Beam Deflection Experiment - Lab Report Example

The Lab Report on Beam Deflection Experiment By Lecturer’s and Table of Contents Contents Table of Contents 2 Abstract 3 Introduction 3 Experimental Setup and Procedure 3 Experimental Results and Analysis 5 Discussion 9 Conclusions and Recommendations 10 Reference List 12 Appendices: Graphical Presentations 13 Figure 1: Graphical presentation on Relationship between Log δ and Log W 13 Figure 2: Graphical presentation on Relationship between Log δ and Log L 14 Figure 3: Graphical presentation on relationship between log δ and log b 14 Figure 4: Graphical presentation on Relationship between Log δ and Log d 15 Abstract This is a comprehensive report on the laboratory experiment that was aimed towards finding out the mutual correlation between the central beam deflections of a supported beam with its proportionate span, width. The other main objectives of this experiment was the aspect of surface strains measurements by use of specific strain gages within a cantilever beam, measurement of the beam’s deflection using LPDT, comparison of both experimental and analytical values of the cantilever beam stress, statistical presentation of values, as well as the aspect of getting acquainted with a wide range of structural testing components (HEILES & SCHÄFER, 2013).  To this extent a number of tools and equipment that were used in the entire experiment have been duly described to a greater extent based on their usage and the conditions that should be kept constant while performing the experiment using those kinds of pivotal tools and equipment. Introduction Objective The main aim of this experiment is to ascertain laws that support deflection of a supported beam in relation to a centrally concentrated load bearing. Experimental Setup and Procedure Apparatus to be used included; the cast iron bed, adjustable supports, mild steel beam, stirrup, mass hanger, Individual mass objects, as well as the dial gauge indicator. The beam of length 1.3 meters was initially placed firmly on the cast iron bed with the assistance of simple supports A and B placed 1 meter apart. The load was then applied by use of the mass hangers at a gradual incremental rate, while the measurements were recorded at each and every stage. The next step that ensued was the aspect of bringing in some sort of variations with regards to the length while the initial procedure was repeatedly done. The material under test was then altered such that, in each and every instance it was only the cross sectional breath that changed. This was repeatedly done at various levels as the mid span deflection at each stage was measured (in mm) with regards to the subjected conditions. The next step that followed suit was the aspect of altering the tested material such that in each and every instance the cross-sectional depth was the only variable that changed. Under this stage, the rate of deflections were also measured and recorded accordingly. All the obtained values were then clearly recorded and compiled so as to assist later during analysis whereby, the values that were arrived at were subjected to massive scrutiny and comparisons with the existing facts and figures under each and every experimented condition. A simple visual view of the entire experiment: Table 1: Tested Independent variables Test Independent Variable S.I Units Symbol 1 Central concentrated load N W 2 Distance between supports (span) mm L 3 Breadth of cross section mm b 4 Depth of cross section mm d 5 Coefficient mm2/N K Experimental Results and Analysis The attained experimental results were recorded as follows based on various variables; a) The mass (N) versus the Deflection (mm) Using 0N as the minimum and 150N as the maximum, the mass of the load was adjusted by increasing each trial consequentially by 25N. All this was done keeping these values constant: L=1m, b=20mm and d=14mm. Values obtained were recorded as below Mass W (N) 0 25 50 75 100 125 150 Deflection δ (mm) 0 56 112 169.5 226.5 284 341 Values of Log δ for Log W Log W - 1.398 1.699 1.875 2 2.097 2.176 Log δ - 1.748 2.049 2.229 2.355 2.453 2.533 b) Length (mm) versus Deflection (mm) Using a minimum length of 0.6m and a maximum of 1.2m, length of the load was varied in split distances of 0.1m per trial. Values kept constant were: W=150N, b=20mm, d=14mm. Results obtained were as recorded in table below. Length L (mm) 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Deflection δ (mm) 72 111 169 249 340 443 571 Values of Log δ for Log L Log L -0.222 -0.155 -0.097 -0.046 0 0.041 0.079 Log δ 1.857 2.045 2.228 2.396 2.531 2.646 2.757 c) Breadth (mm) versus Deflection (mm) Using a minimum breadth of cross section of 10mm and a maximum of 16mm, the breadth of the cross-section was varied consequentially in each trial by 2mm. Values kept constant were: W=150N, d=14mm, L=1m. Results obtained were as recorded in table below. Breadth b (mm) 10 12 14 16 - - - Deflection δ (mm) 224 194 159.5 143 - - - Values of Log δ for Log b Log b 1 1.079 1.146 1.204 - - - Log δ 2.350 2.288 2.203 2.155 - - - d) Depth (mm) versus Deflection (mm) Using a minimum depth of cross section of 10mm and a maximum of 16mm, the depth of the cross-section was varied consequentially on each trial by 2mm. Values kept constant were: W=150N, b=20mm, L=1m. Results obtained were as recorded in table below. Depth d (mm) 10 12 14 16 - - - Deflection δ (mm) 664 536 341 199 - - - Values of Log δ for Log d Log d 1 1.079 1.146 1.204 - - - Log δ 2.822 2.729 2.533 2.299 - - - Analysis: From the above tables of results, the log values were computed for each and every table. This is due to the sense that, linear relationships were expected through comparison of the logs of each pair of variables. The log values more specifically to base 10 are outlined in the separate tables below each subsequent table of results so as to show clear relationship. Those resultant figures were hence graphically presented as shown below in figure 1, 2, 3 and 4 respectively at the appendices segment. The analysis of the resulting linear graphs shows that; the graphs based on the relationship between all these variables with deflection have got varying gradients as well as the y-intercepts. From the results, the constant (K) values can be computed. For instance; the values for each and every variable can be computed as shown below: i. Relationship between Log δ and Log W From the graph; the slope regarding this variable (α) = 0.15; The y-intercept (Log K) = 1.70 Therefore; the linear equation shall be: Log δ = 0.15 (Log W) + 1.70 From this; δ = 101.7.W0.15 With L, d and b kept constant; Read More