Question

Consider a linear elastic rectangular thin sheet of metal, subjected to uniform uniaxial tensile stress of 100 MPa along the length direction. Assume plane stress conditions in the plane normal to the thickness. The Young's modulus E = 200 MPa and Poisson's ratio $v$ = 0.3 are given. The principal strains in the plane of the sheet are

• A. (0.5, - 0.5)
• B. (0.5, - 0.15)
• C. (0.35, -0.15)
• D. (0.5, 0.0)

Answer 1

The correct option is B (0.5, - 0.15)

Given, $E=200MPa,v=0.3$
Assume plane stress condition, ${\sigma }_z=0$ Given, ${\sigma }_y=0$ and ${\sigma }_x\ne 0$ [Uniaxial state of stress condition]
As no shear stress acting on x and y face,
So, ${\sigma }_x={\sigma }_1=100MPa$
${\sigma }_y={\sigma }_2=0$
${\epsilon }_1=\frac{{\sigma }_1}{E}-v\frac{{\sigma }_2}{E}=\frac{100}{200}-0=0.5$
${\epsilon }_2=\frac{{\sigma }_2}{E}-v\frac{{\sigma }_1}{E}=0-0.3\left(\frac{100}{200}\right)$
$=-0.15$
Hence, option (b) is correct.