Damage Detection of Bridges by Using Displacement文明的故事
Data of Two Symmetrical Points世界上最美的离别
Yi-Lin Wang 1;Xi-La Liu,M.ASCE 2;and Cong-Qi Fang 3
Abstract:This paper investigates new damage detection method for bridges to ensure their safety.The idea of using displacement data of two symmetrical points for multiple damage detection is prented for the first time.After introducing the concept of Equivalent Element,a novel index termed as “Symmetrical Displacement Difference Index (SDDI),”is propod.The displacement under static load is ud for constructing the new index.Then the relationship between the local flexural stiffness change caud by damage and SDDI value is generated.In application,SDDI values can be plotted after the measurement of displacement.The relative changes between the intact state and the damage state in the curve shapes can be ud to indicate the position of damage.This new damage detection method bad on SDDI is flexible enough to be applied to real-world bridges with inherent random uncertainty and actual support condition.Numerical and experimental examples have been conducted to examine the suitability of the method.This paper provides a simple,convenient,cost-effective,and nondestructive damage detection method for bridges.DOI:10.1061/(ASCE)CF.1943-5509.0000240.©2012American Society of Civil Engineers.
CE Databa subject headings:Damage;Displacement;Data analysis;Bridges;Structural safety;Static loads.Author keywords:Damage;Detection;Static;Symmetrical;Displacement.
Introduction
Bridges are widely ud in society.Most of them are easily expod to unforeen defects both internally and externally.Therefore,various types of damage may occur in the different regions of the bridge.Reliable and efficient damage detection techniques for existing bridges are esntial to safe operation,cost reduction,and failure prevention.The interest in detecting and locating dam-age at the earliest possible stage has become more and more per-vasive in engineering communities over the last three decades.Damage is considered to be a weakening of the structure that negatively affects its performance and can be defined as any deviation in the structure ’s original geometric or material properties that may cau undesirable stress,displacements,or vibrations on the structure.The weakenings and deviations may be due to cracks,corrosion,fatigue,and so on.In all the cas,damage can verely affect safety and rviceability of the bridges.
Although complex phenomena occur when bridges are dam-aged,the prence of damage is usually expresd by the reduction of flexural stiffness.The assumption is very popular in prent stud-ies (Guo and Li 2009;Chen 2008;Perera et al.2008;Curadelli et al.2008).
This paper attempts to provide a new effective and practical damage detection method for bridges.Finding and testing a proper index for damage detection should be a priority over other work.Over the past few years,considering the complexity of structural behavior and variety of the parameters involved,many indices and corresponding methods have been propod.
One category of indices in common u are vibration-bad in-dices, e.g.,natural frequencies (Morassi 2007),modal shapes (Huth et al.2005),damping (Curadelli et al.2008),modal-shape curvatures (Reynders et al.2007),strain modal (Li et al.2002),and frequency respon function (Liu et al.2009).Although some of the indices have been ud in practical cas,there are four significant limitations associated with the application of the methods in the field:(1)The number of instrumented points is gen-erally limited.Moreover,it is usually extremely difficult to accu-rately measure the needed values using currently available nsor technology;(2)Information from small or even medium levels of damage is usually masked by the noi embedded in measured sig-nals (Trentadue et al.2007);(3)Another difficulty is attributed to extremely low modal nsitivities of the bridge damage (Alvandia and Cremona 2006);(4)Environmental effects such as temperature may induce changes in the measured data that make damage de-tection very difficult (Kim et al.2007).Though intelligent comput-ing techniques with pattern-recognition capability,such as neural
networks (Yeung and Smith 2005)and genetic algorithms (Perera et al.2009)are being adopted more and more frequently as an as-sistant tool of the indices,the above disadvantages cannot be overcome drastically.
Another significant index category is bad on static displace-ment.Corresponding methods are associated with obrved static displacements under prescribed loads.For example,“Partial Eigenstructure Assigned Method ”was prented to identify the parameters of damaged structures by treating the damage detection problem as an optimization task (Feng 2002).Nonlinear regulari-zation and adaptive substructure techniques were introduced to modify the structure model to detect damage.The statistical
1Ph.D.Candidate,Dept.of Civil Engineering,Shanghai Jiaotong Univ.,No.800Dongchuan Rd.,Shanghai 200240,P.R.China (corresponding author).E-mail:xgwang_ 2
Professor,Dept.of Civil Engineering,Shanghai Jiaotong Univ.,No.800Dongchuan Rd.,Shanghai 200240,P.R.China.E-mail:xilaliu@tinghua.edu 3
Associate Professor,Dept.of Civil Engineering,Shanghai Jiaotong Univ.,No.800Dongchuan Rd.,Shanghai 200240,P.R.China.E-mail:cqfang@sjtu.edu
Note.This manuscript was submitted on May 16,2010;approved on April 14,2011;published online on April 15,2011.Discussion period open until November 1,2012;parate discussions must be submitted for individual papers.This paper is part of the Journal of Performance of Constructed Facilities ,V ol.26,No.3,June 1,2012.©ASCE,ISSN 0887-3828/2012/3-300–311/$25.00.
D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y C h o n g q i n g U n i v e r s i t y o n 12/30/12. C o p y r i g h t A S C
E .
F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .
distribution of local stiffness change was acquired by means of data perturbation.The probability of damage occurrence and damage extent in a statistical n could then be ascertained using hypoth-esis testing (Yeo et al.2000;Jang et al.2002).However,while val-ues for static displacement are available at every node in theoretical or numerical simulations,this is typically not the ca in practice.In practical cas,the number of instrumented points is limited,which can significantly reduce the effect of the methods.
Therefore,the problem of finding a more proper index that can reflect the real damage situation of in-rvice bridges remains a challenge.In this paper,a new index bad on static displacement measurement,which is termed as “Symmetrical Displacement Difference Index (SDDI),”will be propod for damage detection of bridges.This index is evidently worthy of interest becau that static displacement measurement is in many cas easier to perform in the field than dynamic characterization of bridge.The study will be carried out to detect the damage-caud local stiffness change by employing displacement data of only two symmetrical points.The feasibility of the propod strategy will be demonstrated through numerical simulation and actual experiments.
Equivalent Element Concept
Generally,three parameters are needed to show the feature of dam-age:x denotes the distance between the damage region and the bridge end,while y denotes the length of the damage region,and z denotes the damage extent:the bending stiffness EI of the damage region,upon the occurrence of damage,becomes zEI .The problem of damage detection thus can be reduced into deter-mining three parameters x ,y ,and z by various means.
It is a heuristic that if we rearrange the damage region in the analytical model of bridge,y in fact can
表示感谢的图片be considered as a con-stant m .The values x and z will then be modified as x 0and z 0accordingly.This kind of transformation can be schematically shown in Fig.1.For example,if we lect m as 1m,a damage with y ¼0:2should be spread within this new region and z ¼0:8will be changed into z 0¼0:96½ð0:2×0:8Þþð0:8×1Þ .It is emphasized that this assumption does not signify that the real damage situation has to be uniform within the element.
数学试卷分析怎么写Other parts of bridge can also be divided by the length m .Then the whole bridge will be partitioned into a number of elements by keeping the length of element m constant.Therefore,this concept can be called Equivalent Element.
This kind of processing does not change the real state of the structure,but it can bring much convenience to the subquent analysis and calculation.Bad on this concept,the following
analysis will reveal information about the damage that occurred in between two element boundaries in an averaged,integral n.Only two unknown parameters,x 0and z 0,are then needed to be solved.
Obviously,the determination of the x 0value is more important than that of the z 0value in practical cas.With a known value of x 0,the damage region can be regarded as a value range [x 0,x 0þm ]a
nd then inspection means are utilized to find the real damage situation within this small region.A wide variety of highly effective non-destructive methods such as ultrasound,eddy-current,acousto-ultrasonic,guided ultrasonic wave,Lamb wave,and X -and gamma-ray inspections have been currently available for the detec-tion of defects.For example,image analysis can provide informa-tion about surface damages;ultrasonic can lead to the detection of voids or other internal defects.
In addition,it should be noted the lection of the m value has an impact on the final solution directly.The optimal value of m is application-dependent.In practical cas,the best way to choo m is to start with a large value and then,depending upon the experience and the result of preliminary inspection,reduce the value of m .
Theoretical Formulation for Simply Supported Bridge
At the beginning,a simply supported single-span bridge is studied to spearhead the introduction of the new index.In addition,the midspan point,which can be en as a special kind of two symmetrical points,is studied first.The midspan point can be en as a special kind of point where two symmetrical points overlap each other.Methodology
The first step is to discretize the whole length of a bridge into a number of regions with the same len
gth as m by resorting to the concept of Equivalent Element.Then a kind of load (e.g.,concen-trated load)can be put and travels on this bridge.Attention is paid to the corresponding midspan point displacement change induced by the load when it occurs on each boundary of equivalent element.Fig.2shows a bridge under an intact state,the incremental val-ues of midspan point displacement follow a symmetrical pattern when a concentrated load F travels from one side to the other side of the bridge.For example,when F occurs at the position denoted as 1,the midspan point displacement incremental value is equiv-alent to the ca when F occurs at the symmetrical position 1′.The same rule can be extended to the rest equivalent element boundaries.
When damage occurs,further analysis should be carried out bad on Fig.3.
When F occurs at x 1¼x 0(x 1is the distance between F and the left end of bridge),Eq.(1)can be obtained bad on the Virtual Work
Principle
Fig.1.Sketch of equivalent
element Fig.2.Analytical model of simply supported bridge
D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y C h o n g q i n g U n i v e r s i t y o n 12/30/12. C o p y r i g h t A S C
E .
F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .
EI Δωx 0¼
Fl 2x 016ÀFx 0ðm þx 0Þ24þFx 0ðm þx 0Þ3þFx 03ðl Àx 0Þ
6l
À
Fmx 0ð2m 2þ6mx 0À3lm þ6x 02À6lx 0Þ12lz 0
ð1Þ
Where l is the whole length of bridge.
Becau common bridges are not deep beam bridges,shear de-formation is a minor factor that can be considered negligible in the analytical process.
When F occurs at x 1¼l Àx 0,the corresponding midspan point
displacement incremental value is denoted by Δω
x 0,which can be solved as
EI Δωx 0¼ Fx 03
l 6l þ
Fx 0ð3l 3À12lx 02À8m 3À24m 2x 0À24mx 02Þ48l
þ
Fmx 0ðm 2þ3mx 0þ3x 02Þ6lz 0
ð2Þ
_Δω
x 0,the difference between Δωx 0and Δωx 0,is reprented as _Δω
x 0¼Δωx 0À Δωx 0
¼
Fmx 0ðz 0À1Þð4m 2þ12mx 0À3lm þ12x 02À6lx 0Þ12EIz 0l
ð3Þ
When F occurs at x 1¼x 0Àm and the corresponding symmetrical position
Δωx 0Àm , Δω
x 0Àm can be obtained similarly as above and then _Δω
x 0Àm is solved as _Δω
x 0Àm ¼Fm ðx 0Àm Þðz 0À1Þð4m 2þ12mx 0À3lm þ12x 02À6lx 0Þ12EIz 0l
ð4Þ
When F occurs at x 1¼x 0À2m and the corresponding symmetrical position
_Δω
x 0À2m can be solved as _Δω
x 0À2m ¼Fm ðx 0À2m Þðz 0À1Þð4m 2þ12mx 0À3lm þ12x 02À6lx 0Þ12EIz 0l
ð5Þ
When F occurs at x 1¼x 0À3m and the corresponding symmetrical position
_Δωx 0À3m can be solved as _Δωx 0À3m ¼
Fm ðx 0À3m Þðz 0À1Þð4m 2þ12mx 0À3lm þ12x 02À6lx 0Þ0ð6ÞThen
_Δω
x 0À_Δωx 0Àm ¼_Δωx 0Àm À_Δωx 0À2m ¼_Δωx 0À2m À_Δωx 0À3m ¼
Fm 2ðz 0À1Þð4m 2þ12mx 0À3lm þ12x 02À6lx 0Þ
12EIz 0l
ð7Þ
Subquently,the right side of the equivalent damage element is considered.When F occurs at x 1¼x 0þm and the corresponding symmetrical position
_Δω
x 0þm À_Δωx 0¼
Fm 2ðz 0À1Þð4m 2þ12mx 0À2lm þ12x 02À3lx 0Þ12EIz 0l ð8Þ
A comparison of Eq.(7)with Eq.(8)gives
ð_Δ
ωx 0þm À_Δωx 0ÞÀð_Δωx 0À_Δωx 0Àm Þ¼Fm 2ðz 0À1Þðm þ3x 0
Þ12EIz 0
ð9Þ
The above results motivate a new index,which can be defined as Δx 1¼_Δωx 1À_Δωx 1
Àm .According to the results above,when F moves and the value of x 1increas,the value of this index will remain constant until reaching the equivalent damaged element.When F gets across the equivalent damaged element,the value of Δx 1
will experience a sudden jump.Subquently,the occur-rence and position of damage can be detected.This new index can be termed as “Symmetrical Midspan Displacement Difference Index (SMDDI).”
When F occurs at x 1¼x 0þ2m and the corresponding symmet-rical position:
_Δωx 0þ2m can be solved as _Δωx 0þ2m ¼
Fm ðz 0À1Þðm 2þ3mx 0þ3x 02Þð4m Àl þ2x 0Þ6EIz 0l ð10ÞThen
Δx 1¼x 0þ2m
¼
Fm 2ðz 0À1Þðm 2þ3mx 0þ3x 02Þ3EIz 0l
ð11Þ
Δx 1¼x 0þ2m ÀΔx 1¼x 0þm ¼Fm 2ðz 0À1Þð2m þ3x 0Þ
12EIz 0
ð12Þ
When F occurs at x 1¼x 0þ3m and the corresponding symmetrical position
_Δω
x 0þ3m ¼Fm ðz 0À1Þðm 2þ3mx 0þ3x 02Þð6m Àl þ2x 0
Þ6EIz 0l
ð13ÞWhen F occurs at x 1¼x 0þ4m and the corresponding symmetrical position
_Δω
x 0þ4m ¼Fm ðz 0À1Þðm 2þ3mx 0þ3x 02Þð8m Àl þ2x 0
Þ6EIz 0l
ð14ÞThen it is found that
Δx 1¼x 0þ2m ¼Δx 1¼x 0þ3m ¼Δx 1¼x 0þ4m
¼
Fm 2ðz 0À1Þðm 2þ3mx 0þ3x 02Þ3EIz 0l
ð15Þ
From the above prented analysis,it is concluded that the SMDDI value of two points (x 1¼x 0þm a
nd the corresponding symmetrical point x 1¼l Àx 0Àm )will be different from the nearby ones when damage occurs within the region [x 0,x 0þm ]or [l Àx 0Àm ,l Àx 0].The esnce of this damage detection method bad on SMDDI can be drawn from this conclusion.In practice,the SMDDI values of equivalent element boundaries can be obtained and then plotted.The sudden jump on this curve can be ud to indicate the position of
damage.
Fig.3.Analytical model of damaged bridge
D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y C h o n g q i n g U n i v e r s i t y o n 12/30/12. C o p y r i g h t A S C
E .
F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .
In addition,it can be en that Eq.(9)controls the magnitude of the sudden jump.According to this expression,this kind of mag-nitude is a function of veral parameters.It is recommended that the value of load F should be as large as possible under the circum-stance that the bridge is intact.With an increa in the value of F ,the magnitude of the sudden jump tends to increa and the damage detection result becomes more stable when the measured data is polluted by noi.If needed,the equivalent damage extent,z 0,can be solved directly by Eq.(9).
Considering the complexity of actual situation,a special ca will be analyzed.Special Ca Analysis
A damage scenario is shown in Fig.4.The position of damage a and b will be adjacent if one of them is displaced symmetrically.The parameters of damage extent are identical to the above ca
_Δωx 0¼
ÀFmx 0½4m 2z 02À28m 2z 01À12x 02ðz 01Àz 02Þþ9mlz 01À3mlz 02À36mx 0z 01 12EIlz 01z 02
þ
ÀFmx 0½12mx 0z 02þ6lx 0ðz 01Àz 2Þþ24m 2z 01z 02À6mlz 01z 02þ24mx 0z 01z 02 0102
ð16Þ
_Δω
催眠王菲x 0Àm ¼Fm ðm Àx 0Þ½4m 2z 02À28m 2z 01À12x 02ðz 01Àz 02Þþ9mlz 01À3mlz 02À36mx 0z 0
1 12EIlz 01z 02
þ
Fm ðm Àx 0Þ½12mx 0z 02þ6lx 0ðz 01Àz 02Þþ24m 2z 01z 02À6mlz 01z 02þ24mx 0z 01z 02
12EIlz 01z 02
ð17Þ
_Δωx 0À2m ¼
Fm ð2m Àx 0Þ½4m 2z 02À28m 2z 01À12x 02ðz 01Àz 02Þþ9mlz 01À3mlz 02À36mx 0z 01 12EIlz 01z 02
þ
Fm ð2m Àx 0Þ½12mx 0z 02þ6lx 0ðz 01Àz 02Þþ24m 2z 01z 02À6mlz 01z 02þ24mx 0z 01z 02 12EIlz 01z 02
ð18Þbreakfast是什么意思
_Δωx 0À3m ¼
Fm ð3m Àx 0Þ½4m 2z 02À28m 2z 01À12x 02ðz 01Àz 02Þþ9mlz 01À3mlz 02À36mx 0z 01 12EIlz 01z 02
þ
Fm ð3m Àx 0Þ½12mx 0z 02þ6lx 0ðz 01Àz 02Þþ24m 2z 01z 02À6mlz 01z 02þ24mx 0z 01z 02 12EIlz 01z 02
ð19ÞThen it is obtained that
Δx 1¼x 0¼ Δx 1¼x 0Àm ¼ Δx 1
¼x 0À2m ¼
ÀFm 2½4m 2z 02À28m 2z 01À12x 02ðz 01Àz 02Þþ9mlz 01À3mlz 02 12EIlz 01z 02
þ
ÀFm 2½À36mx 0z 01þ12mx 0z 02þ6lx 0ðz 01Àz 02Þþ24m 2z 01z 02À6mlz 01z 02þ24mx 0z 01z 02
12EIlz 01z 02
ð20ÞWhen F occurs at x 1¼x 0þm and the corresponding symmetrical position
_Δωx 0þm ¼
ÀFm ½4m 3z 02À28m 3z 01À12x 03ðz 01Àz 02Þþ9mlz 0ðm Àx 0z 02ÞÀ2m 2lz 02þ24mz 02ðm 2z 011þx 02þx 2z 01Þ 12EIlz 01z 02
À
ÀFm ½48mx 0z 01ðx 0Àmz 02Þþ64m 2x 0z 01À16m 2x 0z 02À6lx 02ðz 01Àz 02Þþ7m 2lz 01z 02À15alx 0z 01þ6mlx 0z 02 12EIlz 01z 02
ð21Þ
Then
_Δωx 0þm À_Δωx 0¼
Fm 2½28m 2z 01À4m 2z 02þ12x 02ðz 01Àz 02ÞÀ9mlz 01þ2mlz 02þ36mx 0z 01 12EIlz 01z 02
À
Fm 2½12mx 0z 02À6lx 0z 0À3lx 0z 02þ24m 2z 01z 02À7mlz 01z 02þ24mx 0z 01z 02À3lx 0z 01z 02 0102
ð22ÞD o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y C h o n g q i n g U n i v e r s i t y o n 12/30/12. C o p y r i g h t A S C E . F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .
A comparison of Eq.(20)with Eq.(22)gives
Δx 1¼x 0þm ÀΔx 1¼x 0
¼
Fm 2ðm þ3x 0Þðz 01À1Þ12EIz 01
ð23Þ
Δx 1¼x 0þ2m ¼
ÀFm 2½4m 2z 02À28m 2z 01À12x 02ðz 01Àz 02Þþ5mlz 01ð1Àz 02Þ 12EIlz 01z 02
þ
ÀFm 2½À36mx 0z 01þ12mx 0z 02þ3lx 0z 01ð1Àz 02Þþ24mz 01z 02ðm þx 0Þ
12EIlz 01z 02
ð24Þ
A comparison of Eq.(22)with Eq.(24)gives
Δx 1¼x 0þ2m À Δx 1¼x 0þm ¼
ÀFm 2ð2mz 02À4mz 01À3x 0z 01þ3x 0z 02þ2mz 01z 02Þ12EIz 01z 02
ð25Þ
Then
_Δωx 0þ3m ¼
ÀFm ð6m Àl þ2x 0Þ½m 2z 02À7m 2z 01À3x 02ðz 01Àz 02ÞÀ9mx 0z 01þ3mx 0z 02þ6mz 01z 02ðm þx 0Þ 6EIlz 01z 02ð26Þ
做一个善良的人_Δωx 0þ4m ¼
ÀFm ð8m Àl þ2x 0Þ½m 2z 02À7m 2z 01À3x 02ðz 01Àz 02ÞÀ9mx 0z 01þ3mx 0z 02þ6mz 01z 02ðm þx 0Þ 6EIlz 01z 02ð27Þ
Δx 1¼x 0þ3m ¼ Δx 1¼x 0þ4m ¼
ÀFm 2½m 2z 02À7m 2z 01À3x 02ðz 01Àz 02ÞÀ9mx 0z 01þ3mx 0z 02þ6mz 01z 02ðm þx 0Þ 3EIlz 01z 02
ð28Þ
From the above,it is found that the SMDDI value of two groups of symmetrical points (x 1¼x 0þm ,x
1¼l Àx 0Àm and x 1¼x 0þ2m ,x 1¼l Àx 0À2m )will be different from the nearby ones and the damage region can be identified as [x 0,x 0þ2m ]or [l Àx 0À2m ,l Àx 0].
Further,it can also be en from Eq.(23)that the sudden jump in the graph tends to increa with an increa in F .If needed,z 01and z 02can be solved directly by using Eqs.(23)and (25).Considering Random Uncertainty in Actual Bridges The above work is a necessary step before jumping to its applica-tion to real bridges.It shows advantages but it is very often also accompanied by disadvantages which still leave scientific questions open.Random uncertainty,which occurs due to inherent variabil-ities or randomness in real-world bridges such as uncertainty in geometric and material properties,has been ignored.However,it is particularly important to address the effect of random uncertainties in Young ’s modulus and geometry from a practical point of view.The kinds of uncertainty has been recognized as one of the main barriers against the application of existing damage detection tech-niques on actual bridges.It is usually difficult to determine whether the changes of the damage detection index are caud by random uncertainties or by actual damages.
The existing knowledge cannot be expected to reduce random uncertainty,although it may be uful in quantifying the uncer-tainty.At prent,statistical strategies (Sohn and Farrar 2001and Zhang 2007)and,fuzzy logic (Chandrashekhar and Ganguli 2009;Sawyer and Rao 2000;Pawar and Ganguli
晚饭时间2003)are usually suggested to account for this kind of uncertainty.However,statis-tical strategies can account for only distinct damage features for which the data can have a crisp pointwi quantification.Moreover,the capabilities of detecting damage are restricted to the limitations of probabilistic assumptions.An improper probabilistic mathemati-cal abstract of the actual structure might lead to misleading uncer-tainty analysis.For fuzzy logic approaches,they are mainly suitable for detecting damage occurrence and classifying progressive levels of damage.
Therefore,the application of SMDDI to the ca of random un-certainty will be studied here.It is suggested that the bridge in both an intact and unknown condition is tested.Two ts of SMDDI curves are then generated.Accordingly,damage can be detected by comparing the curves.The gradient of each gment in the curves is examined.A point can be recognized as the damage indication point if the gradients of its two adjacent gments are different in the two curves.Explicit analysis is too complicated to be prented here.Validation and interpretation will be provided by a numerical example directly.
A single-span bridge has span of 10m.The height and width of girder ction are 0.5m and 9m,respectively.The theoretical model is built using the general-purpo finite element analysis software ANSYS (V10.02008,Moaveni 1999).The value of m is lected as 0.2m.A concentrated load F equals 100KN.Midspan point displacement values are solved by ANSYS.
Positions on the bridge can be mapped to the points on a co-ordinate axis where the left side of the bridge is the origin and
the
Fig.4.Special ca
D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y C h o n g q i n g U n i v e r s i t y o n 12/30/12. C o p y r i g h t A S C
E .
F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .
