CEE370L_Lab_05_Shi, He

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University of Hawaii *

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370

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Mechanical Engineering

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Feb 20, 2024

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CEE 370 Mechanics of Materials Lab BEAM BENDING THEORY He Shi University of Hawaii at Manoa CEE 370L Mechanics of Materials Nov 26, 2023 1
CEE 370L Mechanics of Materials Laboratory 1 Fall 2023 EXECUTIVE SUMMARY During an experiment, an aluminum beam was examined to validate the principles of beam bending. The theory suggests that a beam made of flexible & homogeneous material with an equivalent modulus of elasticity in tension and compression will deform equally under the same stress. The moment of inertia (I) was calculated for bending around the horizontal centroid axis using the provided properties of the beam section. The moment about the maximum load at the plane section was determined using a shear force and bending moment diagram. Stresses were computed using the moment of inertia, moment about the plane surface, and distance from the centroid axis. It was proven that the distributed loads on the top and bottom flanges were very close to each other, thus confirming the theory. During the beam experiment, loads were applied which caused sagging. As a result, throughout the beam, there was a positive bending moment. Gauges on the plane section of the beam indicated that a plane section within the beam before bending remains plane after bending throughout a constant moment section of the beam. This proves that the beam bending theory is accurate. The experiment concluded that the material is linearly elastic, as the relationships between stress and strain were directly proportional. When a load was applied, the top of the beam was in compression while the bottom of the beam was in tension. The lowest sagging point of the beam showed the largest strains, and therefore had the largest stresses.
CEE 370L Mechanics of Materials Laboratory 1 Fall 2023 1 Introduction 1.1 Background A transverse load is applied to an aluminum beam in order to test the beam bending theory. A number of electrical resistance strain gauges are attached at various points on the beam to measure strain. The purpose of the testing is to confirm the relationship between moment and bending stresses. 1.2 Reason for Experiment The purpose of this lab was to test the deflection limits of beams that are installed in buildings. The experiment provided valuable information to engineers regarding how beams support and resist loads, which enables them to ensure the safety and stability of structures. Finding the maximum values of quantities and their locations along the beam is essential for beam design. 1.3 Theory When a beam is subjected to loads that are transverse to its length, there is no axial load applied. However, when a transverse load is applied, a relationship can be found between the bending moment and the transverse deflection of the beam. The beam is made of a linearly elastic material, which means it follows Hooke's Law. Therefore, a small deflection should cause small angles due to the deflection. The moment-curvature equation ( is determined by the bending moment divided by the modulus of elasticity times the moment of inertia (also known as the flexural rigidity). The equation given for the moment-curvature is:
CEE 370L Mechanics of Materials Laboratory 1 Fall 2023 where M is the bending moment and EI is the flexural rigidity. The flexure formula ( is determined by the bending moment multiplied by the distance from the neutral distance divided by the inertia of the cross section. The equation given for the flexure formula is: where M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia of the cross section 1.4 Objective The goal of this laboratory experiment was to confirm the correlation between bending moments and bending stresses and assess whether the stress distribution aligns with the principles of beam bending theory.
CEE 370L Mechanics of Materials Laboratory 1 Fall 2023 2 Approach 2.1 Test Setup and Instrumentation The experiment was done with a load cell. There were a total of 20 strains on the steel, five on the back, front, top, and bottom. Each of the strains were 6 inches apart from each other. The strains are then hooked up to three different boxes. The load cell co impressed the aluminum beam at 0 kips to 2 kips in 1 increment and back down to 0 kips
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