Abstract: Based on the plane assumption of bending, this paper analyzes the bending deformation of infinitesimal segments in linearly elastic beams, nonlinearly elastic beams, functionally graded material beams, and beams under thermal gradients. The displacement analysis methods for beams are categorized into two types: one accumulates deformations of infinitesimal segments to obtain the shape of the deflection curve, thereby determining beam section displacements; the other determines beam section displacements by summing the effects of infinitesimal segments deformations. The former belongs to the integral method, while the latter includes energy methods and superposition methods. This paper elaborates on the influence coefficients that characterize the effect of infinitesimal segments deformations on beam section displacements and identifies these coefficients in various analytical methods. Finally, the relationship between the superposition method and infinitesimal segments deformations is discussed. By treating infinitesimal deformation as the fundamental basis for beam displacement analysis, this study aims to guide students in transcending specific calculation methods and understanding the essence of beam displacement analysis from a more holistic and advanced perspective.