$3\mathrm{.}13.$ An extensometer, shown in Fig. $3\mathrm{.}10$b$,$ consists of a semicircular$-$arch clip gage. The dimension of the clip gage is shown in Fig. P$3\mathrm{.}13,$ where $L=\frac{F{L}^3}{16EI}$ and $F$ is the force applied on the clip gage. Place gages $1$ and $2$ in a Wheatstone bridge and determine $\frac{E}{V}$ in terms of $lon,G_f,t,$ and $R$ when $lon=\frac{L}{L}$ is the axial strain of the specimen and $L$ is approximately the length of the clip gage.

FIGURE P$3\mathrm{.}13$