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Beam, column, plate, and any other structure, under full or partial compressive loading, are prone to failure by the buckling phenomenon. At the instant of failure, the structure may be in unpredictable elastic, elastic-plastic, full plastic, cracked, or other forms of deterioration state. Therefore, in spite of so much study, there is no definite solution to the problem. In this paper a unified, simple, and exact theory is proposed where buckling is considered as the change of state of structure between intact and collapsed states, and then the buckling capacity is innovatively expressed via states and phenomena functions, which are explicitly defined as functions of state variable. The state variable is determined by calibration of the structure slenderness ratio. The efficacy of the work is verified via concise mathematical logics, and comparison of the results with those of the others via seven examples. [ABSTRACT FROM AUTHOR]

This paper is a continuation of Survey I [], where the historical background and general remarks on the problem formulation and solution methods were outlined and results related to plane-strain problems were reviewed. In the present paper, a review of axisymmetric and 3D buckling delamination problems is presented. [ABSTRACT FROM AUTHOR]

Buckling-restrained braces (BRBs) have recently become popular in the United States for use as primary members of seismic lateral-force-resisting systems. A BRB is a steel brace that does not buckle in compression but instead yields in both tension and compression. Although design guidelines for BRB applications have been developed, systematic procedures for assessing performance and quantifying reliability are still needed. This paper presents an analytical framework for assessing buckling-restrained braced frame (BRBF) reliability when subjected to seismic loads. This framework efficiently quantifies the risk of BRB failure due to low-cycle fatigue fracture of the BRB core. The procedure includes a series of components that: (1) quantify BRB demand in terms of BRB core deformation histories generated through stochastic dynamic analyses; (2) quantify the limit-state of a BRB in terms of its remaining cumulative plastic ductility capacity based on an experimental database; and (3) evaluate the probability of BRB failure, given the quantified demand and capacity, through structural reliability analyses. Parametric studies were conducted to investigate the effects of the seismic load, and characteristics of the BRB and BRBF on the probability of brace failure. In addition, fragility curves (i.e., conditional probabilities of brace failure given ground shaking intensity parameters) were created by the proposed framework. While the framework presented in this paper is applied to the assessment of BRBFs, the modular nature of the framework components allows for application to other structural components and systems. [ABSTRACT FROM AUTHOR]

The investigation of the effects of cracks or similar weaknesses on the load carrying capacity of structural elements such as columns, beams and shells is an important problem in civil, mechanical and aerospace engineering. In this paper, the buckling of slender prismatic circular columns with multiple non-propagating edge cracks is studied by use of the transfer matrix method. The columns are modeled as an assembly of sub-segments connected by massless rotational springs whose flexibilities depend on the local flexibilities introduced by the cracks. This model enables discontinuity in rotations due to bending moments transmitted by the cracked sections. Eigenvalue equations are established in explicit form for classical columns and written for elastically supported columns. Numerical examples show that the buckling loads are affected considerably by the depths, locations and number of cracks, as expected. In case of a single crack, depending on the support conditions of the columns, the buckling loads show sensitivity or insensitivity to the crack location. For a constant crack depth, a crack located in the section of the maximum bending moment causes the largest decrease in the buckling load. In the study, modifications to take into account the intermediate elastic supports are also presented. [ABSTRACT FROM AUTHOR]

In an attempt to simulate buckling of nonuniform coatings, we consider the problem of an embedded crack in a functionally graded coating bonded to a homogeneous substrate subjected to a compressive loading. The coating is graded in the thickness direction and the material gradient is orthogonal to the crack direction which is parallel with the free surface. The loading consists of a uniform compressive strain applied away from the crack region. The graded coating is modeled as a nonhomogeneous medium with an isotropic stress-strain law. Using a nonlinear continuum theory and a suitable perturbation technique, the plane strain problem is reduced to an eigenvalue problem describing the onset of buckling. Using integral transforms, the resulting plane elasticity equations are converted analytically into singular integral equations which are solved numerically to give the critical buckling strain and the corresponding crack opening displacement shapes. The main objective of the paper is to study the influence of material nonhomogeneity on the buckling resistance of the graded layer for various crack positions and coating thicknesses. [ABSTRACT FROM AUTHOR]

The size-dependent buckling problem of cracked micro- and nanocantilevers, which have many applications as sensors and actuators, is studied by the stress-driven nonlocal theory of elasticity and Bernoulli–Euler beam model. The presence of the crack is modeled by assuming that the sections at the left and right sides of the crack are connected by a rotational spring. The compliance of the spring, which relates the slope discontinuity and the bending moment at the cracked cross section, is related to the crack length using the method of energy consideration and the theory of fracture mechanics. The buckling equations of the left and right sections are solved separately, and the variationally consistent and constitutive boundary and continuity conditions are imposed to close the problem. Novel insightful results are presented about the effects of the crack length and location, and the nonlocality on the critical loads and mode shapes, also for higher modes of buckling. The results of the present model converge to those of the intact nanocantilevers when the crack length goes to zero and to those of the large-scale cracked cantilever beams when the nonlocal parameter vanishes. [ABSTRACT FROM AUTHOR]

The failure and instability of a kind of specific rock structural bodies, such as the spalling-induced thin rock plates and the slender rock pillars, are the key inducing factors of rock engineering disasters and they are closely related to the shape effect, i.e., the height-to-width (H/W) ratio. For application in engineering practice, the strength characteristics and failure modes of the rock structural bodies when their H/W ratios vary in a wide range should be specially concerned, whereas this seems to be seriously ignored in previous studies. To support this purpose, a numerical scheme that integrates the statistical meso-damage constitutive model and the finite deformation formulation is proposed, to consider both the material failure and buckling instability of the rock structural bodies. The numerical results of a series of uniaxial compression tests of rock samples with relatively low H/W ratios (0.5–4) are completely consistent with the findings obtained from experiments. The behaviors of rock samples with high H/W ratios (6–28) show that the failure of rock samples is affected by both the H/W ratio and the strength of the rock material. That is, as the H/W ratio increases, the failure of rock samples gradually transforms from material failure dominated to structural (buckling) instability dominated, and the increase of the strength of rock material can facilitate this transition. The presented results have established an envelope about the failure and instability of rocks, and obtained the critical boundary line (CBL) for distinguishing different failure modes and determining the boundary between low and high H/W ratio. [ABSTRACT FROM AUTHOR]

A discrete lattice based model for the interaction of cracking, delamination and buckling of brittle elastic coatings is presented. The model is unique in its simultaneous incorporation of the coating and of disorder in the interface and material properties, leading to realistic 3D bending (and buckling) behavior. Results are compared to the literature. In the case of cracking, the key role of a stress transfer correlation length ξ in establishing a scaling behavior for the brittle fracture of thin films is shown to extend to all geometrical and material properties involved. In the scaling regime of crack density in uniaxial tension cracking and delamination are found to occur simultaneously. In uniaxial tension of films with an internal biaxial compressive stress, the predicted initiation of buckles above delaminated areas near crack edges in the model is remarkably similar to experimental results. [ABSTRACT FROM AUTHOR]

The strength and size effect of a slender eccentrically compressed column with a transverse pre-existing traction-free edge crack or notch is analyzed. Rice and Levy’s spring model is applied to simulate the effect of a crack or notch. An approximate, though accurate, formula is proposed for the buckling strength of the column of variable size. Depending on the eccentricity, the crack at maximum load can be fully opened, partially opened or closed. The size effects in these three situations are shown to be different. The exponent of the power-law for the large-size asymptotic behavior can be −1/2 or −1/4, depending on the relative eccentricity of the compression load. Whether the maximum load occurs at initiation of fracture growth, or only after a certain stable crack extension, is found to depend not only on the column geometry but also on its size. This means that the definition of positive or negative structural geometry (as a geometry for which the energy release rate at constant load increases or decreases with the crack length) cannot be extended to stability problems or geometrically nonlinear behavior. Comparison is made with a previous simplified solution by Okamura and coworkers. The analytical results show good agreement with the available experimental data. [ABSTRACT FROM AUTHOR]

A new alternative approach to fracture problems for materials and structural elements with cracks is set out. It is based on the mechanism of local instability near defects. The approach is used to study the fracture of materials compressed along interacting cracks and the fracture of thin structural members with cracks under tension with allowance for local buckling. [ABSTRACT FROM AUTHOR]