QUESTION $1-$ Method of consistent deformation: Analysis of indeterminate beam structure The statically indeterminate beam shown in Figure Q$1$ is built$-$in at A and supported on rollers at B and D$.$ Using the method of consistent deformation,

a$)$ Develop the compatibility equations given that the moments at A and B are considered as the redundant actions.

b$)$ Determine the magnitude and sense of the moments at A and B$.$

c$)$ Calculate the other support reactions.

d$)$ Draw the shear force and bending moment diagrams for the beam.