Question

In a piece of stressed material, the principal stress are ${\sigma }_1=3.0kN/m^2$ tensile and ${\sigma }_2=7.0kN/m^2$ compressive as shown in the diagram below.

The line of action of the tensile stress makes an angle $\theta =30°$ to the normal to the plane AB. What is the normal stress ${\sigma }_n$?

• A. $+0.5kN/m^2$
• B. $-1.5kN/m^2$
• C. $+2.0kN/m^2$
• D. $-2.5kN/m^2$

Answer 1

The correct option is A $+0.5kN/m^2$

${\sigma }_n={\sigma }_1{\cos }^2\theta -{\sigma }_2{\sin }^2\theta$

$=3\times {\left(\frac{\sqrt{3}}{2}\right)}^2-7\times {\left(\frac{1}{2}\right)}^2=0.5kN/m^2$