Abstract
This paper is dealt with the analysis of the in-plane elastic buckling of regular polygonal frames which are supported elastically in member directions and subjected to inward concentrated non-follower loads uniformly at all the joints, as approximate models of cylindrical lattice shells under the action of external pressure. The buckling type of this case is bifurcation from uniform prebuckling state because this structure is symmetric to periodic rotation. So, in this paper, the periodic property of the polygonal structures is utilized for the buckling analysis. The main conclusions are as follows. 1) The buckling mode and the buckling load can be expressed in simple formula if the number of members is infinity or members are perfectly rigid. 2) On the condition the number of members is constant, the variation of the ratio between the elastic spring constant and the effective bending rigidity of frames gives all the periodic buckling modes. Especially, in the case of pin-jointed frames, buckling modes are zigzag for the case of stiffer member, and member buckling modes for the other case. 3) The buckling load determined by rigid body rotation, wavy buckling or zigzag buckling, is not affected by the ratio of the member bending softness in the effective bending softness, and the case of rigid members gives the almost lowest limit value of the buckling load. On the other hand, the buckling load determined by member buckling can be estimated by the Euler buckling of pin-supported column. 4) In the condition the effective rigidity of frames and the circumcircle radius of frames are constant, rigid body rotations or lower wavy buckling is scarcely affected by the variation of number of members, but zigzag buckling or higher wavy buckling is considerably affected by the variation of number of members. The zigzag buckling load of the pin-jointed frames can be expressed in Eq. (57). 5) For practical design, the buckling load of frames composed of elastic members can be estimated by member buckling or the buckling load formula for the case composed of rigid members with Eq. (54) for the value of Eq. (55) and Eq. (57).
