Three Moment Equation for Variable Depth Beams

Analysis of continuous beams with variable moment of inertia is simplified by using a general form for the equation of three moments. Influence lines for bending moments, shearing forces, and reactions are directly obtained using this equation. In continuous steel girder bridges with concrete floors, the participation of the concrete deck can take place only in the regions of positive moments in which the concrete is subjected to compressive stresses. The moment of inertia of the composite section is considerably greater than that of the active steel section under negative bending moments. The final bending moment diagram, which fixes the part subjected to the composite action in each span, is itself dependent on the position of these parts when the moment of inertia increases. The exact length and position of these parts, is found to have a comparatively small effect, so that the final bending moment diagram under each particular loading can be obtained from a first suitable trial position of positive moments without further correction.