Mechanical Engineering Lab

BIOEN 4250: BIOMECHANICS I Laboratory 4 – Principal Stress and Strain

Report Guide Due Date: Tuesday, December 4, 2018 by 10:45am (submit via Canvas)

Instructor: Lucas Timmins ([email protected]) TAs: Allen Lin ([email protected]), Kelly Smith ([email protected]) Each student must turn in a separate laboratory report representing his or her own work. The report should be prepared using MS Word or an equivalent word processor. Grammar and style of the written will be evaluated and included in the grading, so please proof your report, rewrite the initial draft as necessary, and check for spelling and other grammatical errors before submission. The report should contain the following sections: Title/Name: Your report must include the following information (in the following format) in the upper-left corner of the first page:

BIOEN 4250 – Laboratory 4, Fall 2018: Principal Stress and Strain <YOUR NAME HERE> <YOUR GROUP ID> <DATE HERE>

Objective (1 paragraph): State the purpose of the lab measurements and analysis. Motivate the need for the measurements. State your perception of the intended educational goals of the laboratory in terms of learning new measurement and analysis techniques. The objective section should be one paragraph. Methods: (no longer than 2 pages)

a) Describe the methods and step-by step procedure to perform the measurements. For example, • Describe the strain gage rosette configuration and orientation of how it was mounted to the beam • Describe how the beam was mounted • State the material the beam was constructed from and provide the elastic modulus • Provide the beam dimensions (e.g., average beam width and thickness, length between rosette

centerline and application of point load • Describe the procedure for application of loads to the beam and capturing strains

b) Describe the methods employed to analyze the data. For example,

• Provide an overview of the analysis (i.e., step-by-step description), including explicitly stating all equations

• Provide an overview of the code/processes used to analyze the data (Matlab is encouraged) • State how the plots were created (e.g., Matlab, Sigmaplot)

Note: You do not need to include your analysis code in your lab report. However, you do need to provide a clear and concise explanation of what you did. Do not give a line by line description of your code.

Results/Discussion (2.5 pages, including a 1 page limit for plots): Discuss the following points, regarding the distribution of stress in the cantilever beam, in connection to the plots requested below. The description of your results and interpretation (excluding plots) should be a maximum of 1.5 pages.

BIOEN 4250: Laboratory 4 – Report Guide

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Basic Discussion Points 1) Where (through the thickness of the beam) is the maximum axial (longitudinal) stress (longitudinal)?

Where is the minimum value? Provide an explanation why. 2) Where (through the thickness of the beam) is the maximum shear stress? Where is it the minimum?

Provide an explanation why. 3) Describe why points 1 and 2 are what they are, and how they are related. 4) If you did not know the elastic modulus of the beam, which was given to you in this case, how would you

go about calculate it from the data you collected in this lab? 5) In the text of the results section, provide the resulting “calibration constant” that you determined in units

of Newtons/strain, as well as your calculated angle of rotation that would bring the axis of gage #1 in line with the axis of the largest principal stress.

6) Address the discussion points specific to each plot as listed below. 7) Interpret your results. Are they what you expected? Why or why not?

Plot 1: Principal Strains vs. Applies Load. Determine all three principal strains in the location of the strain gage rosette and then plot these strains (in micro-strain) as a function of applied load (in Newtons). You should have a single value for each measurement (as you have 6 different loading levels, you should have 6 data points per line in your plot). See the tips below for how to do this in a manner that will be consistent with the answer key.

Discuss: How do the strains differ from each other? Are the values and magnitudes what you expected to see? Plot 2: Principal Stress vs. Applied Load. Calculate the principal stresses (there are only 2 that are non-zero) based on the measured principal strains. Plot these principal stresses (in MPa) as a function of the applied load (in Newtons). You should have a single value for each measurement (as you have 6 different loading levels, you should have 6 data points per line in your plot). See the tips below for how to do this in a manner that will be consistent with the answer key.

Discuss: How do the stresses differ from each other? Are the values and magnitudes what you expected to see, and why? Explain why there is not three principal stresses on this plot. Plot 3: Comparison of Measured and Theoretical Longitudinal Stress. On the same set of axes, plot both the largest principal stress (measured longitudinal stress) and the theoretical longitudinal stress as calculated from the beam flexure equation (both in MPa) as functions of applied load. You should have a single value for each measurement (as you have 6 different loading levels, you should have 6 data points per line in your plot). See the tips below for how to do this in a manner that will be consistent with the answer key.

Discuss: How do these two measures of the same quantity compare? Explain any differences that you see, and what could have caused them. Is this what you expected to see? Notes and Tips:

• Regarding the calculation of strains, you will likely have some noise in the strain gage measurements. Also, as you will be manually starting and pausing the data recording, each group will likely have a different number of data points at each loading case. For example, one group may have 15 data points for the 100 g loading for gage #1, while another has 17 or 20 data points for that same measurement. To ensure that you have a single data point for each loading case for the plots above, take the average of a given measurement rather than dealing with every data point. With 6 loading levels (0 grams through 500 grams) you will have 6 averaged measured values for each of the three strain gages in the strain gage rosette. Please contact your TA if this is not clear.

• Regarding the calculation of Poisson’s ratio, calculate it separately for each of the 5 non-zero loading levels and use the overall average Poisson’s ratio for your calculations when it is needed.

• When item 1 is plotted as a function of item 2, item 2 is on the X-axis and item 1 is on the Y-axis (i.e., 𝑦 = 𝑓(𝑥) denotes 𝑦 is a function of 𝑥, and 𝑦 would be on the Y-axis).