Comparison of Bending of beam

AIM: Comparison of bending in beams and compare the results of stress, displacement and strain for all the three cases and suggest the best out of the three.

Theory:

Bending of Beams:

In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element.

Fig illustrates Bending of an I-beam.

2. Geometry Of Beams(given):

2.1 Rectangular Beam

2.2 I-section Beam

2.3 C-section Beam

3. Procedure:

• Creating the geometry in SolidWorks.
  • Case 1: Rectangular Beam

• Case 2: I-Section Beam

• Case 3: C-Section Beam

• After creating the geometry, extrude it to 400mm.
• Under Simulation, perform a new study for static analysis.
• General steps in FEA problem:
  • Pre-processing:-
    • Defining material property. Here we have defined the material for each beam to be alloy steel.
  • Solving:-
    • Types of Analysis: Static Analysis
    • Beams are fixed at one end of the extrusion along the cross-section.
    • A 1500N load was applied over the top face
    • The Simulation was run using a basic mesh.
  • Post Processing:-
    • Results: Stress, strain, and displacement contours/plots.

4. Output

Case 1: Rectangular Beam

• Observation:-
  • Stress Contour: It achieves maximum yield strength at 6.204e+002N/mm.
  • Displacement Contour: It is quite evident from the contour that fixed end does not experience any changes, as we move to the other end, displacement is maximum at a distance of 3.1e-002mm.
  • Starin Contour: Maximum strain is experienced on the fixed end i.e. 2.402e-005.

Case 2: I-Section Beam

• Observation:-
  • Stress Contour: Here stress is evenly distributed. It achieves maximum yield strength at 6.204e+002N/mm.
  • Displacement Contour: It's quite similar to case 1 stress contour, but slightly higher displacement i.e. 8.537e-002mm, this is due to lose in weight as compared to a rectangular beam(case 1).
  • Starin Contour: Maximum strain is experienced on the fixed end i.e. 7.564e-005.

Case 3: C-Section Beam

• Observation:-
  • The beam experiences a torsion due to the vertical force applied onto the smaller face.
  • Stress Contour: It achieves maximum yield strength at 6.204e+002N/mm.
  • Displacement Contour: Displacement is maximum at a distance of 3.021e-001mm.
  • Starin Contour: Maximum strain is experienced on the fixed end i.e. 1.385e-004.

5 Results/Final Observation:

• If we compare the stress plots, maximum stress induced is less on the rectangular beam then on the I section and is maximum at C-section beam.
• Strain figures indicate that maximum change in length takes place in the C-section beam and minimum change in length occurs in I-section beam and the displacement plots indicate that minimum displacement occurs in the rectangular beam after application of 1500N and maximum displacement occurs in the C-section beam.
• It can be seen that the C-section beam is subjected to torsion, therefore, it is the least preferred among the three beams.
• Since stress induced in both the I-section and rectangular beam is under the yield strength therefore both the beams will sustain the force of 1500N properly without failing, but if we look at the distribution of stress, it is quite evenly distributed in the I-section, which I feel will withstand larger force as compared to rectangular beam.
• So, I would prefer the I-section beam as the best of the three beams