For a multi$-$span bridge find:

a$)$ Check the stability of the frame and the degrees of indeterminacy in figure $1C_{?}$

b$)$ Using slope$-$deflection method, analyse the frame in figure $1$d $($with A and $D$ as fixed supports$)$ and find the moments at the end of the beam $BC$ and columns $AB$ and $DC.$

c$)$ Calculate the reactions at support A using the force method. Assume supports at points A and $D$ are now pinned.

Total factored gravity load on the beam including self$-$weight and live load is $w=1200k\frac{N}{m}.$ Earthquake load is $Q=1500kN$ sideway force.

Concrete material has a modulus of elasticity of $E=30$GPa.

a$)$ real bridge structure

d$)$ simplified analysis model

Figure $1$