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A cantilever beam shown below has a rectangular cross-section, 3/8 in. wide by 1 in. high. The length of the beam is 20 in and the modulus of elasticity (E) of the beam is 10,000 ksi. In an experiment, the following loads were applied at the free end, and observed the deflections of the beam were at each load as shown below. Load (lbs.) 0 5 10 15 20 25 30 35 40 Deflection 0.01 0.045 0.085 0.125 0.175 0.225 0.250 0.300 0.350 (in.) 45 0.385 a. Create a good calibration curve for the deflection gauge using load and deflection. The slope of the resulting curve is the experimental gain in inches/lbs. b. Determine the theoretical gain from the deflection formula. c. Perform the uncertainty analysis on the gain to conclude whether the experimental slope fits inside the bounds predicted by the uncertainty equation. Assume that you were given a yardstick (with the least increment of 1/8th inch) to measure the dimensions of the beam. You can neglect the uncertainty in modulus of elasticity (E) for this problem.

A cantilever beam shown below has a rectangular cross-section, 3/8 in. wide by 1 in. high. The length of the beam is 20 in and the modulus of elasticity (E) of the beam is 10,000 ksi. In an experiment, the following loads were applied at the free end, and observed the deflections of the beam were at each load as shown below. Load (lbs.) 0 5 10 15 20 25 30 35 40 Deflection 0.01 0.045 0.085 0.125 0.175 0.225 0.250 0.300 0.350 (in.) 45 0.385 a. Create a good calibration curve for the deflection gauge using load and deflection. The slope of the resulting curve is the experimental gain in inches/lbs. b. Determine the theoretical gain from the deflection formula. c. Perform the uncertainty analysis on the gain to conclude whether the experimental slope fits inside the bounds predicted by the uncertainty equation. Assume that you were given a yardstick (with the least increment of 1/8th inch) to measure the dimensions of the beam. You can neglect the uncertainty in modulus of elasticity (E) for this problem.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A cantilever beam shown below has a rectangular cross-section, 3/8 in. wide by 1 in. high. The length of the beam is 20 in and the modulus of elasticity (E) of the beam is 10,000 ksi. In an experiment, the following loads were applied at the free end, and observed the deflections of the beam were at each load as shown below. 10 Load (lbs.) 0 5 15 20 25 Deflection 0.01 0.045 0.085 0.125 0.175 0.225 (in.) 30 35 40 45 0.250 0.300 0.350 0.385 a. Create a good calibration curve for the deflection gauge using load and deflection. The slope of the resulting curve is the experimental gain in inches/lbs. b. Determine the theoretical gain from the deflection formula. c. Perform the uncertainty analysis on the gain to conclude whether the experimental slope fits inside the bounds predicted by the uncertainty equation. Assume that you were given a yardstick (with the least increment of 1/8th inch) to measure the dimensions of the beam. You can neglect the uncertainty in modulus of elasticity (E) for this problem.
Transcribed Image Text:A cantilever beam shown below has a rectangular cross-section, 3/8 in. wide by 1 in. high. The length of the beam is 20 in and the modulus of elasticity (E) of the beam is 10,000 ksi. In an experiment, the following loads were applied at the free end, and observed the deflections of the beam were at each load as shown below. 10 Load (lbs.) 0 5 15 20 25 Deflection 0.01 0.045 0.085 0.125 0.175 0.225 (in.) 30 35 40 45 0.250 0.300 0.350 0.385 a. Create a good calibration curve for the deflection gauge using load and deflection. The slope of the resulting curve is the experimental gain in inches/lbs. b. Determine the theoretical gain from the deflection formula. c. Perform the uncertainty analysis on the gain to conclude whether the experimental slope fits inside the bounds predicted by the uncertainty equation. Assume that you were given a yardstick (with the least increment of 1/8th inch) to measure the dimensions of the beam. You can neglect the uncertainty in modulus of elasticity (E) for this problem.
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