Three-Columniation End's Moment Equation of frame with support sinkage and angle

This paper introduces support sinkage and support angle for equation of rigid frame. The methodology was used by analyses columniation end moment and frame parameter bending moment diagram with moment equilibrium at joint and displacement compatibility. Result indicated that Three-Columniation End's Moment Equation (TCEME) is universal. There are three applications for TCEME this paper. First was moved out chord rotation component from two equations at neighbor points to one formula. The result shows the Three-Spans Columniation End Moment Equation (TSCEME) that is formula about columniation end moments with load and support sinkage and support angle in three sans, but without chord rotation component shown. Second was an example for columniation end moment solution of a frame by using TCEME directly. Third was study formula of TCEME and of TSCEME with constant line rigidness. And an example with support sinkage.