1 Column Buckling Test Luis Ramos - 5874829 Ariana Bueno - 5294006 Hassan Zock-Obregon - 2826919 GROUP A2 EML 3702L Section U01 Professor Yu Zhong Mechanics and Materials Science Lab Florida International University – Spring 2017 March 20, 2017 2 Table of Contents Table of Contents 2 List of Figures 3 List of Tables 3 Nomenclature 4 Abstract 5 Introduction 6 Data & Results 8 Discussion and Reccommendations 13 References 15 Appendix A: Apparatus 16 Appendix B: Procedure 17 Appendix D: Experimental Data 19 3 List of Tables: Table 1. Nomenclature……………………………...................................................................................... 4 List of Figures: Figure 1. Tensile Test Apparatus….……..................................................................................................... 6 Figure 2. Specimen Deformation and its behavior........................................................................................6 Figure 3. Tensile Properties of Metals – Stress vs Strain............................................................................. 8 Figure 4. Tensile Properties of Metals – Plastic Deformations and Proportional Limits..............................9 Figure 5. Elastic Modulus using the tangent method……...........................................................................10 Figure 6. Elastic Modulus using the secant method.....................................................................................11 Figure 7. Yield Stress using the 0.2% offset method……………………………………………………...12 Figure 8. Tensile Properties of Metals (Rect bars)………………………………………………………..13 Figure 9. Tensile Testing Machine 1 – left………………………………………………………………..16 Figure 10. Tensile Testing Machine 2 – right……………………………………………………………..16 Figure 11. Dimensions of test specimen…………………………………………………………………..17 Figure 12. Tensile Experiment Poster…………………………………………………………………….18 4 Nomenclature Symbol E I/Imin Description Elastic Modulus Moment of Inertia / Minimum Moment of Inertia Le Effective length Pcr Critical Load r Radius of gyration A Cross sectional area of the column Table 1 Nomenclature SI unit 5 Abstract The purpose of this experiment was to verify the Euler buckling equation for steel columns of various lengths that are subjected to different load applications with certain end conditions. In cases dealing with vertical prismatic members supporting axial loads, stability considerations are important. These structures are known as columns and when they are subject to a load greater than the critical load they will suddenly become sharply curved. We will calculate average bulking critical loads, plot average critical load and deflection, find modulus of elasticity, by using Euler’s formula and collecting experimental data. By measuring the dimensions of the columns and calculating the expected buckling load for the end condition chosen we will be able to calculate and plot the information needed for this experiment as listed above. We will use the Euler buckling apparatus to apply different loads and record deflections at each increment using the dial indicator in order to find the critical load application when specimen undergoes buckling. For this experiment, we will test three different columns and use the one fixed end, one pinned end condition. 6 Introduction Data and Results Discussion Recommendations 7 References “Writing Technical Reports” January 2017. Available at: http://web.eng.fiu.edu/~yzhong/EMA3702L/EMA3702L_WritingReport.html Figure https://upload.wikimedia.org/wikipedia/commons/thumb/4/43/Buckled_column.svg/220pxBuckled_column.svg.png Figure http://www.harborfreight.com/media/catalog/product/cache/1/image/9df78eab33525d08d6e5fb8 d27136e95/i/m/image_18512.jpg 8 Appendix A: Apparatus Figure 9 Column Buckling Testing machine 1 -left Figure 10 Column Buckling Testing machine 2 - right The column buckling testing machine is used for this experiment. The test specimen is positioned and the dial indicator is installed in the brackets and fastened to the center post. The indicator needs to be moved up or down the post so that the indicator point contacts the column at its midpoint. The columns are secured using the fastening screws that don’t need to be tightened too much. 9 Apparatus B: Procedures 1. Measure and record the dimensions of the column on the worksheet. 2. Calculate the expected buckling load for the end condition at hand. 3. Orient the satin chrome blocks on the loading frame for the end condition chosen. 4. Adjust and secure the capstan nut 5. After column is in position, the dial indicator is installed in the brackets and fastened to the center post. Figure 1Dial Indicator 6. Gradually apply increment of load, and check each time column is changed. 7. After each increment of load, record the load and deflection on the data sheet. Suitable increments for the loading of the column may be obtained by rotating the hand wheel. 8. Stop the loading beam when the column starts to curve and reaches critical load. 10 Figure 12 Euler Buckling Experiment Poster 11 Apparatus C: Experimental Data Dimensions of the test specimen and values recorded from indicator dial for applied load. Figure 13 Experimental Data