In non-stiffened CFST specimens, the concrete core can restrict tube inward deformation of the tube which is detected in the hollow tube specimen.
Therefore the steel tube can only buckle outward, which means the existence of concrete changes the buckling mode of the steel tube.
Fig. 11 shows the buckling mode of non-stiffened steel tube in CFST with dotted lines on the basis of finite element analysis conducted by the author.
In the test, the steel tube corners are restricted by the concrete corners.
Therefore in the analysis the steel plate can be approximately considered as fixed at the corners (shown in Fig. 11(a)). Along longitudinal direction, the steel tube takes on multi-wave buckling mode.
The connection of two adjacent buckling waves contacts tangentially to the concrete surface. The steel plate can be approximately supposed to be fixed in rotation at two ends of every buckling wave (shown in Fig. 11(b)), with longitudinal displacement fixed at one end and unfixed at another end.
Fig. 12 is the simplified model of rectangular steel plate subjected to unidirectionally uniformly distributed loading.
The dimensions of the rectangular steel plate are a (in x direction) and b (in y direction).
The line load (px) on neutral surface in x direction represents the axial load on the steel tube.
All the edges of the steel plate are restrained in y direction and rotations, with x directional freedom restrained only at edge AD or edge BC.