For the following beam, $E=30,000$MPa and ignore self$-$weight of the beam. All dimensions are in mm$.$

a$)$ Draw the shear force diagram, bending moment diagram and curvature diagrams.

b$)$ Calculate the location of the centroidal axis and the second moment of area.

c$)$ Draw the flexural stress profile at mid$-$span and at support B$.$

d$)$ Calculate the mid$-$span displacement and the slope of the beam at points B and C$.$ Sketch out the displaced shape and also indicate the points of inflection.