Question

The state of two-dimensional stresses acting on a concrete lamina consists of a direct tensile stress ${\sigma }_x=1.5N/m{m}^2$ and shear stress $\tau =1.20N/m{m}^2$, when cracking of concrete is just impending. The permissible tensile strength of the concrete is

• A. 1.50 $N/m{m}^2$
• B. 2.17 $N/m{m}^2$
• C. 2.08 $N/m{m}^2$
• D. 2.29 $N/m{m}^2$

Answer 1

The correct option is B 2.17 $N/m{m}^2$

${\sigma }_x$ = 1.5 MPa
${\sigma }_y$ = 0
${\sigma }_{xy}$ = 1.2 MPa

${\sigma }_1/{\sigma }_2=\frac{{\sigma }_x+{\sigma }_y}{2}\pm \sqrt{{\left(\frac{{\sigma }_x-{\sigma }_y}{2}\right)}^2+{\tau }_{xy}^2}$

${\sigma }_1=2.17N/m{m}^2$

${\sigma }_2=-0.665N/m{m}^2$
Hence, option (b) is correct.