Lab 2- Google Docs

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University of Texas *

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301

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Mechanical Engineering

Date

Feb 20, 2024

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pdf

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Uploaded by SargentKoalaMaster1021

LAB 2 - Beam Bending Group 1: Adam Fitzgerald, Mo Muhtasim, Clayton Ferguson, Luke Dearborn Introduction Background Theory: Our original background theory was that both of the wood beams would have a larger length of deflection than both metal beams. This is because Metals is often thought of and used as a rigid, hard, and stiff material. This is why it is the foundation for bridges and roads and large structures. On the other hand, wood can also be a very stiff material when the moment of inertia is correctly used. This is why wood is such a good material for supporting buildings and other structures. As far a obtaining the most cost effective beam goes, we think that pine is going to be the best bet, given that it is not too expensive and it has proved to be a very strong material Purpose: The purpose of this lab is to determine the modulus of elasticity and moment of inertia for each cross-sectional size of a pine, douglas fir, aluminum and steel beam in order to find the most cost effective beam. Descriptions of Procedures and Equipment - First we used a tape measure and measured 2 ft out in both directions from the middle of the material so that way we had a 4ft length to work with. - Next we used a caliper in order to measure the width and thickness of the middle and both ends of the material. We then took the average of these three measurements to use as our actual width and thickness. - Then we placed the beam in a stand to span the length of 4 ft. - We placed a deflectometer in the center of the beam. - We used the deflectometer in order to measure how far the material deflected under different loads. - A clamp was used in the center of the beam we were testing in order to hang loads. - We used metal weights in increments of 5 pounds to measure the deflection of the beam. - We recorded the weight and deflection for each trial onto a data table - We transferred this data into visible charts - From these charts, we were able to find the slope (k) which resembled the bending stiffness of the beam. - We were then able to calculate the modulus of elasticity (E) for each beam.

Experimental Data and Discussion

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Modulus of Elasticity Table Experimental Data and Discussion (continued) - (FLAT) We found that the material with the largest bending stiffness (k) is pine, and the material with the smallest bending stiffness (k) is aluminum. - (UPRIGHT) We found that the material with the largest bending stiffness (k) is pine, and the material with the smallest bending stiffness (k) is aluminum. - In the case of both upright and flat beams, the beams that had the largest modulus of elasticity were steel and the beams with the smallest modulus of were pine. - The beam with the largest modulus of elasticity is not the stiffest. The wooden beam with the highest bending stiffness was pine. Reasons for this could be that there is a difference between the density of each of the different types of wood and potentially could’ve been defects in the wooden beam. - Among the wooden beams, pine has the largest bending stiffness. The reason this might be true could be due to the different moments of inertia that each material has; since the moment of inertia is a crucial factor in determining the bending stiffness of a beam. - The steel’s dimensions (other than length) were smaller which means that steel is much more dense than pine. Since the dimensions of the steel were smaller than the dimensions of the pine, it can be concluded that steel is a much more dense material. - The part of the experiment that was prone to the most error was probably ensuring that the beam was perfectly balanced on both sides. While setting up the experiment, it could’ve been very easy for the beam to slide around and for the bases under the boards to slide, meaning that the area we measured in wasn’t perfectly centered. There is also the chance that the deflectometer and the caliper were not 100% accurate when reading the dimensions. Materials Upright Modulus of Elasticity Flat Modulus of Elasticity Combined average Pine 1,753,075.00 2,052,033.59 1,902,554.295 Douglas Fern 2,385,146.50 2,789,831.66 2,587,489.08 Steel 28,708,775.00 30,645,815.88 29,677,295.44 Aluminum 7,583,537.40 9,004,822.65 8,294,180.03

Moment Of Inertia Deflections Deflection-to-cost Material 5.359 0.958 0.2395 2x4 Pine 20.797 0.249 0.0415 2x6 Pine 12.505 0.411 0.0456 4x4 Pine 5.359 0.704 0.1408 2x4 Doug Fir 20.797 0.181 0.0258 2x6 Doug Fir 12.505 0.302 0.0302 4x4 Doug Fir Design Application The least expensive acceptable option is Pine (1.5X5.5) at $6 as when it is upright, its deflection is lower than the maximum acceptable deflection which is 0.5 inches. The most acceptable option that has the lowest deflection-to-cost ratio when it is placed upright is Douglas Fir (1.5X5.5). The overall most reasonable option to choose is Pine (1.5X5.5) as it meets the criteria of having a deflection of ≤ 0.5 inches, and it's also the cheapest option which is considered acceptable. Conclusion This lab's goal is to calculate the moment of inertia and modulus of elasticity for each cross-sectional size of a pine, douglas fir, aluminum, and steel beam in order to identify the most economically efficient beam. As per our background theory, the most reasonable option was Pine (1.5X5.5) as it was the cheapest material which met the criteria of having a deflection ≤ 0.5 inches. This was determined through the calculation of deflections and deflection-to-cost average between the materials. The deflections were affected by the moment of inertia of the materials. Overall, the lab was successful in helping us identify the least expensive acceptable option is Pine (1.5X5.5) at $6 as when it is upright, its deflection is lower than the maximum acceptable deflection which is 0.5 inches..