Laboratory Investigation - Lab Report Example

Lab report Assignment 1: Laboratory Investigation Name: Number: Group members: 1. 2. 3. Abstract Stiffness is important for many applications such as when building bridges, and is dependent on both the geometry of the structure and the material from which it is made. The objective of this experiment was to study the stiffness of different materials such as mild steel, brass and aluminium under the load. In this experiment, we examined the deflection of a beam by increasing the load on the beam for different materials in order to find the relationship between their deflection and the load applied. A material in form of a beam with a rectangular cross section was supported at both ends so as to bear the load. Then a load was applied in a perpendicular direction to the horizontal beam that resulted in to deflection. We found out that the defection increases with increase in load and aluminium deflects more than brass and mild steel for each load. The Young modulus of elasticity obtained from this experiment for mild steel was 172.3GPa, for brass was 109.7 GPa and for aluminium was 69.9 GPa. Stiffness of a material is related to the deflection such that stiffer materials deflect less compared to less stiff ones. (Words = 195) 1. Results Table showing the dimensions for the specimens Mild steel Aluminium Brass Length (mm) 500 500 500 Thickness (mm) 3.3 3.3 3.1 Width (mm) 19 19 18 Table below shows the deflection of the specimens for procedure 1a The graph of load verses deflection is shown below. Figure 1: A graph of Load verses deflection for procedure 1a 2. Results table for 1b Table showing the deflection of the specimens for procedure 1b Mild steel Load (W) Newtons Deflection (Δ) in mm 48ΔI 48ΔI/L3 0 0 0 0 5 0.67 1.8299E-12 2.85923E-11 10 1.37 3.74174E-12 5.84648E-11 15 2.04 5.57165E-12 8.7057E-11 20 2.73 7.45618E-12 1.16503E-10 25 3.46 9.44995E-12 1.47656E-10 Experiment 1b Material B = 19 H =3.3 I = L = 500 L3 = 125000000 The second moment of area, I = mm4 The graph of load verses 48ΔI/L3 for mild steel Figure 2: The graph of load verses 48ΔI/L3 for mild steel Modulus of elasticity for mild steel from the load verses graph = 172.3 Gpa Table showing the deflection of the specimens for Aluminium Load (W) Newtons Deflection (Δ) in mm 48ΔI 48ΔI/L3 0 0 0 0 5 1.65 4.50648E-12 7.04138E-11 10 3.36 9.17683E-12 1.43388E-10 15 5.03 1.37379E-11 2.14655E-10 20 6.57 1.7944E-11 2.80375E-10 25 8.39 2.29148E-11 3.58043E-10 Experiment 1b Material B = 19 H =3.3 I = L = 500 L3 = 125000000 The second moment of area, I = mm4 The graph of load verses 48ΔI/L3 for aluminium Figure 3: The graph of load verses 48ΔI/L3 for aluminium Modulus of elasticity for aluminium from the load verses graph is = 69.9 Gpa Table showing the deflection of the specimens for Brass Load (W) Newtons Deflection (Δ) in mm 48ΔI 48ΔI/L3 0 0 0 0 5 1.36 2.91736E-12 4.55838E-11 10 2.72 5.83473E-12 9.11676E-11 15 4.2 9.0095E-12 1.40774E-10 20 5.37 1.15193E-11 1.79989E-10 25 6.74 1.44581E-11 2.25908E-10 Experiment 1b Material B = 18 H = 3.1 I = L = 500 L3 = 125000000 The second moment of area, I = mm4 The graph of load verses 48ΔI/L3 for brass is shown below Figure 4:The graph of load verses 48ΔI/L3 for brass Modulus of elasticity for brass from the load verses graph is = 109.7 Gpa Discussion 1a From the graphs above, it can be concluded that the load applied is directly propositional to the deflection for the beams for mild steel, brass and aluminium. In other words; Deflection, D  L where, L = the load applied. It means that as the load increase, the deflection increase too (Ashby, 2010). However, the deflection value for aluminium is high for both brass and mild steel for each load. Mild steel has the least deflection among the three materials. 1b From the graphs above, the slopes, as seen from the gradients, vary with the materials being tested. For example, mild steel has 2 x 1011 compared to brass whose gradient is 1.085 x 1011. Thus modulus of elasticity for mild steel is higher compared to that of brass and aluminium. The table below shows the comparison between the theoretical and the experimental values of Young’s modulus. Theoretical value Experimental value % Error Mild steel 200 GPa 172.3GPa 13.85% Brass 108.5 GPa 109.7GPa 1.11% Aluminium 70 GPa 69.9GPa 1.28% As seen from the table above, the values obtained from this experiment were different from the theoretical values (calculated values). The percentage error for brass and aluminium are 1.11% and 1.28% respectively which is low compared to mild steel, which is 13.85%. The factors that may have caused the difference between the experimental values and the theoretical values include the following. a) Temperature – as the temperature increase, the materials used in the experiment soften and expands. b) The impurities in the material may cause difference in Young’s modulus. Holes or substances inside the beam may harden or soften it, thus the deflection is affected. c) Oxidation on the surface layer of the beam may cause may harden the material. For example, the oxide of aluminium is harder than aluminium itself. This affects the deflection which affects the accuracy in the experiment. d) Another factor is the level of the beam. Unbalanced beam affect the moment of the segment. The second moment of the area of the beam affects the stiffness of a material. It can be concluded from this experiment that the higher the value of Young’s modulus, the higher the stiffness and the less the structure deflects. Deflection is useful in our daily lives. Deflection is used to construct buildings and bridges, since a curved beam can support more loads. Some cases where deflection is undesirable include deflection of the shaft of the engine. Such a beam will rotated out of its axis and make it unstable (Duggal, 2009). conclusion From this experiment, it has been shown that the deflection for mils steel, aluminium and brass are directly proportional to the load applied. But aluminium deflects more compared to mild steel and brass. We also found out that the Young’s modulus is related to the stiffness of the material. The materials with higher Young’s modulus are stiffer compared to those with low Young’s modulus. REFERENCES Duggal, S. K. (2009). Design of steel structures. New Delhi: Tata McGraw-Hill. Ashby, M. F. (2010). Materials Selection in Mechanical Design. Burlington: Elsevier Science. Bird J., & Ross C. T. F., (2012). Mechanical Engineering Principles, Routledge Read More