Two wooden studs with cross$-$sectional dimensions $45\backslash$times $145$ mm$2$ are glued together to form a beam with a T$-$section

according to the figure on the right and loaded according to the figure on the left. The beam is loaded in its rigid

direction.

a$)$ Calculate the moment of inertia of the cross$-$section about the centroid axis $($z$-$axis$).$

b$)$ Calculate the maximum normal stress in the beam.

c$)$ Sketch the normal stress distribution over the most loaded cross$-$section of the beam.

All calculations must be clear and handwritten, draw and check so that the answers are correct