Lab 04 - Beam Bending Lab - Datasheet copy

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Dec 6, 2023

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Formatting Legend Day 1 (Lab) Known Young's Modulus Empirical Data - Record during experiments Conversion factors: Conversion Factors - Add reference to other sheet 1 lbf = 453.6 gmf Calculated data - Create functions here Calculated data - Drag functions here Display equation used Task 1 Aluminum Rectangular Beam *Boxes* - Plot data for visualization Table 1.1: Material properties of the aluminum beam Property Variable Value Units Young's Modulus E = 10,000,000 Distance to Force L = 8.750 in Distance to Dial Ind S = 7.500 in Width of beam w = 0.497 in Thickness of beam t = 0.123 in Table 1.2: Calculation of moment of inertia, theoretical deflection, and experimental error (Task 1) Calculation Variable Equation Value Units Moment of Inertia I = 7.707E-05 Moment of Intertia Equation = =(F16*F17^3)/12 Theoretical Deflection in Experimental Error Error = '' % Table 1.3: Measured and theoretical deflection according to various weights for rectangular aluminum beam (Task 1) Total Weight Force Measured Deflection Error Error Analysis (50g each) (gmf) (in) ~ constant ? (lbf) (in) (in) % Average 1% None 0 0.181 0.000 0.000 0.000 0.000 0.00% Standard Deviation 0.025 1 50 0.208 0.027 0.110 0.027 0.025 7.39% 2 100 0.231 0.023 0.220 0.050 0.050 -0.56% 3 150 0.256 0.025 0.331 0.075 0.075 -0.56% Force Equation =D28/$G$6 4 200 0.281 0.025 0.441 0.100 0.101 -0.56% 5 250 0.308 0.027 0.551 0.127 0.126 1.03% Measured Deflection Equation =E29-$E$28 6 300 0.333 0.025 0.661 0.152 0.151 0.76% 7 350 0.359 0.026 0.772 0.178 0.176 1.14% Theoretical Deflection Equation =G29*$F$15^2*(3*$F$14-$F$15)/(6*$F$13*$H$21) 8 400 0.388 0.029 0.882 0.207 0.201 2.92% 9 450 0.417 0.029 0.992 0.236 0.226 4.30% Error Equation =(H29-I29)/I29 10 500 0.434 0.017 1.102 0.253 0.251 0.63% ENGR 1181 - Lab 04 and Application - 02 : Beam Bending Lab Worksheet Day 2 (Analysis) 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. lbf/in 2 (psi) w * t 3 / 12 in 4 δ = F * S 2 * (3L-S) / (6 E I ) Varies with Force See Table 1.3 (δ measured - δ theoretical ) / δ theoretical Number of Weights Dial Indicator Reading Incremental Deflection, ΔX (verify!) Theoretical Deflection 0.050 0.100 0.150 0.200 0.250 0.300 Deflection vs Force for Aluminum Absolute Deflection (in)

Task 2 Copper Rectangular Beam Table 2.1: Material properties of copper rectangular beam Property Variable Value Units Young's Modulus E = 17,000,000 Length of beam L = 8.750 in Distance to Dial Ind S = 7.500 in Width of beam w = 0.499 in Thickness of beam t = 0.123 in Table 1.2: Calculation of moment of inertia and theoretical deflection (Task 1) Property Variable Equation Value Units Moment of Inertia I = 7.7381E-05 Theoretical Deflection see Table 2.3 in Experimental Error Error = '' % Table 2.3: Measured and theoretical deflection according to various weights for rectangular copper beam (Task 2) Total Weight Force Measured Deflection Error Error Analysis (50g each) (gmf) (in) ~ constant ? (lbf) (in) (in) % Average 0.87% None 0 0.146 0.000 0.000 0.000 0.000 0.00% Standard Deviation 1.25% 1 50 0.161 0.015 0.110 0.015 0.015 1.84% 2 100 0.175 0.014 0.220 0.029 0.029 -1.56% 3 150 0.190 0.015 0.331 0.044 0.044 -0.43% 4 200 0.205 0.015 0.441 0.059 0.059 0.14% 5 250 0.221 0.016 0.551 0.075 0.074 1.84% 6 300 0.236 0.015 0.661 0.090 0.088 1.84% 7 350 0.251 0.015 0.772 0.105 0.103 1.84% 8 400 0.265 0.014 0.882 0.119 0.118 0.99% 9 450 0.282 0.017 0.992 0.136 0.133 2.59% 10 500 0.294 0.012 1.102 0.148 0.147 0.48% 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. lbf/in 2 (psi) w * t 3 / 12 = in 4 δ = F * S 2 * (3L-S) / (6 E I )= (δ measured - δ theoretical ) / δ theoretical Number of Weights Dial Indicator Reading Incremental Deflection, ΔX (verify!) Theoretical Deflection 0.000 0.200 0.400 0.600 0.800 1.000 1.200 0.000 Theoretical Deflection (in) Measured Deflection (in) Linear (Measured Deflection (in)) Force (Weight) applied to beam (lbf) 0.000 0.200 0.400 0.600 0.800 1.000 1.200 0.000 0.020 0.040 0.060 0.080 0.100 0.120 0.140 0.160 Delfection vs Force for Copper Square Beam Force (weight) applied to beam (lbf) Measured Deflection (in)

Task 3 Copper Square Beam Table 3.1: Material Properties of Copper Square Beam Property Variable Value Units Young's Modulus E = 17,000,000 Distance to Force L = 8.750 in Distance to Dial Ind S = 7.500 in Width of beam w = 0.253 in Thickness of beam t = 0.250 in Table 3.2: Calculation of moment of inertia and theoretical deflection (Task 3) Property Variable Equation Value Units Moment of Inertia I = 3.2943E-04 Theoretical Deflection F * S2 * (3L-S) / (6 E I )= see Table 3.3 in Experimental Error Error = '' % Table 3.3: Measured and theoretical deflection according to various weights for copper square beam (Task 3) Total Weight Force Measured Deflection Error Error Analysis (50g each) (gmf) (in) ~ constant ? (lbf) (in) (in) % Average 4.26% None 0 0.243 0.000 0.000 0.000 0.000 0.00% Standard Deviation 7.10% 1 50 0.246 0.003 0.110 0.003 0.003 -13.29% 2 100 0.250 0.004 0.220 0.007 0.007 1.16% 3 150 0.255 0.005 0.331 0.012 0.010 15.61% 4 200 0.258 0.003 0.441 0.015 0.014 8.38% 5 250 0.261 0.003 0.551 0.018 0.017 4.05% 6 300 0.265 0.004 0.661 0.022 0.021 5.97% 7 350 0.269 0.004 0.772 0.026 0.024 7.35% 8 400 0.272 0.003 0.882 0.029 0.028 4.77% 9 450 0.276 0.004 0.992 0.033 0.031 5.97% 10 500 0.280 0.004 1.102 0.037 0.035 6.94% 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. lbf/in 2 (psi) w * t 3 / 12 = in 4 δ = (δ measured - δ theoretical ) / δ theoretical Number of Weights Dial Indicator Reading Incremental Deflection, ΔX (verify!) Theoretical Deflection Theoretical Deflection (in) Measured Deflection (in) Linear (Measured Deflection (in)) 0.000 0.200 0.400 0.600 0.800 1.000 1.200 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 Delfection vs Force for Copper Rectangle Beam Theoretical Deflection (in) Measured Deflection (in) Linear (Measured Deflection (in)) Forece (weight) applied to beam (lbf) Measured Deflection (in)

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Task 4 Unknown Beam Beam Description: Black Table 4.1: Material Properties of Unknown Beam Property Variable Value Units Young's Modulus E = 1,866,377 Distance to Force L = 8.750 in Distance to Dial Ind S = 7.500 in Width of beam w = 0.499 in Thickness of beam t = 0.126 in Table 4.2: Calculation of moment of inertia and theoretical deflection (Task 4) Property Variable Equation Value Units Moment of Inertia I = 8.3182E-05 Theoretical Deflection see Table 4.3 in Table 4.3: Measured and theoretical deflection according to various weights for unknown beam (Task 4) Total Weight Force Measured Deflection Error Analysis (50g each) (gmf) (in) ~ constant ? (lbf) (in) Average Error Task 1 1.50% None 0 0.200 0.000 0.000 0.000 Average Error Task 2 0.87% 1 50 0.214 0.014 0.110 0.014 Average Error Task 3 4.26% 2 100 0.227 0.013 0.220 0.027 2.21% 3 150 0.242 0.015 0.331 0.042 4 200 0.256 0.014 0.441 0.056 5 250 0.269 0.013 0.551 0.069 6 300 0.284 0.015 0.661 0.084 7 350 0.299 0.015 0.772 0.099 8 400 0.314 0.015 0.882 0.114 9 450 0.328 0.014 0.992 0.128 10 500 0.342 0.014 1.102 0.142 Observed Slope From Trendline Equation = 0.1294 Calculated Young's Modulus, E= 1,866,377 Youngs Moduls Equation = =((F174^2*(3*F173-F174))/(6*F173*H180)*(1/M201)) Young's Modulus Lower Limit Youngs Modulus Upper Limit Unknown Beam is Copper Rectangle 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. lbf/in 2 (psi) w * t 3 / 12 = in 4 δ = F * S 2 * (3L-S) / (6 E I )= Number of Weights Dial Indicator Reading Incremental Deflection, ΔX (verify!) Estimated Error Task 4 (Average of Average Errors from Tasks 1, 2 and 3) 0.000 0.200 0.400 0.600 0.800 1.000 1.200 0.000 0.020 0.040 0.060 0.080 0.100 0.120 0.140 0.160 f(x) = 0.129397512490909 x − 0.000863636363636 Deflection vs Force for Unknown Beam Measured Deflection (in) Linear (Measured Deflection (in)) Force (Weight) Absolute Deflection (in)

0.000 0.200 0.400 0.600 0.800 1.000 1.200 0.000 0.050 0.100 0.150 0.200 0.250 0.300 Deflection vs Force for all Beams Measured Deflection (in) Measured Deflection (in) Measured Deflection (in) Measured Deflection (in) Force (weight) Measured Deflection (in)

Definitions for using F = m g = The force on a mass m in earth's gravita Standard acceleration of gravity g = 9.8066500 m/s^2 32.174048556430400 ft/s^2 1 N = 1 kg-m/s^2 1 lbm = 0.4535923700 kg Force Metric 1 kgf = = English 1 lbf = = 1 lbf = 4.448221615260500 N 1 gmf = = 1 lbf = 453.5923700 gmf 1 MPa = 145.037737730209 lbf / in^2 The force on a 1 kg mass in gravity The force on a 1 lbm mass in gravity The force on a 1 gm mass in gravity

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