Chapter 2, Problem 2.79HP

Figure P2.79 shows an aluminum cantilevered beam loaded by the force F. Strain gauges $R_1,R_2,R_{3,}$ and $R_4$ are attached to the beam as shown in Figure P2.79 and connected into the circuit shown. The force causes a tension stress on the top of the beam that causes the length (and therefore the resistance) of $R_1$ and $R_4$ to increase and a compression stress on the bottom of the beam that causes the length (and therefore the resistance) of $R_2$ and $R_3$ to decrease. The result is a voltage of 50 mV at node B with respect to node A. Determine the force if
   $\begin{array}{l}{R}_{\sigma }=1\text{k}\Omega v_s=12VL=0.3\text{m}\\ w=25\text{mm}h=100\text{mm}Y=69{\text{GN/m}}^2\end{array}$