4. (a) A unidirectional carbon fibre reinforced composite has the following properties: E 150 GPa; E2=...

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4. (a) A unidirectional carbon fibre reinforced composite has the following properties: E 150 GPa; E2= 8 GPa; G = 10 GPa; v12 = 0.3 where 1 refers to the fibre direction and 2 to the transverse direction. If the 1 direction is aligned with the global x-axis, 1) Determine the reduced compliance matrix for a ply based on this material. ii) Determine the reduced stiffness matrix for a ply based on this material. (b) A unidirectional composite is subjected to a tensile stress of 6 MPa in the fibre direction and a compressive stress of 4 MPa in the transverse direction. Using the properties given in part (a), determine the strain in the fibre direction and the strain in the transverse direction. (c) Determine the transformed reduced stiffness matrix for a unidirectional ply oriented at 45 degrees to the global x-axis for the material outlined in part (a). Useful formulae: [Q] = [7][Q][7]; [5)] = [7][S][7]; cos 8 2 sin 0 cos sin 0 - 2 sin 0 cos 0 cos - sin e -sin cos [T] = [T]- = cos0 sin 0 sin 8 cos 0 sin0 cos 0 sin 0 cos e sin 0 cos 0 - sin cos - 2 sin 0 cos 0 2 sin 0 cos 0 cos e - sin el [8 marks] [8 marks] [6 marks] [8 marks] [30 marks] 4. (a) A unidirectional carbon fibre reinforced composite has the following properties: E 150 GPa; E2= 8 GPa; G = 10 GPa; v12 = 0.3 where 1 refers to the fibre direction and 2 to the transverse direction. If the 1 direction is aligned with the global x-axis, 1) Determine the reduced compliance matrix for a ply based on this material. ii) Determine the reduced stiffness matrix for a ply based on this material. (b) A unidirectional composite is subjected to a tensile stress of 6 MPa in the fibre direction and a compressive stress of 4 MPa in the transverse direction. Using the properties given in part (a), determine the strain in the fibre direction and the strain in the transverse direction. (c) Determine the transformed reduced stiffness matrix for a unidirectional ply oriented at 45 degrees to the global x-axis for the material outlined in part (a). Useful formulae: [Q] = [7][Q][7]; [5)] = [7][S][7]; cos 8 2 sin 0 cos sin 0 - 2 sin 0 cos 0 cos - sin e -sin cos [T] = [T]- = cos0 sin 0 sin 8 cos 0 sin0 cos 0 sin 0 cos e sin 0 cos 0 - sin cos - 2 sin 0 cos 0 2 sin 0 cos 0 cos e - sin el [8 marks] [8 marks] [6 marks] [8 marks] [30 marks]

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The question presented involves the properties of a unidirectional carbon fiber reinforced composite material and how to calculate various matrices re... View the full answer