1. MECH 322 Instrumentation Lab 5 Elastic Modulus of an Aluminum Beam Performed: February 9, 2014 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 factor and beam thickness measurement would reduce the uncertainty in elastic modulus.

3. Table 1 Beam Dimension Measurements and Statistics T (Caliper)T (Micrometer)W (Caliper)W ( Micrometer) [ in ] Mithun0.1840.18420.9940.9923 Mithun0.1830.18410.9920.9932 Venkata0.1840.18390.9970.9951 Venkata0.1840.18530.9920.9932 Sample Average0.18380.18440.99380.9935 Sample Standard Deviation, S0.00050.00060.00240.0012 Instrument Readability,  R min 0.0010.00010.0010.0001 S/  R min 0.56.32.411.8 This table shows measurements by students of the beam thickness T and width W using a Caliper and Micrometer. The Sample Average, Sample Standard Deviation (S), Smallest Increment of each instrument (  R min ), and ratio of S/  R min are tabulated. The caliber gave slightly more consistent reading (smaller S) for T than the micrometer, but less consistent readings for W.

4. Table 2 Micro-strain 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 Micro-strain 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). Only one point is seen 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 Best Estimate Uncertainty Confidence Level Uncertainty Found From W [in]0.99360.0017 0.6826 (1  ) Multiple Measurements T [in]0.184060.00062 0.6826 (1  ) Multiple Measurements L [in]11.0000.031 0.9974 (3  ) Half of Smallest Instrumental Increment S [1]2.0750.010 0.6826 (1  ) Manufacturer specified value a [  m/(m*kg)] 921.31.3 0.6826 (1  ) Statistical Analysis This table summarizes the best estimates and uncertainties of the values used to calculate the elastic modulus –The confidence-levels of the five uncertainties are not the same

7. Table 4 Input Measurement Contributions to the 95%-Confidence-Level Uncertainty in E Based 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