VOLUME: 09, Issue 06, Paper id-IJIERM-IX-VI, December 2022 93 A STUDY BASED ON A CRACKED CONCRETE BEAM
Mr. M. Naresh
Asst. Prof., Civil Engg., Princeton Institute of Engg. and Technology for Womens, Hyderabad
Mr. Md. Nazeem
Asst. Prof., Civil Engg., Princeton Institute of Engg. and Technology for Womens, Hyderabad
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.
1 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
VOLUME: 09, Issue 06, Paper id-IJIERM-IX-VI, December 2022 94 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..
2. Biondini (2004)
The paper presents a three- dimensional finite beam element for damage evaluation and seismic analysis of concrete 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.
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.
4.Salawu (1997)
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
VOLUME: 09, Issue 06, Paper id-IJIERM-IX-VI, December 2022 95 structural assessment technique.
The relationships between frequency changes and structural damage are 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.
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.
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.
9. Lee et al. (2003)
Most of the building structures consist of structural elements such
VOLUME: 09, Issue 06, Paper id-IJIERM-IX-VI, December 2022 96 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.
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.
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
VOLUME: 09, Issue 06, Paper id-IJIERM-IX-VI, December 2022 97 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.
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.
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.
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.
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
VOLUME: 09, Issue 06, Paper id-IJIERM-IX-VI, December 2022 98 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.
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.
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 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.
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.
VOLUME: 09, Issue 06, Paper id-IJIERM-IX-VI, December 2022 99 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.
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.
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 CONCLUSION
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.
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