Solid Mechanic Lab Report 3, Essays (university) of Mechanical Engineering

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EGME 306A Experiment 3 – The Beam

Experiment 3 – The Beam

EGME 306A - Stress Mechanics Laboratory

Szymon Lao

October 21st, 2021

Submitted to: Patrick Phelan

EGME 306A Experiment 3 – The Beam

EGME 306A Experiment 3 – The Beam I Abstract In everyday conditions, load is applied onto every object. How that object reacts to the load is important for every engineer to know. To create a safe and functioning design, the material and geometry of the design must be tested. We tested an I-beam made of 1018 Steel to see how much vertical deflection occurs under load and as well as the bending stresses that it endures during compression. The general process taken was to measure the I-beam’s geometry, then it was fitted with a strain gauge, and a dial gauge. The I-Beam is then set onto roller supports, preparing for it to be compressed by the tensile machine with compression fixtures. Data logging for load, strain and vertical deflection was done and data reduction was done in MATLAB. The results of our data show that the experimental vertical deflection for the I-beam closely matches the theoretical vertical deflection. Graphically, we can also confirm this since both have a similar slope. We ended with roughly a 2-4% error between the vertical deflection graphs. Bending stress v. load had a graph that deviated from each other but kept a positive slope for both graphs as well. We ended with approximately 17% error between the experimental and theoretical values for bending stress. These percent errors were expected since, we were not able to measure the geometry of the actual experimental beam. We were only allowed to measure a similar beam. The combination of possible measurement errors and not being able to measure the experimental beam is the source of the 17% error.

EGME 306A Experiment 3 – The Beam II Results Under compression load, a material will experience vertical deflection and go through bending stresses. We experimented on a beam made of 1018 Steel to see its behavior under load. To study vertical deflection and bending stresses, the following lab equipment is required: Tensile machine, Dial gauge, Strain gauge, and a digital caliper. To start the experiment, geometric measurements of the beam were taken. After it is then outfitted with a strain gauge to measure strain. Alongside it, it is also fitted with a dial gauge to measure the deflection. The beam is then set onto roller supports. The tensile machine fixtures have been installed to induce compression. It is then operated to compress the beam downwards with approximately 1000 lbf and data is collected every 100 lbf from zero. This is only during the elastic range of 1018. The procedure is then repeated for three trials for accuracy. Figure A-1: 1018 Steel vertical deflection under load, trial

EGME 306A Experiment 3 – The Beam Figures A-1 to A-3 show the results of our experiment measuring the vertical deflection of our beam. To reiterate, this was done by collecting data from a dial gauge while the steel beam is compressed downwards. Two graphs are shown in each figure which represent the experimental and theoretical graph. We can see from the graphs that vertical deflection and load have a linear relationship, as load increases as well as the vertical deflection. This was expected since looking at the theoretical equation for deflection we see that it is essentially equal to load over elastic modulus multiplied with moment of inertia The more load you apply, the more it will deform. It is also noted that the graphs do not deviate much from each other, indicating a small percent error in our experiment. Figure B-1: Bending stress vs load on 1018 Steel Trial 1

EGME 306A Experiment 3 – The Beam Figure B-2: Bending stress vs load on 1018 Steel Trial 2 Figure B-3: Bending stress vs load on 1018 Steel Trial 3

EGME 306A Experiment 3 – The Beam III Discussion & Conclusion Under load, any material will undergo deflection with the right amount of load. As deflection comes with load, so does bending stress. Its important study a material’s behavior under load as it is applicable to most engineering designs and a key to designing anything built to function properly safely. To study these behaviors, we have run an experiment testing an I-beam made of 1018 Steel undergoing load. The general procedure was to place the I-beam bonded with a strain gauge and dial gauge onto roller supports and then compressed downwards. Data was then logged three trials for accuracy. The results of our experiments showed that the deflection and bending stress had a uniform relationship with load. As load increases so does vertical deflection and bending stress. This aligns with theory as bending stress is calculated by multiplying the moment by the distance from the neutral axis all over the moment of inertia. The greater the load applied the greater the bending stress will be. For deflection it also aligns with theory as it suggests that deflection is equal to the load over the moment of inertia multiplied with its elastic modulus. It follows the same behavior, the greater the load the greater the deflection will be. Figures A-1 to A-3 were the deflection graphs and we saw that the theoretical and experimental were not too far off, showing a low percent error. It is proven to be right as Table 1 contained the percent errors, which showed that deflection v. load had a 2-4% error for each trial. This small percent error was caused by an error in data logging. The program does not pause every 100 lbf nor does it automatically data log. Our data was collected manually. Figures B-1 to B-3 were our bending stress v. load graphs and were seen to deviate from each other more compared to A-1 to A-3. It was a hint that our percent error was larger for this measurement. Table 1 showed that bending stress graphs had approximately 17% error for each trial. Like stated in our results, we were only allowed to measure an I-beam that was similar to the one used in the trials. Not only was the experimental beam not measured, but the one used for geometric measurements was not symmetric. Combined with the manual data logging and geometric measurement discrepancies, resulted in a high percent error. To alleviate these errors a couple things could have been done. Programing the software to automatically data log, as well as measuring the experimental beam rather than a substitute, can decrease the percent error to a negligible amount.

Bibliography

[1] F. A. B. B. M. & Analytics, F. I. Limited, F. H. International, F. M. S. R.-E. GmbH, F. M. M. E.

FZC, F. L. E. C. O. Corporation, and F. R. V. Systems, “Aisi 1018 mild/low carbon steel,” AZoM.com , 07- Aug-2019. [Online]. Available: https://www.azom.com/article.aspx?ArticleID=6115. [Accessed: 22- Oct-2021]. .

Moment

Distance from neutral axis

Theoretical Bending Stress

IV.2 Datasheets

• I Abstract Contents
• II Results
• III Discussion & Conclusion
• IV Appendix
  • IV.1 Sample Calculations
  • IV.2 Datasheets
  • IV.3 MATLAB Code
    • 101.4 0.0014 Load Deflection Strain
  • 199.76 0.00275
  • 299.69 0.00415
  • 401.03 0.00565
  • 499.92 0.007
  • 601.13 0.0084
  • 700.45 0.00985
  • 801.21 0.01125
  • 905.37 0.01275
• 1000.18 0.0141 - 101.47 0.00155 Load Deflection Strain - 200.75 0.003 - 299.28 0.0044 - 398.85 0.0058 - 501.84 0.00725 - 600.58 0.0086 - 699.15 0.01 - 801.48 0.0115 - 900.14 0.01285 - 999.47 0.0143 - 98.47 0.00155 Load Deflection Strain - 200.78 0.00295 - 300.88 0.0044 - 402.22 0.0058 - 500.78 0.0072 - 597.18 0.0086 - 701.81 0.01 - 802.99 0.0114 - 901.68 0.0129 - 1000.55 0.0143

ylabel('Deflection(in)'); title(['Vertical Deflection vs. Load Trial: ' num2str(i-1)]); exportgraphics(gca,['figures/Deflection' num2str(i-1) '.png'], 'Resolution', 300); %plots - bending vs load fig_b = figure(i); fig_b.Position = [0, 0 , 750, 500 ]; fig.b.Visible = 'on'; plot(data(:,1), bend_stress_exp, 'r-o', 'LineWidth', 2)%Experimental hold on plot(data(:,1),bend_stress_theo, 'b-o', 'LineWidth', 2)%Theoretical hold off legend('Experimental' , 'Theoretical', 'Location' , 'Southeast'); xlabel('Load (lbf)'); ylabel('Bending Stress(PSI)'); title(['Bending vs. Load Trial: ' num2str(i-1)]); exportgraphics(gca,['figures/Bending' num2str(i-1) '.png'], 'Resolution', 300); end