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The historic Wheeling suspension bridge over the Ohio River is one of the 57 long-span suspensionThree dimensional models usually are developed with beamand truss elements to model both the superstructure and thesubstructure (Okamoto 1983; Wilson and Gravelle 1991; Du-manoglu et al. 1992).West Virginia is listed among low seismic risk areas in theUnited States. For West Virginia the American Association ofState Highway and Transportation Ofcials (AASHTO) codeassigns an acceleration coefcientAof 0.05. However, a recentinvestigation concluded that earthquake hazards should be ofconcern to the state. The investigation combined geologicaland historic data from regional earthquakes that caused struc-tural damage in West Virginia. Broad areas of the sate mayhave already experienced modied Mercalli intensity (MMI)scale VII excitations during the 1886 Charleston, S.C. and theNew Madrid, Mo. earthquakes of 1811 and 1812. Similar in-tensity earthquakes also were felt in the southern part of thestate during the 1897 Giles, Va. earthquake. The seismic anal-ysis of the bridge considers both the AASHTO code assignedacceleration coefcient and the intensities based on recentstudies (King et al. 1993).HISTORIC BACKGROUND ANDBRIDGE DESCRIPTIONThe long-span suspension bridge together with the metaltruss and the high-rise building represent three important con-tributions by American engineers to structural engineering inthe nineteenth century. The Wheeling suspension bridge is par-ticularly important in the development of the long-span wiresuspension bridge. When it was opened in 1849 it was thelargest span bridge in the world and ushered in a century-longleadership enjoyed by American engineers. As a result, it isone of the most signicant antebellum civil engineering struc-tures in the nation.Despite the fact that the bridge was not designed to carrytodays live loads resulting from automobile trafc, the bridgehas served as a vital link across the Ohio River for nearly acentury and a half. To protect this internationally signicantbridge and at the same time insure the safety of the travelingpublic, it is necessary to understand how the bridge functionsunder both static and dynamic loads. This paper represents therst comprehensive structural analysis using modern computertechniques and in situ nondestructive measurements of thisbridge.The bridge was designed by Charles Ellet Jr., a leadingnineteenth century civil engineer (Kemp 1975). The originalbridge consisted of a timber deck suspended from wroughtiron suspenders, which in turn were carried by the main cables.VALIDATEDANALYSIS OF WHEELING SUSPENSION BRIDGEBy Constantine C. Spyrakos,1Member, ASCE, Emory L. Kemp,2Fellow, ASCE, andRamesh Venkatareddy,3Student Member, ASCEABSTRACT:bridges in operation in the United States. The bridge was designed and constructed in 1849 by Charles Ellet,Jr., who rightfully may be considered the father of the modern American suspension bridge. Despite the factthat the bridge was not designed to carry todays live loads, the bridge has served as a vital link across the OhioRiver for nearly a century and a half. This paper represents the rst comprehensive structural analysis usingmodern computer techniques and in situ nondestructive testing evaluation of this bridge. Static analysis showedthat deections and stresses caused by present-day loading conditions are within allowable limits. Rating factorsdemonstrated that none of the structural members are overstressed by the posted live load. Seismic analysis tothe American Association of State Highway and Transportation Ofcials loads showed little damage, which wasconned to oor beams at the east tower. Analysis using historic earthquakes showed localized damage of oorbeams and diagonal oor ties at the east tower and top chords of the stiffening truss at midspan. The methodologydeveloped could be applied to a wide range of cable suspension bridges.INTRODUCTIONMost of the suspension bridges built in the 19th centurywere designed for live loads quite different from those theyhave to carry today. Any suspension bridge may have to carryoccasional overloads, as well as loads from natural causes suchas strong winds and seismic loads that were not anticipated inthe original design (Ulstrup 1993). Because many of thesebridges are in use today, it is necessary to evaluate their con-dition and identify necessary stiffening and strengthening tobring them up to modern standards of safety while still re-specting the historic fabric of the bridge. The process requiresin situ testing of the system coupled with analysis.The most frequently used classical theories for static anal-ysis of suspension bridges are the elastic theory and the de-ection theory (Steinman 1929). In addition to these an ap-proximate method by Tsien (1949) also can be used to getpractical answers that are sufciently accurate for design pur-poses (Ulstrup 1993). The major distinction between the elas-tic theory and deection theory is that the deection theorydoes not assume that the ordinates of the cable curve remainunaltered on application of loading (Steinman 1929). The elas-tic theory is sufciently accurate for shorter spans. However,the deection theory is the most accurate and results in moreeconomical and slender bridges.Determining the earthquake response of historic long-spansuspension structures is always a major problem for engineers(Castellani 1987). Research on lateral earthquake response ofsuspension bridges (Abdel-Ghaffer 1983), vertical seismic be-havior of suspension bridges (Abdel-Ghaffer 1982), and sus-pension bridge response to multiple-support excitations (Ab-del-Ghaffer 1982) give in-depth detail about the importance ofearthquake response of suspension bridges. The study on nat-ural frequencies and modes (West et al. 1984) using a nite-element (FE) formulation demonstrates the variation of thefrequencies and mode shapes of stiffened suspension bridges.1Prof. of Civ. Engrg., West Virginia Univ., Morgantown, WV 26506-6103; Nat. Tech. Univ. of Athens, Zografos, 15700, Athens, Greece.2Dir., Inst. for the History of Technol. and Industrial Archaeology, WestVirginia Univ., Morgantown, WV.3Grad. Res. Asst., Civ. Engrg. Dept., West Virginia Univ., Morgantown,WV.Note. Discussion open until July 1, 1999. To extend the closing dateone month, a written request must be led with the ASCE Manager ofJournals. The manuscript for this paper was submitted for review andpossible publication on July 12, 1995. This paper is part of theJournalof Bridge Engineering, Vol. 4, No. 1, February, 1999.qASCE, ISSN1084-0702/99/0001-00010007/$8.00 1 $.50 per page. Paper No.11111.JOURNAL OF BRIDGE ENGINEERING / FEBRUARY 1999 /1bles are supported at each tower by saddles comprised of threecast-iron rollers. The cable ends are connected to anchor barsthat are embedded into concrete anchorages (Lichtenstein1992).Diagonal stay cables comprised of wire ropes of varyingdiameter from 2.54 to 4.45 cm are located within the end-quarter spans. The stay cables pass over the saddles at eachtower and are anchored into the main cable anchorages.The framing plan of the existing bridge is shown in Fig. 3.The oor system is suspended from the main cables by pairsof 2.85 or 3.18 cm diameter hanger rods at each end of theoor beams. The hanger rods are connected to the main cablesby cable bands and attached to the oor beams, which consistof rolled steel wide ange W24376 sections with a spacingof approximately 2.44 m throughout the structure.The deck is stiffened by Howe-type trusses in which the topchords, bottom chords, and diagonals are made of timber (Fig.4). The truss verticals are steel rods with a diameter of 3.18cm, whereas the junction boxes are cast iron. The trusses aresupported by the oor beam extensions at the panel points.The truss bottom chord passes under the extensions and isconnected by vertical steel or wrought-iron rods.The superstructure supports a 12.70-cm-deep open grid steelgrating. A 1.22-m sidewalk of 2.54 cm deep open grid steelgrating exists along each side of the roadway. The timber trussserves as a guardrail for pedestrians (Fig. 4). A woven-wireprotective fence is attached to the stiffening truss to protectpedestrians.The bridge substructure consists of east and west towersconstructed with cut stone masonry. The cables at the top ofthe tower are protected by galvanized sheet metal housings,Figs. 1 and 2 show the elevation of the bridge. In the originaldesign there were 12 independent cables arranged accordingto the French garland system. In 1854, only 4 years after itscompletion, the bridge deck was destroyed and the cables dis-lodged by a tornado that swept up the Ohio valley. It wasquickly rebuilt under the supervision of Ellet.Later the bridge was strengthened and stiffened by the ad-dition of stay cables. This work was undertaken by Washing-ton Roebling who also gathered the 12 cables into two pairsof cables, one pair on each side. This Roeblingized bridgeserved until 1956. In 1956 a major rehabilitation was done inwhich the W24376 oor beams, roadway grating, sidewalkgrating, and lateral bracing system were incorporated in thedeck system. The most recent rehabilitation was performed in1983. At that time a neoprene wrapping system was added tothe main suspension cables, together with miscellaneous struc-tural steel repairs and replacement of damaged stay cables andhanger rods. Additional work included installing new timberstiffening trusses, cleaning and painting of the superstructure,repointing the masonry towers, installing stay-hanger con-nectors, and tensioning the hangers and stay cables. In 1989,additional repairs were performed by the State MaintenanceDepartment.The structure carries the West Virginia state route 251 as itcrosses the main channel of the Ohio River connecting the cityof Wheeling and Wheeling Island. The bridge span is approx-imately 307.50 m and carries a 6.10-m roadway. The mainsuspension cables support the two stiffening trusses of thebridge. Each cable is approximately 19.10 cm in diameter andconsists of approximately 1,650 wires of No. 10 gauge (3.42mm diameter) laid in parallel. The cables are protected with aliquid neoprene paint and an elastomeric cable cover. The ca-FIG. 1. Elevation of Wheeling Suspension BridgeFIG. 2. Part Elevation of Bridge2/ JOURNAL OF BRIDGE ENGINEERING / FEBRUARY 1999TWO- (2D) AND THREE-DIMENSIONAL(3D) MODELSBecause of the complexity of the structure, an FE analysiswas employed to study the behavior of the bridge under staticand dynamic loads. Both 2D and 3D models were used toanalyze the structure. To develop a proper FE model and tocompare the FE results with elastic theory results two 2D mod-els also were developed, one without stay cables and the otherwith stay cables (Figs. 5 and 6, respectively). In the 2D modelsthe stiffening truss is replaced with an equivalent beam. Afterwith elastic theory results, a 2D model with stays and 3DFIG. 5. 2D Model of Wheeling Suspension Bridge withoutStaysFIG. 6. 2D Model of Wheeling Suspension Bridge with StaysFIG. 3. Framing Plan of Existing BridgeFIG. 4. Typical Stiffening Truss Panel and Detailwhereas the main cable anchorages are protected by cut stonemasonry anchorage housings.Currently, the inventory rating and trafc barriers regulatea clearance 2.44 m, and a weight limit of 2 t. No trucks, busesand trailers, are allowed; and automobiles must maintain15.24-m intervals.Based on data provided in the contractors proposal by theDepartment of Highways (1981), the material properties of thesystem components are as follows:comparison of the results from the model without stay cables Timber. Dense select structural Douglas Fir or SouthernPine. Extreme ber in bending (fb) = 13,110 kN/m2; ten-sion parallel to grain (ft) = 7,590 kN/m2; compressionparallel to grain (fc) = 8,970 kN/m2; horizontal shear (fv)= 586.5 kN/m2; compression perpendicular to grain (fct)= 3,139.50 kN/m2. Cable wires. Yield strength = 6.21E5 kN/m2; ultimatestrength = 8.55E5 kN/m2; elongation in 25.4 cm length4%; Youngs modulus E = 2,000 E5 kN/m2. Structural steel. Steel members of the bridge conform toASTM standards.JOURNAL OF BRIDGE ENGINEERING / FEBRUARY 1999 /3that there are 19 stay cables instead of 17. It should be notedthat the bridge is not symmetric, the approach level at theeastern side is approximately 9.50 m higher than that of thewestern side.IN SITU EVALUATION OFSUSPENDER FORCESThe main reason for in situ evaluation was to measure theexisting axial forces in the suspenders with the axial-load mon-itor (ALM), a handheld force-measuring instrument developedat West Virginia University and subsequently used in FE anal-ysis.The operation of the instrument is based on modal testing.It correlates natural frequencies to axial forces. Extensive the-oretical and experimental work has been performed (Siros1992; Nader 1993) in establishing the accuracy of the ALMthrough laboratory testing. Use of the instrument was extendedto eld testing of structural members by Nader (1993).The ALM was used to measure the forces of suspenders thatdid not intersect with diagonal stay cables. Table 1 shows theactual load carried in representative suspenders. By measuringthe actual load carried by the suspenders, the forces in themain cables were calculated using equilibrium equations. Aftercalculating the forces in each element (length between twosuspenders) of the main cable, they were applied as initialforces in the FE model to represent the forces developed inthe main cable caused by the dead load.STATIC ANALYSISStatic analysis of the bridge subjected to present-day load-ings as well as a load rating analysis were performed with 2Dand 3D models. Details on the rating analysis are given inVenkatareddy (1995).For static loads the maximum live load stresses at the mostheavily loaded members such as the main cable (C), suspender(S), stay (ST), top chord (T) and bottom chord (B), oor beam(FB), and diagonal ties (DT) of truss are shown in Table 2,where the negative sign indicates compressive axial loads. TheUpstream side(kN)(1)19.2018.0016.41ST 29,939.10Downstream side(kN)(2)18.3218.3217.64(3)models were developed to represent the actual bridge as itexists at the site as of today. The bridge superstructure, com-prised of two main cables, suspenders, stay cables, oorbeams, a steel grid deck, and a stiffening truss is modeled with3D beam and truss elements. The suspenders and stay cablesare modeled using 3D truss elements. Beam elements are usedto model the stiffening truss, oor beams, and deck. The steelgrid deck and sidewalk were modeled with beam elements towhich equivalent stiffness was assigned to simulate the stiff-ness of the system (Fig. 2). End moment releases were spec-ied at diagonals and verticals to simulate scissors joint con-ditions.Fig. 7 shows the 3D FE model of the western side of thebridge. The parallel wire cables are attened out over a seriesof three rollers, which are mounted at the top of the tower.Inspections over a long period of time have indicated that therehas been no movement of these cables because of the waythey pass over the roller system. Thus, xity has been assumedin the analysis. The stiffening truss is hinged at the supports.The cables in the 3D model have been placed according toplans of the existing bridge. The suspenders are connected tothe channel sections at the bottom of truss joints and the maincable. The spacing between the suspenders is approximately2.44 m. Only translational displacements at the top of the sus-penders are allowed at the junction of the main cable andsuspenders. The ordinates of the cable prole are measuredfrom available drawings and used in the FE model of thebridge.Fig. 8 shows the 3D FE model of the middle portion of thebridge, giving details on the arrangement of the stiffeningtruss, main cable, suspenders, and oor beams. The stiffeningtruss is modeled using beam elements, where the moments arereleased at the end of the diagonals and verticals. The steelgrid deck is represented as a beam with equivalent stiffness.The beams supporting the sidewalk also are shown in Fig. 8.The diagonal ties and oor beams are represented using 3Dbeam elements with six degrees of freedom at each node. Theeastern side of the bridge is identical to the western side exceptmember locations are shown in Figs. 2 and 7 and the T andB are members of the Howe truss. Notice that the stresses inthe members caused by live load plus dead load are much lessthan the allowable stress. Table 3 lists the deection at mid-span resulting from present-day live loads, i.e., 1,026.90 N/muniform load, obtained from the theoretical, a 2D model with-out stays, a 2D model with stays, and a 3D model. The the-oretical results have been obtained based on the elastic theorypresented in Steinman (1929) and also included in Venkata-TABLE 1. Measured Suspender ForcesSuspendernumberFIG. 7. 3D Model of Wheeling Suspension Bridge373839TABLE 2. Static AnalysisLive-load maximum stressMember (kN/m2)(1) (2)C 16,456.5S 21,024.30T 2577.25B 2211.48FB 333.27DT 21,240.76FIG. 8. 3D Model of Central Portion of Bridge4/ JOURNAL OF BRIDGE ENGINEERING / FEBRUARY 1999FIG. 9. Mode Shapes of 2D Model without Staysdemonstrated clearly in Table 4. The corresponding modeshapes are presented in Fig. 9.Modal analysis also was performed on the 2D model withstays for two cases: with and without initial forces in the maincable (Fig. 6). The lowest three natural frequencies and cor-responding mode shapes were evaluated. The frequencies arelisted in Table 5 and the corresponding mode shapes are shownin Figs. 10 and 11. The results indicated that the effect ofinitial forces increased the frequencies by approximately 4%compared with the results without initial forces.Modal analysis was performed on a 3D model of the Wheel-ing suspension bridge to determine the lowest six natural fre-quencies and mode shapes. They are listed in Table 6. As ex-TABLE 5. Wheeling Suspension Bridge (2D Model withStays): Natural FrequenciesWith initial forceNatural frequency(1)v1v2v3FE analysis(rad/s)(2)1.562.303.60Without initial force(rad/s)(2)1.762.103.77(rad/s)(3)1.552.403.30(rad/s)(3)1.691.993.67FIG. 10. Mode Shapes of 2D Model with Stays and InitialForcesTABLE 3. Midspan Deections Caused by Live Load2D withoutTheoretical stays 2D with stays 3D model(1) (2) (3) (4)44.34 cm 42.65 cm 27.48 cm 25.07 cmreddy (1995) for the 2D model. Static analysis with the FEcode included second-order effects for the 3D model. The de-ections clearly indicate the additional stiffness contributed bythe stays and the steel grid deck in the 2D models with staysand the 3D model, respectively. Results from 3D static anal-ysis showed that live load stresses in the stiffening truss andcables are within allowable limits and the deections at mid-span are acceptable. Specically, the span length over the mid-span deection ratio is 1,237 for live load. Rating factors ofhighly stressed structural members were calculated for present-day uniform loading of 1,026.90 N/m. None of them werebelow unity, which indicates that the present-day live load isnot overstressing any structural member (Venkatareddy 1995).MODAL ANALYSISSince the collapse of the Tacoma Narrows Bridge in 1940,considerable amount of research has been conducted to studythe dynamic behavior of cable suspension bridges, e.g., Gadeet al. (1976), Gimsing (1982), Kumarasena et al. (1991), andSeim et al. (1993). Early contributions by Bleich and Steinmanhave adopted an analytical approach. This 2D approach isbased on several assumptions and empirical rules that couldcompromise solution accuracy, such as torsional effects. How-ever, use of FEs, allows accommodation of various complex-ities of the structure. Comparisons between FE results and an-alytical approaches that yielded comparable results for simplemodels of cable suspension bridges have been reported by sev-eral researchers (West et al. 1984; Dumanoglu et al. 1992).In this study the natural frequencies and mode shapes of thestiffened suspension bridge are determined using FE analysis.Because of the complexity of the system and consideration ofthe stiffening effect of the forces in the main cables, the FEprocedure was examined through comparison with the well-documented analytical and experimental studies of the TacomaNarrows Bridge. The results of this research were comparedwith the results by West et al. (1984) and Bleich et al. (1950).Once comparison was completed the procedure was applied toperform modal analysis of the Wheeling suspension bridge.First, a 2D model of the Wheeling suspension bridge with-out stay cables, similar to the one used for the Tacoma Nar-rows Bridge, was developed to compare the FE modal analysisresults with elastic analysis results (Venkatareddy 1995).Transverse deformations were restrained in the 2D models,(Figs. 5 and 6). Beam and truss elements were used to modelthe system with stiffness and inertia properties correspondingto the deck and stiffening truss. The lowest three natural fre-quencies are listed together with the theoretical values ob-tained based on Bleichs elastic theory procedure (Bleich1950; Venkatareddy 1995) in Table 4. The excellent correlationof the 2D FE model without stays and theoretical results isTABLE 4. Wheeling Suspension Bridge (2D Model withoutStays): Natural FrequenciesTheoreticalNatural frequency(1)v1v2v3JOURNAL OF BRIDGE ENGINEERING / FEBRUARY 1999 /5The most severe seismic load combination corresponds to100% in the transverse, 66% in the vertical, and 30% in thelongitudinal direction. ForA= 0.06, the total stresses werewithin the allowable for most of the structure. However, sev-Frequency(rad/s)(2)1.851.992.572.883.334.74the stiffening truss of midspan failed in direct tension. Thestresses developed in the most heavily loaded members arealmost twice the allowable stresses, especially in oor beamsand diagonal ties. Damage also was constrained to the samemembers for the higher intensityA= 0.19. However, inelasticdeformation is expected to alter the response of the system asdetermined by the elastic analysis. Nevertheless, the fact thatno overstressing was imposed on the main cables and sus-penders indicates that catastrophic failure of the bridge forseismic excitations is highly unlikely. The localized damageof several oor beams and truss members could be avoidedthrough proper stiffening and possible installation of dampingdevices.TABLE 7. Displacements Caused by Dead Load and SeismicLoadsDead load Seismic loadDirection(1)XYZTABLE 8. Dead Load and Seismic Load StressesDead Dead loadload (kN/m2)(1) (2)C 15,748.69S 12,720.29T 0.00B 0.00FB 0.00DT 0.00ST 30,569.89eral oor beams would fail at the east tower. They exceededthe allowable stress of 1.38E5 kN/m2by 25%. ForA/= 0.15,the displacements at the midspan of the lower chord resultingfrom dead and seismic loads are given in Table 7. The fourthcolumn of Table 8 lists the stresses developed under dead loadand seismic load forA= 0.15 of the most heavily loadedmembers. For the modal combination of seismic stresses thesquare root of the sum of the squares method was used (Spy-rakos 1994). Floor beams and diagonal ties were overstressed(cm) (cm)(2) (3)0.00 0.8330.00 29.440.00 43.81Seismic load(kN/m2)(3)117,291.40188,803.0068,589.1265,202.606469,338.006211,140.00139,854.40Combined(kN/m2)(4)133,040.091101,523.2968,589.1265,202.606469,338.006211,140.00170,424.29is considered more realistic for cable suspension bridges (Oka-moto 1983; Federal Highway Administration 1987). A seismicanalysis also was performed forA= 0.19, representative of anMMI scale of VII earthquake, to examine the response of thisbridge as a representative suspension bridge of the several his-toric bridges built in the eastern United States with historicearthquakes higher than those predicted for the Wheeling sus-pension bridge.The design loads were obtained by superimposing the deadloads to the seismic forces developed along the longitudinaland transverse directions of the bridge according to AASHTO.The vertical component of the seismic motion also was in-cluded in the analysis (FHWA-IP-87-6). Because it is desirablefor the structure to remain elastic a response modication fac-torR= 1 was assigned to the superstructure. Because of in-sufcient data, the behavior of the towers and abutments wasnot studied.FIG. 11. Mode Shapes of 2D Model with Stays but without Ini-tial ForcesTABLE 6. Modal Analysis ResultsModenumber(1)123456near the supports of the east tower and also several chords ofpected the predominant deformation exhibited by the rstmode is along the transverse direction. A major difference be-tween 2D and 3D models is the representation of the decksystem as well as the inability of the 2D models to capturetorsional and coupled exural-torsional behavior. In the 3Dmodel the bridge is modeled with all load-carrying membersas they exist at the site, only the steel grid deck and the side-walk are replaced with equivalent beams. The 3D model usedin the analysis (Figs. 7 and 8) consists of 6,906 members witha total of over 41,000 degrees of freedom.SEISMIC ANALYSISA multimode spectral analysis was applied to obtain thebridge response to three different spectra. The rst spectra aredeveloped according to current AASHTO specications,whereas the second and third are based on historic earthquakesof the region. Specically, for West Virginia the code assignsa horizontal acceleration coefcient A of 0.05 (AASHTO1992). The ground acceleration corresponds to a 10% proba-bility of being exceeded in 50 years. Because of the historicsignicance of the bridge,Awas increased to 0.06 to corre-spond to a 10% probability of being exceeded in 100 years(Department of the Army, the Navy, and the Air Force 1986).Historically, MMI VI and VII earthquakes have been experi-enced in the area in the early eighteenth century (FederalHighway Administration 1987; King et al. 1993). These his-toric earthquakes can be characterized with an 0.08 A 0.25(Department of the Army, the Navy, and the Air Force 1986).In this studyA= 0.15 was selected as upper bound of an MMIscale of VI earthquake. Modeling of local soil conditions wasnot considered (Spyrakos 1992), and because of limited soildata information, the spectra were developed for site coef-cientS= 1.2. Because in the AASHTO codeCsmis based ona 5% critical damping,Csmwas increased by 25% that corre-sponds to 2% of critical damping (Department of the Army,the Navy, and the Air Force 1986). The 2% critical damping6/ JOURNAL OF BRIDGE ENGINEERING / FEBRUARY 1999buildings. Department of the Army, the Navy, and the Air Force, Wash-ington, D.C.Department of Highways. (1981). Wheeling suspension bridge. Con-tractors Proposal, Department of Highways, Charleston, W. Va.Dumanoglu, A. A., Brownjohn, J. M. W., and Severn, R. T. (1992). Seis-mic analysis of the Fatih Sultan Mehmat (second bosporus) suspensionbridge.J. Earthquake Engrg. and Struct. Dynamics, 21, 881906.Federal Highway Administration (FHwA). (1987). Seismic design andretrot manual for highway bridges.Rep. No. FHwA-IP-87-6, Of-ce of Implementation, HRT-10, Federal Highway Administration,McLean, Va.Gade, R. H., Bosch, H. R., and Podolny Jr., W. (1976). Recent aero-dynamic studies of long-span bridges.J. Struct. 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Congr. XII, American Society of Civil Engineers, NewYork, 762771.members, MS thesis, Coll. of Engrg., West Virginia University, Mor-gantown, W. Va.Spyrakos, C. C. (1992). Seismic behavior of bridge piers including soil-structure interaction.Com. and Struct., 43(2), 373384.Spyrakos, C. C. (1994).Finite element modeling in engineering practice.First Print, West Virginia University Press, West Virginia University,Morgantown, W. Va., Second Print, Algor Press, Pittsburgh, Pa.Steinman (1929).A practical treatise on suspension bridges, 2nd Ed.,Wiley, New York.Tsien, L. H. (1949). A simplied method of analyzing suspensionbridges.Trans. ASCE, 114.Ulstrup, C. C. (1993). Rating and preliminary analysis of suspensionbridges.J. Struct. Engrg., ASCE, 119(9), 26532679.Venkatared