Lab 2 AME 324L

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University Of Arizona *

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324L

Subject

Mechanical Engineering

Date

Jan 9, 2024

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pdf

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8

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Beam Bending Aditya Kannan AME 324L 9/18/2023 NOTE TO GRADER: I spoke with the TA in class today and he allowed me to submit the report before midnight instead of 5 PM. Thank you!
Introduction In this experimental investigation, our focus will be on beam stress and bending. We will employ strain gauges strategically positioned along an I-beam and vary their distances from a fixed clamp as well as a dial gage to measure the deflection of the beam in a simple manner. Subsequently, we will subject the beam to diverse loads applied at two different points near its extremity. By collecting data pertaining to strain, load magnitudes, and distances, we will apply Hooke's law and the flexure formula, accompanied by moment diagrams/equations, to determine the strain response of the beam to a load. Discussion of relevant concepts The primary objective of this experiment is to understand the behavior of a beam when subject to bending by loading a cantilevered I-beam and gathering data on its response. In the following paragraphs, we will go over the equations that govern the response of beams to bending moments. The first among them is the flexure formula, as depicted below, where ? represents the bending moment, ? signifies the location for stress assessment, and 𝐼 stands for the second moment of area. 𝜎 = − ?? 𝐼 Now, below is the equation for shear stress due to bending. 𝑉 is the shear stress due to applied loads, ? is the first moment of area and 𝐼 is the second moment of area. 𝜏 = 𝑉? 𝑏𝐼 The distribution of normal stress is linear, where the max stress is at the top and bottom of the beam pointing in opposite directions. The distribution of shear stress is a parabola with the focus located at the central axis of the beam. Deflection is a useful piece of data gathered from this experiment using a dial gauge, and the theoretical deflection can be calculated as below. 𝛿 = ?? 2 6?𝐼 ∗ (3? − ?) Now, here are drawn shear force and bending moment diagrams for cantilever and 3-point bending configuration beams.
Figure 1: Shear and moment diagrams for different configurations of a loaded beam Experimental Procedure A 6061 Aluminum I-Beam, firmly attached to the testing table, is used as the cantilever beam for experimentation. Two strain gauges each are attached at 3 locations on the beam. The measurements were recorded using LabView and a dial gage. After configuring the LabView software and ensuring that the strain gage connections were in good condition, the dial gauge was placed on the beam at a measured location. Then, the position of the beam was adjusted in order to locate the testing machine head above a specified location. The LabView recording was started and the load was applied up to specific values ( 100, 200, 250 ?𝑏𝑠 ) and a photo of the strain and load data from LabView and the dial gage deflection was recorded. This process was performed again with the beam moved to a different position in order to understand how the deflection changed by varying the distance of the load from the cantilever. Results & Calculations Now we calculate the moment of inertia of the I-beam based on measurements taken during the experiment using the following formula: 𝐼 𝑥 = 1 3 𝑏ℎ 3 1 12 𝑏 1 1 3 1 12 𝑏 2 2 3 Where:
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