Carrying capacity of edge-cracked columns under concentric vertical loads

Abstract

Summary. This paper analyses the carrying capacity of edge-cracked columns with different boundary conditions and cross sections subjected to concentric vertical loads. The transfer matrix method, combined with fundamental solutions of the intact columns (e.g. columns with no cracks) is used to obtain the capacity of slender prismatic columns. The stiffness of the cracked section is modeled by a massless rotational spring whose flexibility depends on the local flexibility induced by the crack. Eigenvalue equations are obtained explicitly for columns with various end conditions, from second-order determinants. Numerical examples show that the effects of a crack on the buckling load of a column depend strongly on the depth and the location of the crack. In other words, the capacity of the column strongly depends on the flexibility due to the crack. As expected, the buckling load decreases conspicuously as the flexibility of the column increases. However, the flexibility is a very important factor for controlling the buckling load capacity of a cracked column. In this study an attempt was made to calculate the column flexibility based on two different approaches, finite element and J-Integral approaches. It was found that there was very good agreement between the flexibility results obtained by these two different methods (maximum discrepancy less than 2%). It was found that for constant column flexibility a crack located in the section of the maximum bending moment causes the largest decrease in the buckling load. On the other hand, if the crack is located just in the inflexion point at the corresponding intact column, it has no effect on the buckling load capacity. This study showed that the transfer matrix method could be a simple and efficient method to analyze cracked columns components.

Cuts Guided Deterministic Buckling in Arrays of Soft Parallel Plates for Multifunctionality

“…ε b increases nonlinearly with the aspect ratio of the plate t / H . Therefore, after cuts the effective thickness of the plates is reduced, leading to a reduced ε b , which is consistent with the reduced critical buckling load when buckling plates with both sides free after introducing a notch . The reduced ε b will speed up the response time.…”

“…Therefore, after cuts the effective thickness of the plates is reduced, leading to a reduced ε b , which is consistent with the reduced critical buckling load when buckling plates with both sides free after introducing a notch. 44 The reduced ε b will speed up the response time. Equation 2 also suggests that λ is proportional to H and independent of t, implying that cuts might have negligible effects on λ.…”

“…When one buckled plate is initially set to be in contact with another straight plate (an output of Logic “1” and lightening of LED, Figure c (i)), buckling of the precut straight plate (an input of Logic “1”) leads to the same buckled phase angle as the initially buckled one to switch from contact to noncontact state, and thus the output of Logic “0” and off of the LED light (Figure c (ii)). Buckling induced contact has been demonstrated in the microelectro-mechanical systems (MEMS), − where a bistable beam clamped at both ends was pushed laterally in the center to enable a snap-through instability. In comparison, our method is more controllable and robust.…”