During a tensile test, the starting gage length is 100.0 mm and the cross-sectional area is 150 mm$^2$. The following force and gage length data are collected during testing:

1. 17,790 N at 100.2 mm
2. 23,040 N at 103.5 mm
3. 27,370 N at 110.5 mm
4. 28,910 N at 122.0 mm
5. 27,400 N at 130.0 mm
6. 20,460 N at 135.1 mm

The final data point (6) occurred immediately prior to failure. Yielding occurred at a load of 19,390 N (0.2\% offset value), and the maximum load (4) was 28,960 N.

(a) Plot the engineering stress-strain curve.
(b) Determine the yield strength.
(c) Determine the modulus of elasticity.
(d) Determine the tensile strength.
(e) Determine the percent elongation.

(a) To plot the engineering stress-strain curve, we need to calculate the engineering stress and engineering strain for each data point. Engineering stress is calculated by dividing the applied force by the original cross-sectional area, and engineering strain is calculated by dividing the change in gage length by the original gage length.

Using the given force and gage length data, we can calculate the engineering stress and strain for each point. Plotting the stress on the y-axis and strain on the x-axis will give us the stress-strain curve.

(b) The is the stress value at which yielding occurs. In this case, yielding occurred at a load of 19,390 N (0.2% offset value). By referring to the stress-strain curve, we can determine the corresponding stress value at that point, which will be the yield strength.

(c) The modulus of elasticity, also known as Young's modulus, can be calculated as the ratio of stress to strain within the elastic region of the stress-strain curve. By taking the slope of the linear elastic region on the stress-strain curve, we can determine the modulus of elasticity.

(d) The tensile strength is the maximum stress value reached during the test. In this case, the maximum load was 28,960 N. By referring to the stress-strain curve, we can determine the corresponding stress value at that point, which will be the tensile strength.

(e) Percent elongation is a measure of how much the material stretched before failure. It is calculated by dividing the change in gage length by the original gage length and multiplying by 100. By comparing the gage length before and after failure, we can determine the percent elongation.

By performing the necessary calculations and analyzing the stress-strain curve, we can determine the yield strength, modulus of elasticity, tensile strength, and percent elongation of the material.

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