Amplification Factors for Beam-Columns

Beam-columns are structural members subject to axial compression and simultaneous bending moments. In practice, the bending moments in such members are often induced by lateral loads. The axial force influences some functions of the beam, such as deflection, slope, shear force and bending moment. These functions are increased by an amplification factor which depends upon the magnitude of the axial compressive force. Since the member used for structural purposes has a variety of applications, it is desirable to have some information readily available for such beam-columns. Formulas for the determination of magnification factors under the most generalized conditions under symmetrical loading are presented herein. In particular, the end slope of a member equal to the small angle of rotation of the end is given, because many statically indeterminate structures can be solved by a proper consideration of angle rotation. Beam-columns which are symmetrically loaded with concentrated, uniformly distributed and triangularly distributed loads are considered. In elementary theory of bending, the principal of superposition is valid provided that Hooks Law holds for the material. In beam-columns, the presence of the axial force shows that the deflection of the member is not directly proportional to the lateral loads. However, the superposition method can be applied in a slightly modified form. Thus results shown in this paper can cover a large area of symmetrical loading.