Comparison of Beams

AIM:

To compare the performance of 3 types of beams under bending loads.

INTRODUCTION: Bending of beams is a frequently encountered loading situation in practice. A slender member subject to traverse loads is termed as a beam under bending. At any cross-section, the traverse loads generate shear and bending moment to maintain equilibrium. The bending causes a change in curvature of the beam and induces tensile and compressive stresses in the cross-section of the beam. Maximum stresses are achieved in layers furthest from the neutral axis, the layer at which strain is zero.

THEORY: This project explains the theory of ultimate load applied to a cantilever beam of rectangular cross section, I- Section and C- Section based on the concept of ultimate load under pure bending.

Pure bending refers to flexure of a beam under a constant bending moment. Therefore pure bending occurs only in regions of a beam where the shear force is zero. In the simplified engineering theory of bending, we make the following assumptions:

1. The beams are assumed to internally statically indeterminate.
2. The strains caused by the deformations have a relationship with stresses.

OBJECTIVE:

To perform an FEA analysis and compare the results for stress, strain and displacement in the beams and to identify the optimum design choice based on the performance parameters.

PROCEDURE:

1. Firstly the design sketch of the beam is made in the SolidWorks, giving appropriate dimensions.
2. All the 3 beams are given the exact extruded length of 400mm, using the mid plane extrusion command.
3. Now we start our Simulation Study on SolidWorks.
4. Before, starting the simulation study, we select the material for the beam. We choose ‘AISI 1010 Steel, Hot Rolled’ an optimum material available on SolidWorks for a beam analysis.
5. Now after starting the simulation study, three factors are important – 1. Fixtures; 2. External loads; 3. Mesh Size.
6. We apply a fixed geometry fixture to the front part of the beam having the dimension of 45 X 80 mm.
7. The external load is applied at the top face of the beam having dimension of 45 X 400 mm.
8. Since, normally the force are not acting entirely on the beam surface, so we use the split command and cut the face of the beam starting from the extreme end to 164mm to the right.
9. This will be our region, where we will apply the force of 1500N, acting vertically downwards.
10. The mesh is kept as fine as possible, to get more accurate results. The SolidWorks is using H- method for mesh generation, where by increasing the mesh size, the triangle are getting finer and finer.
11. These same steps are followed to compute the study for an I-Section and a C-Section respectively.
12. The Stress, Strain, Displacement and Factor of Safety for the all 3 beams are compared.

RESULTS:

X-Section	Stress	Strain	Displacement	FOS	Mass	Volume
Rectangular Beam	15.977	0.000050	0.08203	41.783	11.088	0.00144
I-Section	36.797	0.000124	0.1653	4.8917	2.326	0.0003067
C-Section	61.086	0.000229	0.72693	2.9466	4.950	0.00062

The Tabulation shows the data for all the 3 beams whose parametric study is conducted.

The stress acting on the Rectangular Beam is only 15.977N/mm^2, where the yield strength of the material is 180N/mm^2 having the ‘Factor of Safety = 41.783’ which shows how over-engineered the product is. The mass and volume of this beam is also high as compared to the 3, which shows increase in the material cost thus ultimately increasing the cost of the beam.

The stress acting on the I-Section is 36.797N/mm^2, which is well within the specified limit. This I-Section has an optimum FOS, mass and volume making it an optimum choice among the 3.

NOTE: Since, we do not know what is the practical application of the beam, so we consider to take the Factor of Safety to be at-least ‘greater than 4’.

The C-Section also seems to be an optimum product, but has greater mass and volume than the I-Section ultimately increasing the material cost. The ‘Factor of Safety is only 2.946’, which is below the specified range, thus making the beam less reliable on the panic conditions.

I think in the given condition, the I section is better suited for application because it has optimum mass, volume, fos and stress holding capacity. The rectangular beam has a factor of safety of 41.783, which show how the over-engineered the product is, has higher mass and volume which means increase in the material consumption and thus increasing the cost of the product.