Lab 6 Report

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Community College of Philadelphia *

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102

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Mechanical Engineering

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Jan 9, 2024

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COMMUNITY COLLEGE OF PHILADELPHIA PHILADELPHIA, PENNSYLVANIA Experiment Number: 6 Title: Stress and Strain Performed by: Partners: N/A Engineering Course: Engineering 102 Lab Section No: 901 Lab Day/Hour: Tuesday 1:00 – 3:00 PM Lab Instructor: Dr.W.A.Gontar Date Performed: 11/04/2021 Date Due: 11/09/2021
Purpose The purpose of this experiment is to collect stress and strain data for a geomembrane, graph the data in a spreadsheet, and identify the existence of hysteresis. Procedures After the Power Supply was set to 10 volts DC, mass measurement using a load cell was able to begin with pre-set equipment. First, only pan was weighed, and the voltage for it was recorded. Next, place weights from 50g to 500g in turn on the pan with an increment of 50g, and 10 voltage values corresponding to the weights were carefully recorded. To plot a graph of force and voltage, unit conversion from grams to newton was required. From the graph, a function y = mx + b was collected where m is the slope and b is the intercept. The stress and strain experiment with a flexible substance called geomembrane would be performed in following steps with pre-set equipment. The Power Supply was set to 10 volts DC. The slope, intercept, and cross-sectional area of membrane values were entered into the “Calibration Data” section of the “Stress & Strain.vi” program on the computer. “Data points” was changed to 1, and then run the VI. After the “Read Data” button was pressed and released, the “Force” displayed 0 newtons. After that, stop the VI, copy the value from “Strain Gauge Volts” to “Initial Volts”, and leave the “Lead Resistance” value at 0 ohms. Next, “Data Points” was changed to 10, and the next steps need two people do it at the same time. Run the VI, then the first person pressed and held the “Read Data” button until the “Force” displayed 0 newtons and “Microstrain” displayed small, random values. The second person rotated the knob to stretch the vise until the “Stress” and “Microstrain” displayed positive values and the “Force” showed around 20 newtons. When the desired data was showed, the first person released the “Read Data” button and then pressed the “Accept Data” button. Two people continued to repeat these steps 10 times increasing the force gradually between 0 and 120 newtons to get a line on the screen. “Data points” was changed to 20, and the value of “Strain Gauge Volts” was copied to the box “Initial Volts”. Two people continued to repeat these steps above 10 more times decreasing the force gradually between 120 and 0 newtons to get the remaining line. Save the file “lab6b2.xls”.
Data Sheets Weights and obtained voltages Weight in [g] Weight in [N] Voltage in [V] Only pan 0 -0.000883 50 g 0.49 N -0.000820 100 g 0.98 N -0.000758 150 g 1.47 N -0.000696 200 g 1.96 N -0.000633 250 g 2.45 N -0.000570 300 g 2.94 N -0.000507 350 g 3.43 N -0.000444 400 g 3.92 N -0.000381 450 g 4.41 N -0.000318 500 g 4.90 N -0.000253 Stress and Strain data Microstrain Stress (Pa) Young’s Modulus (MPa) 309.572 482896.7 1560 595.911 708220.1 1188.5 942.857 962432.4 1020.8 1148.186 1121333 976.6 1425.838 1399385 981.4 1665.089 1607798 965.6 1918.51 1847078 962.8 2148.543 2057731 957.7 2434.194 2321993 953.9 2657.053 2534695 953.9 2485.359 2279244 917.1 2284.571 2045037 895.2 2284.571 2045037 895.2 2058.816 1811330 879.8 1830.615 1597200 872.5 1580.305 1365566 864.1 1215.542 1019019 838.3 1021.152 881528.8 863.3 751.637 684022.9 910.0 472.336 478205 1012
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Graphs Graph of Force and Voltage -0.001000-0.000900-0.000800-0.000700-0.000600-0.000500-0.000400-0.000300-0.000200 0.000 1.000 2.000 3.000 4.000 5.000 6.000 f(x) = 7789.58 x + 6.89 Force and Voltage graph Voltage in [V] Force in [N] Graph of Stress and Strain 0 500 1000 1500 2000 2500 3000 0 500000 1000000 1500000 2000000 2500000 3000000 Stress versus Strain Strain Stress
Calculations 1. Convert grams to newton *1 N = 1 kg.m/s 2 (50 g x 1 kg 1000 g ) x 9.8 m/s 2 = 0.49 [N] (100 g x 1 kg 1000 g ) x 9.8 m/s 2 = 0.98 [N] (150 g x 1 kg 1000 g ) x 9.8 m/s 2 = 1.47 [N] (200 g x 1 kg 1000 g ) x 9.8 m/s 2 = 1.96 [N] (250 g x 1 kg 1000 g ) x 9.8 m/s 2 = 2.45 [N] (300 g x 1 kg 1000 g ) x 9.8 m/s 2 = 2.94 [N] (350 g x 1 kg 1000 g ) x 9.8 m/s 2 = 3.43 [N] (400 g x 1 kg 1000 g ) x 9.8 m/s 2 = 3.92 [N] (450 g x 1 kg 1000 g ) x 9.8 m/s 2 = 4.41 [N] (500 g x 1 kg 1000 g ) x 9.8 m/s 2 = 4.90 [N]
Answers to Questions 1. Using the data acquired from this lab find the force in newtons required to stretch your geomembrane a distance of 2.00 mm. Average value of Stress = = 1462487.595 Pa = 1462487.595 N/m 2 Average value of Strain = = 1561.53285 Young’s modulus = / = 1462487.595/1561.53285 = 936.57 Pa F = x A = 1462487.595 N/m 2 x 43.52 x 10 -6 m 2 = 63.65 N 2. The force constant k of a solid object is the ratio of the force applied to the distance x it stretches: k = F/x. Use the result from question 1 above to calculate k for your geomembrane in N/m. x = 2.00 mm x 1 m 10 3 mm = 2 x 10 -3 m k = F/x = 63.65 2 x 10 3 = 31825 N 3. Use algebra to find a formula for the force constant k of the geomembrane in terms of Young’s modulus E, the length L and cross-sectional area A of the geomembrane. (Hint: Set x = ΔL.) x = ΔL F k = FL EA 1 k = L EA k = EA L 4. The workstation was cleaned and all the parts for the lab were returned to the workstation drawer. True
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Analysis and Discussion The accepted value of Young’s modulus for the geomembrane is between 600 to 1500 MPa, so the obtained values of Young’s modulus for the geomembrane in this experiment are correct. From the graph of Stress versus Strain, I conclude that there is hysteresis in the apparatus because the data points corresponding to decreasing force and increasing force are displaced. Moreover, the geomembrane strain is proportional to stress. The purpose of these experiment was achieved.