Question

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?

• A. 160 $N/m{m}^2$
• B. 100 $N/m{m}^2$
• C. 200 $N/m{m}^2$
• D. 250 $N/m{m}^2$

Answer 1

The correct option is C 200 $N/m{m}^2$

According to maximum normal strain theory,

${\sigma }_1-\mu {\sigma }_2\le {\sigma }_y$

$\Rightarrow 200-0.25(-\sigma )\le 250$

$\Rightarrow 200+0.25\sigma =250$

$\Rightarrow \sigma =\frac{50}{0.25}=200N/m{m}^2$
and also

${\sigma }_2-\mu {\sigma }_1>-{\sigma }_y$

$\Rightarrow -\sigma -50>-250$

$\Rightarrow \sigma +50<250$

$\Rightarrow \sigma <200N/m{m}^2$