A modified beam stiffness matrix for interconnected shear walls

Abstract

In the stiffness analysis of plane interconnected shear walls, it is convenient to specify the degrees of freedom at nodal positions defined by the intersection of the centroidal axis of each interconnecting beam and the centroidal axes of the shear walls. These intersection points are positioned a finite distance away from the ends of each interconnecting beam.

A modified stiffness matrix is presented for an interconnecting beam which includes a rigid arm at each end to allow for this finite distance, rotational springs to account for the localised deformations which take place in the zones where the beam adjoins the shear walls and transverse shear springs to allow for shear deformations in the beam. The matrix is presented in a form which permits existing computer programs to be modified with ease.

A stiffness program employing this matrix is used to analyse a series of plane interconnected shear walls, previously tested by MacLeod, in which the beam depth was varied from model to model. The model showing the greatest sensitivity to localised effects was reanalysed keeping the beam depth constant, but varying the number of storeys and in consequence the height of the structure.

The results are presented to show the importance of the rotational springs to the accuracy of the mathematical model and are compared with experimental evidence.