Elastic Deformation and Poisson's Ratio
Information to include in each of the sections in the lab write up
Title Page
Information and format given on page vi of the lab manual
Abstract
What was the experimental value for the modulus of elasticity and Poisson's ratio for the 4140 bar and the aluminum in the cantilever beam. How did these compare to the literature values? Where on the beam was the greatest strain? Was the superposition of stress a valid approximation?
Introduction
Why are the modulus of elasticity and Poisson's ratio important material properties? Please relate to stress and strain.
Procedure
Steel bar: What were the procedures that were followed? What were the increments of the loads on the steel? How were the strain gages mounted on the sample (which directions)? What data was collected (units)?
Aluminum beam: What loads were placed on the beam? At which positions were the loads placed? How was the data collected? At what points on the beam were strain data taken?
Results
2. Results table and comments for tensile test of 4140 steel
3. Complete Table 1 entitled Properties from Tensile Test of 4140 Steel. This includes calculation of Bulk modulus and Shear modulus. Include proper literature citations for literature values.
4. Determine Poisson's ratio for the aluminum in the beam.
5. Results tables and comments for aluminum cantilever beam Appendix
Compare the literature values for the elastic modulus and Poisson's ratio with the values you obtained in the lab.
Include the answers to the following questions.
Please answer each question separately and include the question number before your answer.
Questions:
2. Based on macroscopic properties why is Poisson's ratio always positive?
3. Using literature values for the elastic modulus and Poisson's ratio for 4140 steel calculate the fractional volume change experienced by the gage section of the specimen on being stressed from zero to 25000 pounds.
4. Show that the circumferential strain measured by a transverse gage on a round bar is the same as the radial strain on the same bar. Explain why this is consistent with our definition of Poisson's ratio, why it is equal to the same ratio.
5. Explain superposition of strains? Why is superposition important?
6. For a cantilevered beam is strain dependent upon position from the loaded end of the beam? What is the strain on the "free" end of the beam when only an intermediate load is applied?
7. Is the strain dependent on position across the beam? That is, is the strain significantly different in the center compared to the edges of the beam?
8. How do the strains measured on the top and bottom of the beam correspond to each other? How do the strains relate to those areas of the beam that were in tension or compression?
9. Describe a real system that uses a cantilever beam as a component. Which part of the beam experiences the most deformation (local strain)? Explain. What is done to compensate? Why?
10. Describe a situation or project in which it would be necessary to measure strain (not just an experiment, but something an engineer might make). Would strain gages be needed or useful? Can you think of another way to measure strain? Explain.
What was the value of the modulus of elasticity for
the steel sample. What is the modulus of elasticity for the aluminum cantilever
beam? Did the values match well with published values?
References
Which references were used to obtain literature values. Please use the original reference rather than the lab manual for referencing these literature values.
Appendixes
Results tables and comments for aluminum cantilever beam Appendix
Completed data sheets, rough graphs, and sample calculations.