Comparison of bending in beams.

AIM: Compare three types of beams under loading condition and pick out best one of them according to results.

OBJECTIVES:

• Model three types of beams.
• Perform FEA on three types of beams.
• Obtain stress, strain and displacement as a result.
• Compare the results and conclude which one is best out of the three.

THEORY:

The finite element method (FEM) is the most widely used method for solving problems of engineering and mathematical models. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a particular numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretisation in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain. The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. The FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function.

Stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material. For example, when a solid vertical bar is supporting an overhead weight, each particle in the bar pushes on the particles immediately below it. When a liquid is in a closed container under pressure, each particle gets pushed against by all the surrounding particles. The container walls and the pressure-inducing surface (such as a piston) push against them in (Newtonian) reaction. These macroscopic forces are actually the net result of a very large number of intermolecular forces and collisions between the particles in those molecules. Stress is frequently represented by a lowercase Greek letter sigma (σ).

Strain is a measure of deformation representing the displacement between particles in the body relative to a reference length. A strain is in general a tensor quantity. Physical insight into strains can be gained by observing that a given strain can be decomposed into normal and shear components. The amount of stretch or compression along material line elements or fibers is the normal strain, and the amount of distortion associated with the sliding of plane layers over each other is the shear strain, within a deforming body. This could be applied by elongation, shortening, or volume changes, or angular distortion.

`"Strain=Deformation/Original Shape"`

PROCEDURE:

All the three beams are designed according to given dimensions and extruded to a length of 400mm.

Case 1 Beam:

Case 2 Beam:

Case 3 Beam:

Simulation

Click on SOLIDWORKS Add-Ins and enable simulation

In simulation create new study, name the study and select following options

Study type - Static

Material – Alloy Steel

Fixture – Fixed geometry-> One smaller face of geometry (indicated by green arrows in below image)

External Load – Load of 1500N is applied along the length as UDL (indicated by purple arrows in below image)

Right-click on mesh, select Mesh and Run.

RESULTS:

Case 1

Stress

Displacement

Strain

Case 2

Stress

Displacement

Strain

Case 3

Stress

Displacement

Strain

Observation table:

Case No	Beam Type	Deformation Scale	Maximum Stress (N/m^2)	Maximum Displacement (mm)	Maximum Strain	Mass (Kg)
1	Rectangular	1175.77	7.417e+06	3.430e-02	2.772e-05	11.088
2	I	426.512	2.092e+07	9.442e-02	8.358e-05	2.3637
3	C	293061	2.517e+04	1.527e-04	7.717e-08	3.26736

From the above table we observe that the stress is maximum in rectangular beam but it has minimum strain compared to other beams. The I-beam have maximum displacement among all the beams but have least stress compared to other. The C-beam have the least displacement while stress and strain values lie in between the values of other two beams.

If we compared the deformation scale the I-beam have the lowest value while C-type have the highest value.

Among all the three beams rectangular beam have the highest mass and the I-beam have the lowest mass. The more the mass, the more the weight and more the cost.

CONCLUSION:

By comparing all the parameter, we can conclude that the case 2 beam i.e. I-beam is best option among the three.