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## Using suitable diagrams explain Poisson’s ratio. Give examples of Poisson’s ratio for three common engineering materials.

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Task 1 a. Using suitable diagrams explain Poisson’s ratio. Give examples of Poisson’s ratio for three common engineering materials. b.Your line manager has asked you to investigate the shaft shown in Fig 1. When in service, the shaft will be subjected to an axial load of 100kN. You are required to calculate the reduction in diameter when the loading is applied. This will allow the design engineer to ensure that the bearing fit is such that the bearing inner race maintains suitable contact with the shaft. (E = 100Gpa υ = 0.3) Task 2 You have been asked to ex...

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#### Question Preview:

Task 1 a. Using suitable diagrams explain Poisson’s ratio. Give examples of Poisson’s ratio for three common engineering materials. b.Your line manager has asked you to investigate the shaft shown in Fig 1. When in service, the shaft will be subjected to an axial load of 100kN. You are required to calculate the reduction in diameter when the loading is applied. This will allow the design engineer to ensure that the bearing fit is such that the bearing inner race maintains suitable contact with the shaft. (E = 100Gpa υ = 0.3) Task 2 You have been asked to explain two and three dimensional loading to some final year apprentices. To this end, write down expressions for the strain induced when under: a. Two dimensional mutually perpendicular stresses. b. Three dimensional mutually perpendicular stresses. To demonstrate the principle, calculate the strains in the system shown in Fig 2. Task3 You have been asked to consider a material for use within a pressure vessel. A sample has been carried out by research and development which yielded the following data. Applied pressure was 75MPa. The bulk modulus for the material is 74Gpa. Sample size was a cube of 18mm side. Calculate the reduction in volume of the sample. Task4 a. Define the term bulk modulus. Your answer should include a derivation of the basic expression used to calculate this constant. b. Whilst working on a stress calculation, you find that you need the shear modulus but have values for Young’s modulus and Poisson’s ration only. Using these, calculate: a. the value of the shear modulus for your material. b. The value of the bulk modulus for this material Young’s modulus = 201GPa Poisson’s ratio = 0.3

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## Solution Preview

Poisson’s ratio define by ration of longitudinal strain to transverse strain of solid body

Figure 1. strain distribution

• As   shown in above figure that if elastic body applying load in tensile or compressive manner it will elongate upto body yield limit, if body have elastic properties it can regain its original shape and daimention, this behaviour depend upon body posssion’s  ratio and youngs modulus.

Poisson’s ratio unitless.

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