How Does Biaxial Force Affect Stress and Strain in a Rectangular Bar?

[Confusedbiomedeng]

Homework Statement

consider the rectangular bar undeformed a=b=2cm and c=20cm . The elastic modulus of the bar material is E=100 Gpa and its poissons ratio is u=0.3. The bar is subjected to biaxial forces in the x and y directions such that Fx=Fy=0.4x10⁶ N and that Fx is tensile while Fy is compressive . Assuming that the bar material is linear elastic
Determine:
i)the average normal stresses σx,σy and σz developed in the bar
ii)the average normal strains ∈x,∈y and ∈z
iii)dimension c' of the bar in the x-direction after deformation

Homework Equations

σx=fx/(ab) σy=Fy/(cb) σz=no force no stress
∈x=1/E(σx-u(σy+oz))
∈y=1/E(σy-u(σx+σz))
∈z=1/E(σz-u(σx+σy))
∈=ΔL/L

The Attempt at a Solution

σx=0.4x10⁶/0.02x0.02=1x10⁹
σy=0.4x10⁶/0.2x0.02=1x10⁸
σz=no force no stress

using above equation
∈x=9.7
∈y= -2
∈z= -3.3

new c dimension
.-3.3=ΔL/0.2
-0.66
0.2+-0.66= -0.46
however you can't have negative length??
can anyone show me where I am going wrong?

 

[Chestermiller]

You forgot to divide by the Young's modulus, and the stress in the y direction is negative.