Experiment-7

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University of Central Oklahoma *

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Dec 6, 2023

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University of Central Oklahoma Experiment 7 - Beam Experiment Dylan Robinson, Joshua Jackson, and Kaleb Paddock Dr. Adnan Al-Ibadi Thursday 1:00 PM 11/10/22
ABSTRACT In experiment 7 for the strength of materials lab, we employ the use of strain gauge system in order to determine the static deformation of a cantilever beam structure, as well as learn some of the basics involving the basics of finite element analysis. [1] In aerospace engineering, aircraft wings’ lateral structural elements are similar to that of bridge beams. They are referred to as spars and they carry the main loadings induced from lift. Figure 1 shows equations related to spar shear force and bending moment. Figure 1. Aircraft Wing Spar
THEORY For this experiment,we are asked to consider the deformation of a cantilever beam structure using the theories and concepts behind finite element analysis in conjunction with a strain gauge system. For our particular experiment, we use the strain gage system on a cantilever beam and gather experimental data from that. EQUIPMENT As stated previously, the main piece of equipment that we will be using in this particular experiment is a strain gauge system. This tool is particularly useful when trying to determine deformation on a body, and in this particular experiment in which we are testing on a simple apparatus, it is relatively lightweight work on the end of this device. This device’s main components consist of a single conducting strip on a film that “zig - zags” back and forth along the longitudinal axis of the beam. The gauges are able to detect strain in the beam in that direction, and thus will be able to give us very accurate measurements for the total deformation on the specimen. Shown below is a diagram of the circuit that is used for the strain gauge. Figure 3 shows the exact components used. Figure 2. Strain Gage Diagram EXPERIMENTAL METHOD In this experiment, our part of setting up the experiment was very limited. However, as stated previously, our particular experiment involved a cantilever beam setup with an attachment point for an added load point (weight) towards the end of the beam, and given various loads applied, we measured the deformation of the specimen from the strain gauge system. Shown below in Figure 3 is the apparatus setup. [3]
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Figure 3. Strain Gage Used EXPERIMENT RESULTS Below in figure 3 is the data we collected from the different loads applied on the specimen. The calculations for this table were carried out by using the following formula, shown below in equation 1. EQ: 1 In equation 1 listed above, V 0 is the voltage in the strain gauge, R 2 and R 3 are resistors and are equal in value for this particular instance, and V s is the voltage of the voltage source, which in this case is 15 volts. Using this equation, we are able to calculate the following results for each of the different strain values.
Table 1: Experimental data collected. From the table above, we are able to construct the following graph, which depicts the values of the strain calculated due to the force being applied. This graph was constructed to be able to hopefully more easily display the data we collected. Graph 1. Strain vs. Load Applied
Ansys Results The following figures were the outcome of following the Ansys procedure outlined in the lab manual.[1] Validation and Discussion Comparing Results and Ansys Results, we are able to see the differences between computed and experimentally derived strain between the materials tested. Using this methodology, we could compare many different metals quickly, and cheaply. Conclusion In conclusion, the objective of the experiment was to compare experimental strain and to validate our results using Ansys. We were able to meet these objectives. As discussed in the validation section using the tests mentioned above engineers can perform complex trade studies on many different materials.
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References [1] Khandaker, M. (2021). Laboratory Manual for Strength of Materials Lab. Department of Engineering and Physics (UCO) [2] https://www.sciencedirect.com/topics/engineering/main-spar [3] Hibbeler, R. C. Mechanics of Materials . Pearson, 2022.