Multicomponent tensile buckling
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Multicomponent tensile buckling book
Buckling refers to the jump of a structure from a linear geometry to a distorted one. It occurs when stress applied to the structure overtakes some threshold, making the linear geometry unstable. It has crucial implications in many industries, in particular in civil engineering where buckling instability has to be considered for the resilience of structures and buildings. The buckling phenomenon was first experimentally observed by Musschenborek (1729) and mathematically described by Euler (1744) for a beam experiencing compressive stress. While buckling is almost a synonym for structures under compression, recently it has been demonstrated that buckling can also actually be triggered by tensile loads. The idea of tensile buckling has been brought to light by introducing certain local imperfections to the structures. In order to trigger instabilities in complex structures under tensile increments, experiments and computations have been attempted over the last few decades (Timoshenko & Gere, 1961, Ziegler, 1977, Gajewski & Palej, 1974, Zyczkowski, 1991). However, in those experiments the systems were initially compressed so that the equilibrium bifurcation was not occurring due to pure tension, and only by introduction of an increment of tension. More recently, in 2011, Zaccaria et al. designed a structure exhibiting buckling under tensile load (Zaccaria et al., 2011). Their device consisted of two
One end is rigidly fixed and the end is allowed to freely move horizontally. In a multi-component structure containing N + 1 PVC rods, we place N sliders, with N up to 8. The rods used between the sliders where either 20 cm or 30 cm. Loading was realised manually with the help of a rope attached with the movable extremity of the structures. The other end of the rope was attached to a bucket where loading was realised by slowly pouring glass beads of known calibrated weight. The rope passes over a beam smoothened at the corner to avoid any friction during loading. After buckling occurs, the weight of the grains was measured with a weight machine (fidelity measurement AFM 18(iii)), giving the buckling load. A camera (Nikon D3300) was set above the buckling setup to capture continuously photos as well as movies of the experiment. This has allowed us to study the motion of the structure and its components, i.e. its buckling modes, from the initial instability to the formation of complete buckling. To observe the buckling mode of those structures, videos were processed using a dedicatedly written MATLAB code.