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

Fixed end moments:

Slope deflection sign convention

Counterclockwise fixed end moments are considered as positive, and

Clockwise fixed end moments are considered as negative.

Chord rotation

Slope deflection equations:

Equilibrium equation:

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

and

The third equilibrium equation is established by summing the moments of all the forces and couples acting on the free body of the entire frame about point O.

Applying moment equation:

By solving the equations (6) through (8), we obtain

Member end moments:

Now substituting the value in equation (1) to (5), to get the member end moments; thus

Member end shear:

The member end shears, obtained by considering the equilibrium of each member.

By considering the member AC

Sum of moments about C is zero

By considering the free body of the entire frame

Sum of moments about B is zero

Reaction diagrams: