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why 0.6 x06 + 0.5x0.6x0.40 ??????? I don't understand this please help me to understand it

why 0.6 x06 + 0.5x0.6x0.40 ??????? I don't understand this please help me to understand it

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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why 0.6 x06 + 0.5x0.6x0.40 ??????? I don't understand this please help me to understand it  

A composite structure used for electrical cable ducting on an aircraft carrier is made by the pultrusion technique. The pultrusion consists of 60% S2-glass fibres by volume (V₁ = 0.6). 60% of the fibres are in unidirectional (0°) form and the other 40% consists of a woven fabric. The matrix is a phenolic resin modified with polyvinylbutyral (PVB). The properties of the constituent materials are: Tensile modulus of fibres, E₁ = 86GPa Tensile strength of fibres, of = 4700MPa Tensile modulus of matrix, Em = 4GPa Tensile strength of matrix, σm = 70MPa Calculate the tensile modulus and strength of the pultrusion in the 0° and 90° directions using the simple 'rule of mixtures' approach. ?? Answer: Pultrusion V₁ = 0.6 Vm = (1 -V₁) = 0.4 Vfo (0.6 x 0.6) + (0.5 x 0.4 x 0.6) = 0.48 = Vf90 = V₁ - Vfo = 0.6 - 0.48 = 0.12 Eo = (Vfox Et) + (Vm X Em) = (0.48 x 86) + (0.4 x 4) = 41.28 + 1.6 = 42.88GPa E90 = (Vf90 X Ef) + (Vm + Em) = (0.12 x 86) + (0.4 x 0.4) = 10.32 + 1.6 = = 11.92GPa
Transcribed Image Text:A composite structure used for electrical cable ducting on an aircraft carrier is made by the pultrusion technique. The pultrusion consists of 60% S2-glass fibres by volume (V₁ = 0.6). 60% of the fibres are in unidirectional (0°) form and the other 40% consists of a woven fabric. The matrix is a phenolic resin modified with polyvinylbutyral (PVB). The properties of the constituent materials are: Tensile modulus of fibres, E₁ = 86GPa Tensile strength of fibres, of = 4700MPa Tensile modulus of matrix, Em = 4GPa Tensile strength of matrix, σm = 70MPa Calculate the tensile modulus and strength of the pultrusion in the 0° and 90° directions using the simple 'rule of mixtures' approach. ?? Answer: Pultrusion V₁ = 0.6 Vm = (1 -V₁) = 0.4 Vfo (0.6 x 0.6) + (0.5 x 0.4 x 0.6) = 0.48 = Vf90 = V₁ - Vfo = 0.6 - 0.48 = 0.12 Eo = (Vfox Et) + (Vm X Em) = (0.48 x 86) + (0.4 x 4) = 41.28 + 1.6 = 42.88GPa E90 = (Vf90 X Ef) + (Vm + Em) = (0.12 x 86) + (0.4 x 0.4) = 10.32 + 1.6 = = 11.92GPa
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