Question

In a rectangular strain gauge rosette, if the strains recorded are and ${ϵ}_{90}=100\mu$ then the maximum principal strain at the point is ____________$\mu$
${ϵ}_0=200\mu ,{ϵ}_{45}=150\mu$

• A. 200

Answer 1

The correct option is A 200
${\varphi }_{xy}=2\times {ϵ}_{45}-({ϵ}_0+{ϵ}_{90})$

$=2\times \left(150\right)-(200+100)=0$

${ϵ}_{1,2}=\frac{{ϵ}_0+{ϵ}_{90}}{2}\pm \sqrt{(\frac{{ϵ}_0-{ϵ}_{90}}{2}{)}^2+(\frac{{\varphi }_{xy}}{2}{)}^2}$

$=\left(\frac{200+100}{2}\right)\pm \sqrt{{\left(\frac{200-100}{2}\right)}^2+(0{)}^2}$

$=150\pm 50$

$\therefore$ Maximum principal strain = 200 $\mu$