Maximum Principal Strain Theory

Q. In a two dimensional stress system, the two principal stresses are ${\sigma }_1$ of 180 $N/m{m}^2$ (tensile) and ${\sigma }_2$ (compressive). For the material, yield stress in simple tension and compression is 240 $N/m{m}^2$ and Poisson's ratio is 0.25. According to maximum normal strain theory, the value of ${\sigma }_2$ at which yielding will commence, is

1. 240 $N/m{m}^2$
2. 180 $N/m{m}^2$
3. 195 $N/m{m}^2$
4. 200 $N/m{m}^2$

Q. At a point in a structure, there are two mutually perpendicular tensile stresses of 800 $kg/c{m}^2$ and 400 $kg/c{m}^2$. If the Poisson's ratio $\mu =0.25,$ what would be the equivalent stress in simple tension according to maximum principal strain theory?

1. 1200 $kg/c{m}^2$
2. 900 $kg/c{m}^2$
3. 700 $kg/c{m}^2$
4. 400 $kg/c{m}^2$

Q. At a certain point in a structural member, there are perpendicular stresses 80 $N/m{m}^{2}and20N/m{m}^2$, both tensile. What is the equivalent stress in simple tension, according to the maximum principal strain theory?
(Poisson's ratio = 0.25)

1. Zero
2. $20N/m{m}^2$
3. $60N/m{m}^2$
4. $75N/m{m}^2$

Q. In a two-dimensional stress system, the principal stresses are ${\sigma }_1=200N/m{m}^2$ (tensile) and ${\sigma }_2$ (compressive). The yield stress in both simple tension and compression is 250 N/mm^{2}, with $\mu =0.25$. What will be the value of ${\sigma }_2$ according to the maximum normal strain theory?

1. 160 $N/m{m}^2$
2. 100 $N/m{m}^2$
3. 200 $N/m{m}^2$
4. 250 $N/m{m}^2$

Q. An element of a structure is subjected to two principal stresses ${\sigma }_{1}and{\sigma }_2$.
${\sigma }_1=200N/m{m}^2$ (Tensile)
${\sigma }_2$ is Compressive
The yield stress both in simple tension and compression for the material is 240 $N/m{m}^2$. Poisson's ratio $\mu =0.25$; what is the value of ${\sigma }_2$ in $N/m{m}^2$ as per maximum normal strain theory at which the yield of material will commence?

1. 240
2. 200
3. 180
4. 160

Q. The state of stress at a point in an elastic material, with yield stress of 200 MPa in simple tension, and Poisson's ratio 0.3, is as shown in the figure.

The permissible value of $\sigma$ by maximum principal strain theory is

1. 75 MPa
2. 100 MPa
3. 150 MPa
4. 200 MPa

Q. The limit of proportionality in the material of a structural steel member, when subjected to simple tension, is 280 $N/m{m}^2$. The principal stresses in the member are ${\sigma }_1=122N/m{m}^2$ (Tensile) and ${\sigma }_2=60N/m{m}^2$ (Compressive). $\mu =0.3$. According to maximum strain theory, the factor of safety is

1. 2.5
2. 1.5
3. 2
4. 3

Q. A structural element is subjected to a two-dimensional stress system, wherein ${\sigma }_1=225N/m{m}^2$ (tensile) with ${\sigma }_2$ being compressive. The yield stress in both simple tension $({\sigma }_y{)}_t$ and simple compression $({\sigma }_y{)}_c$ is 250 $N/m{m}^2$ and $\mu$ = 0.25. What is the value of ${\sigma }_2$, according to Maximum Strain Theory?

1. 200 $N/m{m}^2$
2. 150 $N/m{m}^2$
3. 125 $N/m{m}^2$
4. 100 $N/m{m}^2$

Q. In a two-dimensional stress system, the two principal stresses are $p_1=180N/m{m}^2$ (tensile), and $p_2$ which is compressive. For the material, yield stress in simple tension and compression is 240 $N/m{m}^2$ and Poisson's ratio is 0.25. According to maximum normal strain theory, for what values of $p_2$, shall yielding commence?

1. $240N/m{m}^2$
2. $180N/m{m}^2$
3. $195N/m{m}^2$
4. $200N/m{m}^2$