1. MECH 322 Instrumentation Lab 5 Elastic Modulus of an Aluminum Beam Performed: February 13, 2007 Group 0 Miles Greiner Lab Instructors: Mithun Gudipati, Venkata Venigalla

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. The surface strain was measured on the top and bottom surface near the support while a range of weights were loaded on the outer end. The slope of the strain versus mass data was used along with the measured beam dimensions to calculate the elastic modulus and its uncertainty. The calculated Elastic Modulus of the beam was 64.7 + 1.2 GPa (95%) which is 6% below the reference value for alloy 6061-T6. A more precise strain gage and beam thickness measurement would reduce the uncertainty in elastic modulus.

3. Table 1 Beam Dimension Measurements and Statistics This table shows the measurements of the beam thickness (T) and width (W) using two different instruments (Caliper and Micrometer) by different students. The Sample Average, Sample Standard Deviation (S), Smallest Increment of each instrument (  R min ), and ratio of S/  R min are tabulated.

4. Table 2 Microstrain Reading versus Mass As expected, the strain increases as the load increases. The reading is not the same for the same mass on the ascending and descending cycles

5. Figure 1 Microstrain Reading versus Mass The slope of the best fit line is 921.3  m/(m*kg). The uncertainty of the slope with a 68% -confidence level is 1.3  m/(m*kg). We see only one point in the figure for each mass because the ascending and descending strain values are approximately same.

6. Table 3 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 quantities.

7. Table 4 Input Measurement Contributions to the 95%-Confidence Level Uncertainty in E Base on these measurements, E = 64.7+1.2 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 does not include this value. The uncertainties in T and the strain gage factor make the largest contributions to the uncertainty in E. More precise measurements of these properties would improve the measurement.