MEE 324 Lab 2

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Arizona State University, Tempe *

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324

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Mechanical Engineering

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Apr 3, 2024

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docx

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Lab 2: Material Characterization Fabian Ameen Lab Number: Thursday 10:30 - 11:35 AM Date of Experiment: 2/8/2024 Due Date: 2/23/2024 Abstract:
This lab experiment focused on conducting bending tests on 7075 Aluminum beams in cantilever configurations equipped with strain gauges. The objective was to obtain load-strain data for beams of uniform and variable cross-sections, analyze the effects of variable geometry on stress, strain, and curvature, and compare experimental results with theoretical expectations. Load-strain data was collected for beams with strain gauges mounted at various positions, ensuring elastic behavior. For the sample with constant cross-section, axial and transverse strains were measured, while for variable cross-section beam, strain measurements focused on the upper fibers to calculate stress and curvature. The experiment utilized a specially designed rig for load measurement. Through this experiment, Young’s modulus and Poisson’s ratio were determined for uniform cross-section beams, and the validity of beam theory regarding variable cross-sections was tested. Data Analysis: A) Shear force and Bending moment diagram of load 4 Shear Force 3.565 N R y x3 x2 x1 P = 3.565 N Bending Moment x3 x2 x1 P -0.94116 N-m P = I E y max x gauge ε axial (3) B) After plotting the data of microstrain 1 vs the load (Figure 1) a linear regression can be performed, the slope of which (44906) is equal to the I E y max x gauge term from equation 3 that was provided in the lab handout (shown
above). Plugging in the known variables y, x, and I, E can be solved for giving the calculated elastic modulus 44906 = I E y max x gauge 44906 = 20.54 6.27 3 12 E 3.135 264 E = 88 GPa This value of Young’s Modulus is above the literature value of 71 GPA [1] . This discrepancy is most likely due to a measuring inaccuracy as a small error can largely impact the calculated value. 0 0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 f(x) = 44906.22 x R² = 1 Load vs Axial Strain Strain Load C) Poisson’s ratio can be calculated by dividing the lateral strain by axial strain. By calculating the Poisson’s ratio for each loading the average and standard deviation can be determined through excel. Mean: 0.403 STD: 0.00963. This value is also slightly higher than the literature value of 0.33, which could also be due to measurement errors. D) Based on the data collected theory of the constant stress beam is valid. Based on the data collected both pairs of segments (1 with 2 and 3 with 4) have a constant strain at both points. This supports the idea that the stress is constant as well because stress is related linearly with strain. (Figure 2) Index Force (N) microstrain 1 microstrain 2 microstrain 3 microstrain 4 1 0.721 20.037 20.595 11.331 12.49 2 1.44 38.754 40.424 21.938 23.971 3 1.983 57.472 59.99 33.045 36.122 4 2.798 77.706 80.268 44.579 49.4
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5 3.615 96.387 100.044 55.447 61.551 Figure 2 (Data collected from constant stress beam) Conclusion In conclusion, the bending tests conducted on 7075 Aluminum provided important insight into the theory behind Young’s Modulus and beam theory. The first experiment gave proof of the theory that stress and strain can be linearly related with a constant (E). Also, the second experiment’s results proved that by varying the cantilever width a constant stress can be applied to a beam. The calculated values of the modulus of Elasticity and Poisson’s ratio were both slightly higher than the literature values. This is most likely due to a measurement error when the dimensions of the beam were taken, as a change in dimension can have a large impact on the calculation. References ASM Material Data Sheet , asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA7075T6. Accessed 23 Feb. 2024. [1]