Question

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?

• A. $240N/m{m}^2$
• B. $180N/m{m}^2$
• C. $195N/m{m}^2$
• D. $200N/m{m}^2$

Answer 1

The correct option is C $195N/m{m}^2$

Yielding may occur either in tension or compression.
For yielding in tension
$p_1+\mu p_2=f_y$(Maximum normal strain theory)
$\therefore p_2=(240-180)/0.25=240N/m{m}^2$
For yielding in compression
$p_2+\mu p_1=f_y$
$\therefore$ $p_2=240-0.25\times 180=195N/m{m}^2$
So the yielding will commence at
$p_2=195N/m{m}^2$