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 $\tau =1.20N/m{m}^2$, which cause cracking of concrete. Then the tensile strength of the concrete in $N/m{m}^2$ is

• A. 1.50
• B. 2.08
• C. 2.17
• D. 2.29

Answer 1

The correct option is C 2.17

${\sigma }_x=1.5N/m{m}^2$;
$\tau =1.2N/m{m}^2$

Tensile strength will be the maximum principal stress in the concrete.

${\sigma }_{max/min}=\frac{{\sigma }_x+{\sigma }_y}{2}\pm \sqrt{{\left(\frac{{\sigma }_x-{\sigma }_y}{2}\right)}^2+{\tau }_{xy}^2}$
${\sigma }_x=1.5,{\sigma }_y=0,{\sigma }_{xy}=1.2N/m{m}^2$
${\sigma }_{max}=\frac{1.5}{2}+\sqrt{(\frac{1.5}{2}{)}^2+(1.2{)}^2}$
${\sigma }_{max}=2.165$
$=2.17N/m{m}^2$