The aim of this experiment is to obtain and graph deflections and bending stresses for a cantilever beam under a point load and observe the affect that changing the mass of the point load has on the deflection and bending stress graphs. Hypothesis As the loading on the bar Increases, the magnitude of deflection and bending stresses will become greater. Procedure 1 . Clamp the strain gauge instrumented steel beam to the rig. Place the dial gauge at ammo and zero it. 2. First acquire a reading with a zero load then load the beam tit different weights (4 different weights is recommended) at ammo. Enter the mass into the corresponding box and ‘Acquire’ the data point. 3. Enter the parameters of the beam Including the conversion factor to plot the theoretical deflection and stress curves. Note: to delete an Individual data point, click on that row on that table and then click ‘delete row’. Remember to label your plot including units. Diagram Results Discussion The experiment has shown that as the loading mass is increased, the magnitude of the deflection and bending stress became greater, thus confirming the hypothesis.
However there was a clear amount of error between the experimental and theoretical results. For deflection versus load the error was very small implying that the bar used for this Investigation had not lost much of It original properties or suffered much permanent deformation prior to experimentation. The error Incurred with this part measuring the equipment used. For bending stress versus load the error was quite significant. There is a clear difference in the gradient of experimental and theoretical data. An average percentage error was calculated to be 64. % 0. As shown in the results, when the bar had a zero mass loading applied, there was still a stress force of 0. 018 Amp, demonstrating that the stress gauge did not take into account the mass of the bar itself. Also there could be error within the readings that the stress gauge taking due to fatigue of the materials used in the make of the device. Fatigue of the material would result in the readings being much higher than they are. These factors, along with a certain degree of human error are why the theoretical and experimental results are not exact.
Repeating the experiment multiple times for each mass and taking the average of the measurements could have improved the consistency of the results. Doing this would decrease the amount of human error associated with the investigation. Also calibrating the computer to take into account the mass of the bar would greatly improve the accurateness of the measurements. Calculations and Uncertainty Analysis An uncertainty value was put on measurements taken from the investigation that have a direct correlation to the equipment used to take each measurement. ‘ (keg) h’ (meter’s) ‘ (meter’s) 0. 0005 0. 00001 Using the formula: From this formula the second moment of area about the Z-axis, with an uncertainty, can be obtained. Where: h = 2. Mom b=19. Mm Hence uncertainty would have an affect on the theoretical calculations of bending stress and deflection as shown in the calculation below. Bending stress plus uncertainty: where P=mass * g L = 0. Mm X = 0. Mom (distance from fixed point to stress gauge).