Comparison of bending in beams

Comparison of bending in beams

Aim: To model the three beams in provided dimensions and to load the beam at the smaller face to compare the bending of beams with each other.

Beams

Beams are generally structures that are capable of withstanding loads applied over them. Usually beams are supported at it ends depending on its type. The load that acting over the beams leads to shear force and bending momentum which leads to displacement, stress, strain induction of the beams.

Beams can be classified on their shapes and the way in which they are supported.

The types of beams depending upon their support are:

• Simply supported beam
• Fixed beam
• Cantilever beam
• Over hanging beam
• Double over hanging beam
• Continuous beam
• Trussed beam

The beams are also classified depending upon the shape of the cross section of the:

• Rectangular beam
• I-Shape beam
• H-Shape beam
• L-shape beam
• C-Shape beam

Objective of the project

• To create three beams of I, H, C shaped in the given dimension.
• To extrude the beam cross sectional geometry to a length of 400 mm.
• To perform a loaded analysis over the beam with a load of 1500 N on the smaller face of the cross-section.
• To obtain the Stress, Displacement and Strain of the loaded beam and to compare them.

Body:

All the three beams are modeled in the required dimensions

Simply supported beam

Figure 1: Cross section of rectangular beam in mm

Figure 2: Solid model of rectangular beam in mm

I-Shaped Beam

Figure 3: Cross section of I-Shaped beam in mm

Figure 4: Solid model of I-Shaped beam in mm

C-Shaped Beam

Figure 5: Cross section of C-Shaped beam in mm

Figure 6: Solid model of C-Shaped beam in mm

Constrains and Loading of the Beam

Figure 7: The Rectangular beam is fixed at its cross section and loaded at the smaller top face

Figure 8: The I-shaped beam is fixed at its cross section and is loaded at the smaller top surface of the beam

Figure 9: The C-Shaped beam is fixed at its cross section and is loaded at the smaller top surface of the beam

Meshing

The meshing of the beam is done at 6 mm mesh fineness

Stress:

Displacement:

Strain:

Beam Maximum Stress (N/m^2) Maximum Displacement (mm) Maximum Strain

Simple 9488774 0.026 2.648e-05

I-Shape 25324830 0.566e-02 8.926e-05

C-Shape 46104006 0.304 6.643e-04

Conclusion:

From the chart and the table we can say that the Stress produced is less for the simple beam as the material density of simple beam is much higher than the rest three which helps to resist the bending movement produced by the load. In view with the Displacement the maximum is with the C-shape, because the load acting on the upper face had very less material down which lead to maximum load acting on the hanging surface with made the lip of the c beam to bend very large. The strain produced is low in the C-shape beacuse the compressive force acting on the beam changed into torsion that made the no change in length, were as the loads on other two beam made them to extend little.