Explain volumetric strain and state the expression

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Reference no: EM132164933

Task 1

(a) When a rigid body is subjected to a direct stress system dimensional changes take place.

I. State the relationship that connects the longitudinal and lateral axes.

II. List the Poisson value for five common engineering materials. (b) A metal bar is axially loaded

(b) A metal bar is axially loaded such that its extension is measured and found to be 0.4 mm. The diameter was measured and found to have reduced by 0.02 mm. If the original diameter was 100 mm, determine Poisson's ratio for the material assuming that the elastic limit was not exceeded.

C) This provides evidence for [1.1] (c) If the limits of modulus of elasticity and modulus of rigidity are known for the metal bar in part (b), suggest an analytical method that could be used to calculate the Poisson ratio. This provides evidence for.

Task 2

(a) A high carbon steel strip of dimensions 200mm x 100mm and thickness of 3 mm is subjected to a two-dimensional loading system. The axial load being 12kN and the lateral load being 9kN, both loads are tensile. Determine the change in both the x and y directions under these loading conditions (ignoring the thickness change) using values of Poisson's Ratio and Youngs Elasticity Modulus for the given material.

(b) A three-dimensional/cuboid Malleable Iron shape, of dimensions 100 mm long x 50mm high x 100mm wide, is loaded as follows: Load x-axis = 800 kN tensile Load y-axis = 500 kN compressive Load z-axis = 100 kN compressive Determine the strain in each axis, using values of Poisson's Ratio and Youngs Elasticity Modulus for the given material.

Task 3

(a) A substance that is subjected to an external force or pressure experiences changes!

- Explain volumetric strain and state the expression for volumetric strain
- Define Bulk modulus and relate this to other elastic moduli.
(b) A stainless-steel bar of circular cross-section, 1500mm long x 25mm diameter, is subject to a tensile load of 100kN, which is within the elastic range. Determine using values of Poisson's Ratio and Youngs Elasticity Modulus for the given material:
i) the extension of the bar,
ii) the decrease in diameter of the bar,
iii) the increase in volume of the bar,
iv) the volumetric strain.

Task 4

A pressure vessel of dimensions, 0.5m high x 0.5m long x 0.5m wide, contains a pressurised liquid that subjects the vessel to a volumetric (hydrostatic) stress. Show, stating all assumptions, that, Elastic Modulus, Bulk Modulus and Poisson's ratio are related by the expression:

K = E 3(1 -2v)

Reference no: EM132164933

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