Slope deflection method

In the book, "The Theory and Practice of Modern Framed Structures", written by J.B Johnson, C.W.

According to this book, professor Otto Mohr introduced this method for the first time in his book, "Evaluation of Trusses with Rigid Node Connections" or "Die Berechnung der Fachwerke mit Starren Knotenverbindungen".

By forming slope deflection equations and applying joint and shear equilibrium conditions, the rotation angles (or the slope angles) are calculated.

Substituting them back into the slope deflection equations, member end moments are readily determined.

Deformation of member is due to the bending moment.

The slope deflection equations can also be written using the stiffness factor

These rotation angles can be calculated using the unit force method or Darcy's Law.

The statically indeterminate beam shown in the figure is to be analysed.

There are no chord rotations due to other causes including support settlement.

Fixed end moments are: The slope deflection equations are constructed as follows: Joints A, B, C should suffice the equilibrium condition.

Therefore The rotation angles are calculated from simultaneous equations above.

Substitution of these values back into the slope deflection equations yields the member end moments (in kNm):