A solid circular bar of diameter $d=50mm$ is subjected to an axial force $P$ and a torque $T($see Figure $1\mathrm{.}1).$ Strain gages A and B mounted on the surface of the bar $($Point C $)$ give readings ${}_a=100{10}^{-6}$ and ${}_b=-55{10}^{-6}.$ The bar is made of steel having $E=200$GPa and Poisson's ratio $v=0\mathrm{.}3.$

$($a$)$ Determine the axial force $P$ and the torque $T.$

$($b$)$ Determine the maximum in$-$plane shear strain at Point C$.$

Answer

Figure $1\mathrm{.}1$

$($a$)P=39\mathrm{.}27kN$;$T=-339\mathrm{.}84N-m$

$($b$){}_{\text{m}\text{a}\text{x}}=222{10}^{-6}$