This document contains solutions to 4 problems from H.W(5). Problem 5.1 calculates fiber volume fraction and fiber orientation tensors. Problem 5.2 calculates the safety factor of a composite material with given fiber orientation. Problem 5.3 calculates average stress in a composite with 45 degree fiber orientation. Problem 5.4 calculates average stress in a composite with 90 degree fiber orientation.

1. H.W(5)
Problem (5.1):
Givens: and
Required: [Q] , [S] , [ ] and [ ]
Solution: = = 0.03
Δ= 1- = 1-(0.3*0.03) = 0.991
[ [ ] = [ ]
[S] = [ ] = [ ]
[ ] = [ ] = [ ]
[ ] = [ ] = [ ]
Problem (5.2):
Givens: θ = 60 , , and
Required: safety factor

2. Solution:
Cos(θ) = C = 0.5 and Sin(θ) = S = 0.866
[T] = [ ] = [ ]
[ ] = [T]*[ ] = [ ]
From table 1.1 using material carbon epoxy (AS43501-6)
and and
By comparing results:
And and
so, F.S = = = 8.656
Problem (5.3):
Given: θ = 45 Cos(θ) = C = 0.707 and Sin(θ) = S = 0.707
Required: [ ̅]
[T] = [ ] = [ ]
[ ̅] = [ ]*[Q]*[T] = [ ]

3. Problem (5.4):
Given: θ = 90 Cos(θ) = C = 0 and Sin(θ) = S = 1
[T] = [ ] = [ ]
[ ̅] = [ ]*[Q]*[T] = [ ]