1. MECH 322 Instrumentation Lab 5 Elastic Modulus of an Aluminum Beam Performed: February 9, 2004 Sinan Ozcan: I believe I performed 50% of the work for this laboratory experience. Participation grade __/50 Soma: I believe I performed 50% of the work for this laboratory experience. Participation grade __/50

2. Abstract The purpose of this lab was to measure the Elastic Modulus of an Aluminum Beam in bending. An aluminum beam was supported horizontally in a jig. The surface strain was measured near the support while a range of weights were loaded on the outer end. The slope of the strain versus load mass line was used along with the measured beam dimensions to calculate the elastic modulus and its uncertainty. The calculated Elastic Modulus of the beam was 70.0 + 1.8 GPa (95%) which is in agreement with a reference value for alloy 6061-T6. A more precise strain gage would improve the measurement.

3. Table 1 Resistance Change Under Tension and Compression Loading The unloaded resistance is greater in the tension configuration than the one in the compression configuration due to bending of the beam under its own weight. The magnitude of the fractional change in the resistance is 0.097%. The magnitude of the fractional change in tension and compression is approximately same.

4. Table 2 Beam Dimension Measurements and Statistics This table shows the measurements of the thickness (T) and width (W) using two different instruments (Caliper and Micrometer) by different students. The Average Values, Sample Standard Deviation (S), Smallest Increment of each instrument (I) and the ratio of S to I are tabulated. The Micrometer measurements appear to be slightly more consistent.

5. Table 3 Gage Strain Load Mass Data This table presents the strain measured for different load masses. As expected, the strain increases as the load increases.

6. Figure 1 Measured Strain vs. Load Mass The slope of the best fit line is 0.00030432 [1/kg]. Since the ascending and descending strain values are approximately same, we see only one point in the figure for each loading. The confidence interval of the slope with a 68% -confidence level is 0.00000054 [1/kg].

7. Table 4 Best Estimate and Uncertainty of Quantities Used to Calculate Elastic Modulus This table summarizes the best estimates and uncertainties of the values used to calculate Elastic Modulus. The confidence levels of the uncertainties are not the same for all five measured quantities.

8. Table 5 Input Measurement Contributions to the 95%-Confidence Level Uncertainty in E Base on these measurements, E = 70.0 ± 1.8 GPa (95%) For alloy 6061-T6, E = 68.9 GPa (Van Vlack, L.H. Elements of Material Science and Engineering, 3rd edition, Addison-Wesley, 1975). The measured confidence interval includes this value The uncertainty in the strain gage factor makes the largest contribution to the uncertainty in E. A more precise strain gage would improve the measurement.