Question

For the state of stress shown in the figure, the maximum and minimum principal stresses (taking tensile stress + and compressive stress as -) will be

• A. 95 MPa and (-35) MPa
• B. 60 MPa and 30 MPa
• C. 95 MPa and (-30) MPa
• D. 60 MPa and 35 MPa

Answer 1

The correct option is A 95 MPa and (-35) MPa

${\sigma }_x=90MPa,$

${\sigma }_y=-30MPa,$

${\tau }_{xy}=25MPa$

$\therefore$ Principal stress,

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

$=30\pm \sqrt{{60}^2+{25}^2}$

$=95and-35MPa$