Cracked Columns Research Articles

Retrofitting of Thermally Affected Structural Compression Member Using Basalt FRP Laminates

Concrete structures exposed to high temperatures often experience thermal damage, which can significantly reduce their structural integrity. Fiber-Reinforced Polymer (FRP) wrapping is a common retrofitting technique used to restore the strength and durability of thermally affected concrete. This study investigates the effectiveness of Basalt Fiber-reinforced Polymer wrapping on different concrete specimens with varying orientations of wrapping. This study mainly focuses on various parameters as fiber orientation and wrapping methodology. A series of 15 columns of dimension 150mm x 150mm with a length of 700mm are cast and subjected to axial compression loading in a pre-heated condition until the initial cracking occurs. These cracked columns are made to strengthen using Basalt Fiber with different patterns of orientation of laminates. The retrofitted columns are subjected to axial compression loading to determine their maximum load-bearing capacities. The test results of this experiment is assessed and compared with conventional RC columns of same grade. The strength of retrofitted columns versus conventional ones are compared and analyzed. The maximum load bearing capacity for a particular pattern of wrapping is determined.

Variation of Corrosion Rate, Vcorr, during the Carbonation-Induced Corrosion Propagation Period in Reinforced Concrete Elements.

The structural systems of residential buildings in many developed countries have widely utilized reinforced concrete as the most common solution in construction systems since the early 20th century. The durability of reinforced concrete columns and beams is compromised, in most cases, by pathologies caused by the corrosion of their reinforcements. This study analyses the corrosion processes induced by carbonation in 25 buildings with reinforced concrete structures. The models estimate the service life of reinforced concrete elements by differentiating between the initiation period and the propagation period of damage, considering two possible stages: the time of corrosion propagation until the cracking of the concrete cover, and the time of propagation until a loss of section is considered unacceptable for structural safety. However, the mathematical expressions that model the propagation periods consider the same corrosion rate in both cases. This research has found that the average corrosion rate in elements with an unacceptable loss of reinforcement section was in the order of 8 times higher than the corrosion rate in cracked columns and beams without a loss of reinforcement. This opens up a path to improve the definition of the different stages experienced by a reinforced concrete element suffering corrosion of its reinforcements due to carbonation, because once the concrete has cracked, the corrosion rate increases significantly.

Eccentrically Loaded Slender Columns Strengthened by High-Strength Fiber Reinforced Concrete Jackets.(Dept.C)

The behavior of eccentrically loaded cracked slender High-Strength Concrete (HSC) columns strengthened by HSC jackets contain steel fibers and have cube compressive strength equal to 89.3 MPa has been studied experimentally. The results of these tests have been used to examine the applicability of the design requirements of slender columns of the Eurocode 2 (EC-2), the Egyptian code (ECCS-2001) and ACI 318-99 building eode, when applied to the strengthened columns. The testing p rogram included 11 columns with slenderness ratios before strengthening ranged between 17.3 and 69.3. The main variables considered in this study were the slenderness ratio of the strengthened columns, the type of the steel fibers, the end eccentricity of the applied axial load and the transverse reinforcement ratio of the HSC jackets. The results showed that, eccentrically loaded slender and short cracked columns strengthened by HSC jackets contain 1% steel fibers (by volume) can be treated as new integral columns. Using a steel fibers into the HSC mix of the jackets reduces to a great extent the early cover spalling of the tested columns and increases the ultimate loads comparing with the same columns strengthened with HSC jackets without steel fibers. The three different methods for design of slender columns required by the ECCS-2001, EC-2 and ACI 318-99 building code can be safely used for design of slender columns strengthened by HSC jackets contain steel fibers.

Approximate analytical solution of buckling of multi-damaged column-like structures using a continuous diffused crack model by variational iteration method

Compressive structural members can be locally damaged by overloading, corrosion, car crash and fire. In this work, a continuous diffused crack model is proposed to study the static stability of Euler–Bernoulli rectangular column-like structures under different boundary conditions. The governing differential equation is formulated by adopting a diffused crack model. The powerful variational iteration method is implemented to find the approximate analytical buckling modes and buckling loads based on the buckling response of the intact column. A novel generalized Lagrange multiplier is derived. The proposed method incorporates the effects of the crack width into consideration when deriving the buckling modes. The stability equation allows addressing the influences of multiple damages and can be applied to both concentrated and distributed cracks. The famous Rayleigh–Ritz method is utilized to verify the computed buckling loads. The proposed diffused crack model and the application with VIM is efficient and accurate for handling buckling problems of cracked columns under different boundary conditions.

A Lagrange Multiplier-based Technique within the Nonlinear Finite Element Method in Cracked Columns

In this research, two energy-based techniques, called Lagrange multiplier and conversion matrix, are applied to involve crack parameters into the non-linear finite element relations of Euler-Bernoulli beams made of functionally graded materials. The two techniques, which divide a cracked element into three parts, are implemented to enrich the secant and tangent stiffness matrices. The Lagrange multiplier technique is originally proposed according to the establishment of a modified total potential energy equation by adding continuity conditions equations of the crack point. The limitation of the conversion matrix in involving the relevant non-linear equations is the main motivation in representing the Lagrange multiplier. The presented Lagrange multiplier is a problem-solving technique in the cracked structures, where both geometrical nonlinearity and material inhomogeneity areas are considered in the analysis like the post-buckling problem of cracked functionally graded material columns. Accordingly, some case-studies regarding the post-buckling analysis of cracked functionally graded material columns under mechanical and thermal loads are used to evaluate the results.

Three-dimensional finite element modeling for post-buckling analysis of cracked columns

Purpose – The purpose of this paper is to investigate the effect of crack surfaces contact on the post-buckling behavior of a slender column with a non-propagating crack. Design/methodology/approach – In this paper a 3D finite element model has been implemented to study the post-buckling behavior of a slender column with a non-propagating crack. According to this model, the column is discretized into three-dimensional solid elements. Contact conditions are considered between the crack surfaces. The non-linear equations for this model are solved using an incremental-iterative procedure, and the equilibrium path of the cracked column is extracted. Findings – Load-displacement curves are presented for a cantilever column with a transverse surface crack of either uniform or non-uniform depth across the column cross-section. For both crack shapes, the load-displacement curves are presented for various values of crack depth and position. The results of this study are in good agreement with the results available in the literature. Comparisons with the results of the always-open crack were performed. The post-buckling behavior of a column with a uniform depth crack is more sensitive to variations in crack depth and position than the post-buckling behavior of a column with a non-uniform depth crack. Originality/value – A 3D finite element approach for the post-buckling behavior of a transversely cracked column including contact between crack surfaces.

A new simplified method for anti-symmetric mode in-plane vibrations of frame structures with column cracks

This paper is on the natural frequency and mode shape computation of frame structures with column cracks. First, a model of intact frame structures is built to perform vibration analysis. Beam elements are considered as lumped masses and rotational springs at the storey levels of frames. Equivalent model of columns and lumped mass-stiffness effects of beams have been combined to carry out continuous solution for the anti-symmetric mode in-plane vibrations of frames. In addition, frame systems with multiple column cracks are analyzed in terms of anti-symmetric mode vibration characteristics. Cracks are considered as massless rotational springs in compliance with the local flexibility model. Compatibility and continuity conditions are satisfied at crack and storey locations of the equivalent column, modeled using the Euler–Bernoulli beam theory. The proposed method is tested for single-storey single- and multi-bay, H-type and double-storey single-bay frame systems with intact and cracked columns. Results are validated by those given in the current literature and/or obtained by the finite element analyses.

Investigation of vibration and stability of cracked columns under axial load

In this paper, an analytical method is proposed to study the effect of crack and axial load on vibration behavior and stability of the cracked columns. Using the local flexibility model, the crack has been simulated by a torsional spring with connecting two segments of column in crack location. By solving governing eigenvalue equation, the effects of crack parameters and axial load on the natural frequencies and buckling load as well as buckling load are investigated. The results show that the presents of crack cause to reduction in natural frequencies and buckling load whereas this reduction is affected by the location and depth of the crack. Furthermore, the tensile and compressive axial load increase and decrease the natural frequencies, respectively. In addition, as the compression load approaches to certain value, the fundamental natural frequency reaches zero and instability occurs. The accuracy of the model is validated through the experimental data reported in the literature.

Compressive capacity of longitudinally cracked wood columns retrofitted by self-tapping screws

This paper presents the results of an experimental and numerical study of the compressive capacity of longitudinally cracked wooden columns retrofitted using self-tapping screws. The screws were driven into the wood perpendicular to the wood grain to alleviate the propagation of existing cracks and to improve the structural integrity of the cracked columns. Full-scale concentric and eccentric compression tests were conducted to investigate the failure modes and maximum load carrying capacity of such columns. A 3D finite element model was developed, verified, and then used for a parametric study. The test results indicated that the cracks (of 6 mm wide) caused a resistance loss of up to 19% compared with an intact column, but most of this resistance loss can be remedied by using self-tapping screws. It was also found that such resistance loss and recovery are dependent on the seriousness of the cracking, and generally increase with the increased initial mid-height deflection and decreased screw spacing, whereas a screw spacing of 100 mm would be sufficient for most cases considered in this study.

Anti-floating problem and retrofit measures for a damaged basement

Through comprehensive investigation of a building accident, this paper analyses the reason of unevenly floating phenomenon in an underground garage subjected to a rainstorm and puts forward some reinforcement measures to the damaged members in the structure accordingly. The damaged status investigation of the garage structure is focused on the pile corresponding to the largest deformation column. Coring samples from damaged piles, the status of them can be obtained accordingly. Checking the garage design with investigated data, the cause of the uneven rise is concluded. Combined with the damage degree difference between structure components, the retrofit measures are put forward. First, cover the garage roof with proper depth of soil pressure, and then reinforce the cracked beams, columns and slabs, respectively. Second, plant bar into the broken pile and inject grout around the pile with high pressure. Finally, add prestressed anchors in the deformation foundation floor.

New Finite-Element Formulation for Buckling Analysis of Cracked Structures

AbstractA crack in a steel structure will cause a local change in its stiffness. The change in stiffness will lead to a change in buckling loads and a discontinuity in the associated buckling modes. The changes in the buckling characteristics of columns cause a change in the buckling stability of the structure. The effect of cracks on the buckling load of structural systems can be investigated through numerical methods. The FEM is a well-known method for this work. In this paper, a new and innovative finite-element (FE) formulation for the buckling analysis of cracked columns is presented. The method presented is simpler and, at the same time, more accurate and practical than those available in the literature. The proposed FE formulation for cracked columns has the same format as that for intact columns. The formulation is used successfully in efficient and accurate buckling analysis of cracked frames.

Dynamic stability of cracked columns; the stiffness reduction method

A new formulation for the dynamic stability of cracked columns is proposed. In this formulation, a differential equation governing the free vibration of a cracked column subjected to compressive axial force is derived. The solution of the proposed equation needs only the end conditions for its solution (similar to that of intact beam columns). The equation is solved using the Laplace Transform. Both conservative and non-conservative forces are considered. The closed form solution is then used in the dynamic stability investigation of the cracked column with different boundary conditions. The accuracy, efficiency and robustness of the work are verified through numerical examples.

Comparison of ANFIS and NN models—With a study in critical buckling load estimation

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, earthquake and aerospace engineering. In this paper, adaptive neuro-fuzzy inference system (ANFIS) and artificial neural network (ANN) model have been successfully used for the buckling analysis of slender prismatic columns with a single non-propagating open edge crack subjected to axial loads. The main focus of this work has been to study the feasibility of using ANFIS and neural network (NN) trained with the non-dimensional crack depth and the non-dimensional crack location parameters to predict the critical buckling load of fixed-free, pinned-pinned, fixed-pinned and fixed-fixed supported, axially loaded compression rods. A comparative study is made using the neural nets and neuro-fuzzy techniques. Statistic measures were used to evaluate the performance of the models. Based on comparison of the results it is found that the proposed ANFIS architecture with Gaussian membership function is found to perform better than the multilayer feed forward ANN learning by backpropagation algorithm. The final results show that especially the ANFIS modeling may constitute an efficient tool for elastic buckling analysis of edge cracked columns. Architectures of the ANFIS and NN established in the current study perform sufficiently in the estimation of critical buckling loads, and particularly the ANFIS estimates closely follow the actual values for the whole data sets. These model architectures can be used as a non-destructive procedure for health monitoring of structural elements.

Carrying capacity of edge-cracked columns under concentric vertical loads

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.

Crack effect on the elastic buckling behavior of axially and eccentrically loaded columns

A close form solution of the maximum deflection for cracked columns with rectangular cross-sections was developed and thus the elastic buckling behavior and ultimate bearing capacity were studied analytically. First, taking into account the effect of the crack in the potential energy of elastic systems, a trigonometric series solution for the elastic deflection equation of an arbitrary crack position was derived by use of the Rayleigh-Ritz energy method and an analytical expression of the maximum deflection was obtained. By comparison with the rotational spring model (Okamura et al. 1969) and the equivalent stiffness method (Sinha et al. 2002), the advantages of the present solution are that there are few assumed conditions and the effect of axial compression on crack closure was considered. Second, based on the above solutions, the equilibrium paths of the elastic buckling were analytically described for cracked columns subjected to both axial and eccentric compressive load. Finally, as examples, the influence of crack depth, load eccentricity and column slenderness on the elastic buckling behavior was investigated in the case of a rectangular column with a single-edge crack. The relationship of the load capacity of the column with respect to crack depth and eccentricity or slenderness was also illustrated. The analytical and numerical results from the examples show that there are three kinds of collapse mechanisms for the various states of cracking, eccentricity and slenderness. These are the bifurcation for axial compression, the limit point instability for the condition of the deeper crack and lighter eccentricity and the fracture for higher eccentricity. As a result, the conception of critical transition eccentricity (e/ h)c , from limit-point buckling to fracture failure, was proposed and the critical values of (e/h)c were numerically determined for various eccentricities, crack depths and slenderness.

Caustics and Buckling of Cracked Columns

The experimental method of caustics is applied to buckling behaviour of straight cracked columns. Two major parameters of the problem may be defined through the caustics method: the SIF and the high strain internal region. The knowledge of these parameters may be used to improve predictions of the buckling behaviour of cracked columns.

Finite element analysis for fracture behavior of cracked beam-columns

The fracture behavior of cracked beam-columns with different load eccentricities is studied. A cracked beam-column element, developed previously by Tharp (Int. J. Numer. Methods Eng. 24 (1987) 1941) is implemented into a finite element code to study the behavior of cracked beam-columns subjected to axial and lateral loads. Assuming that failure occurs due to crack propagation when the mode I stress intensity factor reaches the fracture toughness of the material, the failure load of cracked columns are determined for different crack depths and slenderness ratios. It is observed that the presence of crack decreases the critical load of columns and this decrease is small for short cracks and long columns. The presence of crack has no effect on the critical load for columns with slenderness ratios 180 and above. In addition, the presence of crack makes the relation between lateral load and lateral deflection bi-linear in a beam-column subjected to axial compressive load.

Cracked Column Flanges in Steel Moment Frame Buildings: Considerations for Their Repair including Report on Tests on Volumetric Weld Repairs

This paper presents recommendations on the repair of cracked columns based upon the writers' experiences, found from repair of cracked column flanges following the 1994 Northridge Earthquake. This paper also describes tests carried out using volumetric weld repairs on thick plates to evaluate acceptable procedures for the repair of column flanges with partial cracks damaged from earthquakes. Cracks were often found in the bottom flange of welded joints. In some cases, cracks propagated into column flanges, and in a few cases into their webs. Repairs of cracked welded joints are discussed at some length in other documents and thus are not part of the scope of this paper. One method for the repair of cracked columns involves replacement of the column flange with a new plate. Another method of repair involves the use of volumetric welds to replace the cracked portion of the column flange. This paper includes a description of the development of procedures and limited testing to assess the adequacy of the volumetric repair method of partial column cracks.

Buckling of multi-step cracked columns with shear deformation

The governing differential equation for buckling of a one-step cracked column with shear deformation is established and its solution is found first. Then a new approach that combines the exact buckling solution of a one-step column and the transfer matrix method is presented for solving the entire and partial buckling of a multi-step column with various end conditions, with or without cracks and shear deformation, subjected to concentrated axial loads. The main advantage of the proposed method is that the eigenvalue equation for buckling of a multi-step column with an arbitrary number of cracks, any kind of two end supports and various spring supports at intermediate points can be conveniently determined from a system of two linear equations. Due to the decrease in the determinant order as compared with previously developed procedures, the computational time required by the present method for solving the title problem can be reduced significantly. A numerical example is given for explaining the proposed procedure and investigating the effects of shear deformation and the number, depth and location of cracks on critical buckling force of a multi-step column. It is shown through the numerical example that the proposed procedure is a simple, exact and efficient method.

Stress intensity calibrations for closed cracks

A powerful method is described for determining stress intensity factors for plane cracks intersecting a free edge and where the bulk stress field is such that the crack faces are pressed together along at least part of their length. This configuration occurs widely in problems where the crack is propelled by a contact stress field, but the simpler example given here for illustration purposes involves a cracked column undergoing compression and shear.