Lab 04 PDF

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Ohio State University *

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Mechanical Engineering

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Dec 6, 2023

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Conversion factors: 1 lbf = gmf Task 1 Variable Value Units E = 10,000,000 lbf/in 2 (psi) L = 8.750 in S = 7.500 in w = 0.497 in t = 0.123 in Variable Value Units I = in 4 Moment of Intertia Equation = δ = Varies with Force See Table 1.3 in Error = '' % Number of Weights Total Weight Dial Indicator Reading Incremental Deflection, ΔX (verify!) Force Measured Deflection Theoretical Deflection Error (50g each) (gmf) (in) ~ constant ? (lbf) (in) (in) % Average None 0 0.181 0.000 0.000 0.000 0.00% Standard Deviation 1 50 0.208 0.027 2 100 0.231 0.023 3 150 0.256 0.025 Force Equation 4 200 0.281 0.025 5 250 0.308 0.027 Measured Deflection Equation 6 300 0.333 0.025 7 350 0.359 0.026 Theoretical Deflection Equation 8 400 0.388 0.029 9 450 0.417 0.029 Error Equation 10 500 0.434 0.017 Day 2 (Analysis) Moment of Inertia Day 1 (Lab) Display equation used *Boxes* - Plot data for visualization Formatting Legend Known Young's Modulus Conversion Factors - Add reference to other sheet Empirical Data - Record during experiments Calculated data - Create functions here Error Analysis Calculated data - Drag functions here ENGR 1181 - Lab 04 and Application - 02 : Beam Bending Lab Worksheet Property Young's Modulus Distance to Force Distance to Dial Ind Table 1.1: Material properties of the aluminum beam Width of beam Thickness of beam Aluminum Rectangular Beam Instructions: Take all Task 1 measurements with your partner. Measure the width and thickness of the aluminum beam using calipers. Fasten beam into apparatus. Record initial reading on dial indicator in Table 1.3. Add a weight and record new reading. Repeat for each of 10 weights. Table 1.2: Calculation of moment of inertia, theoretical deflection, and experimental error (Task 1) Theoretical Deflection Calculation w * t 3 / 12 F * S 2 * (3L-S) / (6 E I ) Experimental Error (δ measured - δ theoretical ) / δ theoretical Table 1.3: Measured and theoretical deflection according to various weights for rectangular aluminum beam (Task 1) Equation Day 2 (Analysis) Activity: INSERT GRAPH HERE Create an X-Y Scatter plot Measured deflection vs. force plot should be discrete Theoretical deflection vs. force plot should be continuous Add a trend line for the measured deflection vs. force plot Include a chart title (e.g. Deflection vs. Force for [beam identifier]) Include axis titles with units "Absolute deflection (in)" and "Force (weight) applied to beam (lbf)" Include a legend

Task 2 Variable Value Units E = 17,000,000 lbf/in 2 (psi) L = 8.750 in S = 7.500 in w = 0.499 in t = 0.123 in Variable Value Units I = in 4 δ = see Table 2.3 in Error = '' % Number of Weights Total Weight Dial Indicator Reading Incremental Deflection, ΔX (verify!) Force Measured Deflection Theoretical Deflection Error (50g each) (gmf) (in) ~ constant ? (lbf) (in) (in) % Average None 0 0.146 0.000 0.000 Standard Deviation 1 50 0.161 0.015 2 100 0.175 0.014 3 150 0.190 0.015 4 200 0.205 0.015 5 250 0.221 0.016 6 300 0.236 0.015 7 350 0.251 0.015 8 400 0.265 0.014 9 450 0.282 0.017 10 500 0.294 0.012 Task 3 Variable Value Units E = 17,000,000 lbf/in 2 (psi) L = 8.750 in S = 7.500 in w = 0.253 in Instructions: Take all Task 2 measurements with your partner. Measure the width and thickness of the rectangular copper beam using calipers. Fasten beam into apparatus. Record initial reading on dial indicator in Table 2.3. Add a weight and record new reading. Repeat for each of 10 weights. Table 2.3: Measured and theoretical deflection according to various weights for rectangular copper beam (Task 2) Length of beam Thickness of beam Copper Rectangular Beam Moment of Inertia Error Analysis w * t 3 / 12 = Theoretical Deflection F * S 2 * (3L-S) / (6 E I )= Property Young's Modulus Experimental Error (δ measured - δ theoretical ) / δ theoretical Table 3.1: Material Properties of Copper Square Beam Distance to Force Distance to Dial Ind Width of beam Copper Square Beam Instructions: Take all Task 3 measurements with your partner. Measure the width and thickness of the square copper beam using calipers. Fasten beam into apparatus. Record initial reading on dial indicator in Table 3.3. Add a weight and record new reading. Repeat for each of 10 weights. Property Equation Table 1.2: Calculation of moment of inertia and theoretical deflection (Task 1) Property Young's Modulus Distance to Dial Ind Width of beam Table 2.1: Material properties of copper rectangular beam Day 2 (Analysis) Activity: INSERT GRAPH HERE Create an X-Y Scatter plot Measured deflection vs. force plot should be discrete Theoretical deflection vs. force plot should be continuous Add a trend line for the measured deflection vs. force plot Include a chart title (e.g. Deflection vs. Force for [beam identifier]) Include axis titles with units"Absolute deflection (in)" and "Force (weight) applied to beam (lbf)" Include a legend

t = 0.250 in Variable Value Units I = in 4 δ = see Table 3.3 in Error = '' % Number of Weights Total Weight Dial Indicator Reading Incremental Deflection, ΔX (verify!) Force Measured Deflection Theoretical Deflection Error (50g each) (gmf) (in) ~ constant ? (lbf) (in) (in) % Average None 0 0.243 0.000 0.000 Standard Deviation 1 50 0.246 0.003 2 100 0.250 0.004 3 150 0.255 0.005 4 200 0.258 0.003 5 250 0.261 0.003 6 300 0.265 0.004 7 350 0.269 0.004 8 400 0.272 0.003 9 450 0.276 0.004 10 500 0.280 0.004 Task 4 Beam Description: Black Variable Value Units E = lbf/in 2 (psi) L = 8.750 in S = 7.500 in w = 0.499 in t = 0.126 in Variable Value Units I = in 4 Table 3.2: Calculation of moment of inertia and theoretical deflection (Task 3) Equation Property Thickness of beam Thickness of beam Table 4.2: Calculation of moment of inertia and theoretical deflection (Task 4) Property Equation Moment of Inertia w * t 3 / 12 = Property Young's Modulus Distance to Force Distance to Dial Ind Error Analysis Width of beam Experimental Error (δ measured - δ theoretical ) / δ theoretical w * t 3 / 12 = F * S 2 * (3L-S) / (6 E I )= Unknown Beam Instructions: Take all Task 4 measurements with your partner. Select a description for your unknown beam. Measure the width and thickness of unknown beam using calipers. Fasten beam into apparatus. Record initial reading on dial indicator in Table 4.3. Add a weight and record new reading. Repeat for each of 10 weights. Table 3.3: Measured and theoretical deflection according to various weights for copper square beam (Task 3) Moment of Inertia Theoretical Deflection Table 4.1: Material Properties of Unknown Beam Day 2 (Analysis) Activity: INSERT GRAPH HERE Create an X-Y Scatter plot Measured deflection vs. force plot should be discrete Theoretical deflection vs. force plot should be continuous Add a trend line for the measured deflection vs. force plot Include a chart title (e.g. Deflection vs. Force for [beam identifier]) Include axis titles with units "Absolute deflection (in)" and "Force (weight) applied to beam (lbf)" Include a legend

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δ = see Table 4.3 in Number of Weights Total Weight Dial Indicator Reading Incremental Deflection, ΔX (verify!) Force Measured Deflection (50g each) (gmf) (in) ~ constant ? (lbf) (in) Average Error Task 1 None 0 0.200 0.000 0.000 Average Error Task 2 1 50 0.214 0.014 Average Error Task 3 2 100 0.227 0.013 Estimated Error Task 4 (Average of Average Errors from Tasks 1, 2 and 3) 3 150 0.242 0.015 4 200 0.256 0.014 5 250 0.269 0.013 6 300 0.284 0.015 7 350 0.299 0.015 8 400 0.314 0.015 9 450 0.328 0.014 10 500 0.342 0.014 Observed Slope From Trendline Equation = Calculated Young's Modulus, E= Youngs Moduls Equation = Young's Modulus Lower Limit Youngs Modulus Upper Limit Unknown Beam is Table 4.3: Measured and theoretical deflection according to various weights for unknown beam (Task 4) Theoretical Deflection F * S 2 * (3L-S) / (6 E I )= Error Analysis Day 2 (Analysis) Activity: INSERT GRAPH HERE Create an X-Y Scatter plot Measured deflection vs. force plots of three known beams and the unknown should all be discrete Include a chart title (e.g. Deflection vs. Force for [beam identifiers]) Include axis titles with units "Absolute deflection (in)" and "Force (weight) applied to beam (lbf)" Include a legend Day 2 (Analysis) Activity: INSERT GRAPH HERE Create an X-Y Scatter plot Measured deflection vs. force plot should be discrete Add a trend line and trendline equation for the measured deflection vs. force plot Note down the slope from the trendline equation Include a chart title (e.g. Deflection vs. Force for [beam identifier]) Include axis titles with units "Absolute deflection (in)" and "Force (weight) applied to beam (lbf)" Include a legend