Question

A point in two-dimensional stress state subjected to biaxial stress is shown in figure below. What is the normal stress acting on the plane AB?

• A. Zero
• B. $\sigma$
• C. $\sigma co{s}^2\theta$
• D. $\sigma sin\theta .cos\theta$

Answer 1

The correct option is B $\sigma$

Normal stress acting on plane AB is given by

${\sigma }_n=\frac{{\sigma }_1+{\sigma }_2}{2}+\left(\frac{{\sigma }_1-{\sigma }_2}{2}\right)\times \cos 2\theta$

$=\frac{\sigma +\sigma }{2}+\left(\frac{\sigma -\sigma }{2}\right)\times \cos 2\theta$

$=\sigma +0$

$=\sigma$