How slope deflection equation is applied in continuous beam

In this construction video tutorial, the eminent engineer Parag Pal provides brief information on slope deflection equation for continuous beam.

A continuous beam refers to a statically indeterminate multispan beam that is supported with hinged connection. A continuous beam is similar to simply supported beam. The end spans are cantilever and freely supported or fixed supported. As a minimum one of the supports of a continuous beam can develop a reaction across the beam axis.

Slope deflection method is useful for various types of statically indeterminate beams and frames. With this method the unidentified joint rotations which are described by means of the applied loads & bending moments. Deflections because of shear and axial stresses are not taken into consideration because the effects are small.

With the formation of slope deflection equations and application of joint and shear equilibrium conditions, the rotation angles (or the slope angles) are computed. Replacing them back into the slope deflection equations, member end moments are instantly defined.

Deformation of member occurs because of the bending moment. The slope deflection method applies displacements as unknowns, that's why this method is known as displacement method.

To get detailed information on slope deflection equation, go through the following video tutorial.

Video Source: Parag Pal