Periods of vibration of braced frames with outriggers

This paper presents simple equations for the natural lateral and rotational periods of vibration for high-rise steel structures comprising braced frames with outrigger trusses. The structural floor plan can be symmetric or asymmetric combinations of identical bents. Each braced frame is modelled by a cantilever with a bending stiffness and racking shear stiffness. The outriggers are represented by a rotational spring. The stiffness of the outrigger spring is dependent on three specific modes of behaviour: bending and racking shear in the outrigger truss and axial lengthening or shortening of the exterior columns. This yields a simple calculation of the maximum horizontal deflection of the structure. For the rotational frequencies, the bending, racking shear and spring stiffness parameters of the steel structure each are combined to yield a torsional stiffness, a warping stiffness and a warping spring stiffness which allow an assessment of the rotation at the top. The approximate method of analysis relates the natural frequencies of the structure to the top deflection and rotation when the self-weight is taken as a distributed horizontal load. In the calculations a braced frame is represented by a rigid stick model with its overall flexibility assigned to a rotational spring at the base. Results obtained by the simplified method are compared to those from a finite element analysis. The approximate method gives acceptable conservative results for preliminary analysis.