CIVL2201 Second Moment of Area Lab Report.docx - 1 CIVL2201...

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CIVL2201 – Structural Mechanics: Laboratory Report 2 SECOND MOMENT OF AREA REPORT FROM LABORATORY EXPERIMENT CONDUCTED ON 16 MAY 2017 AS PART OF THE UNIT OF STUDY CIVL2201 STRUCTURAL MECHANICS ABSTRACT This report details the loading and displacement measurements of a simply supported beam. The objective was to use the catalogue description, cross-sectional dimensions, and deflections of a simply supported beam to calculate and compare different values for the second moment of area ( I value) using a 75 x 40 x 3.8 cold-formed steel channel section. The experimental I value was calculated using the rate of load per deflection (assuming pure bending deflection), and the calculated value by using the measured cross-sectional dimensions. The nominal, calculated and experimental I values were found to be 0.0840, 0.0915 and 0.0892 x10 6 mm 4 respectively. The mid-span load-deflection curve of the section was linear, revealing that deflections of a simply supported beam subject to a point load at mid-span increase at a constant rate in the elastic range. For this specific section, the rate of load per deflection was found to be 58.96 N mm . The second moment of area is a geometric property representing the exact distribution of cross- sectional area from the centroid. Thus the best estimate to this “true” distribution should be the I value based on measured cross-sectional dimensions. However, when the theoretical deflections of the beam using the different I values mentioned were compared to the actual deflection, the calculated I value was inconsistent with the data. Furthermore, the nominal I value was inconsistent with the rest results as well. The experimental value was consistently the most accurate; thus appearing to be the most reliable estimate. These results reveal the discrepancies that may arise through alternate methods of calculating I values, and explore which is the most reliable. The different results illustrate the importance of using conservative nominal values, for otherwise the manufacture of overly flexible or weak members may compromise the safety of structures. 1
CIVL2201 – Structural Mechanics: Laboratory Report 2 Table of Contents ABSTRACT ...................................................................................................................... 1 1. Introduction .................................................................................................................. 3 2. Method .......................................................................................................................... 3 2.1. Equipment and Set-up .......................................................................................................... 3 2.2. Testing Procedure ................................................................................................................. 4 3. Results ........................................................................................................................... 4 3.1. Nominal and calculated I ...................................................................................................... 4 3.1.1. Dimensions .......................................................................................................................... 4 3.1.2. Calculated I value ................................................................................................................ 5 3.2 Deflection and Experimental I ............................................................................................... 5 4. Discussion ...................................................................................................................... 7 4.1. Measurements ....................................................................................................................... 7 4.3. Deflection .............................................................................................................................. 8 4.4. Assumptions and accuracy ................................................................................................. 10 5. Conclusion ................................................................................................................... 12 6. References ................................................................................................................... 13 Appendices ...................................................................................................................... 14 Appendix A – Calculated Centroid ............................................................................................ 14 Appendix B – Calculated I value ............................................................................................... 14 Appendix C – Raw Deflection Data ........................................................................................... 15 Appendix D – Load-Deflection Curves and Trend Line Regression Analysis .......................... 15 Appendix E – Figure 4 MATLAB code ..................................................................................... 17 Appendix E – Figure 6 MATLAB code ..................................................................................... 18 2
CIVL2201 – Structural Mechanics: Laboratory Report 2 1. Introduction The aim of this report was to calculate the second moment of area of a channel section in various ways, and conclude which is the best estimate to the true I value of a section. Understanding different methods for calculating I

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