Beam Deflection

Topics: Young's modulus, Cantilever, Stiffness Pages: 12 (2631 words) Published: April 22, 2014
Summary
The primary goal of the experiment was to determine the structural stiffness of two cantilevered beams composed of steel and aluminum while maintaining both beams at a constant thickness and cross sectional area. The experiment also investigated material properties and dimensions and their relationship to structural stiffness. The experiment was divided into two separate parts. The results for the first part of the experiment were obtained by clamping the beam at one end while applying different masses at a specified length across the beam and then measuring deflection. The measuring device was set a specified distance from the clamped end. The following procedure was employed for both the steel and aluminum beam. The second part of the experiment required placing a single known mass at various lengths across the supported beam and then measuring the resulting deflection. This method was only completed for the steel beam. The deflections from both parts of the experiment were then averaged independently to ascertain final conclusions. The first part of the experiment resulted in a much greater deflection for the aluminum beam, with its greatest deflection spanning to an average of 2.8 mm. Moreover, the deflection for the steel beam was much less, concluding that steel has a larger structural stiffness. In fact, the structural stiffness that was found for steel was 3992 N/m, compared to aluminum, which was 1645 N/m. In addition, the theoretical values of structural stiffness for steel and aluminum were calculated to be 1767.9 N/m and 5160.7 N/m, respectively. There was a large error between the theoretical and experimental values for steel, close to 29%. This could have been due to human error, or a defective beam. The second part of the experiment resulted in validating the fact that the values of deflection are proportional to length cubed. It was also determined that deflection is inversely proportional to the elastic modulus and that structural stiffness is proportional to the elastic modulus. Despite the fact that there was considerable error between some of the theoretical and experimental values, the experiment still proved to be effective in determining a reasonably accurate value for structural stiffness as well as verifying its relationship between material properties and beam dimensions.

Table of Contents

Summary 2

List of Figures 4

List of Tables 5

List of Equations 6

Introduction 7

Theory 8

Test Setup & Procedures 11

Results 14

Discussion 19

Conclusion 20

References 21

Appendix 22

List of Figures

Figure 1 – The Fourth Bridge in Scotland, United Kingdom, an Example of a Cantilever Beam 7

Figure 2 – Cantilever Beam of Length l, Clamped at One End and Loaded at the Other End 8

Figure 3 – Apparatus 12

Figure 4 – Displacement Meter 12

Figure 5 – Masses and Beams 12

Figure 6 – Testing 12

Figure 7 – Load vs....
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