Further studies on the elastic stability of curved beams

Abstract

In a previous article, 1 the authors investigated the instability of circular curved beams, the ends of which were hinged to fixed supports. For simplicity the loading was assumed to consist of equal but opposite end moments which tend to increase the span, and hence induce compression forces in the beam. The ranges of validity of three theories were investigated, viz. linear, extensible and nonlinear, inextensible and extensible theories. The present article extends the investigation to the more complicated problem of a circular curved beam with central concentrated loading. It was shown that buckling cannot occur if the initial rise span ratio λ 2l <0·96p (see Notation). Curves of critical loads t cr vs. initial rise span ratio were calculated for the three theories and comparisons made for values of p = 0·025 and 0·05. Finally, the effects of end restraints on the stability of small initial rise curved beams were studied by the linear theory. It is concluded that the translational restraint influences the buckling loads to a considerable extent whereas the rotational restraint has little effect.