Decoupling of Lateral Equilibrium Equations for Asymmetric Multistory Structures

Abstract

The authors of the paper presented a methodology for the decoupling of the differential equations describing the lateral static equilibrium of eccentric multistory buildings with orthog­ onal framing, employing the continuum model. For the monosymmetric systems. which are analyzed in the paper, the total response to static forces is computed as a superposition of a pure translation and a rotation around a twist axis. The commonly employed differential equation for mixed systems is used for the pure translation, whereas, for the rotation. a new fifth-order differential equation (seventh order for the general case of double eccentricity) is considered. Moreover, the employed twist axis does not constitute an intrinsic property of the structure, but depends on the external loading. The writer has developed and presented a more general method for the decoupling of the differential equations describing the lateral static equilibrium of eccentric multistory buildings with a mixed structural system (Anastasiadis 1987). According to this method, in the general case of double eccentricity, the total response for static forces is computed as a superposition of three rotational responses around three principal torsional axes, which are independent of the external loading and constitute an intrinsic property of the structure. For each one of these principal torsional axes the classic differential equation of mixed torsion can be written ac­ cording to the well-known Vlassov theory. In addition, for applying this method to practical cases, a series of tables that correspond with four types of external loading (with uniform distribution, linear distribution, parabolic distribution, and for a concentrated force) are pre­ sented; moreover, the elastic fixity of the shear walls on the ground level was also considered, (Anastasiadis 1991). Finally, with this method, one succeeds in analyzing (in the same manner) both the two-dimensional and three-dimensional structural systems, taking into account the axial deformations of the vertical members in an approximate way. APPENDIX. REFERENCES