ESDU 79005:2010

INTRODUCTION

The construction techniques employed in modern high-rise
buildings lead to structures of relatively high flexibility and low
mass so that the effect of dynamic loads on the structure become
increasingly important. A knowledge of the natural frequency
parameters is necessary for the investigation of the response of a
building to such loads. The natural frequency parameters, required
for the calculation of the response of a building to fluctuating
loads by the modal superposition method, are natural frequencies,
mode shapes, and normal-mode generalised masses (or inertias) and
stiffnesses. In considering lateral modes, generalised masses and
lateral stiffnesses are used and for torsional modes, generalised
rotational inertias and rotational stiffnesses are required. The
way in which these data are used in the case of the calculation of
the response of a building under the action of a fluctuating wind
load is described in the Data Items in Sections 7, 8 and 9.

This Item provides a means of estimating the natural
frequencies, mode shapes and normal-mode generalised masses* for
both lateral and torsional undamped modes of vibration of shear
buildings. A relationship is given from which the generalised
stiffnesses for lateral and torsional modes might be obtained using
other data provided. This Item is primarily intended for use with
uncoupled modes of vibration although coupling between lateral and
torsional modes is considered in Appendix B where expressions for
the estimation of coupled mode parameters are given for a special
class of shear building.

The data provided are restricted to use for those buildings that
may be modelled as shear type buildings. A shear building is
defined as a building that has inextensible columns and rigid
floors which prevent joint rotations. In this Item it is assumed
that the reductions in column stiffness due to the axial loads
applied by the supported structure are negligible. This stiffness
effect causes a reduction in frequency and may modify the mode
shapes but is generally small. Further, it is assumed that the
buildings have a rigid base. Thus, by implication, the displacement
at ground level is assumed to be zero and it is assumed that no
soil/structure interaction takes place.

The mathematical model of the shear building, illustrated in
Sketch 3.1, is further idealised (as described in Section 4) to
provide a graphical solution for the natural mode of vibration
parameters. A computer program is provided in the
Wind Engineering Series via
the website that allows the solution of the shear
building model without the necessary further idealisation imposed
by the graphical solution. A number of modes of vibration may
significantly contribute to the dynamic loads on a building
although it is generally the lowest frequency mode which has the
greatest influence on the dynamic response. Graphical data are
provided for the first four natural modes of vibration for both
lateral and torsional oscillations.

* The terms mass, stiffness and displacement are used in the
generic sense to include rotational inertia, rotational stiffness
and rotational displacement, respectively, for the torsional
vibration case.