Solid Beams Lab Report

Abstract

The main aim of this experiment was to explore the properties of 6 different types of Cantilever Beams provided to us. 3 Hollow and 3 Solid beams were provided to us, and they were loaded with weights, to note the deflection produced. The first Experiment showed the linear relationship between Deflection and Load of the Solid Beams. The second Experiment showed a linear relationship between Mean Stiffness and Diameter of the Solid Beams. Experiment 3 was carried out to prove the linear relationship between stiffness, specific stiffness and diameter. The 4th experiment showed the Inverse relationship between Stiffness and (Length) 3 whereas the 5th experiment proved the relationship between Deflection and the Length of the Beams.

Step by step Loading was done so as to avoid Plastic Deformation.

Experiment 2

This only involved Solid beams and a graph was plotted after calculating Mean Stiffness.

Mean Stiffness vs Diameter was plotted.

Mean Stiffness = (Total sum of Stiffness for the beam) / (No. of readings taken)………… (3)

Experiment 3

In this experiment, Stiffness and Specific stiffness was compared to Diameter for both Hollow and Solid Cylinders.

Specific stiffness = Stiffness/ Mass ……… (4)

Experiment 4

This experiment was carried out to find out whether Stiffness is inversely proportional to Length3. Beams 3 and 4 were used for this experiment.

Experiment 5

Load was applied to different parts of the Beam, and then the Deflections were noted. The setup in Figure 2 was used. Results

Minimum and Maximum stiffness was calculated for each beam because of a very minimal error of ±0.00025.

Experiment 1 Beam One

Table no. 2 : Showing Calculations for Beam 1

Mass used (Kg) Load (N) Deflection (m) S (N/m) Minimum S (N/m) Maximum S (N/m)

0.2 0.91 0.091 10.77 10.74 10.8

0.4 1.68 0.168 11.67 11.65 11.68

0.6 2.51 0.251 11.71 11.7

However, due to excessive loading, the Solid Beams went through partial Plastic Deformation, which had an impact on the Stiffness factor of the Beams since Hooke’s law was not obeyed.

The first experiment, which was carried out successfully, proved that there is a linear relationship between Load and Diameter. There was an exponential increase in the Task two when Diameter and Stiffness were compared. The third experiment Mean stiffness for Solid beams was more, whereas the opposite was true for Hollow beams; i.e. Hollow beams had higher Specific stiffness than solid beams. The fourth experiment was conducted to prove that Stiffness is inversely proportional to L3, so a graph between Stiffness and L3 was plotted and the nature of the graph was linear.

Conclusion

The Experiments were a success and taught us a lot, with practical experiences accounting for all the theoretical knowledge we were provided with beforehand.

But due to some errors in apparatus (plastic deformation), a lot of variations occurred in the calculation of Stiffness for the beams.

Data