The built$-$up T$-$beam has a fixed end condition with applied loads as shown and has elastic material properties E$=200$ GPa, v$=0\mathrm{.}32.$ The top flange is secured to the web of the T$-$beam with tack$-$fasteners along its length as shown in the cross section diagram. For the given loading, geometry and material properties, determine the following:

A$.$ The maximum normal stress $($using the coordinate system provided$)$ that occurs in the beam and normal strain at that location. Make sure you correctly indicate the sign of the stress and strain.

B$.$ The maximum shear stress $($using the coordinate system provided$)$ that occurs in the beam and shear strain at that location. Make sure you correctly indicate the sign of the stress and strain.

C$.$ Where in the beam does the highest maximum principal stress occur? Please clearly and completely describe the location in $3$D$.$