Comparison of bending in beams

Aim:

To model and made a finite element analysis on three different beams under bending load.

Objectives:

• To model three different beams in the solidworks.
• The rectangular beam, I-section beam and the C-section beam is modelled.
• The finite element analysis was done in the solidworks simulation.
• The stress, strain and the displacement of the object is analysed.

Finite Element Analysis:

Finite Element Analysis is a widely used study which deals with various analysis like thermal, structural etc on the mathematical and engineering model. The main principle of this analysis is to divide the model into various smaller elements and then the analysis are made on each element.

Beams:

Beam is a structural element in which the force is acted laterally on it. The beams play a major role in the construction of various buildings and the chasis construction. Based on the load applied on it and the maximum load withstand by the beam, beams are designed with various cross sections.

Rectangular beam:

Rectangular beams are widely used in various applications. It allows for fast construction in the form work. It can withstand high tension and the shear reinforcing.

I-section beam:

The I-section beam are often called as H beam has a specific applications. Based on the euler-bernoulli beam equation, the I-section is specially designed to withstand the bending and shear loads.

C-section beam:

The C-section beam is designed to carry the small span or light duty applications. The C-section beams are applied in brackets, railings, inserts, joints etc.

Input parameters:

• The drawings for designing the three different beams are attached below,

• These sketches should made an extrude of 400mm.
• Apply a load of 1500N on the smaller face(i.e. 45mm face for rectangular beam, 40mm face for I-section beam and 45 mm face for C-section beam)
• Compare the results of stress, displacement and strain for all the three beams.

Beams modelling:

The rectangular beam is designed based on the given input parameters.

The I-section beam is designed based on the given input parameters.

The C-section beam is designed based on the given input parameters.

Simulation setup:

Fixed geometry:

The bending analysis is initiated by fixing a particular face of the beam.

Force application:

The transverse load is applied on the particular face based on the input parameter.

Meshing:

Meshing is a major prameter in the simulation aspects. Meshing make the model into smaller elements. Based on the meshing number, the accuracy of the simulation results get vary.

All beams are provided with the general mesh of 6mm.

Results and discussions:

Rectangular beam:

The stress, strain and the displacement image of the rectangular beam after analysis were shown below,

Stress diagram:

Strain diagram:

Displacement diagram:

• The stress diagram express that the stress and strain are maximum at the fixed end of the rectangular beam.
• The yield strength is given as 6.204e+08. The stress value has a minimum value of 2.072e+02 to the maximum value of 9.626e+06.
• The strain value has a minimum value of 9.317e-10 to the maximum value of 2.997e-05.
• The displacement simulation result has a minimum value of 1.000e-30 to 3.102e-02.
• The displacement value is maximum at the opposite end of the fixture.

I-section beam:

The stress, strain and the displacement image of the I-section beam after analysis were shown below,

Stress diagram:

Strain diagram:

Displacement diagram:

• The yield strength of the beam is obtained as 6.204e+08. The stress has the minimum value of 1.518e+03 to the maximum value of 2.358e+07.
• The strain has the minimum value of 7.955e-09 to the maximum value of 7.814e-05.
• The displacement of the beam has a minimum value of 1.000e-30 to the maximum value of 8.719e-02.
• The stress and strain values are maximum at the fixed end of the beam.
• The displacement value is maximum at the opposite end of the fixed beam.

C-section beam:

The stress, strain and the displacement image of the C-section beam after analysis were shown below,

Stress diagram:

Strain diagram:

Displacement diagram:

• The stress of the C-section beam has the minimum value of 6.352e+04 to the maximum value of 4.028e+07. The yield strength is obtained as 6.204e+08.
• The strain of the beam has a minimum value of 2.621e-07 to the maximum value of 1.426e-04.
• The displacement has a minimum value of 1.000e-30 to the maximum value of 3.093e-01.
• The stress and strain are higher at the fixed end and also at the inner side of the C-section beam.
• The displacement is maximum at the two end point on the opposite side of fixed end in the C-section.

Comparion Table:

Beams	Max. Stress (MPa)	Max. Strain	Max. Displacement (mm)
Rectangular beam	9.626	2.997e-05	3.102e-02
I-section beam	23.58	7.814e-05	8.719e-02
C-section beam	40.28	1.426e-04	3.093e-01

From the results of the simulation, the I-section beam withstand a maximum stress of 23.58 MPa and the maximum strain of 7.814e-05. The maximum displacement of the I-section beam is 8.719e-02 and it is the maximum value among all the three beams. The I-section beam also consumed less material when compared with rectangular beam. The C-section beam also consumes less material but the quality differs. Thus, the I-section beam is good at economy and quality aspect.

Conclusion:

Thus, the three different beams are modelled and the FEA was done on each beam using solid works.