Modulus of Elasticity - Lab Report Example

Modulus of Elasti Theory Stress is a measure of an internal force that an object experiences per unit cross sectional area while strain. Mathematically, this can be expressed as (Lees, 2011): Where σ -is the stress in newton per meter F- Force A-Crosse-sectional area Other terms related to stress are tensile strength and yield strength. The tensile strength refers to the level of stress that a material fractures (Lees, 2011). For this reason, tensile strength is also called fracture stress. A material is said to be brittle if it fractures by crack propagation. On the other hand, yield stress is the point at which a material permanently deforms (Lees, 2011). Stress often causes a material to stretch, which ultimately makes it to strain. In this case, strain it measures the extent a material is stretched. Mathematically, it is expressed as Where Lo is the material’s original length, L is the length after the material has stretched, Δl as the difference between the two lengths.   Young’s Modulus is the measure of the material’s stiffness. The Young’s Modulus indicates the extent to which a material stretches as a result of stress. Mathematically, the Young’s Modulus can be expressed as The SI units of Young’s Modulus is Pa or N/M2. This experiment focused on finding Young’s Modulus from the stress-strain graph and comparing the young’s modulus of the steel to that of aluminium. Results In two graphs below shows the experimental results of values of stress plotted against strain (stress-strain graph) for steel and aluminium. From the two graphs, the Young’s modulus for the two materials: Steel and aluminium were determined. Hook’s law of elastic states that Load or Force is directly proportional to the extension of the material so long as the given load does not exceed an elastic limit. This relationship is often expressed as the word done or Elastic Potential Energy required to stretch a material and it is equal to the area of the Tension/extension graph and can be expressed as Steel We therefore, used the above principle to find the area under the curve. This way, the area is the cross section area of the steel which is 10.12 mm2 (12.49 mm X 0.81 mm). Equally, the modulus of elasticity of steel was found from the stress-strain graph as:  Figure 1 - Stress-Strain graph for steel Aluminium Similarly, based on the Hook’s law, the cross sectional area of aluminium was found to be equal to 24.64mm2 (12.51mm x 1.97mm). Equally, based on the elastic region of the stress-strain graph the Young’s Modulus of elastically (E) =   Figure 2 - Stress-Strain graph for aluminium Timber For timber, the force on the specimen was applied axially and the graph below is plotted from the data provided. Figure 3 - Timber (Axially loaded) On the other hand, the force on the specimen was applied laterally and the graph below was plotted from the data provided Figure 4 Timber (Laterally loaded) Discussion The results of this experiment shows that steel has a higher Modulus of Elasticity compared to Aluminium. Based on the results of this experiment the Modulus of Elasticity of Steel is , which is higher to the Aluminium’s Modulus of Elasticity 70.8KN/mm2. This are in conformity with what has been found in literature. Studies show that for steel, the Modulus of Elasticity is 180 x 109N/m2 which is equivalent to 180 KN/mm2 (Krueger, 2007). On the other hand, literature gives the value for Modulus for Elasticity for Aluminium as 69x 109N/m2, which is an equivalent of 69Nmm2 (Krueger, 2007). This clearly demonstrates that modulus of elasticity for Steel is higher than that for Aluminium. However, what is appalling is that the experimental Modulus of Elasticity values (both steel was and aluminium) are slightly higher than what has been documented. To ascertain the accuracy of the measured value it is prudent to conduct an error analysis as shown Relative error was used to ascertain the accuracy of the measured value For aluminium = [(70.8-69) Nmm2/69 = 0.026 For steel = [(203.3-180)/ 180= 0.129 The relative error shows that the graphical value for the metals deviated from the expected values. However, the error was greater in steel than in Aluminium. These deviations from the theoretical value may be attributed errors may be attributed to among others lag time and hysteresis, physical variations, instrument resolution, environmental factors, and failure to account for a factor. In the construction industry, Young’s modulus is very important as it is helps predict the compression and elongation of an object as long as the material stresses is found to be less than the material’s yield strength. Modulus of elasticity (E) or Young’s Modulus measures the material’s stiffness (Sauveur, 2006). It also measures the materials’ ability to resist elastic deformation under load. This means that Aluminium with a somewhat lower E can easily deform if subjected to force as compared to steel with a higher E. Modulus of elastic deformation is more often used in applications involving stresses, deformations and deflections and can be a good indicator of whether a material can withstand certain force (Krueger, 2007). Stiffness is often explored to design structures with a limited allowable deflection. The high modulus of elasticity of steel makes it widely applicable in the construction industry. For instance, steel is used in earthquake prone areas. Besides, there are a wide variety of materials that are made of steel. There are key attributable characteristics of steel that make it widely favoured in the construction industry. These include its attributable decidability, which makes it to avoid collapse. Its low weight and flexibility. It’s associated mechanism of energy dissipation (Sauveur, 2006). In conclusion, Stress is a measure of an internal force that an object experiences per unit cross sectional area while strain. On the other hand, strain it measures the extent a material is stretched. Young’s Modulus is the measure of the material’s stiffness besides indicating the extent to which a material stretches as a result of stress. This experiment demonstrated that Aluminium has a higher Modulus of Elasticity than steel. This higher modulus of steel makes it widely applicable in the construction industry. References Lees, E. (2011). Cyclic torsion testing. New York, NY: National Aeronautics and Space Administration (NASA). Krueger, G. (2007). Techniques for Determining the Modulus of Rigidity of and Applications of Engineered Adhesive. New York, NY: University of Wisconsin--Madison Sauveur A. (2006). The Torsion Test. New York, NY: University of Michigan Read More