Experiment B lab

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Carleton University *

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2202

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Mechanical Engineering

Date

Dec 6, 2023

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pdf

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11

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Experiment B Stresses In a Thin Walled Pressure Vessel Lab 2 MAAE2202 section B Department of Mechanical and Aerospace Engineering Carleton University Prepared by: George Grivas (101273448) (georgegrivas@cmail.carleton.ca) Lab Performed: November 2nd, 2023 Lab Submitted: November 9th, 2023
Summary The main objective of this lab was to gain a better understanding about how strain gauges work and their function. To do this, strain gauges were used on a standard 355 mL soda can and the strain in the hoop as well as the strain in the longitude axis were recorded. This was done twice, the first time had the soda in its normal state and the second was after the soda can had been shaken. After all the strain values were recorded, stress and internal pressure of the can were calculated using data for aluminium collected from trusted sources. The calculated stress was in two parts that being the hoop stress and longitude stress, the ratio of these values was recorded and compared to the actual known property that hoop stress will be twice that of longitude stress. The lab appears to have been successful as the experimental ratio was close to that of the actual ratio. Nomenclature
Theory and Analysis Stress ( 𝜎 ) Defined as F/A, The two kinds of stress are normal and shear where normal describes force perpendicular to the cross sectional area and where shear describes force parallel to the cross sectional area. This experiment only focuses on normal stress, more specifically normal compressive stress. The unit of stress is newtons (N) divided by metres (m) also known as Pascals (Pa). In this experiment stress will be calculated from strain alongside the young’s modulus of aluminium using the derived equations for hoop and longitude stress: Strain (ϵ) As force is applied to an object there will always be some sort of deformation this is where strain is used. Defined as Δl/l o . Strain represents the unitless ratio of the change in length divided by the original length. Young’s Modulus (E) The young’s modulus is used in hooke's law which is defined as 𝜎 = ϵE. When hooke’s law is rearranged E represents the ratio of stress and strain. E is known as a material
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elasticity or in other terms its stiffness. The material used in this experiment is aluminium which has an elasticity of E = 70 GPa [2]. Internal Pressure (P) Pressure is the force that acts perpendicular to the surface of the soda can, similar to stress it uses the same units (MPa) as it describes force over area. In this lab the can will experience a pressure from the fluid inside of it. Poisson’s ratio (v) Poisson’s ratio depicts how much an object deforms in both axis relative to each other. For aluminium this ratio is v = 0.35 Ultimate tensile strength ( 𝜎 ) The ultimate tensile strength describes the maximum amount of pulling/stretching of a material before it eventually fails. For aluminium the ultimate tensile strength is 600 Mpa Experimental Setup and Procedure The Procedure went as the lab manual describes. Soda can dimensions
Strain gauge/Soda can setup Actual Experimental Setup
Results and Discussion Strain Table µε hoop µε long Undisturbed -1000 -186 Disturbed -1319 -188 1. Undisturbed (stress) Disturbed (stress)
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Undisturbed (internal pressure) Disturbed (internal pressure) The hoop stress in the undisturbed can is around twice that of longitude stress, and the hoop stress in the disturbed can is three times that of the longitude stress; there is little change between the disturbed and undisturbed longitude stress. The negative stresses represent that the can is in compression and the negative pressure describes that the pressure outside the can is greater than the pressure inside the can. The pressure values seem to make sense as that value represents the pressure the fluid exerted on the walls of the can, therefore since we know fluid will exert more pressure it makes sense. It is expected that the hoop stress is to be twice that of the longitude stress which appears to almost be the case here with these values. 2. Undisturbed Disturbed Take the Allowable strength of 600 Mpa [2] The safety factor is greater for the undisturbed can, which makes sense as it has a smaller internal stress. The longitudinal safety factors do not differ much from each other. Overall the safety factors for all four results are pretty high which goes to show that the design of the soda can is pretty solid and aluminium is a very versatile material. It would take a much larger pressure before the can becomes structurally compromised which adds up considering these soda cans often are transported via aircraft.
3. Actual Ratio Undisturbed The undisturbed hoop to longitude stress ratio is 1.96 which is an expected and accurate result. This means there was not that much error during the procedure especially when attaching the strain gauges. Disturbed The disturbed ratio is a little less accurate than that of the undisturbed ratio although still not too far off the expected value. Some discrepancy is noticed here most likely due to some error during the procedure, the strain gauges could potentially have not fully been parallel to their respective axis leading to strain being measured in two dimensions instead of the desired one dimension measurement. 4. The can possess a concave bottom which allows it to increase its maximum pressure tolerance. The concave ends dissipate pressure around the rim of the can, in fact it does so well at resisting pressure that it withstands the rapid atmospheric pressure change during transportation via aircraft. Conclusion The strain gauge provided the necessary strain values for both hoop and longitude direction. From these strain values the compressive stress was calculated along with the internal pressure. Overall the experiment was successful as the error was small and nothing unexpected occurred. References [1]“MAAE 2202 Lab Manual .”
[2]“Aluminium - Strength - Hardness - Elasticity - Crystal Structure,” Material Properties , Nov. 02, 2020. https://material-properties.org/Aluminium-mechanical-properties-strength-hardness-crys tal-structure/#:~:text=Summary%20%20%20Element%20%20%20Aluminium%20 [3]“How thick is a soda can wall in inches? – TipsFolder.com.” https://tipsfolder.com/thick-soda-wall-inches-d58f7775c53cbef80b633dc29be340e5/ (accessed Nov. 08, 2023). [4]“Why beverage cans have concave bottoms (idea) by originalzin - Everything2.com,” everything2.com . https://everything2.com/user/originalzin/writeups/Why+beverage+cans+have+concave+ bottoms (accessed Nov. 08, 2023).
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Appendices Appendix A (lab data)
Appendix B (sample calculations) All calculations done in discussion