The values for the upright beam all fall within error of each other, while for the flat orientation one value while still very close was just outside of the error of the other two, which are nearly identical.
The plots also contain the standard deviation of the experimental results and the theoretical values for comparison. The experiment was repeated using the second beam. Experiment 1 began with measuring and recording the width and Beam deflection essay of each of the beams using a caliper.
Therefore, the reading of the height might be different from time to other, so, the calculation of deflection is different from the theoretical.
Method three approaches the problem in a different way.
To further strengthen these results, the measurements for both of the specimens maintained a fairly low standard deviation, showing great consistency and accuracy throughout the individual measurements.
There are some errors between the theoretical and the experimental deflection. Three trials were conducted for each mass.
In method three, error comes from the lack of a perfect fit of a deflection graph to our data; our E value minimized the error between predicted and actual deflection, which was then represented as rms Beam deflection essay. In method one, there is error from fitting a line to a set of data that is not precisely linear.
The resulting values of E were then averaged to determine the best value of E for method two. Therefore the final conclusion can be made that structural stiffness is directly proportional to the inverse of length cubed see table 6.
Furthermore, it is easily seen that the quantity length cubed is directly proportional to deflection, as shown in figure The clearance between the middle of the beam and another beam placed on the top of the stand was measured.
The considerable error, We also observed the deflection and the location of maximum deflection, and calculated values of I the second moment of inertia for each orientation. Conclusion Overall, both experiments were effective in validating the primary trends within the derived theoretical equations.
The theoretical value of stiffness was also calculated using equation 7. Nonetheless, Experiment 1 proved effective in determining fairly accurate values for structural stiffness. Flat Orientation 10 ksi ksi 3 0.
The graphs will show the relationship between the load applied and deflection, in addition to compare the experimental deflection and theoretical deflection. This is partially a result of the composition of the beam, as, upon inspection, the grain of the wood is pronouncedly evident see Appendix F.
If we increase the loads, deformation will Beam deflection essay decrease. Starting from the lowest mass g, g, g, g, and geach mass was hung using the hanger from the selected length.
In addition, it was also concluded that force was linearly proportional to displacement, as shown in figures 7, and 8. When the system was stabilized, the deflection length was recorded. Table 3 Force and Experimental and Theoretical Deflections for the Aluminum Beam Table 4 Force and Experimental and Theoretical Deflections for the Steel Beam In order to determine the experimental structural stiffness, the average experimental deflections for both beams were plotted.
This means that because the flat side has less inertia there will be less resistance in changing its position, so it will deflect more.
Making these assumptions, we can apply the general equation for beam flexure to our experiment. Because the thin side has more inertia, it will have more resistance in changing its state. Instead of assuming that! Error in our values comes partially from universal measurement error, and from flaws and inconsistencies in the beam i.
However, although the material does perform more rigidly according to grain orientation, the difference in the value of I made a more significant impact on our final values of E and, thus, the beam behaved more rigidly in the flat orientation, where the I value was significantly smaller.
Experiment 1 setup procedures were repeated for experiment 2. From this experiment we learned that when when a beam will be placed with the wide side on supports it will show les deflection and is more efficient to use.
We also used Matlab values as a check of accuracy. The best value of E for method three was found by determining where the rms error was minimized.
This error might have happened because of the inaccuracy in measuring the length between the beam and the ground, which happens because of not measuring the length perpendicular to the beam itself. The theoretical deflection, theoretical stiffness, average, and standard deviation were calculated for each mass using equations 1, 7, 8, and, 9, respectively.
Table 2 Test Specimen Properties Note:It is found that the deflection of the beam changes linearly with the load and as the beam thickness increases, the beam deflection decreases Show More More about Bending of Beam Lab Report Essay.
beam deflection under the anticipated design load and compare this figure with the allowable value to see if the chosen beam section is adequate. Alternatively, it may be necessary to check the ability of a given beam to span between two supports and to carry a given load system before.
The beam deflection experiment was designed to investigate the structural stiffness of cantilever beams made of steel and aluminum. Cantilever beams are fixed at one end and support applied loads throughout their length. BEAM DEFLECTION FORMULAS BEAM TYPE SLOPE AT ENDS DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM AND CENTER DEFLECTION 6.
Beam Simply Supported at Ends – Concentrated load P at the center 2. Read this essay on Beam Deflection. Come browse our large digital warehouse of free sample essays. Get the knowledge you need in order to pass your classes and more.
Only at ultimedescente.com". The Report of Deflection of a Beam Essay The Report of Deflections of Beams and Cantilevers Summary: There are four parts in this big experiment, including deflection of a cantilever, deflection of a simply supported beam, the shape of a deflected beam, and circular bending.
In these four parts, a.Download