A Simplified Method for Evaluating the Natural Frequencies and Corresponding Modal Shapes of Multist

With limit state design, sidesway of buildings may become more critical than collapse; there is considerable difficulty in specifying ‘safe’ sidesway, since wind gusts are dynamic and opposed by inertia as well as by frame stiffness. Dynamic analysis necessitates using large computers but many designers prefer simplified ‘desk’ methods of analysis. Two such methods for static behaviour have already been developed at the
Building Research Station, employing substitute frames, and have been accepted in recent British and European Codes of Practice. This paper describes an analogous method for dynamic behaviour of multistorey frames, in particular the natural frequencies and modal shapes that could be developed to study the effects of forced vibration. The largest matrices involved are now only of size 2 x 2 irrespective of the number of members in the multistorey frame. It is shown how composite stiffening
effects of walls and floors can be introduced into the design, which highlights the need for more tests in real buildings.

E.H. Roberts and R.H. Wood