Vol.04, Issue 09, September 2019 Available Online: www.ajeee.co.in/index.php/AJEEE MODAL ANALYSIS OF A CRACKED CONCRETE BEAM: A CONCEPTUAL REVIEW
Pratik Verma1, Rahul Sharma2
1M. Tech Research Scholar, 2Assistant Professor Department of Civil Engineering,
Prashanti Institute of Technology and Science, Ujjain (M.P) India
Abstract - Cracks in vibrating component can initiate catastrophic failures. The presences of cracks change the physical characteristics of a structure which in turn alter its dynamic response characteristics. Therefore there is need to understand dynamics of cracked structures. Crack depth and location are the main parameters for the vibration analysis. So it becomes very important to monitor the changes in the response parameters of the structure to access structural integrity, performance and safety, and to examine the effect of the crack to the natural frequency of beams. In present research work, contributions of researchers in the field of concrete with varying depths are acknowledged and gaps in the research as well as objectives of new research are proposed.
Keywords: Concrete, crack depth, location.
I. INTRODUCTION
The most common structural defect is the existence of a crack. Cracks are present in structures due to various reasons. The presence of a crack could not only cause a local variation in the stiffness but it could affect the mechanical behavior of the entire structure to a considerable extent.
Cracks may be caused by fatigue under service conditions as a result of the limited fatigue strength. They may also occur due to mechanical defects. Another group of cracks are initiated during the manufacturing processes. Generally they are small in sizes. Such small cracks are known to propagate due to fluctuating stress conditions. If these propagating cracks remain undetected and reach their critical size, then a sudden structural failure may occur. The cracks present in the structure interrupt the continuity of the assembly in most of the engineering structures like beam, columns in which geometrical properties can also be altered.
Cracks caused due to fatigue stresses or stress concentration reduces the natural frequency and change mode of vibration due to local flexibility induced by the crack. All these effects due to concentrated cracks have been exclusively discussed in this literature. A crack is modeled by describing the variation of the stiffness matrix of the member in the vicinity of a crack. The presence of a crack in a structural member introduces a local compliance that affects its response to varying loads. The change in dynamic characteristics can be measured and lead to identification of structural alteration, which at the end finally might lead to the detection of a structural flaw.
Considering above mentioned facts, present research work is devoted to investigations contributions of researchers in the field of cracked concrete beams.
2. CONTRIBUTIONS OF THE RESEARCHERS
Following are the details of research contributions in the field of cracked beams.
1. Heydari et al. (2014)
In this paper, forced flexural vibration of a cracked beam is studied by using a continuous bilinear model for the displacement field. The effects of shear deformation and rotary inertia are considered in the model. The governing equation of motion for the beam is obtained using the Hamilton principle and based on the proposed displacement field.
The equation of motion is given for a general force distribution. Then, the equation of motion has been solved for a concentrated force to present a numerical simulation of the method. The frequency response diagrams obtained from this study are compared with the finite element results to demonstrate the accuracy of the method. The results are also compared to results of a similar model with Euler-Bernoulli assumptions to confirm the advantages of the proposed model in the case of short beams.
2. Biondini (2004)
The paper presents a three-dimensional finite beam element for damage evaluation and seismic analysis of concrete
Vol.04, Issue 09, September 2019 Available Online: www.ajeee.co.in/index.php/AJEEE structures. The proposed formulation
takes both mechanical and geometrical non-linearity into account. The measure of the seismic structural performance is based on a set of damage indices defined at different scales. The accuracy of the finite beam element is proven with reference to the results of experimental tests on reinforced concrete columns under complex loading histories. An application to the seismic analysis and evaluation of the structural performance of a concrete bridge is finally presented.
3. Shahnewaz et al. (2012)
A predominant failure mode in deep beams is shear failure which is a brittle and sudden and can lead to catastrophic consequences. Therefore, it is necessary to investigate the shear deficiency of deep beams under seismic loads. This paper aims to investigate the seismic performance of reinforced concrete deep beams structure. A reinforced concrete structure with a deep beam in the first storey was selected from the literature and was analyzed. The capacity of the structure was calculated using non-linear displacement based Pushover Analysis (POA) and the seismic demand was calculated for ten different earthquake records using non-linear Time History Analysis. The study showed a significant strength deficit in the deep beam at the first storey level under different earthquake records. While the drift of the structure and the inter-storey drift ratio were found in the tolerable limits the base shear capacity of the structure was found insufficient.
4. Salawu (1997) of natural frequency as Assessment procedures using vibration monitoring is discussed in the paper. The approach is based on the fact that natural frequencies are sensitive indicators of structural integrity. Thus, an analysis of periodical frequency measurements can be used to monitor structural condition.
Since frequency measurements can be cheaply acquired, the approach could provide an inexpensive structural assessment technique. The relationships between frequency changes and structural damage are discussed. Various methods proposed for detecting damage using natural frequencies are reviewed.
Factors which could limit successful application of vibration monitoring to
damage detection and structural assessment are also discussed.
5. Ghodge et al. (2018)
This paper presents the numerical results of Vibration analysis of a cantilever beam with load at the tip and simply supported beam with the center load. Modal analysis of a cantilever beam and simply supported beam were carried out in ANSYS for different materials. The results were compared and it was found that for the same cross-section and for both configurations (i.e. cantilever and simply supported) structural steel gives higher natural frequencies.
6. Dive et al. (2017)
Experimental Modal Analysis (EMA) is a method to predict the behavior of a system by effectively using the modal or vibration data. It helps in understanding and evaluating the dynamic behavior of a system in actual scenario. In this paper, an attempt is made to study the free vibration analysis of the cantilevered beams of different materials and lengths.
The results obtained theoretically are cross checked using the ANSYS simulation package.
7. Vishwarkarma and Bhaskar (2017) In reinforced concrete structures, portions of columns that are common to beams at their intersections are called Beam- Column Joint. Beam-column joint is an important part of reinforced concrete frames in terms of seismic lateral loading.
The two major failure at joints are, joint shear failure and end anchorage failure.
As we know that nature of shear failure is brittle so the structural performance cannot be accepted especially in seismic conditions. This study presents design as well as detailing of beam-column joint of the structure. From this paper we get a review on the behavior of joints under ACI 352R-02 and IS13920:1993 code. Design and detailing provisions on beam-column joints in IS13920:1993 do not adequately address prevention of anchorage and shear failure during severe earthquake shaking. A careful study and understanding of joint behaviour is essential to arrive at a proper judgement of the design of joints. This paper focus on the seismic action on various type of joints and even on the parameters which
Vol.04, Issue 09, September 2019 Available Online: www.ajeee.co.in/index.php/AJEEE affect joints and all component parts will
be check for strength and stability.
8. Mekalke and Sutar (2016)
Structural elements, supporting motors or engines are frequently seen in technological applications. The operation of a machine may introduce additional dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. This paper aims at determining the natural frequencies and mode shapes of a cantilever beam of different material and geometries with different methods. The model allows analyzing the influence of the shear effect and spring-mass systems on the dynamic behavior of the beams by using equation, software and experimentation. The effects of attached spring-mass systems on the free vibration characteristics of the beams are studied.
The natural frequencies of cantilever beam calculated by using equation and compared with the natural frequencies of beam calculated by using software and experimentation, the mode shapes are presented in graphs.
9. Lee et al. (2003)
Most of the building structures consist of structural elements such as beams, columns, braces, shear walls, foundations, and floor slabs. In general, the models used for the analysis of building structures are prepared without the floor slabs assuming that they would have negligible effects on the response of a structure. Therefore, the floor slabs are simply replaced by rigid floor diaphragms for the efficiency in the analysis. Several researchers attempted to study the effects of floor slabs using finite element models with refined plate element meshes to account for the flexural stiffness of floor slabs. Since beams and floor slabs are not located in a common plane, in general, rigid bodies shall be introduced to represent the T-beam effects. Therefore, the model used in the analysis of building structures with floor slabs would have refined finite element meshes with too many degrees of freedom to be used for the practical engineering purpose. The analytical model was proposed in this study for the efficient seismic analysis of building structures considering the
flexural stiffness of the floor slabs. The proposed model employs super elements, rigid diaphragms, and the sub structuring technique to minimize the number of degrees of freedom to be used in the analysis. Analyses of example structures were performed to verify the efficiency and the accuracy of the proposed model in the seismic analysis of multistory building structures. The proposed model could provide seismic response of the example structures in significantly reduced computational times while the accuracy in the analysis results such as vibration periods and response time histories were very close to those obtained from the refined model.
10. Sharma et al. (2011)
Seismic performance of reinforced concrete (RC) framed structure can be assessed with various analytical tools that may broadly be classified as linear elastic procedures and non-linear or inelastic analysis procedures. Since the reinforced concrete structures generally go in the inelastic range due to seismic loading, inelastic procedures predict the performance of the structures in a much better and realistic way than the linear elastic procedures. However, at the same time, the inelastic procedures are computationally much more demanding.
Thus, a good balance between accuracy and computational effort is often sought for. Often, important structures are analyzed using inelastic procedures so that the actual performance of the same can be assessed under earthquakes, whereas less important structures are analyzed using linear procedures. To assess the seismic behavior of RC framed structures, various experimental procedures are used. Monotonic pushover tests give information about the load carrying and deformational capacity of the structure along with sequence of failure modes but only in one direction. Static cyclic tests, where inertia effects are not included give the above mentioned information for to and fro loading direction along with the information on energy consumption. Shake table tests, which are closest to the real life earthquake tests provide almost all the information required to understand the seismic behavior but the scale of such tests are usually limited by the capacity of the shaking table facility.
Vol.04, Issue 09, September 2019 Available Online: www.ajeee.co.in/index.php/AJEEE 11. Jain et al.(2016)
Present study presents comparative analysis of flat slab system and wide beam system in reinforced concrete buildings. The comparison is performed with reference to conventional moment resisting frame. A G+3 building model is selected and is modeled as conventional beam column system, flat slab system and wide beam system. These models are then analyzed for gravity loads and seismic loads. For seismic analysis, two different methods- linear static and linear dynamic are used.
12. Chati et al. (2017)
This paper addresses the problem of vibrations of a cracked beam. In general the motion of such a beam can be very complex. This phenomenon can be attributed to the presence of the nonlinearity due to the opening and closing of cracks. The focus of this paper is the modal analysis of a cantilever beam with a transverse edge crack. The nonlinearity mentioned above has been modeled as a piecewise linear system. In an attempt to define natural frequencies for this piecewise linear system\ the idea of a bilinear frequency is utilized. The bilinear frequency is obtained by computing the associated frequencies of each of the linear pieces of the piecewise linear system. The Finite element method is used to obtain the natural frequencies in each linear region. In order better to understand the essential nonlinear dynamics of the cracked beam\ a piecewise linear two degrees of freedom model is studied. Perturbation methods are used to obtain the non linear normal modes of vibration and the associated period of the motion. Results of this piecewise linear model problem are shown to justify the definition of the bilinear frequency as the natural frequency. It is therefore expected that calculating piecewise mode shapes and bilinear frequencies is useful for understanding the dynamics of the infinite degree of freedom cracked beam.
13. Akbani and Verma (2013)
The presence of microstructural defects such as cracks is known to have resulted in catastrophic failures. These failures lead to enormous loss of resources including human lives. To help prevent such losses, the scientific community has
been studying the mechanics of crack propagation and trying to develop methods for early detection of cracks. Out of the various alternative techniques being explored, study of the impact of crack presence on the flexibility and vibration response of the structural or machine elements has gained popularity in past few decades. It is based on the theory, supported by observations, that the presence of crack in any structure/machine element alters its dynamic response and thus, this change in the response can be used as an indicator to predict presence of cracks. In order to have an insight into the effects of crack on the response parameters, one has to carry out several repeated simulations. Various analytical and numerical methods have been applied by researchers working in this direction. But the usual approach adopted is very tedious and time consuming. In this paper, the authors have applied artificial neural network to a vibration analysis problem of a cantilever beam with surface crack using Finite Element Method (FEM) formulation. The results show that Artificial Neural Network (ANN) helps to reduce the efforts involved in simulations while providing solutions with fairly reasonable accuracy.
14.Sutar (2012)
This paper describes the finite element analysis of a cracked cantilever and analyzes the relation between the modal natural frequencies with crack depth, modal natural frequency with crack location. Also the relation among the crack depth, crack location and natural frequency has been analyzed. Only single crack at different depth and at different location are evaluated. And the analysis reveals a relationship between crack depth and modal natural frequency. As we know when a structure suffers from damage its dynamic property can change and it was observed that crack caused a stiffness reduction with an inherent reduction in modal natural frequencies.
Consequently it leads to the change in the dynamic response of the beam. The analysis was performed using ALGOR software. Modal natural frequency was found to be decreasing with increase in crack depth. And the same was found to be increasing with increase in crack location from the fixed end.
Vol.04, Issue 09, September 2019 Available Online: www.ajeee.co.in/index.php/AJEEE 15. Choudhari and Patil (2016)
Every faulty structure subjected to change in local flexibility which affects vibration response of the structure.
Therefore it is necessary to detect the faults in the structure with its position. In this paper, aluminum un-crack and crack cantilever beam is used for analysis.
Firstly, theoretical calculations had been done to obtain first three natural frequencies by solving the Euler equation for un-crack beam and cracked beam considering various crack positions for the beam. Secondly, static and modal analysis of un-crack and crack beam is performed to find deflection and natural frequencies of beam. Finally, the results are presented in tabular form to show the effect of crack in change of deflection and lower natural frequencies. ANSYS software was used for the analysis of un- crack and crack beam.
16. Waghulde and Kumar (2014)
Vibration analysis of a beam is an important and peculiar subject of study in mechanical engineering. Many developments have been carried out in order to try to quantify the effects produced by dynamic loading. Examples of structures where it is particularly important to consider dynamic loading effects are the construction of tall buildings, long bridges under wind- loading conditions and buildings in earthquake zones, etc. Dynamic structures subjected to periodic loads compose a very important part of industrial machineries. One of the major problems in these machineries is the fatigue and the cracks initiated by the fatigue. These cracks are the most important cause of accidents and failures in industrial machinery. In addition, existing of the cracks may cause vibration in the system. Thus an accurate and comprehensive investigation about vibration of cracked dynamic structures seems to be necessary. On the base of these investigations the cracks can be identified well in advance and appropriate measures can be taken to prevent more damage to the system due to the high vibration level. Typical situations where it is necessary to consider more precisely the response produced by dynamic loading are vibrations due to equipment or machinery, impact load produced by traffic, snatch loading of cranes,
impulsive load produced by blasts, earthquakes or explosions. So it is very important to study the dynamic nature of structures.
17. Batihan (2011)
In this thesis, transverse vibration of a cracked beam on an elastic foundation and the effect of crack and foundation parameters on transverse vibration natural frequencies are studied.
Analytical formulations are derived for a beam with rectangular cross section. The crack is an open type edge crack placed in the medium of the beam and it is uniform along the width of the beam. The cracked beam rests on an elastic foundation. The beam is modeled by two different beam theories, which are Euler-Bernoulli beam theory and Timoshenko beam theory. The effect of the crack is considered by representing the crack by rotational springs. The compliance of the spring that represents the crack is obtained by using fracture mechanics theories. Different foundation models are discussed; these models are Winkler Foundation, Pasternak Foundation, and generalized foundation. The equations of motion are derived by applying Newton's 2nd law on an infinitesimal beam element. Non- dimensional parameters are introduced into equations of motion. The beam is separated into pieces at the crack location. By applying the compatibility conditions at the crack location and boundary conditions, characteristic equation whose roots give the non- dimensional natural frequencies is obtained. Numerical solutions are done for a beam with square cross sectional area. The effects of crack ratio, crack location and foundation parameters on transverse vibration natural frequencies are presented. It is observed that existence of crack reduces the natural frequencies. Also the elastic foundation increases the stiffness of the system thus the natural frequencies. The natural frequencies are also affected by the location of the crack.
18. Ramachandran and Ponnudurai (2017)
If a crack appears in the structure it will cause catastrophic failure in the structure. It also affects natural frequency of the structure. Cracks in the structure are identified early to avoid catastrophic
Vol.04, Issue 09, September 2019 Available Online: www.ajeee.co.in/index.php/AJEEE failure. Changes in vibrational parameters
are required to be analysed to identify the crack. Location and depth of crack are the important parameters to change the vibrational parameters of the structure.
Modal analysis is the most widely used method for crack identification of structures. In this work modal analysis of beam with single edged notch having various depth was done by Finite Element Analysis software ANSYS Mechanical APDL 15.0. Vibrational parameters like mode shape and natural frequency of the beam were found by modal analysis. From these results inferred that the fundamental frequency of the beam reduces when the crack depth increases and it is due to reduction in stiffness of the beam.
19. Quila et al.(2014)
The presence of cracks causes changes in the physical properties of a structure which introduces flexibility, and thus reducing the stiffness of the structure with an inherent reduction in modal natural frequencies. Consequently it leads to the change in the dynamic response of the beam. This paper focuses on the theoretical analysis of transverse vibration of a fixed beam and investigates the mode shape frequency. All the theoretical values are analyzed with the numerical method by using ANSYS software and co relate the theoretical values with the numerical values to find out percentage error between them. Also in this paper, a model for free vibration analysis of a beam with an open edge crack has been presented. Variations of natural frequencies due to crack at various locations and with varying crack depths have been studied. A parametric study has been carried out. The analysis was performed using ANSYS software.
20. Prabhakar (2009)
In the present study, vibration analysis is carried out on a cantilever beam with two open transverse cracks, to study the response characteristics. In first phase local compliance matrices of different degree of freedom have been used model transverse cracks in beam on available expression of stress intensity factors and the associated expressions for strain energy release rates. Suitable boundary conditions are used to find out natural frequency and mode shapes. The results
obtained numerically are validated with the results obtained from the simulation.
The simulations have done with the help of ANSYS software.
21. Meshram and Pawar (2015)
This paper describes finite elemental analysis of a cracked cantilever beam and analyzes the relation between the modal natural frequencies with crack depth, modal natural frequency with crack location. Also the relation among the crack depth, crack location and natural frequency has been analyzed. Only single crack at different depth and at different location are evaluated and the analysis revels relationship between crack depth and modal natural frequency. As we know when a structure suffers from damage its dynamic property can change and it was observed that crack caused a stiffness reduction with an inherent reduction in modal natural frequencies. Consequently it leads to change in dynamic response of the beam. The analysis was performed using ANSYS software. The material of the beam is taken as aluminum. The proposed technique represents actually a modal analysis having great benefits for health monitoring of structures. For this 3D model of cantilever beam with single crack is created in ANSYS. Total 49 model of crack cantilever beam has been analyzed. Thus result obtained from ANSYS software we can draw the graph of modal natural frequency Vs crack depth for constant crack location and modal natural frequency Vs crack location keeping crack depth constant. And finally the value obtained from ANSYS is checked with result obtained from analytical method.
22. Yamuna and Sambasivarao (2014) The importance of the beam and its engineering applications is obvious, and it undergoes different kinds of loading. Such loading may cause cracks in the beam.
Crack depth and location are the main parameters for the vibration analysis of such beams. These cracks and their locations effect on the shapes and values of the beam frequency. So it becomes very important to monitor the changes in the response parameters of the beam to access structural integrity, performance and safety. In the current work, the natural frequency of a simply supported beam with a triangular crack, is
Vol.04, Issue 09, September 2019 Available Online: www.ajeee.co.in/index.php/AJEEE investigated numerically by finite element
method using of FE analysis software ANSYS. Different crack location effects are considered and the results are compared with that of the simply supported beam without crack. The results obtained from the vibration analysis of the beam show that the lowest fundamental frequency of the beam without crack is higher than the lowest frequency obtained for beam with cracks. When the location of the crack varies from the either end of the simply supported beam to the centre of the beam the lowest natural frequency decreases.
23. Al-Waily (2013)
In this research the natural frequency of a cracked beam with different supported, simply and clamped beam, is investigated analytically and numerically by finite element method with using of ANSYS program ver. 14 with different crack depth and location effect and the results are compared. The analytical results of the effect of a crack in a continuous beam are calculated the equivalent stiffness, EI, for a rectangular beam to involve an exponential function with depth and location of crack effect, with solution of assuming equivalent stiffness beam (EI) by using of Fourier series method. And, the beam materials studied are low carbon steel, Alloys Aluminium, and Bronze materials with different beam length and depth. A comparison made between analytical results from theoretical solution of general equation of motion of beam with crack effect with numerical by ANSYS results, where the biggest error percentage is about (1.8 %).
Also it is found that the frequency of beam when the crack is in the middle position is less than the frequency with crack near the end position and the natural frequency of beam decreasing with increasing of crack depth due to decreasing of beam stiffness at any location of crack in beam.
24. Jagdale & Chakrabarti (2013) The presence of cracks causes changes in the physical properties of a structure which introduces flexibility, and thus reducing the stiffness of the structure with an inherent reduction in modal natural frequencies. Consequently it leads to the change in the dynamic response of the beam. In this paper, A model for free vibration analysis of a beam with an open
edge crack has been presented. Variations of natural frequencies due to crack at various locations and with varying crack depths have been studied. A parametric study has been carried out. The cracked beams with different boundary conditions have been analyzed. The results obtained by experiments performed by previous studies are compared with those obtained by finite element analysis. The analysis was performed using ABAQUS software.
25. Mao (2016)
The Adomian decomposition method (ADM) and high-pass filters are employed in this study to investigate the free vibrations and damage detection of cracked Euler-Bernoulli beams. Based on the ADM and employing some simple mathematical operations, the closed-form series solution of the mode shapes can be determined for beams consisting of an arbitrary number of cracks under general boundary conditions in a recursive way.
Then, a highpass filter is used to extract the irregularity profile from the corresponding mode shape. The location and size of the cracks in the beam can be determined by the peak value of the irregularity profile. The numerical results for different locations and depths of cracks on the damaged beam under different boundary conditions are presented. The results show that the proposed method is effective and accurate. The experimental work for aluminium cantilever beams with one and two cracks was performed to verify the proposed method. The successful detection of cracks in the beam demonstrates that the proposed method has great potential in crack detection of beam-type structures, as it is simple and does not require the mode shapes of an uncracked beam as a baseline.
26. Mazaheri et al. (2018)
In this paper, a simple method for defining the effects of cracks on elastic behavior of beam is presented. The cracked sections were modeled as rotational springs and the problem was solved using the finite element method.
The global stiffness matrix of a beam with multiply cracked section was then assembled. For calculation of rotational spring stiffness equivalent to uncracked and cracked sections, finite element models and experimental test were used.
Vol.04, Issue 09, September 2019 Available Online: www.ajeee.co.in/index.php/AJEEE The natural frequencies and mode shape
of beams with multiple single-edge cracks were obtained and a new simple formula was proposed. Published numerical examples for cracked beams were used for validation.
27. Banerjee & Pohit (2014)
Cracks reduce the service life of structures. A crack in a structural member introduces local flexibility that would affect vibration response of the structure. Both the mode shape and frequency change significantly due to the presence of crack. The objective of this paper is to obtain information about the location and depth of transverse open multiple cracks in a rotating cantilever beams. Vibration parameter in the form of mode shape of damaged rotating beam is obtained using finite element simulation.
Using fractal dimension of mode shape profile, damage is detected. It is also shown that this method can produce satisfactory results with some limitation based on profile.
28. Nobile and Viola (2001)
In this paper, a finite element model for a cracked prismatic beam, under bending moment, axial and shear forces, is developed. The stiffness matrix is derived starting from an integration of stress intensity factors. Translational and rotational mass matrices are the same both for cracked and uncracked Timoshenko beam finite element. The stiffness matrix of the cracked element can be used in any finite element formulation to study static and dynamic behaviour of cracked structures. In the present study the transverse crack has been considered as open.
29. Mia et al. (2017)
Any structure in presence of crack is susceptible to failure depending on the mode of vibration. Failure is due to the resonance formed by the superposition of frequency of periodic force acting on structure and the natural frequency of the structure. To be alert about resonance due to periodic load, it is important to determine natural frequency. In this study of modal analysis, natural frequency and mode shapes of transverse vibration for both un-cracked and cracked cantilever beam has been extracted for first three modes. The analysis has been
extended to investigate the effect of crack opening size and mesh refinement. For cracked beam, analysis is performed for various crack depth and crack location.
As structural discontinuity problems are difficult to solve analytically, leading commercial Finite Element Analysis software Abacus is used to perform all the analysis computationally. For modeling un-cracked beam, hexahedral element is used whereas for cracked beam modeling, both hexahedral and wedge elements are selected for better result. In our study we observed that natural frequency reduces with the presence of crack. The amount of reduction varies depending on crack location, depth and crack opening size.
Non-dimensional representation highlights that failure criteria largely depend on mode of vibration. The findings of this study can be applied to predict the structural sustainability under varying loads.
3 GAPS IN THE RESEARCH AND OBJECTIVES OF PROPOSED RESEARCH
Following section is devoted to gaps in the research and objectives of the proposed research, the details of which are presented as follows:
i. Gaps in the Research
Following are the research gaps investigated.
a) There is very limited research which focuses on modal analysis of cracked concrete beams;
b) There is very limited research work which tells about rankings of crack locations in the concrete beams.
ii. Objectives of the Research
Following are the objectives of present research work.
a) Modal analysis of cracked concrete beams; and
b) Rankings of cracked beams with respect to crack locations.
4 CONCLUSIONS
Present research work is devoted to academic aspects of the research work and investigates gaps in the research.
Considering the contributions and practical applications of the targeted system, a new research may be expected in this field.
Vol.04, Issue 09, September 2019 Available Online: www.ajeee.co.in/index.php/AJEEE REFERENCES
1. Heydari, M., Ebrahimi, A., & Behzad, M.
(2014). Forced vibration analysis of a Timoshenko cracked beam using a continuous model for the crack. Engineering Science and Technology, an International Journal, 17(4), 194-204.
2. Biondini, F. (2004, August). A three- dimensional finite beam element for multiscale damage measure and seismic analysis of concrete structures. In 13th World Conference on Earthquake Engineering (pp. 1- 6). Vancouver, BC,, Canada: Paper No. 2963.
3. Shahnewaz, M., Rteil, A., & Alam, M. (2012, June). Seismic Effects on Deep Beams in a Reinforced Concrete Building. In 3rd International Structural Specialty Conference.
4. Salawu, O. S. (1997). Detection of structural damage through changes in frequency: a review. Engineering structures, 19(9), 718- 723.
5. Ghodge, V., Bhattu, A. P., & Patil, S. B.
(2018). Vibration Analysis of Beams.
International Journal of Engineering Trends and Technology (IJETT) – Volume 55 Number 2, 81-86.
6. Vikas Dive, Mayur Bhosale, Vipil Chavan, Niranjan Durugkar (). Analysis of Natural Frequencies of Cantilever Beam Using ANSYS. International Research Journal of Engineering and Technology, 4 (5), 2724- 2728. Anant S. Vishwakarma, Gitadevi Bhaskar (2017). Analysis of Beam-Column Joint subjected to Seismic Lateral Loading” – A Review. International Research Journal of Engineering and Technology, 4 (11), 1350- 1353.
7. Lee, D. G., Ahn, S. K., & Kim, D. K. (2003).
An Efficient Model for Seismic Analysis of Building Structures with The Effect of Floor Slabs. In 7th Pacific Conference on Earthquake Engineering-7PCEE.
8. Akanshu Sharma1, G.R. Reddy, R.
Eligehausen, J. Hofmann, K.K. Vaze (2011).
Transactions, SMiRT 21, 6-11 November, 2011, New Delhi, India.
9. Mohit Jain, Sudhir S. Bhadauria, Danish Khan (2016). Seismic analysis of flat slab and wide beam system. American Journal of Engineering Research 5 (10), 91-95.
10. Chati, M., Rand, R., & Mukerhjee, S. (1997).
Modal analysis of a cracked beam. Journal of sound and vibration, 207(2), 249-270.
11. Akbani, I., & Varma, I. Dynamic Analysis of a Structural Beam with Surface Crack Using Artificial Neural Network. International Journal of Scientific & Engineering Research Volume 6, Issue 5, 1975-1979.
12. Sutar, M. K. (2012). Finite element analysis of a cracked cantilever beam. International Journal of Advanced Engineering Research and Studies, 1(2), 285-289.
13. Chaudhari, J. R., & Patil, C. R. (2016). Study of Static and Modal Analysis of Un-Crack and
Crack Cantilever Beam Using
FEA. International Journal of Engineering Research and Technololgy, 5(4), 534-542.
14. Waghulde, K. B., & Kumar, B. (2014).
Vibration analysis of cracked cantilever beam
with suitable boundary
conditions. International Journal of Innovative Science, Engineering and Technology, 1(10), 20-24.
15. Kumar, A., & Kumar, V. Numerical Analysis of Crack Effect on Natural Frequency of Cantilever Composite Beam. International Journal of Engineering Research, 1 (3), 1-6.
16. Al Çagri Batihan (2011). Vibration analysis of cracked beams on elastic foundation using Timoshenko beam theory (Doctoral dissertation, Middle East Technical University).
17. Ramachandran, C., & Ponnudurai, R. (2017).
Modal Analysis of Beam with Varying Crack Depth. International Journal of Engineering Research and Technololgy, 452-458.
18. Quila, M., Mondal, S. C., & Sarkar, S. (2014).
Free Vibration Analysis of an Un-cracked &
Cracked Fixed Beam. Journal of Mechanical and Civil Engineering, 11(3), 76-83.
19. Prabhakar, M. S. (2009). Vibration analysis of cracked beam. Master Thesis, National Institute of Technology Rourkela, Rourkela.
20. Meshram, N. A., & Pawar, V. S. (2015).
Analysis of crack detection of a cantilever
beam using finite element
analysis. International Journal of Engineering Research & Technology, 4(04).
21. Yamuna, P., & Sambasivarao, K. (2014).
Vibration analysis of beam with varying crack location. International journal of engineering research and general science, 2(6), 1008-17.
22. Al-Waily, M. (2013). Theoretical and Numerical Vibration Study of Continuous Beam with Crack Size and Location Effect. International Journal of Innovative Research in Science, Engineering and Technology, 2(9), 4166-4177.
23. Jagdale, P. M., & Chakrabarti, M. A. (2013).
Free vibration analysis of cracked beam. Int.
J. Eng. Res. Appl, 3, 1172-1176.
24. Mao, Q. (2016). Vibration analysis of cracked beams using Adomian decomposition method and non-baseline damage detection via high- pass filters. International Journal of Acoustics and Vibration, 21(2), 170-177.
25. Mazaheri, H., Rahami, H., & Kheyroddin, A.
(2018). Static and Dynamic Analysis of Cracked Concrete Beams Using Experimental Study and Finite Element Analysis. Periodica Polytechnica Civil Engineering, 62(2), 337-345.
26. Banerjee, A., & Pohit, G. (2014). Crack investigation of rotating cantilever beam by fractal dimension analysis. Procedia Technology, 14, 188-195.
27. Nobile, L., & Viola, E. (2001). Cracked beam element formulation for structural analysis. Transactions, SMiRT, 16.
28. Mia, M. S., Islam, M. S., & Ghosh, U. (2017).
Modal Analysis of Cracked Cantilever Beam by Finite Element Simulation. Procedia engineering, 194, 509-516.
