$(8$ points$)$ A metallic specimen is subjected to a bending moment $\backslash ($ M $\backslash )$ and an axial load $\backslash ($ F $\backslash ),$ as shown in the figure below. The bending, axial, and thermal strains on the upper surface of the specimen are denoted using $\backslash (\backslash$varepsilon$\_\{$b$\},\backslash$varepsilon$\_\{$a$\}\backslash ),$ and $\backslash (\backslash$varepsilon$\_\{$T$\}\backslash ),$ respectively.

Design a strain measurement experiment to sense the bending strain only. In the design, you are only allowed to use two strain gages.

You are asked to

$($i$)$ Show on the graph how the strain gages are affixed to the specimen;

$($iv$)$ Write down the expressions of measured strains by each gage;

$($iii$)$ Draw the bridge circuit and indicate how the gages are connected into a

$($iv$)$ standard bridge circuit;

$($iv$).$ Present the output expression of the bridge circuit;

$($V$)-$ Find the bridge constant.