The Estimation of the Critical Loads of Certain Frameworks

IT HAS long been known that the approach of elastic instability in a framework results in the amplification of bending actions due to transverse loads on the component members, to eccentricities and to other imperfections which may be present. This amplification can cause premature yielding in extreme fibres and it may therefore affect adversely the load carrying capacity of the structure. The moment-distribution
method used in the analysis of these bending actions has been extended in the past to provide a means of estimating critical loads.1 In its usual form the method can be tedious, particularly in the region of the critical load, where convcrgencc is slow. In a recent paper the writer has dcvelopcd a method which is direct in its approach and which enables the stiffnesses and hence the criticaloads of plane braced structures to be calculated with ease. For continuous beam and certain building frame problems the method has a parallel in the techniques adopted by Wood, when these are
extended to deal with the effects of end-thrust. Such methods of estimation of critical loads are briefly reviewed here, and it is demonstrated that they correspond
to a convenient physical interpretation of the process of condensing a determinant.

H.G. Allen