A unified principle of multiples for lateral deflection,buckling and vibration of multi-storey, multi-bay, sway frames

摘要

Cheap computing has rightly eliminated tedious hand methods from taught courses.Unfortunately,this has often unintentionally resulted in the elimination of procedures which give useful structural behavioural insights into whole families of structures using simplified models which give good approximate results.Such procedures help designers both to check that computer results are reasonable and also to gain insight from parametric studies with a manageable number of parameters.The present paper seeks to rescue one such procedure from relative obscurity and presents almost its only recent extension.It is the use of substitute one bay (or alternatively Grinter) frames to obtain results for unbraced and lightly braced multi-storey,multi-bay,sway frames which are exact when they are unbraced,ahve inextensible members and obey the Principle of Multiples and otherwise are good approximations.these results can incorporate cladding and are for: deflections caused by static lateral (e.g.wind) loading; critical buckling and; natural vibrations.These three types of problem are unified herein and,because adequate published results exist for the first two types,only (new) natural frequency results are given.These show that,for unbraced frames,the substitute frame gives acceptable accuracy for most purposes regardless of how closely the frame obeys the Principle of Multiples.They also apparently justify a new application,namely to analyse multi-storey,multi-bay Multiples.They also apparently justify a new application,namely to analyse multi-storey,multi-bay frames with one or more braced bays by using a substitute frame which represents the bracing as cladding.Exceptionally,when all bays are cross-braced,the Principle of Multiples may be obeyed.