Problem $1$: Analysis of a continuous beam by the Slope$-$Deflection method.

Determine the reactions and draw the shear and bending moment diagrams for the three$-$span continuous beam shown in Fig $1$ using the slope$-$deflection method. The same structural profile is used for all spans: E$=200$GPa,I$=120$ xx$106$mm$4.$ The loads and dimensions are given in Fig $1.$ The ends A and D of the beam are fully fixed. The supports B and C are sliders allowing horizontal movement.

n$1=3,$ n$2=1,$ n$3=0$

The following tasks are to be performed and reported:

Identify the spans, nodes and degrees of freedom. Derive slope$-$deflection equations for each span. Apply equilibrium conditions at each unknown degree of freedom and solve them for unknown rotations. Calculate the member end moments. Calculate the end shears and support reactions. Draw the shear and bending moment diagrams