QUESTION $2-$ Conjugate Beam Method

The beam ABCD is loaded as shown in Figure Q$2.$

a$)$ Calculate the reactions at supports A and C $.$

b$)$ Draw the shear force and bending moment diagrams of the beam.

c$)$ With the aid of the concept of bending moment diagrams by parts, where necessary, draw

the $\frac{M}{EI}$ diagram and the elastic curve for the beam under the applied loading.

d$)$ Use the conjugate beam method to determine the slopes and deflections at points B and D

of the beam.