The square deforms into the position shown by the dashed lines in $($Figure $1).$ The dimensions are S$=52$ mm

$,$ S$=57$ mm

$,\backslash$Delta x$1=3$ mm

$,$ and $\backslash$Delta x$2=8$ mm

$.$ Side D$\text{'}$B$\text{'}$

remains horizontal.

Figure$1$ of $1$

The x axis is directed horizontally to the right. The y axis is directed vertically upward. In the x y plane, square plate $\text{'}$A$\text{'}$ C B D has base $\text{'}$A$\text{'}$ C and height $\text{'}$A$\text{'}$ D of length S$.$ Vertex $\text{'}$A$\text{'}$ is at the origin. Vertex C is on the x axis. Vertex D is on the y axis. A deformed plate is shown with dashed lines. The vertices of the deformed plate are positioned as follows. The lower left vertex coincides with $\text{'}$A$\text{'}.$ Vertex C prime is to the right of C at distance Delta x subscript $2.$ Vertex B prime is upward and to the left of B$.$ The horizontal distance between B and B prime is Delta x subscript $1.$ Vertex D prime is upward and to the left of D$.$ Side D prime B prime is horizontal. Side $\text{'}$A$\text{'}$ D prime has a length of S prime. Angle C $\text{'}$A$\text{'}$ D prime measures $91\mathrm{.}5$ degrees.

Part A

Part complete

Part B

Determine the shear strain at B

relative to the x

$,$ y

axes.

Express your answer in radians to three significant