
• In short, a beam is a structural member the length of which is considerably more than the other 2 dimensions (i.e. width & depth).
• A beam gets bent-up or deformed when subjected to Bending moment and shear force. As, it undergoes deformation, internal resistances are set up & the process of deformation (bending) stops when every cross section sets up full resistance (stress) to the shear force & bending moment acting on it.
• The stresses induced to resist the bending moment are called as bending stresses. Bending action in a beam is called as flexure.
• Beams are characterized by their manner of support, shape of cross-section or profile, equilibrium conditions, length, and their material.

TYPES OF BEAMS -

1. Simply supported –

• A beam which is freely supported on the walls or columns at its both the ends is known as simple supported beam.

2. Cantilever –

• A beam fixed at one end & free at the other is called cantilever beam.

3. Fixed –

• A beam supported on both ends and ridigly fixed is called fixed beam or encastre beam.

4. Over hanging –

• A simple beam extending beyond its support on one end is over hanging beam.

5. Continuous –

• A beam extending over more than two supports is called continuous beam.

• 3 CASES OF BEAMS used for analysis are -

1. RECTANGULAR BEAM
2. I SECTION BEAM
3. C SECTION BEAM

• All the 3 cases of beams will act as a cantilever beam.
• The beam bends under the action of transverse loading on it & thus, a cantilever beam bends in a hogging pattern.
• For a cantilever beam the tension zone is above the Neutral axis(N.A) whereas the compression zone is below the N.A.

PROCEDURE :

1. Create a 2 D geometry sketch for beam in Solidworks and convert it to 3 D geometry by extrusion from features.
2. Select the type of Analysis to perform on 3D Model.
3. Apply material to the part model as required.
4. Apply the fixture at certain area or edge in Model as required to fix the part at particular position.
5. Apply load at certain face or edge of model as needed to anlayze the force impact.
6. Create a Mesh of the 3D Model.
7. Run the simulation and display the results for Stress, Displacement & Strain or any other parameter as per given statement.
8. Compare the Results for stress, strain and displacement.

CASE SETUP –

GEOMETRY :

1. RECTANGULAR BEAM

• 2D SKETCH

• The above image shows the 2 dimensional sketch for the rectangular beam with overall dimensions.

• 3D MODEL

• The 2D Sketch of rectangular beam is extruded by 400 mm which now represent as a 3D model with 400 mm in length.

2. I SECTION BEAM

• 2D SKETCH

• The above image shows the 2 dimensional sketch for the I section beam with overall dimensions.

• 3D MODEL

• The 2D Sketch of I Section beam is extruded by 400 mm which now represent as a 3D model with 80 mm in width 400 mm in length.

3. C SECTION BEAM

• 2D SKETCH

• The above image shows the 2 D sketch for the C section beam with overall dimensions.

• 3D MODEL

• The 2D Sketch of C Section beam is extruded by 400 mm which now represent as a 3D model with 400 mm in length.

MATERIAL

• The material selected for all the 3 cases is same i.e. Alloy steel is used. Alloy steel having the yield strength 620.422 N/mm^2 and further properties are mentioned below.

MESH :

• RECTANGULAR BEAM MESH

• In rectangular beam auto mesh has been generated with medium mesh quality for beam and get a developed mesh of element size around 11 mm. Here, triangular type mesh is used with structured grid.

• Overall computational time taken for meshing of this Rectangular section is around 0.2 s.

• I SECTION BEAM MESH

• In I Section beam auto mesh has been generated with medium mesh quality for beam and get a developed mesh of element size around 7 mm. Here, triangular type mesh is used with structured grid.

• Overall computational time taken for meshing of this I section is around 0.5 s.

• C SECTION BEAM MESH

• In C Section beam auto mesh has been generated with medium mesh quality for beam and get a developed mesh of element size around 7.5 mm on model. Here, triangular type mesh is used with structured grid.

• Overall computational time taken for meshing of this C section is around 0.3 s.

FIXTURES :

1. RECTANGULAR BEAM

• The rectangular beam is fixed at 1 end on the Left side face of the beam and is free at the other end.

2. I SECTION BEAM

• The I Section beam is fixed at 1 end on the Left side I shaped face of the beam and is free at the other end.

3. C SECTION BEAM

• The C Section beam is fixed at 1 end on the Left side C shaped face of the beam and is free at the other end.

LOAD :

1. RECTANGULAR BEAM

• In this rectangular beam a load of 1500 N is applied on the top of the smaller face i.e 45 mm face entirely over 400 mm length for bending of beam.

2. I SECTION BEAM

• In this I Section beam a load of 1500 N is applied on the top of the smaller face i.e 40 mm face entirely over 400 mm length for bending of beam.

3. C SECTION BEAM

• In this C Section beam a load of 1500 N is applied on the top of the smaller face i.e 45 mm face entirely over 400 mm length for bending of beam.

RESULTS :

STRESS

• RECTANGULAR BEAM

• After fixing the beam at 1 end and applying a udl load of 1500 N the beam starts bending. Thus, the bending stress are produced in the beam whose stress variation is shown by a coloured region over the beam. The blue region shows the starting or minimum amount of stress produced while it goes on increasing till the maximum stress is reached which is represented by the red region. The legend shown indicates the stress variation of the plot for rectangular beam. Maximum amount of stress is produced around 7.557e N/mm near the fixed support region.

• I SECTION BEAM

• After applying a load of 1500 N the beam starts bending and thus, the bending stresses are produced in the I section beam whose stress variation is shown by a coloured region over the beam. The stresses goes on increasing from minimum at free end blue region till the other end at fixed position red region. The legend shown indicates the stress variation of the plot for I Section beam. Maximum amount of stress is produced around 5.563e N/mm near the fixed support region.

• C SECTION BEAM

• After applying a udl load of 1500 N the beam starts bending and thus, the bending stresses are produced in the C section beam whose stress variation is shown by a coloured region over the beam. The legend shown indicates the stress variation of the plot for C Section beam. Maximum amount of stress is produced around 3.883e+01N/mm near the fixed support region.

DISPLACEMENT

• RECTANGULAR BEAM

• The rectangular beam acts as a cantilever beam thus, the displacement is minimum at its fixed end shown by blue colored region and gradually increases till maximum displacement is reached which is at other free end. Here, the maximum displacement is indicated by the red colored region in beam and its max. value in the legend in mm.

• I SECTION BEAM

• The I Section beam acts as a cantilever beam thus, the displacement is minimum at its fixed end shown by blue colored region and gradually increases till maximum displacement is reached which is at other free end. Here, the maximum displacement is indicated by the red colored region in beam and its max. value in the legend in mm.

• C SECTION BEAM

• The C Section beam acts as a cantilever beam thus, the displacement is minimum at its fixed end shown by blue colored region and gradually increases till maximum displacement is reached which is at other free end. Here, the maximum displacement is indicated by the red colored region in beam and its max. value in the legend in mm.

STRAIN

• RECTANGULAR BEAM

• The maximum value of strain is 2.586e-05 shown by red region near the fixed support and minimum strain developed at the other free end.

• I SECTION BEAM

• The maximum value of strain is 2.070e-05 shown by red region near the fixed support and minimum strain developed at the other free end.

• C SECTION BEAM

• The maximum value of strain is 1.262e-04 shown by red region near the fixed support and minimum strain developed at the other free end.

COMPARISON OF BEAMS :

• RECTANGULAR BEAM

• I SECTION BEAM

• C SECTION BEAM

• The above images shown the final results for comparison of stress, strain and displacement produced in Rectangular, I section and C section beam.

Case No.	Max. stress(N/mm^2)	Max. strain	Max. Displacement(mm)
1.	7.557e+00	2.586e-05	3.102e-02
2.	5.563e+00	2.070e-05	0.0228
3.	3.883e+01N	1.262e-04	3.018e-01

Observation :

• The same material is applied for all the 3 cases of the beam that is common material Alloy steel with its specific yield strength. We could observe that the maximum amount of stress is around 3.883e+01N/mm in C section beam also, the strain and displacement is maximum in C section as compare to Rectangular and I section beam. The Minimum stress, strain and displacement produced among all the 3 cases is in I section beam. Even less material is required for I section beam as compare to Rectangular beam.

CONCLUSION :

In the analysis and comparison of beam on the basis of their results for stress , displacement and strain generated at overall beam section for alloy steel material the I section beam is the best one to use rather than other. We had briefly understood the bending of beams for different cross sections with a specific load acting on it and how the beam behave after the bending stresses are developed in the material of beam. Comparison of beam gave us the fundamentals for Beam bending and the relation of stress , strain and displacement within the elastic limit as all the beams material yield strength is more and the generated results have minimum value than it respectively which means none of the beam goes above the yield strength and fails.

ANIMATION :

Animation for analysis of an I section.