Buckling of a Weakened Column

Localization in the buckling or in the vibration of a two-span weakened column

“…It is clear however that the second-order perturbation (Eqs. (18) and (19)) has to be questioned when γ tends towards zero, thereby indicating that the buckling modes undergo a dramatic change (this result is similar to the one of Pierre [10] where the stiffness of the torsional spring at the intermediate support is large).…”

“…It is assumed that the rotational spring, whose flexibility is denoted by k, is located at the intermediate support. It is recalled that this rotational spring may model a one-sided crack (see the cited paper [15][16][17][18][19][20][21]) or more generally a semi-rigid connection in civil engineering. The column is subjected to axial compressive load P.…”

“…It is shown that the equivalent flexibility depends on the depth of the crack and on the height of the cross section of the beam. Recent papers on buckling of weakened columns are the one of Li who considers an arbitrary number of cracks in a non-uniform column [17] or Wang et al [18] who optimize the location of the equivalent crack, from the buckling load sensitivity. In the connected field of vibration of weakened column, Binici investigates the effect of axial force on the vibration of beams with multiple open cracks [19].…”

First-Order Solutions for the Buckling Loads of Euler-Bernoulli Weakened Columns

“…1͒. Following the method proposed by Freund and Herrmann 1976 and further followed by many others ͑Adams et al 1978;Morassi 1993;Narkis 1994;Fernández-Sáez et al 1999;Fernández-Sáez and Navarro 2002;Krawczuk et al 2003;Wang et al 2004;Loya et al 2006͒, we can model the cracked beam as two beams connected at the cracked section by a rotational spring whose stiffness is related to the crack size and the geometry of the cross section.…”

Nonlinear dynamic response of an edge-cracked functionally graded Timoshenko beam under parametric excitation

“…The dynamic behavior of cracked structures has been a topic of active research over the last few decades. A large number of studies on the free and forced vibration of cracked structures, using analytical or numerical methods or both, are available in open literature [1][2][3][4][5][6][7][8]. For Timoshenko beams in which the effect of transverse shear deformation is nonnegligible, Kisa et al [9] analyzed the free vibration of cracked Timoshenko beam using a combination of finite element and mode synthesis method.…”