Crack Detection Of Simply Supported Beam Using Dynamic Analysis

Transcription

1 International Journal of Technical Research an Applications e-issn: , Volume 3, Issue4 (July-August 205, PP Crack Detection Of Simply Supporte Beam Using Dynamic Analysis Reshmi Revi, Inu. V. S. 2 PG Stuent, 2 Assistant Professor, Civil Engineering Department Sree Buha College of Engineering, Pattoor, Noorana, Alappuzha, Kerala, Inia revi.reshmi90@gmail.com 2 inhuunnithan@gmail.com Abstract This paper eals with a methoology for the use of ynamic response as an inspection an surveillance tool for the amage in a structure. The metho is base on finite element iscretisation to ientify the stiffness characteristics (relate to cracking starting from moal ynamic parameters (natural frequency an moe shape erive from ynamic tests. Any amage in the structure alters its ynamic characters. The amage reuces the stiffness of the structure an increases its amping value, at the same time it will ecrease the natural frequency an the corresponing moe shape changes. The present thesis work aims at etecting the cracks of a simply supporte beam an to stuy the effects of cracks in its ynamic characteristics. The beam use here is a Reinforce Concrete Simply Supporte Beam. Crack is inuce by applying incremental. Curvature Factor (CDF using curvature moe shape was use to locate the amage positions. Keywors: Crack Detection, Simply Supporte Beam, Dynamic Analysis, Curvature moe shape, Curvature Factor, Ansys I. INTRODUCTION Engineering structures uner repeating ing conitions unergoes amage or crack in overstresse zones. The presence of cracks in a structural member such as beam causes the reuction in stiffness of the structure which in turn mainly epens on the location an epth of the cracks. These variations in turn have a significant effect on the vibrational behaviour of the entire structure. To ensure the safety of the structures, it is important to know whether their members are free of cracks an shoul any be present, to etect their location an provie safety measures. Any amage in a structure alters its ynamic characteristics or the moal parameters such as natural frequency, associate moe shapes an amping values. The amage reuces the stiffness of the structure an increases the amping value. The reuction in stiffness is associate with ecrease in natural frequencies an changes in corresponing moe shapes. The moe shape of the amage structure may seem to be similar as the moe shape of the unamage structure. But the erivatives of the moe shapes show a iscontinuity at the amage location. This hien feature of the moe shape gives the motivation to use it as a amage etection tool. Cracks occurring in structural elements are responsible for local stiffness variations, which in consequence affect their ynamic characteristics. This problem has been a subject of interest for the past few years. Curvature moe shape metho is use as a amage etection tool in this thesis work. Finite element analysis of the Reinforce concrete simply supporte beam was one in Ansys to obtain the isplacement moe shapes of the moels. The ynamic properties of a amage structure an an unamage structure are compare. A. Moelling of Beam II. FINITE ELEMENT MODELLING The selection of finite element moel to simulate the response of a structure is very important task in any analysis. The Finite Elemental Metho (FEM iscretize the structure into a iscrete number of elements from which an approximate numerical solution is obtaine. With the easy of simulating the mathematical moel in FEM on personal computer, this approach provies an accurate solution for many structural analysis problems. The accuracy of result epens on the selection of suitable elements with the appropriate material characteristics moelling. In this paper simply supporte beam was moelle using the FEM with the commercial software package ANSYS. The material property assigne for the simply supporte beam is given in Table I. TABLE I. MEMBER PROPERTY OF THE MATHEMATICAL MODEL er al Memb Materi Beam Length 3.23m Reinforce concrete 279

2 International Journal of Technical Research an Applications e-issn: , Volume 3, Issue4 (July-August 205, PP With 0.5m Depth 0.3m Concre te Eleme Concre nt type te 65 Poisso n s ratio Mass ensity Moul us of elasticity Reinforce ment bar kg /m GPa B. Moelling of s Link kg/m GPa There are a number of approaches to moel amage in a mathematical moel. Although the geometry of the amage can be very complicate, the conition is that for lower frequency vibration only an effective reuction in stiffness is require. Thus for comparison, a simple moel of a amage is require. can be introuce into the finite element moel by applying incremental. III. DYNAMIC ANALYSIS USING ANSYS A ynamic analysis is first performe for beam with self weight only. The frequency an moe shapes are rea from the analysis. This test results serves as a reference for later comparison of ynamic characteristics at the ifferent amage stages. Then ynamic analysis is performe by applying incremental. After each ing phase, the beam is une, an the ynamic analysis is performe. Formation of crack can also be seen in this analysis. IV. LOCATING THE DAMAGES BY USING MODE SHAPE CURVATURE AND CURVATURE DAMAGE FACTOR It is likely that amage inicators base on erivatives of the moe shape will amplify the localize amages in a structure.the curvature moe shape has emerge as one of the best way to amplify the effect of the amage on the moe shape. The curvature moe shapes are base on flexural stiffness of the beam cross section. Base on beam theory the curvature at a point in the beam is given by V = M / (Ebxx Iyy Where M is the bening moment at the section an (Ebxx Iyy is the flexural stiffness of the beam. The presence of amage in a beam at a given location reuces the flexural stiffness of the beam an hence increases the magnitue of curvature at the amage location. Typically amages occurre ue to impact an are likely to be localize at some point in the structure. The changes in curvature are local in nature an can be use to fin the amage location in the beam. To obtain curvature moe shape of a amage beam finite element analysis is one to get the isplacement moe shape. Then using isplacement moe shape, curvature moe shapes are obtaine numerically by a central ifference approximation as: V i,j = Φ (i+,j-2φ i,j+φ (i-,j he 2 Where Vi,j represents curvature moe shape, subscript i represent the noe number an subscript j represents the moe represents the mass normalize isplacement moe shape for the ith moe shape. Absolute ifference in curvature moe shape between amage an unamage structure is obtaine as; Δ V i,j = V i,j ( - V i,j (u The Curvature Factor (CDF is obtaine by averaging the first few curvature moe shape. In general CDF of ith noe is obtaine by consiering the first n curvature moe shape an is given as; CDF i = The CDF at each noe is obtaine by consiering the first five curvature moe shape. With increase in amage ensity, the peak magnitue of CDF at the amage location also increases an hence inicates the extent of amage. V. RESULTS AND DISCUSSIONS The results obtaine from the two beams were compare. The control beams (Un- amage state provies the reference reaings which form the basis of the comparison of the moal parameters obtaine in successive amage states as escribe below. A. Natural Frequency When a system is subjecte to certain egree of amage or eterioration, it experiences a change in stiffness. Subsequently it causes the natural frequency to change. The magnitue of the changes is also an inicator of the severity or state of the amage experience. This is apparent in the changes in the natural frequencies of the amage beams as compare to the control beam. The values of natural frequencies for the test beams are tabulate in Table II, Table III an in Table IV. TABLE II: CHANGE IN NATURAL FREQUENCIES OF BEAM FOR MODE Loaing conitions 280

3 International Journal of Technical Research an Applications e-issn: , Volume 3, Issue4 (July-August 205, PP Loa only Unam age + Live Freque ncy (Hz Decre ase (% Loa only Unam age + Live Frequ ency (Hz se Decrea (% TABLE III: CHANGE IN NATURAL FREQUENCIES OF BEAM FOR MODE 2 Loaing conitions Loa only Unam age + Live 2 Freque ncy (Hz Decre ase (% B. Moe shapes A moe shape is a specific pattern of vibration execute by a mechanical system at a specific frequency. Different moes will be associate with ifferent frequencies. The moe shapes of test beams are shown below. Fig.. Moe shape of unamage beam TABLE IV: CHANGE IN NATURAL FREQUENCIES OF BEAM FOR MODE 3 Loaing conitions 3 Fig. 2. Moe shape 2 of unamage beam 28

4 International Journal of Technical Research an Applications e-issn: , Volume 3, Issue4 (July-August 205, PP C. Difference in Curvature Moe Shape Locating the amage positions using Difference in Curvature Moe Shape, 2, an 3 of ing conition are shown in Figure. 7, 8, an 9. Fig. 3. Moe shape 3 of unamage beam Fig. 7. Difference in curvature moe shape Fig. 4. Moe shape of beam at amage conition Fig. 8. Difference in curvature moe shape 2 Fig. 5. Moe shape 2 of beam at amage conition Fig. 9. Difference in curvature moe shape 3 D. Curvature Factor Locating the amage positions using Curvature Factor for ing conition are shown in Figure. 0. Fig. 6. Moe shape 3 of beam at amage conition 282

5 International Journal of Technical Research an Applications e-issn: , Volume 3, Issue4 (July-August 205, PP VII. ACKNOWLEDGMENT First an foremost, I woul like to thank the Almighty go who blesse me to overcome all the obstacles I came across while proceeing with this thesis. I am eeply inebte to my thesis guie Mrs. Inu. V. S, Assistant Professor, Department of Civil Engineering, Sree Buha College of Engineering for her sincere guiance, timely help an much appreciate correction uring every step of this work. Finally, yet importantly, I woul like to express my heartfelt thanks to my belove parents for their blessings, an my friens for their help an wishes for successful completion of this thesis. Fig. 0. Curvature amage factor for ing conition VI. CONCLUSIONS The purpose of the current stuy is to obtain the ynamic behaviour of Reinforce concrete beam uner various amage conitions. s are introuce by applying incremental an ynamic analysis is one. Moe shape curvature metho is use for locating crack in the beam. Base on the results, the following conclusions can be erive: As amage level on the beams increase, Natural frequency ecrease. Moe shape curvature metho using curvature amage factor is an effective metho for locating cracks. The numerical results show the high efficiency of the propose metho for accurately locating structural amages. Dynamic analysis is an economical an time saving metho than experimental metho for crack etection. Preiction of formation an location of crack can be one before casting. REFERENCES [] L.S. Srinath, Avance Mechanics of Solis, thir eition, Tata McGraw Hill Eucation private Limite, 20, pp [2] Dr. R. K. Bansal A text book of Strength of Materials revise fourth eition, Laxmi publications (P Lt, 20, pp - 0. [3] D. R. Prasa, an D. R. Sheshu, Stuy on change in moal parameters of RC beams ue to fatigue type amage Asian Journal of Civil Engineering(Builing an Housing Vol, NO 4 (200 pages [4] X. Wang a,n. Hu b, Hisao Fukunaga b, an Z.H. Yao. A Structural amage ientification using static test ata an changes in frequencies, Engineering Structures 23 (200, pp [5] Paney, A.K., Biswas, M an Samman, M.M. (99. etection from changes in curvature moe shapes, Journals of Soun an Vibration,45(2: [6] Wolff, T. An Richarson, M. (989. Fault etection in structures from changes in their moel parameters, proceeings of the 7 th International Moal Analysis Conference, Las Vegas, Nevaa, USA, pp,