Determine the member end moments and reactions for the frames shown in figure by using t...

Chord rotation

Slope deflection equations:

Calculating for remaining beams:

Calculating for remaining beams:

Calculating for remaining beams:

Equilibrium equation:

Sum of moments at a joint is zero. Thus, we obtain the equilibrium equation

and

The remaining two equilibrium equations is established by passing a horizontal section just above the lower ends of the column of each story of the frame and, apply the horizontal equilibrium

By solving the equations (13) through (18), we obtain

Member end moments:

Now substituting the value in equation (1) to (12), to get the member end moments; thus

Calculating member end moments:

Calculating member end moments:

Reaction diagrams