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The purpose of this paper is to develop, for use in everyday design, a procedure that incorporates the effect of concrete cracking in reinforced concrete (RC) beams at service load and requires computational efforts which is a fraction of that required for the available methods. Further for ease of use in everyday design the reinforcement input data is minimized. The procedure has been demonstrated for continuous beams and is under development for tall building frames.

The procedure is analytical at the element level and numerical at the structural level. A cracked span length beam element consisting of three cracked zones and two uncracked zones has been used. Closed form expressions for flexibility coefficients, end displacements, crack lengths, and mid-span deflection of the cracked span length beam element have been presented. In order to keep the procedure analytical at the element level, average tension stiffening characteristics are arrived at for cracked zones.

The proposed procedure, at minimal computation effort and minimal reinforcement input data, yields results that are close to experimental and finite element method results.

The procedure can be used in everyday design since it requires minimal computational effort and minimal reinforcement input data.

A procedure that requires minimal computational effort and minimal reinforcement input data for incorporating concrete cracking effects in RC structures at service load has been developed for use in everyday design.

In this paper, an approximate analytical approach is developed for the determination of natural longitudinal frequencies of a cantilever-cracked beam based on the Lagrange inversion theorem.

The crack is modeled by an equivalent axial spring with stiffness according to Castigliano's theorem. Thus, an implicit frequency equation corresponding to cantilever-cracked bar is obtained. The resulting equation is solved using the Lagrange inversion theorem.

Effect of different crack depths and crack positions on natural frequencies of the cracked beam is analyzed. It is shown that an increase in the crack depth ratio produces a decrease in the fundamental longitudinal natural frequency of a cracked bar. Furthermore, approximate analytical results are compared with those obtained numerically as well as from experimental tests.

A new approximate analytical expression of a fundamental longitudinal frequency, as a function of crack depth and crack location, is obtained.

This study aims to perform dynamic response analysis of damaged rigid-frame bridges under multiple moving loads using analytical based transfer matrix method (TMM). The effects of crack depth, moving load velocity and damping on the dynamic response of the model are discussed. The dynamic amplifications are investigated for various damage scenarios in addition to displacement time-histories.

Timoshenko beam theory (TBT) and Rayleigh-Love bar theory (RLBT) are used for bending and axial vibrations, respectively. The cracks are modeled using rotational and extensional springs. The structure is simplified into an equivalent single degree of freedom (SDOF) system using exact mode shapes to perform forced vibration analysis according to moving load convoy.

The results are compared to experimental data from literature for different damaged beam under moving load scenarios where a good agreement is observed. The proposed approach is also verified using the results from previous studies for free vibration analysis of cracked frames as well as dynamic response of cracked beams subjected to moving load. The importance of using TBT and RLBT instead of Euler–Bernoulli beam theory (EBT) and classical bar theory (CBT) is revealed. The results show that peak dynamic response at mid-span of the beam is more sensitive to crack length when compared to moving load velocity and damping properties.

The combination of TMM and modal superposition is presented for dynamic response analysis of damaged rigid-frame bridges subjected to moving convoy loading. The effectiveness of transfer matrix formulations for the free vibration analysis of this model shows that proposed approach may be extended to free and forced vibration analysis of more complicated structures such as rigid-frame bridges supported by piles and having multiple cracks.

This study aims to investigate the size effect of the patched repairing material applied to the cracked beam.

Numerical analysis was conducted on a simply supported cracked beam with a dimension of 200 × 25 × 15 cm using ABAQUS software. The behavior of concrete and engineered cementitious composites (ECC) in the simulation are described as concrete damage plasticity model. Linear elastic-plastic model was used to represent the behavior of rebar steel. The type of patching consisted of the varying ratio of lengths and depths, including patching length to total length ratios of 0.2, 0.3 and 0.4, and patching depth to total depth ratios of 0.2, 0.3, 0.4 and 0.5.

Results show that variations in the patching length and depth ratios affect the maximum flexural load, stiffness and ductility of the repaired beam. It was also found that repairing the cracked beam by using ECC provides higher flexural load of the beam than the use of conventional concrete, owing to the superior tensile strength of ECC.

ECC is the cementitious-based mortar that contains the special selected poly vinyl alcohol fiber having high tensile strength. ECC has been known to exhibit high ductility, high tensile strength and improve durability performance. Thus, ECC is suitable as repairing material for patching cracked beam. By investigating the size of the patched repairing material applied to the cracked beam, the structural performance of repairing beam and the effectiveness of the various patching size were achieved.

In the case of machines, structures and assemblies, the crack generation and propagation is becoming a great concern, especially in airplane wings, turbine blades and such other applications. This is because these parts are very large in size and the crack size is very small, i.e. in microns. Hence, there is an important need to locate the crack and to find its severity before it starts to propagate and also to detect these parameters by on-site non-destructive testing methods. This paper aims to develop and test the methodology to locate an unknown single open crack in steel cantilever beam along with its severity.

This study covers analytical, numerical and experimental analysis for healthy and cracked beams. Vibration-based approach and finite element analysis (FEA) approach is used for analytical and numerical study respectively. Own designed and dedicated experimental set-up is used for testing purpose along with fast fourier transform analyzer. An anti-resonance technique is used to locate and to find the severity of unknown crack. The statistical approach helps to validate the results.

The comparison of the natural frequency of healthy and cracked steel cantilever beam shows that the crack in the beam reduces its natural frequency. The accuracy of results is achieved by finding actual density and Young's modulus of steel specimen under consideration. It is helpful to verify the health of the non-cracked beam by applying dye testing. The study of natural frequency and anti-resonance gives the location of crack and its depth also. The FEA approach proved to be an important tool for numerical analysis of cracked beam.

The research is limited to steel material and surface cracks only.

Practically, this study highlights how to locate a surface crack in steel beam along with its depth, i.e. severity with great accuracy. Identification of the factors such as location and depth of a crack provide the severity of damage in airplane wings, turbine blades, bridges and many more, and thereby, it helps in safety at working vicinity.

The identification and solutions of current research helps to predict the operational life of machine elements such as airplane wings, turbine blades, bridges and many more, and thereby, it helps in the safety of people in working vicinity of such structures.

The work presented, is based on original research and experimentation. This work is valued contribution in the field of methodologies applied for fault detection in structures and also determining its correctness by numerical and experimental work.

The purpose of this paper is to develop an organized structure for damage detection of a cracked cantilever beam using finite element method and experimental method technique.

Due to presence of cracks the dynamic characteristics of structure change. The change in dynamic behavior has been used as one of the criteria of fault diagnosis for structures. Major characteristics of the structure which undergo change due to presence of crack are: natural frequencies, the amplitude responses due to vibration and the mode shapes. Therefore, an attempt has been made to formulate a smart technique for minimizing the amplitude of vibration for crack cantilever beam structures. In the analysis both single and double cracks are taken into account.

The results of the active vibration control experiments proved that piezoelectric sensor/actuator pair is an effective sensor and actuator configuration for active vibration control to reduce the amplitude of vibration for closed-loop system.

It is necessary that structures must safely work during its service life, but damages initiate a breakdown period on the structures which directly affect the industrial growth. It is a recognized fact that dynamic behavior of structures changes due to presence of crack. It has been observed that the presence of cracks in structures or in machine members leads to operational problem as well as premature failure.

Modelling methods can be helpful for understanding vibrations of beam structures including cracks, as well as for early detection of crack. This study aims to provide an analytical modelling approach for a cantilever beam considering a slant vertical crack along its height. However, previous uniform crack methods cannot be used for describing this case. The results from the analytical, finite element (FE) and experimental methods are compared to verify the vibration problem.

A massless rotational spring model is adopted to describe the crack. An extended method based on the calculation method for a uniform vertical edge crack is proposed to obtain the stiffness of the slant case. The beam is divided into a series of independent thin slices along the beam height. An Euler–Bernoulli beam model is applied to formulate each slice. The crack in each slice is considered as a uniform one. The transfer matrix method in the literature is used to obtain the beam vibration frequencies and mode shapes. Influences of crack location and sizes on the natural frequencies for the cantilever beam, as well as the mode shapes, are analysed. An established FE model and test results in the listed references are used to validate the developed method.

The numerical results show that the rotational stiffness at the cracked section and the natural frequencies of the beam decrease by increasing the crack sizes; the natural frequencies for the beam are greatly influenced by the crack sizes and location; the first natural frequency decreases with the distance from the beam fixed end to the crack location; the value of the first natural frequency reaches a minimum value when the crack is at the beam fixed end; the value of the second natural frequency is a minimum value when the crack is at the beam middle; and the value of the third natural frequency is a minimum value when the crack is at the beam free end. Saltation is observed in some mode shapes at the crack location, especially for larger crack depths; but, the mode shapes of the beam are slightly influenced by the vertical crack.

This study gives a useful analytical modelling method for free vibration analysis for the cantilever beam with a vertical crack, which can overcome the disadvantages of the previous uniform crack methods.

This study aimed to solve the engineering problem of free vibration disturbance and local mesh refinement induced by microcrack damage in circularly curved beams. The accurate identification of the crack damage depth, number and location depends on high-precision frequency and vibration mode solutions; therefore, it is critical to obtain these reliable solutions. The high-precision finite element method for the free vibration of cracked beams needs to be developed to grasp and control error information in the conventional solutions and the non-uniform mesh generation near the cracks. Moreover, the influence of multi-crack damage on the natural frequency and vibration mode of a circularly curved beam needs to be detected.

A scheme for cross-sectional damage defects in a circularly curved beam was established to simulate the depth, location and the number of multiple cracks by implementing cross-section reduction induced by microcrack damage. In addition, the h-version finite element mesh adaptive analysis method of the Timoshenko beam was developed. The superconvergent solution of the vibration mode of the cracked curved beam was obtained using the superconvergent patch recovery displacement method to determine the finite element solution. The superconvergent solution of the frequency was obtained by computing the Rayleigh quotient. The superconvergent solution of the eigenfunction was used to estimate the error of the finite element solution in the energy norm. The mesh was then subdivided to generate an improved mesh based on the error. Accordingly, the final optimised meshes and high-precision solution of natural frequency and mode shape satisfying the preset error tolerance can be obtained. Lastly, the disturbance behaviour of multi-crack damage on the vibration mode of a circularly curved beam was also studied.

Numerical results of the free vibration and damage disturbance of cracked curved beams with cracks were obtained. The influences of crack damage depth, crack damage number and crack damage distribution on the natural frequency and mode of vibration of a circularly curved beam were quantitatively analysed. Numerical examples indicate that the vibration mode and frequency of the beam would be disturbed in the region close to the crack damage, and a greater crack depth translates to a larger frequency change. For multi-crack beams, the number and distribution of cracks also affect the vibration mode and natural frequency. The adaptive method can use a relatively dense mesh near the crack to adapt to the change in the vibration mode near the crack, thus verifying the efficacy, accuracy and reliability of the method.

The proposed combination of methodologies provides an extremely robust approach for free vibration of beams with cracks. The non-uniform mesh refinement in the adaptive method can adapt to changes in the vibration mode caused by crack damage. Moreover, the proposed method can adaptively divide a relatively fine mesh at the crack, which is applied to investigating free vibration under various curved beam angles and crack damage distribution conditions. The proposed method can be extended to crack damage detection of 2D plate and shell structures and three-dimensional structures with cracks.

This study aims to develop an adaptive finite element method for structural eigenproblems of cracked Euler–Bernoulli beams via the superconvergent patch recovery displacement technique. This research comprises the numerical algorithm and experimental results for free vibration problems (forward eigenproblems) and damage detection problems (inverse eigenproblems).

The weakened properties analogy is used to describe cracks in this model. The adaptive strategy proposed in this paper provides accurate, efficient and reliable eigensolutions of frequency and mode (i.e. eigenpairs as eigenvalue and eigenfunction) for Euler–Bernoulli beams with multiple cracks. Based on the frequency measurement method for damage detection, using the difference between the actual and computed frequencies of cracked beams, the inverse eigenproblems are solved iteratively for identifying the residuals of locations and sizes of the cracks by the Newton–Raphson iteration technique. In the crack detection, the estimated residuals are added to obtain reliable results, which is an iteration process that will be expedited by more accurate frequency solutions based on the proposed method for free vibration problems.

Numerical results are presented for free vibration problems and damage detection problems of representative non-uniform and geometrically stepped Euler–Bernoulli beams with multiple cracks to demonstrate the effectiveness, efficiency, accuracy and reliability of the proposed method.

The proposed combination of methodologies described in the paper leads to a very powerful approach for free vibration and damage detection of beams with cracks, introducing the mesh refinement, that can be extended to deal with the damage detection of frame structures.

The early detection of cracks, corrosion and structural failure in aging structures is one of the major challenges in the civil, mechanical and aircraft industries. Common inspection techniques are time consuming and hence can have strong economic implications due to downtime. The paper aims to discuss these issues.

As a result, during the past decade a number of methodologies have been proposed for detecting crack in structure based on variations in the structure's dynamic characteristics. This work showcases the efficacy of particle swarm optimization (PSO) and genetic algorithm (GA) in damage assessment of structures.

Efficiency of these tools has been tested on structures like beam, plane and space truss. The results show the effectiveness of PSO in crack identification and the possibility of implementing it in a real-time structural health monitoring system for aircraft and civil structures.

The methodology presented establishes the PSO as robust and competent tool over GA for crack identification using changes in natural frequencies.