A prismatic cantilever beam of rectangular cross-section is subjected to a tip-force P as shown in figure. Assume that the angle θ for the direction of the force in the x - y plane is variable. Calculate the minimum required value of the cross-section width a such that the maximum normal stress in the beam does not exceed an allowable value of σ<sub>a</sub>. (6 marks)
y
A
AP
4
y
A
P
4
2
2a
θ
X
1
a