COMPARISON OF BENDING IN BEAMS

COMPARISON OF BENDING IN BEAMS

AIM – To compare stress, strain and displacement in same loading conditions and select best among rectangular, I section and channel beam.

OBJECTIVES-

1. Create parts of all three beams.
2. Run static analysis for all of them. Compare the results.

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. It deforms and stresses develop inside it. In the quasi-static case, the amount of bending deflection and the stresses that develop are assumed not to change over time.

Compressive and tensile forces develop in the direction of the beam axis under bending loads. These forces induce stresses on the beam. The maximum compressive stress is found at the uppermost edge of the beam while the maximum tensile stress is located at the lower edge of the beam. Since the stresses between these two opposing maxima vary linearly, there therefore exists a point on the linear path between them where there is no bending stress. The locus of these points is the neutral axis. Because of this area with no stress and the adjacent areas with low stress, using uniform cross section beams in bending is not a particularly efficient means of supporting a load as it does not use the full capacity of the beam until it is on the brink of collapse.

PROCEDURE-

1. Create 3d models of different beams with help of sketches provided.
2. Extrude each beam to 400mm thickness.
3. Click on Simulation tab. Select Linear>static. Apply material alloy steel to beams.

4. Select Fixed geometry of one of the end faces of each beam
5. Apply a load of 1500N on the smaller side face (i.e. 45mm face for case 1, 40mm face for case 2 and 45 mm face for case 3).
6. Click on mesh and set parameter to 6mm to generate fine mesh.
7. Click on run.
8. Compare the results.

RESULTS -

Case1: Rectangular cross section beam

Case2: I cross section beam

Case3: Channel cross section beam

CONCLUSIONS & EXPLANATIONS-

1. Comparing stress values in each case we can see that minimum stress is developed in rectangular cross section beam while maximum stress is observed in channel cross section beam.
2. Comparing displacement values we can see that minimum displacement is observed in rectangular cross section beam while maximum displacement is observed in channel cross section beam.
3. Comparing strain values in each case we can see that minimum strain is developed in rectangular cross section beam while maximum strain is observed in channel cross section beam.

So, from above data we can easily say it is safest to use rectangular beam.

Mass of rectangular cross section beam= 9.856kg

Mass of I cross section beam = 2.401kg

Mass of channel cross section beam= 3.223kg

Clearly, I cross section beam gives best result in lowest mass and hence is cost effective.

I cross section beam is the most preferred one.