Principal Strains and Maximum Shear Strain

Q. 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

1. (0.5, - 0.5)
2. (0.5, - 0.15)
3. (0.35, -0.15)
4. (0.5, 0.0)

Q. If the two principal strains at a point are 1000 x ${10}^{-6}$ and -600 x ${10}^{-6}$, then the maximum shear strain is

1. 800 x ${10}^{-6}$
2. 500 x ${10}^{-6}$
3. 1600 x ${10}^{-6}$
4. 200 x ${10}^{-6}$

Q. An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal strain in the plane of maximum shear strain is.

1. 0.0050
2. Zero
3. 0.0025
4. 0.0010

Q. If $p_{1}and{p}_2$ are the principal stress at a point in a strained material with Young's modulus E and Poisson's ratio 1/m, then the principal strain is?

1. $\frac{p_1+p_2}{mE}$
2. $\frac{p_1-p_2}{mE}$
3. $\frac{p_1}{E}-\frac{p_2}{mE}$
4. $\frac{p_1}{m}-\frac{p_2}{mE}$

Q. The principal strains at a point are +800 × ${10}^{-6}$ cm/cm, +400 × ${10}^{-6}$ cm/cm and -1200 × ${10}^{-6}$ cm/cm. The volumetric srain is equal to

1. +1200 × ${10}^{-6}$ cm/cm
2. +800 × ${10}^{-6}$ cm/cm
3. -1200 × ${10}^{-6}$ cm/cm
4. zero

Q.

$M{L}^{-1}{T}^{-2}$ is the dimensional formula of?

1. Coefficient of friction

2. Energy

3. Modulus of Elasticity

4. Force