Deflection of an Eccentric Tie free essay sample

Figures and Diagrams/15| | Materials and Method/10| | Results Discussions/45| | References/10| | Total| | School of Engineering Taylor’s University Malaysia 28 September 2012 Table of Contents Abstract3 1. Introduction3 2. Experiment design4 2. 1 Materials4 2. 2 Methods4 2. 3 Procedure4 3. Results amp; Discussion5 3. 1 Tables5 3. 2 Graphs 6-7 3. 3 Discussion of results8 4. Analysis9 4. 1 Guidelines for error analysis9 5. Conclusions amp; Recommendations9 6. References 10 ABSTRACT The aim of doing this experiment is to compare the transverse bending deflection of the tie bar and the theoretical values that obtain from the simplified formula and the exact formula when the eccentricity of the load is 75m, 55mm and 35mm. The experimental values of the deflection of the tie are obtained by reading the results of dial gauge during the experiment. 1. INTRODUCTION Eccentric loading is the pressure directed anywhere on a component other than where the component is designed to accept the force. Sometimes the design of a mechanism or a structure demands that a tension member has to be offset from the line of the pull. This means that the member has to carry combined tension and bending, the latter increasing with the eccentricity of the load. When the load line is going out the middle third of a square tie bar, as in this experiment, the bending moment predominates and bending deflection may be considerable. The more rigorous mathematical solution of an eccentrically loaded tie bar requires some knowledge of differential equation. An approximate solution could be obtained by regarding the tie bar as a beam with equal and opposite couples applied, thus producing circular bending. The experiment provides an exaggerated demonstration of an eccentric tie to make possible a visual appreciation of the problem. It also gives an opportunity to check the order of accuracy that can be achieved by using the simple theory. 2. EXPERIMENT DESIGN Dial Gauge Aluminum Tie Bar Apply Load Figure 1. Eccentric Tie Bar Dial Gauge Aluminum Tie Bar Apply Load Figure 1. Eccentric Tie Bar The experiment is designed as followed. . 1 Materials 1. Eccentric Tie Apparatus 2. Load hanger 2N 3. Weight sets 50N, 20N, 10N and 2N. 2. 2 Methods First, the gauges readings are obtained by calculate the dial gauge at the centre of the eccentric tie apparatus. The dial gauge contain of 100 divisions, to get the central of deflection, is the gauge readings multiply by the sensitivity of the dial gauge which is 0. 01mm. Besides that, the central defle ction also obtains by using the simple formula and exact formula. The comparison between the results will be shown in the form of graph. 2. 3 Procedure ) The apparatus with the greatest eccentric of loading (75mm) was set up and the â€Å"zero† load reading of the dial gauge was noted. b) 90N of load was added in nine increments of 10N, the reading of the central deflection for each increment was recorded in Table 1. c) The above procedure was repeated with the load at 55mm eccentric, and 120Nof load was added in increment of 20N, the results were recorded in Table 2. d) The above procedure with the load at 35mm eccentric was repeated, and 140N of load was added in increment of 20N, the results were recorded in Table 3. 3. RESULTS amp; DISCCUSION 3. 1 Tables Applied Load (N)| End Moment (KN. mm)| Gauge Reading (No of divisions)| Central Deflection (mm)| Central Deflection,? from simple formula (mm)| ? /e| Central Deflection from exact formula (mm)| | | | | | | | | | | | | | | | | | | | | | 0| 0. 00| 0| 0. 00| 0. 00| 0. 000| 0. 00| 10| 0. 75| 79| 0. 79| 1. 28| 0. 017| 1. 26| 20| 1. 50| 289| 2. 89| 2. 56| 0. 034| 2. 49| 30| 2. 25| 321| 3. 21| 3. 84| 0. 051| 3. 69| 40| 3. 00| 411| 4. 11| 5. 12| 0. 068| 4. 85| 50| 3. 75| 513| 5. 13| 6. 41| 0. 085| 5. 98| 60| 4. 50| 618| 6. 18| 7. 69| 0. 02| 7. 08| 70| 5. 25| 719| 7. 19| 8. 97| 0. 120| 8. 15| 80| 6. 00| 821| 8. 21| 10. 2| 0. 137| 9. 20| Table 1: 75mm eccentric Applied Load (N)| End Moment (KN. mm)| Gauge Reading (No of divisions)| Central Deflection (mm)| Central Deflection,? from simple formula (mm)| ? /e| Central Deflection from exact formula (mm)| | | | | | | | | | | | | | | | | | | | | | 0| 0. 0| 0. 0| 0. 0| 0. 00| 0. 000| 0. 00| 20| 1. 1| 147| 1. 47| 1. 88| 0. 034| 1. 83| 40| 2. 2| 300| 3. 00| 3. 76| 0. 068| 3. 56| 60| 3. 3| 448| 4. 48| 5. 64| 0. 102| 5. 19| 80| 4. 4| 600| 6. 00| 7. 52| 0. 137| 6. 5| 100| 5. 5| 730| 7. 30| 9. 39| 0. 171| 8. 22| Table 2: 55mm eccentric Applied Load (N)| End Moment (KN. mm)| Gauge Reading (No of divisions)| Central Deflection (mm)| Central Deflection,? from simple formula (mm)| ? /e| Central Deflection from exact formula (mm)| | | | | | | | | | | | | | | | | | | | | | 0| 0. 00| 0. 0| 0. 0| 0. 00| 0. 000| 0. 00| 20| 0. 70| 85| 0. 85| 1. 20| 0. 034| 1. 16| 40| 1. 40| 194| 1. 94| 2. 39| 0. 068| 2. 26| 60| 2. 10| 396| 3. 96| 3. 59| 0. 102| 3. 30| 80| 2. 80| 481| 4. 81| 4. 78| 0. 137| 4. 29| 100| 3. 50| 570| 5. 7| 5. 98| 0. 171| 5. 23| 20| 4. 20| 645| 6. 45| 7. 17| 0. 205| 6. 12| Table 3: 35mm eccentric 3. 2 Graphs The results of the experiment are plotted and as shown in the 3 graph above, the eccentricity of load which is 75mm, 55mm and 35mm gave us the different results. The equation that used to calculate the Central deflection is: Simplified Formula ?=ML28EI Exact Formula 3. 3 Discussion of results 1. After compared both theoretical and experimental results, it shows that the values of central deflection is related to the end moment, as the end moment increases, the central deflection also increases. The behaviour of the graph central deflection against end moment also clearly showed that the central deflection is directly proportional to end moment. The results of the central deflection for the experimental values is smaller than the simplified and exact formula, this is because, there might be some errors occur during the experiment. The errors are listed in 4. 1 Guidelines for error analysis. 2. There are significant different between the values obtained from Simplified Theory and the Exact Formula, this is because the eccentricity of the tie bar that used in the Simplified Theory is only considered the applied load. On the other hand, the Exact Formula is considered as a whole depending on the effective load, Young’s modulus, length, and second moment of inertia. Therefore the values that obtain by using the Exact Formula are more accurate. 3. If an error of 10% was allowed (by using a larger factor of safety in design), the experimental results which are after 80N are not adequate, this is because the tensile strength of the tie bar that used in the lab is not that strength. Therefore, the different between the Theoretical central deflection and the central deflection that calculate using Simplified Theory for the heavier loads shouldn’t be ignored. . 0 ANALYSIS 4. 1 Guidelines for error analysis 1. Parallax error might be occurred when reading the dial gauge when taking different results. 2. The load is not applied directly on the normal axis will also cause some error on our results. 3. Slight vibration of the table might also affect the accuracy of the result. 5. 0 CONCLUSION A ND RECOMMENDATION From the experiment, the accuracy of the experimental values is less accurate if compare to the Theoretical values, this is because there might be errors that occurred during the experiment. In order to increase the accuracy of the experimental results, a digital dial gauge with smaller scale and more sensitive should be used and the experiment should we repeated more times to get the average reading. 6. 0 References 1. M. Zaina, S. J. Foster (2005), â€Å"Testing of Concentric and Eccentrically Loaded Fibre-Reinforced HSC Columns†, School of Civil and Environmental Engineering, UNSW. 2. Hugh D. Young, Roger A. Freedman (2008), â€Å"University Physics with Modern Physics†, 12th Edition, p. 363-370. 3. W. A. Bassali, M. N. Y. Anwar, K. M. Mosleh (1985), â€Å"Deflection of an Eccentrically Loaded and Concentrically Supported Thin Circular Annulus†, Journal of Pure and Applied Maths, 16(2), 189-212. 4. Beer, Johnston, Dewolf 2002. Mechanics of Materials 3rd Ed. (Reference list) 1. http://www. engineeringtoolbox. com/area-moment-inertia-d_1328. html 2. http://www. ecourse. ou. edu/cgi-bin/ebook. cgi? doc=†amp;topic=meamp;chap_sec=09. 3? amp;page=theory 3. http://www. toolingu. com/definition-570240-28512-eccentric-loading. html 4. http://www. freestudy. co. uk/statics/beams/beam%20tut3. pdf