Comparison of Bending in Beams using FEA Analysis

Aim:- Comparison of Bending in Beams using FEA Analysis

Objective:-

1. To compare the performance of three types of the beam under the bending load.
2. To compare the results of stress, displacement, and strain for all three cases and suggest 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. The loads applied to the beam result in reaction forces at the beam's support points. The total effect of all the forces acting on the beam is to produce shear forces and bending moments within the beam, which in turn induce internal stresses, strains, and deflections of the beam. Beams are characterized by their manner of support, profile (shape of cross-section), equilibrium conditions, length, and material.

Classification of beams:-

In engineering, beams are of several types:

1. Simply supported – a beam supported on the ends which are free to rotate and have no moment resistance.
2. Fixed – a beam supported on both ends and restrained from rotation.
3. Over hanging – a simple beam extending beyond its support on one end.
4. Double overhanging – a simple beam with both ends extending beyond its supports on both ends.
5. Continuous – a beam extending over more than two supports.
6. Cantilever – a projecting beam fixed only at one end.
7. Trussed – a beam strengthened by adding a cable or rod to form a truss

Study Parameters:-

In this study, we will compare 3 types of beams which are

1. Rectangle cross-section beam
2. C-section beam
3. I-section beam

All beams are of 400mm length and are made of Alloy Steel.

A force of 1500 Newton is applied on the smaller face of each beam and relevant data is then compared for all the cases.

All the beams are in cantilever condition (one end of the beam to be fixed) with an average mesh size of 10mm.

Properties of Alloy Steel are given below:-

Material type = Linear elastic isotropic

Default failure criterion = Max von mises stress

Elastic Modulus = 2.1e+11 N/m^2

Poisson's Ratio = 0.28

Shear Modulus = 7.9e+10 N/m^2

Mass Density = 7700 kg/m^3

Tensile Strength = 723825600 N/m^2

Yield Strength = 620422000 N/m^2

Thermal Expansion Coefficient = 1.3e-05 /K

Thermal Conductivity = 50 W/(m·K)

Specific Heat = 460 J/(kg·K)

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Rectangle Beam:-

Mass properties of this model:-

Stress plot:-

Displacement plot:-

Strain plot:-

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C - section Beam:-

The structural channel, also known as a C-channel or Parallel Flange Channel (PFC), is a type of (usually structural steel) beam, used primarily in building construction and civil engineering. Its cross-section consists of a wide "web", usually but not always oriented vertically, and two "flanges" at the top and bottom of the web, only sticking out on one side of the web.

The structural channel is not used as much in construction as symmetrical beams, in part because its bending axis is not centered on the width of the flanges. If a load is applied equally across its top, the beam will tend to twist away from the web. This may not be a weak point or problem for a particular design, but is a factor to be considered.

Channels or C-beams are often used where the flat, backside of the web can be mounted to another flat surface for maximum contact area. They are also sometimes welded together back-to-back to form a non-standard I-beam.

Mass properties of this model:-

Stress plot:-

Displacement plot:-

Strain plot:-

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I - section Beam:-

An I-beam, also known as H-beam (for universal column, UC), w-beam (for "wide flange"), universal beam (UB), rolled steel joist (RSJ), or double-T (especially in Europe), is a beam with an I or H-shaped cross-section. The horizontal elements of the I are flanges, and the vertical element is the "web". I-beams are usually made of structural steel and are used in construction and civil engineering.

The web resists shear forces, while the flanges resist most of the bending moment experienced by the beam. The Euler-Bernoulli beam equation shows that the I-shaped section is a very efficient form for carrying both bending and shear loads in the plane of the web. On the other hand, the cross-section has a reduced capacity in the transverse direction, and is also inefficient in carrying torsion, for which hollow structural sections are often preferred.

Mass properties of this model:-

Stress plot:-

Displacement plot:-

Strain plot:-

Data comparison:-

Beam type		Max. Stress(N/m^2)	Max. Strain(mm)	Max. Displacement(mm)	Mass (kg)	Factor of Safety
Rectangle		7,374,519	0.000026 (0.26*10^-4)	0.031	11.09	84.13
C - section		41,611,864	0.000149 (1.49*10^-4)	0.310	3.20	14.90
I - section		19,366,096	0.000073 (0.73*10^-4)	0.085	2.36	32.03

The factor of safety = Yield stress / Max. Working stress

On comparing the three cases, we concluded that the maximum stress is induced in C - section beam, and the minimum stress is induced in a rectangle beam.

The maximum strain is observed in C - section beam and the minimum strain is induced in a rectangle beam.

The maximum displacement is observed in C - section beam and the minimum displacement is induced in a rectangle beam.

Here the maximum factor of safety is for the rectangle beam and the least is for C - section beam.

Overall, the minimum variations of stress, strain, and displacement are observed in the Rectangle beam whereas the maximum stress, strain, and displacement is observed in C - section beam, and I - section beam lies in between both with average values.

If the mass is considered, the rectangle beam having maximum mass will be costly among others but is well suited in this case as per the parameters, if the mass is neglected.

I - section beam being least in mass will be cheap for this case being average in stress, strain, displacement, and factor of safety.

C - section beam will not be considered as a good choice for this case due to maximum stress, strain and displacement values.

Conclusion:-

1. Most beams in reinforced concrete buildings have rectangular cross-sections, but a more efficient cross-section for a beam is an Ior H section which is typically seen in steel construction. Because of the parallel axis theorem and the fact that most of the material is away from the neutral axis, the second moment of area of the beam increases, which in turn increases the stiffness. An I-beam is only the most efficient shape in one direction of bending: up and down looking at the profile as an I. If the beam is bent side to side, it functions as an H where it is less efficient.
2. In this study, the I - section beam is considered a good choice because it has the least mass due to which it be cheaper among others. Moreover, the values of stress, strain and displacement are quite feasible for a uniform distributed load of 1500 Newton.
3. If the mass and the cost are not considered then the rectangle beam is the best choice because of the least stress, strain, and displacement induced in it and also the factor of safety is maximum for the rectangle beam.

Reference:-

https://en.wikipedia.org/wiki/Beam_(structure)

https://en.wikipedia.org/wiki/Bending