Memorandum

To: Andy Theiss
From: Kevin Geohegan (Seat 9), Karthik Pillalamarri (Seat 16), Sam Reifsteck (Seat 3), Justin Sikkema (Seat 6)
Date: 11/4/2015
Re: Materials Testing
1. Introduction
The arm supports for Office Spaces’ newest chairs need to be strong, yet not overly heavy or overly expensive. There were four combinations of materials and cross-section designs for the arm supports available to us for testing: rectangular steel, brass, and aluminum, as well as hollow, square aluminum. The purpose of the first part of the experiment was to directly analyze these options and determine which one would work the best in the chairs. There were three other materials not available, but still considered for use: Titanium, pure gold, and …show more content…
Results and Description
For the first part of the experiment, the results were recorded as a table of deflection measurements from each beam resulting from various loads. This table can be seen in Table 1, in Tables and Figures. The data from this table was then plotted using MATLAB. After plotting, trendlines were drawn to model the data. The graph of the trendlines for each beam, as well as their respective equations can be seen in Figure 1, in Figures and Tables. The best representation of the beam’s strength is its Young’s Modulus, or Modulus of Elasticity, which models an object’s resistance to strain under stress. The higher the value of a beam’s Modulus of Elasticity, the stronger it will be. Using the data described above, the Modulus of Elasticity of each beam can be calculated using Equation 1. Table 2, in Tables and Attachments, shows the Modulus of Elasticity of each of the four beams analyzed.

For the second part of the experiment, the results of the Finite Element Analysis yielded displacement values in the same way as in the material analysis in part 1 of the experiment. From these displacement values, the same calculations can be made, and non-experimental values for the Modulus of Elasticity of each material result. These values are shown in Table …show more content…
Discussion
After researching the Moduli of Elasticity of the 6 materials, it is apparent that our experimental data varies. The variances between the measured values of Young’s Moduli and the accepted values can be seen in Table 2. While aluminum (rectangular cross-section) had its value close to accepted, brass, steel, and aluminum (square cross-section) were significantly different from their theoretical values. These differences may have been caused by plastic strain (strain that is not reversed when load is removed), or they may have been caused by conditions such as temperature or humidity.

The slopes of the curves in Figure 1 show the ratios of displacement to load for the four tested designs. As the slope increases, the displacement per unit force increases, meaning the Modulus of Elasticity decreases. Cross-sectional area, area moment of inertia, and the material’s Modulus of Elasticity are all inversely related to the slope, meaning as cross-sectional area or Modulus of Elasticity increases, the displacement decreases. An example of this concept is the difference between the two aluminum beams. The area moment of inertia of the hollow square beam is greater than that of the rectangular beam, and its displacement was much less than its rectangular counterpart of the same