This problem involves loading from two directions, and thus requires at least the 2-D Hooke's Law. The 3-D Hooke's Law could be used, but since σ_{z} is zero, those equations will reduce to the 2-D equations. The equations are,
ε_{x} = (σ_{x} - ν σ_{y})/E
ε_{y} = (σ_{y} - ν σ_{x})/E
The strains and stresses in the x and y direction need to be calculated.
σ_{x} = P_{x}/A_{x} = 5/[(0.05)(0.005)]
= 20 MPa
σ_{y} = P_{y}/A_{y} = 9/[(0.10)(0.005)]
= 18 MPa
ε_{x} = 0.021/10 = 0.0021 cm/cm
ε_{y} = 0.009/5 = 0.0018 cm/cm
Substituting the stresses and strains into the 2-D Hooke's Law equations, gives
0.0021 E = 20 - ν 18
0.0018 E = 18 - ν 20
Solving for ν gives,
ν =
0.1876 |