CEE370L_Test5_Report_Vergara, Kailah Reign

.docx

School

University of Hawaii *

*We aren’t endorsed by this school

Course

370

Subject

Mechanical Engineering

Date

Dec 6, 2023

Type

docx

Pages

Uploaded by MinisterTank8797

CEE 370 Mechanics of Materials Lab Beam Bending Theory Kailah Reign Vergara University of Hawaii at Manoa CEE 370L Mechanics of Materials November 14, 2023

CEE 370L Mechanics of Materials Fall 2020 Laboratory (No.) EXECUTIVE SUMMARY During the laboratory experiment, a large steel beam specimen with simple support was exposed to a transverse load. The steel beam was equipped with multiple electrical resistance strain gauges at different locations to track the strain in the steel. These gauges were employed to assess the specimen's response under various loads. By calculating the theoretical stresses based on the measured microstrains, we could observe the behavior of the plot. The outcomes of the test will be utilized to validate the correlation between bending moment and bending stresses, commonly referred to as the beam bending theory. Page

CEE 370L Mechanics of Materials Fall 2020 Laboratory (No.) TABLE OF CONTENTS EXECUTIVE SUMMARY………………...……………………………………………………………...i 1 INTRODUCTION ............................................................................................................................. 1 1.1 B ACKGROUND .............................................................................................................................. 1 1.2 R EASON FOR E XPERIMENT ........................................................................................................... 1 1.3 T HEORY ........................................................................................................................................ 1 1.4 O BJECTIVE ................................................................................................................................... 1 2 APPROACH ...................................................................................................................................... 1 2.1 T EST S ETUP AND I NSTRUMENTATION ........................................................................................... 1 2.2 T EST S PECIMENS .......................................................................................................................... 2 2.3 T EST P ROCEDURE ......................................................................................................................... 3 3 RESULTS ........................................................................................................................................... 3 3.1 ............................................................................................................................................................... 3 3.2 ............................................................................................................................................................... 3 4 ANALYSIS ......................................................................................................................................... 3 4.1 ............................................................................................................................................................... 4 4.2 ............................................................................................................................................................... 4 5 CONCLUSIONS/RECOMMENDATIONS ..................................................................................... 4 6 REFERENCES .................................................................................................................................. 5 APPENDIX TABLE OF FIGURES FIGURE 1.3.1: DIAGRAM FOR A TYPICAL STEEL BEAM SUBJECTED TO AN EXTERNAL LOAD FIGURE 2-2: DIAGRAM OF THE BEAM WITH THE DISTANCES AND LAYOUT OF THE VARIOUS GAGES FIGURE 2-3: CROSS SECTION OF THE BEAM Figure 2-4: BEAM BENDING THEORY TEST SETUP Figure 3.1: Stress vs Load Relationship of Top and Bottom Gages Figure 3.2: Average Stress vs Distance Relationship of Front and Back Gages Figure 3.3: Stress vs Distance Relationship from Center of Beam Page

CEE 370L Mechanics of Materials Fall 2020 Laboratory (No.) 1 Introduction 1.1 Background Beam bending arises when external forces act on a beam, inducing deformation. This phenomenon is prevalent in the construction of diverse structures. To assess a beam's ability to bear loads, shear force and bending moment diagrams are employed to pinpoint areas of peak shear force and moment. Steel, widely utilized for beams, exhibits proficiency in both tension and compression. Its versatility in being shaped into various forms with distinct capabilities further enhances its appeal. By scrutinizing stress distribution across the cross-section, the highest stress occurs farthest from the neutral axis. Additionally, when assessing stress variation along the beam span, stress peaks align with maximum bending moments. 1.2 Reason for Experiment The objective of conducting this laboratory experiment was to aid a civil engineering professional in the design phase by identifying the most suitable variation of a specific material for a project. The stress-strain curve generated through the experiment provides essential characteristics that play a vital role in the material selection process. This careful consideration is crucial for ensuring the safety and stability of the structure being worked on. The broader public stands to gain valuable insights from the outcomes of this experiment. Knowledge of how various materials behave and respond to applied forces can instill confidence in the public regarding the safety and structural integrity of their surrounding environment. 1.3 Theory Page 1

CEE 370L Mechanics of Materials Fall 2020 Laboratory (No.) The fundamental principle of beam bending theory, also known as Bernoulli Euler beam theory, plays a crucial role in mechanical engineering. It elucidates the behavior of a beam when subjected to external loads. As a beam undergoes deformation or bending under loading, we can compute the resulting stresses and deflections. Notably, any cross-section of the beam that is initially perpendicular to the neutral axis will maintain this perpendicular orientation throughout the deformation process. The core tenet of beam bending theory asserts that a beam will deform in a manner that minimizes its potential energy under the given external loads. This principle holds as long as the cross-section remains constant during bending, and the material exhibits consistent mechanical properties in all directions. Figure 1.3.1: Diagram for a typical steel beam subjected to an external load 1.4 Objective The goal of this laboratory experiment was to confirm the correlation between bending moment and bending stresses. Furthermore, the validity of the assumption that plane sections remain flat will be assessed. Page 2

CEE 370L Mechanics of Materials Fall 2020 Laboratory (No.) 2 Approach 2.1 Test Setup and Instrumentation This test used a steel beam and electrical gages to identify the strain in the beam. Figure 2-2: Diagram of the beam with the distances and layout of the various gages. Figure 2-3: Cross section of the beam. Page 3

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version