Civil Engineering Association

Torsional analysis of multi-storey building structures under horizontal load

New closed-form formulae are presented for the torsional analysis of asymmetrical multi-storey buildings
braced by moment-resisting (and/or braced) frames, (coupled) shear walls and cores. The analysis is based
on an analogy between the bending and torsion of structural systems. A closed-form solution is presented
for the rotation of the building. The torsional behaviour is defi ned by three distinctive phenomena: warping
torsion, Saint-Venant torsion and the interaction between the two basic modes. Accordingly, the formula
for the maximum rotation of the building consists of three parts: the warping rotation is characterized by
the warping stiffness of the bracing system, St Venant rotation is associated with the St Venant stiffness
of the building and the third part is responsible for the interaction. It is demonstrated that the interaction
between the warping and St Venant modes is always benefi cial, as it reduces the rotation of the structure.
It is shown how the proposed formula for torsion can be used for the determination of the maximum defl ection
of multi-storey asymmetrical building structures. The results of a comprehensive accuracy analysis
demonstrate the validity of the method. A worked example is given to show the ease of use of the procedure.