Extradosed Bridges Assessment of seismic damage using Ground Acceleration and Displacement correlations

Transcription

1 Internationa Refereed Journa of Engineering and Science (IRJES) ISSN (Onine) 39-83X, (Print) 39-8 Voume 3, Issue (November 4), PP Extradosed Bridges Assessment of seismic damage using Ground Acceeration and Dispacement correations M V Sardesai, Dr A K Desai (Appied Mechanics Department, Sardar Vaabhbhai Nationa Institute of echnoogy, Surat,India) (Appied Mechanics Department, Sardar Vaabhbhai Nationa Institute of echnoogy, Surat,India) Abstract:- Forced vibration of structure for given Earthquake time history is governed by peak acceeration. For cabe stayed structures such as Extradosed cabe stayed bridge it is difficut to predict dynamic response using usua methods of dynamic anaysis as appied to some other bridge structures ike response spectrum anaysis, accurate anaysis ike time history anaysis is time consuming and has time and cost effects. Noninearities can ony be considered in time history anaysis. he proposed method correates the peak ground acceeration (PGA) and earthquake deformation ratio (EDR) which can be used for simpified dynamic anaysis and can prove handy too for structura engineers to know earthquake reated serviceabiity without much compicated anaysis at initia stages. his ratio can be used to present seismic damage indices. he method is proposed considers Extradosed bridge for exampe. Keywords:- Extradosed cabe stayed bridge; Structura Behavior; Earthquake; Dynamic response; PGA-EDR; Seismic Damage index. I. INRODUCION Dynamic response prediction has been the matter of research for many authors, in particuar as the structura design of many structures is governed by the earthquake oad cases or combinations thereof. he commony used simpified methods used for anaysis are based of theory of dynamics pertaining to SDOF systems. Rues of moda combinations viz SRSS, CC are used for MDOF systems. hese combinations rues are fairy accurate and hepfu since exact methods such as time history anaysis invoves significant ski, time and cost. Athough it is acceptabe that having tempora response parameters proves hepfu, the structura design is aways governed by peak response. he peak vaues correspond to peak ground motions. he approach as presented here gives fairy accurate estimation of earthquake response and may prove hepfu for quick response prediction at the time of preiminary designs and further serves as a too for seismic damage index for higher intensity ground motions for which the structure is not designed he recent research has shown that a Extradosed bridge, variant of cabe stayed bride where cabes add substantia prestress to the deck because of the shaow pyon, are found to be economica for spans upto 5m. he intrados is defined as the interior curve of an arch, or in the case of cantiever-constructed girder bridge, the soffit of the girder. Simiary, the extrados is defined as the uppermost surface of the arch. he term Extradosed was coined by Jacques Mathivat in 988 [9] to appropriatey describe an innovative cabing concept he deveoped for the Arrêt-Darré Viaduct, in which externa tendons were paced above the deck instead of within the cross-section as woud be the case in a girder bridge. o differentiate these shaow externa tendons, which define the uppermost surface of the bridge, from the stay cabes found in a cabe-stayed bridge, Mathivat caed them Extradosed prestressing. Some features of Extradosed bridge as given beow; Externa appearance resembes cabe-stayed bridge but structura characteristics are comparabe to those of conventiona girder bridge he Girder Depth are esser than that of conventiona girder bridges he stay cabes (prestressing tendons outside the girder) need no tension adjustment necessary for cabestayed bridges, and can be treated as usua tendons as in girder bridges he height of pyon is haf as that of cabe-stayed bridge and hence easier to construct With sma stress fuctuation under ive oad the anchorage method for stay cabes can be same as that of tendons inside girder and thereby achieve economy 59 Page

2 Extradosed Bridges Assessment of seismic damage using Ground Acceeration and Dispacement correations Fig. Figure showing Cabe arrangements in Girder Bridge, Extradosed Bridge and Cabe stayed bridge With the rapid increase in span ength, combined trend and aso trend of using high strength materias have resuted in sender structures and a concern is being raised over dynamic behavior of such structures, in case of cabe supported structures it is more pronounced as this further incudes vibrations of cabe eements aso. An accurate anaysis of natura frequencies is fundamenta to the soution of its dynamic responses due to seismic and wind and traffic oads. Seismic anaysis of structure is important aspect of structura design as overa economy and safety of structure is most of the time governed by the oad cases invoving seismic forces. Many studies associated with this have been performed over ast few decades. However, number of researches on dynamic behavior of Extradosed Bridge is very imited. o gauge the exact dynamic response of structure, time history anaysis is used. But this method is found to be time consuming and invoves considerabe cost. Further it is sometimes required to know the approximate resuts beforehand prior to proceeding to extensive anaysis such as time history anaysis. he Proposed Earthquake- Dispacement Ratio (EDR) is defined as ratio of maximum seismic dispacement to maximum static dispacement. hese both dispacements measured at the same point. Earthquakedispacement ratio can be evauated as seismic damage index. he aim of this paper is to present work reating to dynamic behavior of Extradosed bridge and the proposed PGA EDR reationship. II. FORMULAION OF PROBLEM SIFFNESS AND MASS MARIX FORMULAION FOR EXRADOSED BRIDGE Fig. Eevation ypica Extradosed bridge Consider a typica Extradosed bridge as shown in figure, et us take a sma section as shown in the figure 3 beow. he boundary conditions for this eement can be considered as that of beam on eastic foundation to reate effect of eastic support provided by cabe. Further this beam wi be subjected to prestressing force due to horizonta component of cabe forces, as shown in figure 3 6 Page

3 Extradosed Bridges Assessment of seismic damage using Ground Acceeration and Dispacement correations Fig.3 Beam on eastic foundation Now, consider an eement ij of ength L of a beam on an eastic foundation as shown in Figure.3 having a uniform width b and a ineary varying thickness h(x) It wi be a simpe matter to consider an eement having a ineary varying width if the need arises. Negecting axia deformations this beam on an eastic foundation eement has two degrees of freedom per node a atera transation and a rotation about an axis norma to the pane of the paper and thus possesses a tota of four degrees of freedom. he (4x4) stiffness matrix k of the eement is obtained by adding the (4x4) stiffness matrices kb, kf and k pertaining to the usua beam bending stiffness and foundation stiffness and stiffness due to prestressing force () respectivey Since, there are four end dispacements or degrees of freedom a cubic variation in dispacement is assumed in the form v Aa Eq. () Where, A= ( x x x 3 ) and a = (a a a 3 a 4 ) (Dispacement variation within eement) he four degrees of freedom corresponding to the dispacements v, v 3 and the rotations v v 4 at the ongitudina nodes are given by q=ca (Noda dispacements) Eq. () Where q = (v v v v 3 ) and C is the connectivity matrix for an eement ij between x= and x=l as given in Figure 3 From equations (Eq.) and (Eq.) V=AC - q Eq. (3) If E is the Young s moduus and I=bh(x) 3 / is the second moment of area of the beam Cross-section about an axis norma to the pane of the paper\ the bending moment M in the eement is given by v M D DBC q Eq. (4) x Where D=EI(x) and B=d A/dx =(,,, 6x) A. Stiffness due to bending he potentia energy U B due to bending is U B d v Mdx dx Eq. (5) And the stiffness is given by U B kb Eq. (6) d From equations (Eq.5) and (Eq.6) we get, kb B DBdx (Eementa) Eq. (7) Kb ( C ) kb C (Assmebed) Eq. (8) B. Stiffness due to eastic foundation he potentia energy of foundation stiffness is given by, 6 Page

4 Extradosed Bridges Assessment of seismic damage using Ground Acceeration and Dispacement correations U f V kfvdx and then the stiffness is given by, kf U d f Eq. (9) Eq. () From equations (Eq.9) in (Eq.) we get, kf A kfadx (Eementa) Eq. () Kf ( C ) kfc (Assembed) Eq. () C. Stiffness due to Prestressing force he potentia energy of prestressing force is given by, U v dx Eq. (3) x hen the stiffness is given by, k U Eq. (4) d Substituting equation (3) in (4) we get, k A k Adx Eq. (5) ( C ) kc Eq. (6) K Finay compete stiffness is given by, K K K K Eq. (7) B f Eement mass matrix is the equivaent noda mass that dynamicay represents the actua distributed mass of the eement. his is kinetic energy of the eement. v dvv Where, v = Latera veocity and = mass density q C A hxadx C q hen, the mass matrix is given by, m C mc Eq. (8) Eq. (9) Eq. () and m A hxadx Eq. () for free vibration of this beam, M q C q K q Eq. () and for forced vibration, Eq. (3) M q C q K q f N f For Extradosed bridge, since the cabe are shaower and the effect of prestressing force is more the effecting of prestress sha be taken in to account as shown in the equation above. III. ANALIICAL SUDY FORCED VIBRAION BEHAVIOUR o study static as we as dynamic behavior of Extradosed Bridge, 3 numbers of modes with variabe parameters are prepared. Basic span configuration as appicabe for Extradosed span is seected to be, and 6m main span, the side span is about.45 of main span. he pyon height is varied from 8 to to 6 Page

5 Extradosed Bridges Assessment of seismic damage using Ground Acceeration and Dispacement correations account for the effect of varying cabe incinations. he cabe incination varies from 7 to 3 degrees. he requirement of cabe area and prestressing is as per preiminary design. Box beam superstructure is adopted with soid rectanguar pyon designed by working stress method. For detais of mode refer tabe- Since, Extradosed bridges take part in an intermediate zone between prestressed bridges and cabestayed bridges, their structura behavior may be simiar to these kinds of typoogies, depending on design criteria adopted during the project stage. Generay a rigid deck Extradosed bridge sha have a simiar behavior to the prestressed bridges, thus avoiding high stress osciations of stay cabes and, consequenty, avoiding fatigue conditions associated with anchorages and tendons present in a sender deck extradosed bridge, which behavior is quite cose to the cabe-stayed bridge. Its construction demands the acquaintance of technoogies currenty appied on straight course-prestressed concrete bridges and cabe-stayed bridges, which is generay deveoped by means of the consecutive cantiever method but counting with the assistance of tension rods that are not paced on temporary, but on permanent basis. In order to anayticay study structura behavior of Extradosed bridges with respect to ground acceeration numerica studies were conducted for forced vibration on typica Extradosed bridge. he parameters were non-dimentionaised using equivaent factors. he earthquake time histories used are having Koyna (PGA-.49g), Bhuj (PGA-.3g) and E-Centro (PGA-.6g). abe- Detais of Earthquake time histories used for this study; Sr No Span (L) configuration Pyon ht (H) Remarks On pie foundation,.5 wide deck 9++9 On pie foundation, 4 wide deck On pie foundation, 8 wide deck Non-Dimensionaizing of parameters Forced vibration anaysis for three earthquake time histories having different characteristics are undertaken. o compare the resuts a parameter have been non dimensionaised using equivaent factors as mentioned beow; Where, V & M are non dimensioning factors for shear force, bending moment. Where, = Mass Density, g= Gravitationa acceeration, A= Cross section area of component and L= Haf span ength of the component. Span and pyon height are non-dimensionaized by using parametric ength. he resuts obtained from the time history anaysis in terms of bending moment and shear forced in the structure are non-dimensionaised and superimposed and presented in Fig 4 to 8 Variation of bending moment-across Span E-Centro +ve E centro -ve -.35 Bhuj +ve Bhuj -ve Koyna +ve Koyna -ve Fig.4 Variation of bending moment across span for +6+m span (Non-dimentionaized) 63 Page

6 Pyon height (Parametric) Bending moment Bending Moment Extradosed Bridges Assessment of seismic damage using Ground Acceeration and Dispacement correations Variation of Bending mometn across span E-Centro +ve E-Centro -ve Bhuj +ve Span Bhuj -ve Koyna +ve Koyna -ve Fig.5 Variation of bending moment across span for 9++9m span (Non-dimentionaized) Variation on BM across span for m Span -.5 Koyna +ve Koyna -ve Bhuj +ve Bhuj -ve Ecentro +ve E Centro -ve Fig.6 Variation of bending moment across span for m span (Non-dimentionaized) Fig 7 to 9 gives resuts for BM across pyon height. Variation of bending moment-across Pyon-Hybrid Koyna +ve Koyna -ve Bhuj +ve Bhuj -ve Ecentro +ve Ecentro -ve Dimensioness Bending moment Fig.7 Variation of bending moment across pyon height for +6+m span (Non-dimentionaized) 64 Page

7 Pyon height (Parametric) Pyon height (Parametric) Extradosed Bridges Assessment of seismic damage using Ground Acceeration and Dispacement correations. Variation of Bending moment across pyon height m span Koyna +ve Koyna -ve Bhuj +ve Bhuj -ve Ecentro +ve Ecentro -ve Dimensioness bending moment Fig.8 Variation of bending moment across pyon height for 9++9m span (Non-dimentionaized) Variation of bending.moment across pyon Extradosed Koyna +ve Koyna -ve Bhuj +ve Bhuj -ve Ecentro +ve Ecentro -ve Dimensioness Bending moment Fig.9 Variation of bending moment across pyon height for m span (Non-dimentionaized) Forced vibration studies of deck and pyon of three types of bridges reaffirms foowing facts for extradosed bridge, Magnitude of bending moment / shear force is directy proportiona to the magnitude of forcing function / Peak Ground Acceeration (PGA). With increase in the distance between cabes supports the shear force in deck aso increases. Pyon stiffness does not have any effect on the deck moments/shear. It is observed that ony for cabe stayed bridge with harp shape cabe arrangement the shear force reduces at the junction of deck IV. ANALIICAL SUDY PGA-EDR RELAIONSHIPS It is seen in above sections that for time history anaysis generay the magnitude of structura actions are directy proportiona to magnitude of forcing function ie. Its Peak ground acceeration. Hence it wi be possibe to reate these quantities as a function of forcing frequency. he term EDR as expained beow is used for this purpose. 65 Page

8 Extradosed Bridges Assessment of seismic damage using Ground Acceeration and Dispacement correations A data of earthquake records are now days processed using Seismosigna software. Seismosigna processes strong motion seismic data. It wi generate strong motion parameter such as Fourier and Power spectra, Eastic response spectra and pseudo spectra, over damped and constant ductiity in eastic response spectra. Spatia earthquake represents ie. ime history components or a the three direction viz. ongitudina, transverse and vertica are specified. his is data can be obtained from various agencies and can be cassified by the Peak Ground Acceerations. Earthquake Deformation ratio (EDR) Every structure has its stiffness characteristics which contros the behaviour of structure. o account for this variabe, the ratio EDR is defined as ratio of maximum seismic dispacement to maximum static dispacement. hese both dispacements measured at the same point. he vaues of PGA and EDR can be potted against each other to get correation by curve fitting. o obtain the vaues of EDR for various PGA it is required to simuate earthquake Ground acceerations on anaytica mode in computer anaysis using ime histories which is the time variation of ground acceeration. It is the most usefu way of defining the shaking of ground during earthquake. his ground acceeration is descriptive by numerica vaues at discrete time intervas. Integration of this time acceeration history gives veocity history, integration of which intern gives dispacement history. V. DISCUSSIONS & CONCLUSIONS Forced vibration studies of three different Extradosed bridges are done. It is noted that;. Forced vibration is governed by peak acceerations. Design of structures is most often governed by seismic cases and combinations thereof. 3. For cabe stayed structures it is difficut to predict dynamic response using usua method 4. Accurate anaysis viz. ime history anaysis invoves time, cost and ski requirements 5. Effect of seismic transmission units or isoators can not be considered in coda methods. 6. he commony used simpified methods used for anaysis are based of theory of dynamics pertaining to SDOF systems. Rues of moda combinations viz SRSS, CC are used for MDOF systems. 7. It is observed that there is some reationship between Peak Ground Acceerations and the response of structure, reationship between these needs to be estabished by further study. Forced vibration studies of deck and pyon of three types of bridges need to be done to find out correation between peak ground acceeration and Earthquake dispacement ratio. he correations can be used to quicky predict the expected dynamic response of the highy indeterminate structures ike Extradosed cabe stayed bridge during preiminary design as exact dynamic anaysis at this stage is time and cost consuming and aso not very much desired. Exact time histories at a ocations are not avaiabe and design can be done for expected PGA. Using these reations dispacement based design can be done for structure ie. By appying obtained defections on static structura mode. Apart from this the EDR vaues can be used as a too for seismic damage index for earthquakes beyond designed vaues and provides ess conservative approach than response spectrum anaysis. ACKNOWLEDGEMENS Authors acknowedge the immense hep received from the schoars whose artices are cited and incuded in references of this manuscript. he authors are aso gratefu to authors / editors / pubishers of a those artices, journas and books from where the iterature for this artice has been reviewed and discussed. REFERENCES []. Katsuhiko akami and Sumio Hamada (5); Behavior of extradosed bridge with composite Girder; ASCE / Journa Of Bridge Engineering []. H. Otsuka,. Wakasa, J. Ogata, W. Yabuki and D. akemura (3); Comparison of structura characteristics for different types of cabe-supported prestressed concrete bridges; Structura Concrete Mar- [3]. F K Au, Y S Cheng, Y K Cheung, D Y Zheng (); On determination of natura frequency and mode shapes of cabe stayed bridges; Appied methametica modeing [4]. A K Desai, J A Desai, H S Pati (5); Co-reationship of Seismic (EDR) & (PGA) for Cabe Stayed Bridge; NMB media [5]. Ani K Chopra. (3), Dynamics of Structures. Pearson Education, Inc. Second edition 844, Singapore 66 Page

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