MET211 Lab 10 Report

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Purdue University *

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Course

21100

Subject

Mechanical Engineering

Date

Apr 3, 2024

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pdf

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10

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MET 21100 Memo Lab Report Grading Sheet Expectations: The complete draft lab report was read/reviewed by ALL group members. Suggestions and corrections were considered, and incorporated where appropriate. The final version of the complete lab report was then reviewed by ALL group members prior to submission. Names : Peter Catizone M,W,F 11:30-12:20 Nate Montanari M,W,F 11:30-12:20 Quinn Steinkamp M,W,F 11:30-12:20 Lab Date - 11/16/2023 Lab Div# - 211000-008 Format/Grammar/Spelling 6 points Title Information 2 points Executive Summary 10 points Results 40 points Conclusions 10 points Data Sheet(s); references 2 points Subtotal: Attendance: Total score:
To: Dr. Sunghwan Lee From: Peter Catizone, Nate Montanari, and Quinn Steinkamp Cc: Shuning Yin Date: November, 30, 2023 Re: MET 211 3 Point Bending & Beam Deflection Executive summary This lab was completed as part of the MET 211 Lab curriculum. It was conducted to show the lab groups the effects that material, size, and quantity have on deformation while conducting a 3 point bending test. To conduct the experiment the lab group was given access to a United Electromechanical Test Machine (UTM), a 500 lb f capacity load cell, a Vishay Measurements Group P 3500 Strain Indicator, a 24 inch steel scale, dial caliper, micrometer, digital multimeter, screwdriver, Lab view software with computer and connection box, and 6 different specimens including : 7 - ¼ in x 1 in x 36 in 6061-T6511 Aluminum bar, ½ in x 1 in x 36 in 6061-T6511 Aluminum bar, ¾ in x 1 in x 36 in 6061-T6511 Aluminum bar, 1-¾ in x 1 in x 36 in 6061-T6511 Aluminum bar, ¼ in x 1 in x 36 in AISI 1018 Steel, and ¼ in x 1 in x 36 in CA 260 Brass. Within this lab the group set up the UTM with the 3 point bending apparatus to test the given samples. The group was given a few elected samples from the list to test while other lab groups collected the other data. To start the bar of choice was put into the 3 point bending apparatus. Then the data acquisition equipment was zeroed in preparation for the test. To conduct the test the group set the setting on the UTM machine in accordance with a data table that was provided in lab. Then one person started the test while another filmed bot the strain indicator and the screen on the UTM to collect the deformation of the beam in inches and the strain that the UTM applied in lb f . The data acquired from the lab was then analyzed by the group and determined that materials known for their stiffness such as steel, deformed less than materials that are known to be more flexible such as brass or aluminum. The test of 7 stacked pieces of aluminum compared to a bar of the same thickness yielded interesting results. The bar mode up of 7 different bars deformed more than that of the one which was one solid piece.
Results
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Table 1: Modulus of Elasticity Using Deflection From Three-Point Bending Specimen b (in) h (in) I (in 4 ) L (in) M py (lb f /in) E exp (psi) E pub (psi) % Diff ¼” Steel 1 0.25 0.001 30 70.311 39.55*10^6 29*10^6 36.4 ¼” Brass 1 0.25 0.001 30 20.909 11.76*10^6 16*10^6 26.5 ¼” Al 1 0.25 0.001 30 24.089 13.55*10^6 10*10^6 35.5 ½” Al 1 0.5 0.010 30 1807.9 10.1*10^6 10*10^6 1 ¾” Al 1 0.75 0.035 30 6632.5 10.6*10^6 10*10^6 6 1-¾” in Al 1 1.75 0.447 30 5182 6.52*10^6 10*10^6 34.8 7 Al Stack 1 1.75 0.009 30 157.57 9.84*10^6 10*10^6 1.6
Table 2: Area Moment of Inertia Using Deflection From Three-Point Bending Specimen E pub (psi) L (in) M py (lb f /in) I EXP (in 4 ) I THEO (in 4 ) % Diff Al Stack 10*10^6 30.0 157.57 0.008 0.009 11.1
Sample Calculations: E exp : (M*L^3)/(48*I) = [70.311*(30^3)]/[48*(0.001)] = 39.55*10^6 psi I EXP : (b*(h^3))/12 = [1*(0.25^3)]/12 = 0.001 in^4 I THEO : (M*L^3)/(48*E) = [157.57*(30^3)]/[48*(10*10^6)] = 0.008 in^4 % Diff Between I or E: (Iexp-Itheo)/Etheo *100% = (0.008-0.009)/0.009 *100 = 11.1%
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Conclusion In conclusion the results yielded in the lab provided great insight on how material properties such as size, shape, stiffness are affected at different loads. The data that was acquired proved the group's theories correct. Using the tests of bars of different materials showed that materials of different stiffness deform differently under the same load. Using the test of a stack of bars and one solid bar yielded results that show how a solid bar will deform less than a stack of bars totaling the same thickness. This showed that choosing different materials of different sizes is important to consider when designing different products, structures, or anything that involves bending forces. The lab manual for MET 211 poses some questions for the lab group to think about to further their understanding of the lab. The first question the lab manual asks is “Do the empirical values for modulus of elasticity support the validity of the formula for deflection of a simply supported beam experiencing three-point bending?” The group's data do support the validity of the formula to an extent. To have the values be perfect you have to have the perfect condition which the group found the the lab equipment and specimens was not exact so there will be some variance from the modulus of elasticity. The second question the lab manual poses is “Do the empirical values for area moment of inertia support the validity of the formula for deflection of a simply supported beam experiencing three-point bending?” To answer this question the group answered in the same manner as before, the results showed that the empirical values helped prove the validity of the equation to an extent but due to the lab equipment and specimens not being perfect the results will be slightly different. The final question the lab manual poses is “Comment your observations, similarities, and differences, regarding the area moment of inertia of a stacked beam and a solid beam made of the same material.” According to the group's calculations both beams have a moi of .447. The group found this interesting because they had the same moi but differing amounts of deformation at the same loads. So in conclusion the group has a deeper understanding of deformation under load utilizing a 3 point bending test. The group found that factors such as material, size, and load applied affect the amount of deformation an object such as the beam tested within the lab experiences and can now relate these findings to other real life applications.
Sources Roach, Thelen; MET 21100 Laboratory Manual , Purdue University: West Lafayette, IN, 2023 “Aisi 1018 Steel, Cold Drawn - Matweb.” MatWeb , www.matweb.com/search/DataSheet.aspx?MatGUID=3a9cc570fbb24d119f08db22a53e2 421. Accessed 29 Nov. 2023. “Aluminum 6061-T6; 6061-T651.” MatWeb , www.matweb.com/search/DataSheet.aspx?MatGUID=b8d536e0b9b54bd7b69e4124d8f1 d20a. Accessed 29 Nov. 2023. “Cartridge Brass, UNS C26000 (260 Brass), Os070 Temper Flat Products.” MatWeb , www.matweb.com/search/datasheet_print.aspx?matguid=83677ae92338456da4dafe8fe4b 815c5. Accessed 29 Nov. 2023.
Data Sheet ¼” 1018 Steel ¼” Al ¼” Brass Load, P (lb) Def, y (in) Load, P (lb) Def, y (in) Load, P (lb) Def, y (in) 1 3 0.034 3 0.127 3 0.178 2 6 0.087 6 0.248 6 0.338 3 9 0.123 9 0.369 9 0.469 4 12 0.170 12 0.499 12 0.588 5 15 0.208 15 0.619 15 0.768 6 18 0.250 18 0.750 18 0.898 ½” Al ¾” Al Load, P (lb) Def, y (in) Load, P (lb) Def, y (in) 1 16 0.008 30 0.005 2 32 0.017 60 0.01 3 48 0.027 90 0.014 4 64 0.033 120 0.018 5 80 0.044 150 0.023 6 96 0.052 180 0.028 7 Stack ¼” Al 1-¾” Al Load, P (lb) Def, y (in) Load, P (lb) Def, y (in) 1 25 0.182 25 0.007 2 50 0.348 50 0.014 3 75 0.509 75 0.018 4 100 0.669 100 0.023
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5 125 0.819 125 0.028 6 150 0.978 150 0.031