The Structural Systems oF Tall Buildings - Tall Buildings: Structural Systems and Aerodynamic Form - page 59

Columns
in tension
Columns
in compression
\p
6
d/2 d/2
Figure 3.49 Axial deformation of the perimeter columns on two facades perpendicular
to the bending direction
core under lateral loads. Thus, by reducing the rotation of the core, both the bending
moment of the core ( Figure 3.48 ) and the lateral drift at the top of the building
are reduced. Columns on two facades perpendicular to the bending direction are
subjected to axial tension or compression, and so are elongated on one side and
contracted on the other ( Figure 3.49 ).
The behaviour of outriggered frame systems is analysed below, taking the lateral
drift at the building top as a basis, in cases where the outriggers are located throughout
the height of the building at one or two levels. Assuming that the outriggers are so stiff
that rotation in the outriggers due to axial deformation of the columns and the rotation
of the core at the same level under lateral loads are equal, the restoring moment
created by the outrigger and the lateral drift of the outrigger are obtained with the help
of compatibility equations. Below, an approximate analysis is presented, assuming
uniform columns, uniform core and uniform outriggers, hoping to be helpful to create
a rough estimation in preliminary design stage.
The analysis has been made with the following assumptions:
• The core is a vertical cantilever rigidly ixed at the base and rigid against shear.
• Outriggers are rigidly ixed to the core, have hinged connections to the perimeter
columns to induce axial forces only, and are rigid against shear and flexure.
• The cross-sectional areas of the columns are constant from the top outrigger down
to foundation and the moment of inertia of the core is constant throughout the
building height.
• The lateral load on the building is constant throughout the building height.
• The structure is linearly elastic.
Outriggers can be represented by an equivalent spring of rotational stiffness K at the
core. The rotational stiffness of this spring (the moment per unit of rotation) for a
couple of columns (working on opposite sides perpendicular to the bending direction)
under an axial load pi: i :