The specimen is $5$ m long and, when a force of $2\mathrm{.}2$ kN is applied, it should stretch no more than $2\mathrm{.}5$ mm $.$ The stress acting on the specimen must be less than the yield strength of the epoxy matrix, which is $80$ MPa $.$ The epoxy has a modulus of elasticity of $3\mathrm{.}5$ GPa.

a$)$ Calculate the following parameters the specimen can obtain if there are no carbon fibres present.

Maximum strain

Maximum stress $($in MPa$)$

Area $($in $\backslash (\backslash$mathrm$\{$mm$\}^\{\backslash$wedge$\}\backslash ))$

b$)$ If the maximum strain is still to be maintained with a stress of $76$ MPa $,$ calculate the modulus of elasticity of the specimen $($in GPa$).$

GPa

c$)$ If the carbon fibre volume fraction is $0\mathrm{.}195,$ what is the diameter of the specimen $($in mm $)$ to achieve the above$-$given properties?

Maximum stress $($in GPa$)=$

Diameter $\backslash ((\backslash$mathrm$\{$mm$\})=\backslash )$

d$)$ Calculate the percentage of waste material removed from the specimen by the reinforcement of the carbon fibres using the specimen area values.