At a point in a stressed body the state of stress on two

At a point in a stressed body the state of stress on two planes 45° apart is as shown below. Determine the two principal stresses in MPa.

σ_x = 8 MPa
τ_xy = 3MPa
σ_n = 2 MPa
θ = 45°

σ_n =	σ_x + σ_y	+	σ_x - σ_y	cos2θ - τ_xysin2θ
	2		2

2 =	8 + σ_y	+	8 - σ_y	(0) - 3sin(90)
	2		2

( σ_y = 2 MPa )

σ_{1 , 2} =	σ_x + σ_y	+ √			σ_x - σ_y		²	+ τ²_xy
	g				2

=	8 + 2	± √			8 - 2		²	+ 3²
	2				2

= 5 ± 4.242
σ_{1 / 2} = 9.242, 0.758 MPa