Rephrasing a lab

TABLE OF CONTENTS

Abstract………………………………………………………………………………2

Table of contents…………………………………………………………………….3

Introduction and Theory…………………………………………………………….4-5

Procedures…………………………………………………………………………..6-7

Summary of Important Results………………………………………………………8

Sample Calculations and Error Analysis……………………………………………9-10

Discussion and Conclusion…………………………………………………………..11

References……………………………………………………………………………12

Appendix……………………………………………………………………………..13

INTRODUCTION AND THEORY

Calculating the strain using the strain gauge is the based on the change in the electrical resistance of the thin wire when it deforms. The resistance R of a wire depends on its length L and area A as follows:

(II-1)

Where is the resistivity of the wire. Since the volume of the wire is V=LA, (II-1) can also be written as:

(II-2)

If the wire is bonded securely to an object which is being strained, this strain will change the length of the wire from L to . According to equation (II-2), this change in length will cause a change in resistance. Assuming the volume V does not change, and the resistivity of the material remains the same, it follows from eq. (II-2) that:

And

(II-3)

For finite, but small, changes eq. (II-3) becomes

(II-4)

And

(II-5)

Where F=2.14 is the factor, since the strain is defined ε= ∆L/L. The strain from the strain gauge is directly proportional to the fractional change in resistance. The set up reads the strain directly when the gauge factor is 2, so whenever F differs from this value it is necwssary to correct the strain, as follows:

(II-6)

Where,

= corrected strain

= strain read by the data acquisition

PROCEDURES

First we ensured that the “Emergency Stop” is released and not activated then we turned on the PC and the power switch at the bottom panel of the MTS frame. After that we ensured that the Wedge Action Grips are installed on the MTS frame. We double clicked the TestWorks 4 icon on the PC which is the software that operates the MTS and collects information from the extensometer. Then, we logged in under “306A lab.” We clicked on “Open Method” drop down list after that then highlighted “Exp.2 Tensile with extensometer Mod9-15-X,” the clicked OK.

After that we clicked on the “Calibrate Device” icon and highlighted the load cell serial number associated with the load cell that is installed on our MTS machine, and then clicked Calibrate. We clicked Next the waited until the process is completed then clicked Finish then OK. After that, we measured the diameter of the Aluminum bar using the calipers and recorded it. Then we used the handset on the side of the MTS machine to install the Aluminum sample simply by lowering the grips using the arrow buttons. Then, we connected the wires from the strain gauge, which is attached to the Aluminum bar, to the terminals identified as “#1 Strain” on the ADC interface box and ensured that the internal ribbon cable is installed on the right side connector of the interface box. After that we attached extensometer at narrow section of the test sample. We connected the cable of the extensometer to J1 DC Cond 1 (behind the MTS frame). We went to the computer and right clicked inside the load and the Extensometer windows then left clicked on “Zero Channel.” Then, we double clicked on the National Instruments or Measurement & Automation icon on the desktop after minimizing the TestWork 4 window and the LabView opened. After that, we clicked on the :down arrow” in the open box and clicked on the file specified by the lab manual. Then, on LabView, we clicked the run arrow then the Zero Strain box. The we opened the windows for the “TestWorks” and “LabView” side-by-side and clicked on the “Motor Reset” button. Then we clicked on the “Green Arrow” in the TestWork 4 window when prompted type in the Aluminum bar diameter. After doing all of the that we were able to collect screen data from the following sources (1) Load & length increase from TestWork 4, and (2) Strain from LabView. Then, we paused the load in an increments of 100 lb and recorded the elongation from the extensometer and the strain using the strain gauge. After reaching 1500 lbs, which is below the elastic limit for Aluminum, we stopped both calculations and saved the results on our flash drives.

SUMMARY OF IMPORTANT RESULTS

Figure 1

Figure 2

SAMPLE CALCULATION AND ERROR ANALYSIS

Calculating Stress:

Calculating Strain:

Standard Error from strain gauge:

=

Standard Error from extensometer:

Modulus of Elasticity:

Analytical Error:

The uncertainty of the strain gauge method of measurement is that the wires are not attached properly or the wires are old which will not give us accurate results. While, the uncertainty of the extensometer method could be wrong calculation or the extensometer is not installed properly. The values of the modulus of elasticity are both off the published value for aluminum. However, the percent error from the strain gauge method (9.12%) is way off compared to the percent error from the extensometer (2.6%).

DISCUSSION AND CONCLUSION

After finishing the experiment, calculating the data, and graphing them, we noticed that the extensometer method is more precise and accurate, but the strain gauge method is more convenient and fast. In the strain gauge method, we got a modulus of elasticity of 9087543.4 psig which 9.12% off the actual value, while we got 10261703 psig for the method of extensometer which was 2.6% off the actual value. The standard error for the strain gauge method was 50.42, while for the extensometer method was 41.62 which also proves that the extensometer is more accurate.

REFRENCES

[1] CSUF EGME 306A Lab Manual.

[2] Modulus of Elasticity – Young Modulus for Some Common Materials