Abstract: This paper examines the role of member stiffness by summarizing the effects of material properties, cross-sectional geometry, member length, and support conditions. Revisiting Timoshenko’s discussion of load-transfer mechanisms, it highlights the distribution of internal forces by relative stiffness in statically indeterminate structures. Distinctions between axial and flexural stiffness are used to analyze triangular truss stability and the rationality of truss models, while the influence of support conditions is applied to the critical buckling of rigid frames and the bending instability of tape-like structures. The study demonstrates the advantages of the mechanics of materials approach in engineering practice and emphasizes the importance of comprehensively understanding fundamental concepts and systematically mastering basic principles in structural mechanics education.