• Journal of the Korean Society for Precision Engineering
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• v.26 no.9
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• pp.112-120
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• 2009

In this paper the purpose is to investigate the stability and variation of natural frequency of a cracked Timoshenko cantilever beams subjected to subtangential follower force. In addition, an analysis of the stability of a cantilever beam as the crack effect and slenderness ratio is investigated. The governing differential equations of a Timoshenko beam subjected to an end tangential follower force are derived via Hamilton's principle. The two coupled governing differential equations are reduced to one fourth order ordinary differential equation in terms of the flexural displacement. By using the results of this paper, we can obtain the judgment base that the choice of beam models for the effect of slenderness ratio and crack.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.22 no.6
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• pp.950-956
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• 2013

This paper describes a sensitivity-coefficient-based iterative method for detecting cracks in a structure. The sensitivity coefficients of a cracked structure are obtained by changing its eigenvectors. The proposed method is applied to a cracked cantilever. The crack is modeled as a rotational stiffness. The predicted cracks are in good agreement with those from a structural reanalysis of the cracked structure.

• Journal of the Korea institute for structural maintenance and inspection
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• v.2 no.4
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• pp.177-185
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• 1998

This paper deals with the flexural behaviors of R.C beams strengthened by carbon fiber sheets. The behaviors of strengthened beams which were preloaded up to 50%, 60% and 70% of the ultimate load of unstrengthened beam are compared with that of a beam which was not preloaded. The structural behaviors of strengthened beams are compared with analytical method in terms of load-strain of concrete, load-strain of steel bar, load-strain of CFS and falilure load. Four cases of analytical method are investigated according to cracked section or partially cracked section and including strain hardening effect of steel bar or not. Comparing the results of test and analysis, both are similar in terms of load-strain of concrete, and falilure load, the results of analytical method underestimate the failure load. But each results of load-strain of steel bar, load-strain of CFS near at failure is some different, thus near at failure the composite action between CFS and upper concrete is assumed to be disturbed. Consequently, the analytical method was proved to be efficient and accurate in estimating the flexural response of CFS strengthened RC beams.

• Structural Engineering and Mechanics
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• v.40 no.1
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• pp.105-120
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• 2011

The strengthening and rehabilitation of reinforced concrete structures with externally bonded carbon fibre reinforced polymer (FRP) laminates has shown excellent performance and, as a result, this technology is rapidly replacing steel plate bonding techniques. This paper addresses this issue, and presents results deals with the influence of external bonded CFRP-reinforcement on the time-dependent behavior of reinforced concrete beams. A total of eight reinforced concrete beams with cracked and un-cracked section, with and without externally bonded CFRP laminates, were investigated for their creep and shrinkage behavior. All the beams considered in this paper were simply supported and subjected to a uniform sustained loading for the period of six months. The main parameters of this study are two types of sustained load and different degrees of strengthening scheme for both cracked and un-cracked sections of beams. Both analytical and experimental work has been carried out on strengthened beams to investigate the cracking and deflection performance. The applied sustained load was 56% and 38% of the ultimate static capacities of the un-strengthened beams for cracked and un-cracked section respectively. The analytical values based on effective modulus method (EMM) are compared to the experimental results and it is found that the analytical values are in general give conservative estimates of the experimental results. It was concluded that the attachment of CFRP composite laminates has a positive influence on the long term performance of strengthened beams.

• Structural Engineering and Mechanics
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• v.41 no.2
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• pp.285-297
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• 2012

An inverse approach is presented for calculating the flexibility coefficient of open-side cracks in the cross sectional of beams. The cracked cross section is treated as a massless rotational spring which connects two segments of the beam. Based on the Euler-Bernoulli beam theory, the differential equation governing the forced vibration of each segment of the beam is written. By using a mathematical manipulation the time dependent differential equations are transformed into the static substitutes. The crack characteristics are then introduced to the solution of the differential equations via the boundary conditions. By having the time history of transverse response of an arbitrary location along the beam, the flexibility coefficient of crack is calculated. The method is applied for some cracked beams with solid rectangular cross sections and the results obtained are compared with the available data in literature. The comparison indicates that the predictions of the proposed method are in good agreement with the reported data. The procedure is quite general so as to it can be applicable for both single-side crack and double-side crack analogously. Hence, it is also applied for some test beams with double-side cracks.

• Advances in Computational Design
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• v.1 no.1
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• pp.61-77
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• 2016

Seismic performance of structures depends on the force flow mechanism inside the structure. Discontinuity regions, like beam-column joints, are often affected during earthquake event due to the complex and discontinuous load paths. The evaluation of shear strength and identification of failure mode of the joint region are helpful to (i) define the strength hierarchy of the beam-column sub-assemblage, (ii) quantify the influence of different parameters on the behaviour of beam-column joint and, (iii) develop suitable and adequate strengthening scheme for the joints, if required, to obtain the desired strength hierarchy. In view of this, it is very important to estimate the joint shear strength and identify the failure modes of the joint region as it is the most critical part in any beam-column sub-assemblage. One of the most effective models is softened strut and tie model which was developed by incorporating force equilibrium, strain compatibility and constitutive laws of cracked reinforced concrete. In this study, softened strut and tie model, which incorporates force equilibrium equations, compatibility conditions and material constitutive relation of the cracked concrete, are used to simulate the shear strength behaviour and to identify failure mechanisms of the beam-column joints. The observations of the present study will be helpful to arrive at the design strategy of the joints to ensure the desired failure mechanism and strength hierarchy to achieve sustainability of structural systems under seismic loading.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1360-1365
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• 2006

In this paper the vibration analysis of cantilever beams having a concentrated tip mass and an open crack are performed. The influences of a concentrated tip mass, the crack depth, and the crack position on the natural frequencies of the cracked cantilever beam are investigated by a numerical method. The cracked cantilever beam is modeled based on the Euler-Bernoulli beam theory. The flexibility due to crack is calculated using a fracture mechanics theory. The crack is assumed to be opened during the vibrations. The results obtained by the present method were compared with experimental results to verify the theory. As inspected, as the crack depth and the concentrated tip mass increase, the natural frequencies of the beam decrease. In general, the natural frequencies of the cantilever beam are more sensitive to the depth of the crack than the position of the crack.

• Structural Engineering and Mechanics
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• v.38 no.1
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• pp.81-97
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• 2011

In this research, the wavelet transform is used to analyze time response of a cracked beam carrying moving mass for damage detection. In this respect, a new damage detection method based on the combined use of continuous and discrete wavelet transforms is proposed. It is shown that this method is more capable in making damage signature evident than the traditional two approaches based on direct investigation of the wavelet coefficients of structural response. By the proposed method, it is concluded that strain data outperforms displacement data at the same point in revealing damage signature. In addition, influence of moving mass-induced terms such as gravitational, Coriolis, centrifuge forces, and pure inertia force along the deflection direction to damage detection is investigated on a sample case. From this analysis it is concluded that centrifuge force has the most influence on making both displacement and strain data damage-sensitive. The Coriolis effect is the second to improve the damage-sensitivity of data. However, its impact is considerably less than the former. The rest, on the other hand, are observed to be insufficient alone.

• Steel and Composite Structures
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• v.29 no.5
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• pp.635-645
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• 2018

Beam-column joints play a significant role in static and dynamic performances of reinforced concrete frame structures. This study contributes a numerical approach of topologically optimal design of carbon fiber reinforced plastics (CFRP) to retrofit existing beam-column connections with crack patterns. In recent, CFRP is used commonly in the rehabilitation and strengthening of concrete members due to the remarkable properties, such as lightweight, anti-corrosion and simplicity to execute construction. With the target to provide an optimal CFRP configuration to effectively retrofit the beam-column connection under semi-failure situation such as given cracks, extended finite element method (X-FEM) is used by combining with multi-material topology optimization (MTO) as a mechanical description approach for strong discontinuity state to mechanically model cracked structures. The well founded mathematical formulation of topology optimization problem for cracked structures by using multiple materials is described in detail in this study. In addition, moved and regularized Heaviside functions (MRHF), that have the role of a filter in multiple materials case, is also considered. The numerical example results illustrated in two cases of beam-column joints with stationary cracks verify the validity, benefit and supremacy of the proposed method.

• Steel and Composite Structures
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• v.46 no.4
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• pp.565-575
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• 2023

This study represents a numerical research in vibration and buckling of functionally graded material (FGM) beam comprising edge crack by using finite element method (FEM) and multilayer perceptron (MLP). It is assumed that the material properties change only according to the exponential distributions along the beam thickness. FEM and MLP solutions of the natural frequencies and critical buckling load are obtained of the cracked FGM beam for clamped-free (C-F), hinged-hinged (H-H), and clamped-clamped (C-C) boundary conditions. Numerical results are obtained to show the effects of crack location (c/L), material properties (E₂/E₁), slenderness ratio (L/h) and end supports on the bending vibration and buckling properties of cracked FGM beam. The FEM analysis used in this paper was verified with the literature, and the fundamental frequency ratio ($\overline{P_{cr}}$) and critical buckling load ratio ($\overline{{\omega}}$) results obtained were compared with FEM and MLP. The results obtained are quite compatible with each other.