Applied Stress Analysis - Report Example

A REPORT FOR PRACTICAL SESSION 2: STRESS ANALYSIS Student Name Student ID Unit Lecturer Date Start Date of Submission Table of Contents Introduction 4 Experiment 1: The Deflections for a Simply Supported Beam 4 Aim 4 Measurement Method 4 Method Used in the Calculation 5 Discussion 8 Conclusion 9 Experiment 2: Characteristics of Cantilever Beams when a Point Load is Applied 10 Aim 10 How Measurement was carried out 10 Calculation Method Used 10 Discussion 12 Conclusion 12 Experiment 3: How Beam Span and Beam Deflection are Related 13 Aim 13 Measurement Methods Applied 13 Calculation Method 14 Discussion 16 Conclusion 17 Experiment 4: Effect of Torsion loading on a Circular rod 18 Aim 18 Method Used in Carrying Out the Experiment 18 Method of calculation 18 Explanation for Table 5 20 Discussion 21 Conclusion 21 Experiment 5: Loading & Tension in a Suspension Bridge 22 Aim 22 Measurement Methods 22 Method of Calculations: 23 Discussion 24 Conclusion 24 Experiment 6 25 Aim: 25 Method of measurement 25 Method of Calculation: 25 Discussion: 26 Conclusion: 27 Experiment 7: Tension on a Suspension bridge with some point load at different positions. 28 Aim 28 Measurement Method Used 28 Results Obtained 28 Discussion 29 Conclusion 29 Introduction This report covers the practical sessions for semester two on stress analysis. The report focuses on examining the characteristics and deflection variations under different aspects including different loads, different types of beams, load position, angle of twists, and tensions. For each experiment, the report covers on the aims, methods of measurement, method of calculation, discussion and conclusion. Further, the report explores the differences between the actual values and the theoretical values. The total number of experiments covered herein are seven. Experiment 1: The Deflections for a Simply Supported Beam Aim The principle aim for Experiment 1 is to illustrate the deflection variation for a simply supported beam under the application of different loads, and the relationship between beam deflection and length. Measurement Method Experiment 1 has been divided into two sets, where the first set involves the use of a 400mm length whereas the second set uses a beam of 200mm length. In order to carry out effective measurement, the equipment has to be arranged as shown in Figure 1. Before load application, the display meter has to be adjusted to zero. Different loads are then applied, from 100g to 500g, with an interval increase of 100g for every repetition, and values obtained from the meter are recorded in Table 1. A graph of deflection against load is also plotted. Method Used in the Calculation For the purpose of calculating the deflection of a given Cantilever beam, the equation below should be considered: Where; L = the distance between the supports E = Young’s Modulus the material used in the cantilever material (in Nm-2). For aluminium, it is 69 x 10 9 Nm-2 I = the Moment of inertia of the material Moment of inertia is given by I = bd3/12 m4 W = Load (N) = mg where g = 0.9806 m/s2 The value of can be obtained from the information provided about the beam. The values obtained on deflection are listed in Table 1.0 and Table 1.1 for the first and second sets respectively. E = 69Gpa, I = bd3/12 = (0.0211 x 0.0034 4)/12 m4 = 6.91095E-11 m4 Width (b) = 0.0211m and depth (d) = 0.0034 m, and Length of the beam is 400mm Mass (g) Load (N) Actual Deflection (mm) Theoretical Deflection (m) 0 0 0 0 100 0.9806 0.33 0.274184926 200 1.9612 0.62 0.548369852 300 2.9418 1.03 0.822554777 400 3.9224 1.37 1.096739703 500 4.903 1.73 1.370924629 Table 1.0 Results for the First Set of Experiment 1 Figure 1.1: A Plot of Actual Deflection and Theoretical Deflection versus Load In the second set of experiment 1, a beam whose length is 200mm is used. The results for both actual and theoretical deflections are as shown in Table 1.2 and a plot of the same is shown in Figure 1.3 Mass (g) Load (N) Actual Deflection (mm) Theoretical Deflection (mm) 0 0 0 0 100 0.9806 0.05 0.034273116 200 1.9612 0.11 0.068546231 300 2.9418 0.14 0.102819347 400 3.9224 0.21 0.137092463 500 4.903 0.29 0.171365579 Table 2: Results for Set 2 of Experiment 1 Figure 1.3: A Plot of Actual Deflection and Theoretical Deflection versus Load (L = 200mm) Discussion From the graphs in Figure 1.2 and 1.3, it can be concluded that changes in both actual and theoretical deflections is proportional to load and that deflection is proportional to length of the beam. The first set of experiment was conducted using the length of 400mm whereas set two was conducted by use of a 200mm length. From the results, it is clear that the theoretical values for deflection in the 400mm beam are four times as more as those for the experiment conducted using 200mm long beam. In terms of length, 400mm is twice more than 200mm. Table 1.0 and 1.1 shows that there is a difference between theoretical & actual values, and this gets more clear for masses above 200g. In set two of experiment 1, there is more difference between the actual and theoretical differences. Primarily the differences are due to human errors such as rounding off of figures, poor adjustment of lengths between the supports, and inaccurate settings on the meter. Conclusion Thus, experiment 1 illustrates the relationship between deflection and load application. Further, there is a difference between the actual and the theoretical values. The differences could be due to human or random errors. Further, it can be deduced that deflection is a function of length because it increases with increase in length. Experiment 2: Characteristics of Cantilever Beams when a Point Load is Applied Aim Primarily, this experiment is meant to assist in the understanding of some of the characteristics of cantilever beams once a point load is applied and continually increased. The experiment also shows the relationship drawn between deflections and the load. How Measurement was carried out Before application of any load, the meter for displaying the deflection was adjusted to zero. The point of load was positioned away from the left part of the Cantilever beam by a distance of 200mm. The loads were then applied from the minimum of 100g to a maximum of 500g, and at an increasing interval of 100g. The values displayed on the meter for each experiment are recorded in Table 2.0 Calculation Method Used The deflection of the cantilever is given by the equation: Where; E = the material’s Young Modulus. In this case aluminium is used and therefore, E = 69GPa W = Load (N) but W = m.g with g = 9.806 m/s2, and is mass L = the distance from the point of support I = The Moment of Inertia, I = bd3/12 m4 Through the application of the right method for measurements, Table 2.0 below was obtained: I = 6.91E-11, depth (d) = 0.0034m, Width (w) = 0.0211m and E = 69GPa Mass (g) Load (N) Actual Deflection (mm) Theoretical Deflection (mm) 0 0 0 0 100 0.9806 0.85 0.548369852 200 1.9612 1.71 1.096739703 300 2.9418 2.69 1.645109555 400 3.9224 3.7 2.193479407 500 4.903 4.56 2.741849258 Table 2.0: Table of Results for Experiment 2 Discussion Cantilever beams have a number of uses, and some of these uses include bridge, cantilever balcony and traffic lights. As such, the experiment is crucial towards understanding various experimental parameters, especial the relationship between load and deflections. From the plot above, it is clear that there is a difference between the actual deflection and the theoretical deflection. In general, actual deflection is more than the theoretical deflection. The two deflections show a trend that is approximately linear. The main explanation as to why there is a massive difference between the actual and theoretical deflection would be attributed by human errors. For instance, the beam length would be set to exactly 200mm or the meter would not have yielded a proper display. Further, failure to follow experiment instructions in the proper way attributes to experimental errors. Conclusion This experiment illustrates, to a large extend, the relationship between the load applied to a cantilever beam, and deflection. Despite the human and experimental errors associated with the experiment, the plot of load against deflections shows a continuous trend line. Basically, the results and the plot shown in this experiment highlight the effect on deflection when a point of increasing load is applied to a Cantilever beam. Experiment 3: How Beam Span and Beam Deflection are Related Aim The study carried out in experiment 3 focuses on how beam deflection and beam span are related. The study goes ahead to explore the application of deflections limit to a beam that has been subjected to some loads. Measurement Methods Applied This experiment employs a number of measurement methods. For instance, all the weights or hangers are to be eliminated from the bar and a rig is hooked to the centre of the bar as shown in Figure 3.0 The meters for measuring deflection are adjusted to zero, and positioned along a beam excluding the load that is applied. Further, the negative and positive buttons are expressed. The knife-edge hangers are adjusted as in experiment 2.1, and the datum is noted down for every turn of repositioning of the knife-edge. Just like in experiment 2, a load of 500g is applied at the centre of 400mm beam and at the end of every turn; the meters are turned to zero. In this experiment, this step is repeated using a load of 500g but is applied to a knife edge hanger. All the results obtained by the digital meter are recorded in Table 2.1 Calculation Method Deflection variances are based on changing of distance of the knife-edge hanger and have to load an attached load of 500g once the beam is simply supported. Under such circumstances, the right equation for computations of deflection is: Where; W = load=gm where g = 9.806 m/s2 X = the distance for the left side of the beam (mm) L =t he length between the beam’s supports =400mm = 0.04 E = Young’s modulus of elasticity of the beam material. For aluminium = 69Gpa I = Momentum of inertia = bd3/12 m4 The equation above is used for performing calculations for 0 Read More