208 128 0

Thêm vào bộ sưu tập

- Loading ...

Tài liệu hạn chế xem trước, để xem đầy đủ mời bạn chọn Tải xuống

Ngày đăng: 01/06/2018, 15:19

v = 110 km/h 335 m 146 m 25 15 -5 the truck leaves the **bridge** Mid-point vertical displacement (mm) - 146 m -15 -25 -35 -45 with tuned mass damper (TMD) without tuned mass damper (TMD) -55 10 20 30 40 Time (s) **Response** **of** Cable-Stayed **and** Suspension Bridges **to** Moving **Vehicles** Analysis methods **and** practical modeling techniques Raid Karoumi Royal Institute **of** Technology Department **of** Structural Engineering TRITA-BKN Bulletin 44, 1998 ISSN 1103-4270 ISRN KTH/BKN/B 44 SE Doctoral Thesis **Response** **of** Cable-Stayed **and** Suspension Bridges **to** Moving **Vehicles** Analysis methods **and** practical modeling techniques Raid Karoumi Department **of** Structural Engineering Royal Institute **of** Technology S-100 44 Stockholm, Sweden Akademisk avhandling Som med tillstånd av Kungl Tekniska Högskolan i Stockholm framlägges till offentlig granskning för avläggande av teknologie doktorsexamen fredagen den 12 februari 1999 kl 10.00 i Kollegiesalen, Valhallavägen 79, Stockholm Avhandlingen försvaras på svenska Fakultetsopponent: Huvudhandledare: Docent Sven Ohlsson Professor Håkan Sundquist TRITA-BKN Bulletin 44, 1998 ISSN 1103-4270 ISRN KTH/BKN/B 44 SE Stockholm 1999 **Response** **of** Cable-Stayed **and** Suspension Bridges **to** Moving **Vehicles** Analysis methods **and** practical modeling techniques Raid Karoumi Department **of** Structural Engineering Royal Institute **of** Technology S-100 44 Stockholm, Sweden _ TRITA-BKN Bulletin 44, 1998 ISSN 1103-4270 ISRN KTH/BKN/B 44 SE Doctoral Thesis **To** my wife, Lena, **to** my daughter **and** son, Maria **and** Marcus, **and** **to** my parents, Faiza **and** Sabah Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm framlägges till offentlig granskning för avläggande av teknologie doktorsexamen fredagen den 12 februari 1999 Raid Karoumi 1999 KTH, TS- Tryck & Kopiering, Stockholm 1999 Abstract This thesis presents a state-of-the-art-review **and** two different approaches for solving the moving load problem **of** cable-stayed **and** suspension bridges The first approach uses a simplified analysis method **to** study the dynamic **response** **of** simple cable-stayed **bridge** models The **bridge** is idealized as a Bernoulli-Euler beam on elastic supports with varying support stiffness **To** solve the equation **of** motion **of** the bridge, the finite difference method **and** the mode superposition technique are used The second approach is based on the nonlinear finite element method **and** is used **to** study the **response** **of** more realistic cable-stayed **and** suspension **bridge** models considering exact **cable** behavior **and** nonlinear geometric effects The cables are modeled using a two-node catenary **cable** element derived using “exact” analytical expressions for the elastic catenary Two methods for evaluating the dynamic **response** are presented The first for evaluating the linear traffic load **response** using the mode superposition technique **and** the deformed dead load tangent stiffness matrix, **and** the second for the nonlinear traffic load **response** using the Newton-Newmark algorithm The implemented programs have been verified by comparing analysis results with those found in the literature **and** with results obtained using a commercial finite element code Several numerical examples are presented including one for the Great Belt suspension **bridge** in Denmark Parametric studies have been conducted **to** investigate the effect of, among others, **bridge** damping, bridge-vehicle interaction, cables vibration, road surface roughness, vehicle speed, **and** tuned mass dampers From the numerical study, it was concluded that road surface roughness has great influence on the dynamic **response** **and** should always be considered It was also found that utilizing the dead load tangent stiffness matrix, linear dynamic traffic load analysis give sufficiently accurate results from the engineering point **of** view Key words: cable-stayed bridge, suspension bridge, Great Belt suspension bridge, bridge, moving loads, traffic-induced vibrations, bridge-vehicle interaction, dynamic analysis, **cable** element, finite element analysis, finite difference method, tuned mass damper –i– – ii – Preface The research presented in this thesis was carried out at the Department **of** Structural Engineering, Structural Design **and** Bridges group, at the Royal Institute **of** Technology (KTH) in Stockholm The project has been financed by KTH **and** the Axel **and** Margaret Ax:son Johnson Foundation The work was conducted under the supervision **of** Professor Håkan Sundquist **to** whom I want **to** express my sincere appreciation **and** gratitude for his encouragement, valuable advice **and** for always having time for discussions I also wish **to** thank Dr Costin Pacoste for reviewing the manuscript **of** this report **and** providing valuable comments for improvement Finally, I would like **to** thank my wife Lena Karoumi, my daughter **and** son, **and** my parents for their love, understanding, support **and** encouragement Stockholm, January 1999 Raid Karoumi – iii – – iv – original configuration - convergence study number **of** increments Dynamic Amplification Factors (DAF) Vertical displacement at node 14 Vertical displacement at node 18 Horizontal displacement **of** node 43 Axial force in deck element 30 at node Shear force in element 52 at node 36 Axial force in element 52 at node 36 Bending moment in element 52 at node 36 Axial force in **cable** Axial force in **cable** 13 Absolute maximum vertical accel at node 14 (m/s2) Maximum normalized bridge-vehicle contact force 1000 500 1500 1000 linear dynamic - 30 modes all modes 1.186 1.179 1.207 1.186 1.243 1.234 1.270 1.243 1.086 1.065 1.057 1.065 1.404 1.393 1.391 1.394 1.212 1.174 1.164 1.160 1.270 1.268 1.284 1.268 1.180 1.166 1.222 1.159 1.316 1.294 1.284 1.284 1.157 1.133 1.125 1.133 0.125 0.123 0.160 0.125 1.049 1.039 1.036 1.039 Dynamic Amplification Factors (DAF) trucks Vertical displacement at node 14 Vertical displacement at node 18 Horizontal displacement **of** node 43 Axial force in deck element 30 at node Shear force in element 52 at node 36 Axial force in element 52 at node 36 Bending moment in element 52 at node 36 Axial force in **cable** Axial force in **cable** 13 Absolute maximum vertical accel at node 14 (m/s2) Maximum normalized bridge-vehicle contact force Table 10.6 elem/cable nonlinear 1.087 1.289 1.272 1.237 1.272 1.272 1.268 1.101 1.208 0.316 1.078 v = 50 v = 70 simply supported 1000 1500 500 nonlinear dynamic 1.208 1.187 1.180 1.240 1.235 1.230 1.094 1.060 1.053 1.374 1.390 1.387 1.205 1.154 1.149 1.279 1.301 1.275 1.210 1.152 1.150 1.240 1.275 1.268 1.164 1.135 1.126 0.158 0.140 0.124 1.049 1.039 1.036 v = 110 v = 130 = girder linear nonlin 1.131 1.130 1.119 1.112 1.250 1.247 1.360 1.364 1.222 1.087 1.270 1.290 1.431 1.442 1.240 1.238 1.232 1.234 0.121 0.136 1.041 1.041 = = trucks trucks moving linear nonlin 1.060 1.056 1.286 1.265 1.279 1.274 1.237 1.246 1.285 1.271 1.251 1.202 1.276 1.262 1.086 1.035 1.239 1.242 0.336 0.316 1.071 1.073 = = force model linear nonlin 1.048 1.048 1.171 1.162 1.202 1.199 1.205 1.214 1.198 1.181 1.229 1.173 1.207 1.188 1.358 1.345 1.211 1.213 0.275 0.266 1.000 1.000 bump TMD km/h km/h km/h km/h 0.01 0.015 0.02 0.03 30 mm v = 110 nonlin nonlin nonlin nonlin nonlin nonlin nonlin nonlin nonlin nonlin nonlin 1.041 1.132 1.282 1.204 1.220 1.164 1.143 1.124 1.093 1.188 1.245 1.057 1.003 1.427 1.060 1.285 1.202 1.170 1.143 1.102 1.233 1.378 1.178 1.086 1.131 1.205 1.106 1.032 1.010 0.992 0.984 1.059 1.065 1.112 1.176 1.414 1.427 1.401 1.381 1.372 1.362 1.329 1.601 1.413 1.195 1.100 1.331 1.230 1.211 1.127 1.102 1.097 1.087 1.172 1.266 1.189 1.241 1.511 1.461 1.395 1.258 1.222 1.193 1.168 1.329 1.463 1.178 1.104 1.323 1.244 1.239 1.123 1.103 1.097 1.087 1.211 1.260 1.024 1.101 1.206 1.408 1.300 1.258 1.241 1.226 1.202 1.331 1.205 1.082 1.008 1.104 1.205 1.180 1.107 1.082 1.063 1.038 1.138 1.083 0.067 1.024 0.091 1.042 0.145 1.059 0.202 1.060 0.195 1.039 0.118 1.039 0.099 1.039 0.086 1.039 0.075 1.040 0.141 1.446 0.137 1.059 Dynamic amplification factors (DAF), absolute maximum vertical acceleration at node 14, **and** maximum normalized bridge-vehicle contact force Note that even the linear dynamic analysis referred **to** in this table is based on the dead load tangent stiffness matrix obtained from a nonlinear static analysis Chapter Conclusions **and** Suggestions for Further Research 11.1 Conclusions **of** Part B The conclusions from the study conducted in Part B **of** this thesis are presented in the following two subsections In the first subsection, conclusions concerning the nonlinear finite element modeling **of** **cable** supported bridges are presented, **and** in the second subsection, conclusions are presented concerning the **response** due **to** moving **vehicles** 11.1.1 Nonlinear finite element modeling technique The present work has presented a method for modeling **cable** supported bridges for the nonlinear finite element analysis A two-node catenary **cable** element was adopted for modeling the cables **and** a beam element for modeling the girder **and** the pylons This study has shown that the adopted elements are accurate **and** efficient for nonlinear analysis **of** cable-stayed **and** suspension bridges It has been confirmed that the main advantages **of** the **cable** element are the simplicity **of** including the effect **of** pretension **of** the **cable** **and** the exact treatment **of** **cable** sag **and** **cable** weight Moreover, the iterative process adopted, **to** find the internal force vector **and** tangent stiffness matrix for the **cable** element, was found **to** converge very rapidly According **to** the author’s opinion, linear analysis utilizing the traditional equivalent modulus approach, is not satisfactory for modern cable-stayed bridges Modern cablestayed bridges built today or proposed for future bridges are, as they are highly flexible, subjected **to** large displacements The equivalent modulus approach however – 181 – accounts only for the sag effect but not for the stiffening effect due **to** large displacements [7] It was found that the catenary **cable** element is simple **to** formulate, accurate, **and** can correctly model the geometric change **of** the **cable** at any tension level This makes the element very attractive, especially for static **response** calculations, **and** the author strongly recommends the use **of** this element However, one drawback is when using commercial finite element codes for analysis, as only few commercial codes, e.g ABAQUS, enable the users **to** define their own elements This disadvantage applies also **to** the one bar element equivalent modulus approach It has been demonstrated that **cable** supported bridges have a hardening characteristic with respect **to** the applied load Furthermore, due **to** the highly nonlinear behavior during the static application **of** the dead load, a nonlinear static analysis is required **to** arrive at the deformed dead load tangent stiffness matrix Replacing each **cable** by several catenary **cable** elements has demonstrated that, in addition **to** obtaining new pure **cable** modes **of** vibration, **cable** motions are also associated with every bending mode **of** vibration **To** simplify the data input process when utilizing the multi-element **cable** discretization, one can start from a straight **cable** configuration **and** during analysis the **cable** configuration under its own weight is determined accurately after few iterations Finally, this work has only focused on two-dimensional modeling **of** **cable** supported bridges However, the catenary **cable** element used in this study is also applicable for modeling cables in other types **of** **cable** structures [35, 63, 64], such as: suspended roofs, guyed masts, electric transmission lines, moored floating bridges, etc Moreover, with some minor modifications **of** the **cable** element matrices this element can also be used for modeling cables for three-dimensional analysis For such analysis, threedimensional catenary **cable** **and** beam elements can be found in [35, 61] 11.1.2 **Response** due **to** moving **vehicles** An investigation was conducted **to** analyze the **response** **of** realistic two-dimensional cable-stayed **and** suspension **bridge** models under the action **of** moving **vehicles** For the analysis **of** the dynamic response, two approaches were implemented: one for evaluating the linear dynamic **response** **and** one for the nonlinear dynamic **response** Further, nonlinear geometric effects, “exact” **cable** behavior, **and** realistically – 182 – estimated **bridge** damping, were considered This investigation has mainly focused on comparing linear **and** nonlinear traffic load dynamic responses **and** also on the effect **of** bridge-vehicle interaction, road surface roughness, vehicle speed, **bridge** damping, **cable** modeling, **and** tuned vibration absorbers Based on this investigation **of** the traffic load **response** **of** cable-stayed **and** suspension bridges, the following conclusions can be made: • utilizing the tangent stiffness matrix (obtained from a nonlinear static analysis under dead load), linear static **and** linear dynamic traffic load analysis **of** **cable** supported bridges give sufficiently accurate results from the engineering point **of** view Moreover, the mode superposition technique was found **to** be very efficient as accurate results could be obtained based on only 25 **to** 30 modes **of** vibration Thus, this linear dynamic procedure is especially appropriate for analyzing **bridge** models with many degrees **of** freedom • **bridge** deck surface roughness **and** irregularities in the approach pavements **and** over bearings have a tremendous effect on the dynamic **response** **To** reduce damage **to** bridges not only maintenance **of** the **bridge** deck surface is important but also the elimination **of** irregularities (unevenness) in the approach pavements **and** over bearings It is also suggested that the formulas for dynamic amplification factors specified in **bridge** design codes should not only be a function **of** the fundamental natural frequency or span length (as in many present design codes) but should also consider the road surface condition • for more detailed **and** accurate studies where the most accurate representation **of** the true dynamic **response** is required, it is recommended **to** consider the cables motion **and** modes **of** vibration in the dynamic analysis by utilizing the multielement **cable** discretization This is also necessary **to** avoid an underestimation **of** the **bridge** dynamic **response** • **bridge** damping has a significant effect upon the **response** **and** should always be considered in such analysis Some dynamic amplification factors are very sensitive **to** **bridge** damping ratio **and** the relationship is not always linear **Bridge** damping ratios should be carefully estimated **to** insure more correct **and** accurate representation **of** the true dynamic **response** **To** obtain realistic damping ratios, such estimation should be based on results from tests on similar bridges Unfortunately, results from many studies **of** the dynamic **response** **of** cable-stayed – 183 – bridges found in the literature are not useful, as they have been conducted using either unrealistically high damping ratios for such bridges or no damping at all • a tuned mass damper is not very effective in reducing the maximum dynamic **response** during the forced vibration period (i.e when the vehicle is on the bridge) In fact, such a device can even increase some **of** the dynamic amplification factors However, the reduction **of** the vibration level in the free vibration period is significant as the tuned mass damper increases the overall damping **of** the **bridge** by working as an additional energy dissipater • the moving force model (constant force idealization **of** the vehicle load) can lead **to** unnecessary overestimation **of** the dynamic amplification factors compared **to** the sprung mass model It is believed that the sprung mass vehicle models are causing this by acting as vibration absorbers • the dynamic amplification factors **of** **cable** supported bridges can reach high values, higher than 1.30, even if maintenance **of** the road surface is made regularly This situation should be considered in the design practice **of** such bridges For the studied cable-stayed bridge, high dynamic amplification factors were obtained for the axial force in the girder near the pylons **and** for the tension in the shortest cables in the side spans For this bridge, the designer should consider installation **of** **cable** dampers especially for the shortest cables **to** increase the fatigue life **of** the cables 11.2 Suggestions for further research Based on the performed investigation, the following suggestions for further research can be given: • The effect **of** **cable** modeling **and** tuned mass dampers should be more thoroughly investigated using realistic trains **of** moving **vehicles** **and** considering road surface roughness **and** different vehicle speeds, as this could not be accomplished in this study due **to** time limitation Moreover, for future research it is suggested **to** use simulated trains **of** moving traffic based on collected statistical traffic data • The dependency **of** **bridge** **response** **and** dynamic amplification factors on the way in which the girder is connected **to** the pylons **and** on other modern girder supporting conditions, should be investigated – 184 – • Further work is needed **to** study the effect **of** using finer models (i.e more elements for discretizing the **bridge** girder **and** pylons) **of** the two studied **cable** supported bridges **and** also three-dimensional models **to** include torsional effects **and** torsional modes **of** vibration in the analysis • Extensive testing on a **cable** supported **bridge** should be performed **to** assess the validity **of** the analysis methods **and** the theoretical findings • Research is needed **to** thoroughly study active structural control **of** **cable** supported bridges **and** examine the effectiveness **of** active devices on suppressing **bridge** vibrations due **to** moving **vehicles** As discussed earlier in section 8.4, the performance **of** a tuned mass damper (TMD, passive device) significantly deteriorates when the dynamic characteristics **of** the **bridge** changes (i.e are different from the original characteristics assumed during the optimal design **of** the TMD) Thus, a superior solution can be obtained by using a socalled active tuned mass damper (ATMD) Such a damper comprises computer controlled servo-hydraulic actuators that can, when needed, modify the TMD properties **to** improve its efficiency The computer continuously monitors the dynamic characteristics **of** the **bridge** using e.g sensors attached **to** the **bridge** deck Active control **of** structures using cables was proposed by Freyssinet as early as 1960 [67] Today, active control is applied in advanced airplanes for suppression **of** aerodynamic instability, in high-speed trains like the Swedish train X2000 **to** improve riding comfort, **and** in modern cars like the Mercedes A-class **to** improve stability Active controls, e.g active modification **of** **bridge** deck edge shape **to** enhance resistance **to** aerodynamic instabilities like flutter, are also considered for new **cable** supported bridges with very long spans such as for the Messina crossing **and** the Gibraltar crossing It is believed that, as the cost **of** such active systems is high, they can only be economical for long span bridges where they can induce big saving in construction material Furthermore, since some people are perhaps not ready **to** rely on computers when crossing a bridge, active control should as a first step only be used **to** improve serviceability aspects such as riding comfort, whereas e.g the stability **of** the **bridge** have **to** rely entirely on the **bridge** structure itself For cable-stayed bridges real time vibration control can be achieved by e.g computer controlling the tension in some cables, so-called active cables, in order **to** counteract – 185 – traffic loads at any time Such control system is based on the idea **of** constantly monitoring movements **of** the **bridge** using attached sensors **and** via computer controlled tensioning jacks, the pretensioning force in the cables is changed Such bridges can be referred **to** as smart bridges as they have the capability **of** modifying their behavior during the dynamic loading The author believes that active vibration control **of** long span cable-stayed **and** suspension bridges will be an area **of** significant interest in the future Till now analysis **and** application **of** active vibration control **of** structures excited by moving loads have attracted limited research efforts For the interested reader, excellent literature review **and** state-of-the-art review on control **and** monitoring **of** civil engineering structures are found in [30, 67] Recent studies describing active control **of** bridges are presented in [5, 62, 69] – 186 – Appendix Maple Procedures The Maple procedures, used **to** generate the Fortran code for the elements presented in Chapter 7, are given below Each comment line starts with the symbol # A.1 **Cable** element # Tangent stiffness matrix Kt for; # the catenary **cable** element; readlib(fortran); with(linalg); Ly:=1/(2*E*A*w)*(Tj^2-Ti^2)+(Tj-Ti)/w; Lx:=-P1*(Lu/E/A+1/w*ln((P4+Tj)/(Ti-P2))); P3:=-P1; P4:=w*Lu-P2; Ti:=sqrt(P1^2+P2^2); Tj:=sqrt(P3^2+P4^2); f11:=diff(Lx,P1): f12:=diff(Lx,P2): f21:=diff(Ly,P1): f22:=diff(Ly,P2): f:=matrix(2,2,[f11,f12,f21,f22]): k:=inverse(f): k1:=k[1,1]: k2:=k[1,2]: k4:=k[2,2]: – 187 – Kt:=matrix(4,4,[-k1,-k2,k1,k2,-k2,-k4,k2,k4,k1,k2,-k1,-k2,k2,k4,-k2,-k4]): fortran(Kt,optimized): A.2 Beam element # Internal force vector p and; # tangent stiffness matrix Kt for; # the beam element; readlib(fortran); with(linalg); ux:=(u4-u1)/L; wx:=(u5-u2)/L; t:=(u3+u6)/2; tx:=(u6-u3)/L; e:=(1+ux)*cos(t)+wx*sin(t)-1; g:=wx*cos(t)-(1+ux)*sin(t); k:=tx; PIe:=1/2*L*E*A*e^2; PIg:=1/2*L*G*A*g^2; PIk:=1/2*L*E*I*k^2; PI:=PIe+PIg+PIk; p:=grad(PI,[u1,u2,u3,u4,u5,u6]); Kt:=hessian(PI,[u1,u2,u3,u4,u5,u6]); fortran(p,optimized); fortran(Kt,optimized); – 188 – Bibliography **of** Part B [1] ABAQUS User’s Manual, Hibbitt, Karlsson & Sorensen, Inc., Providence, Rhode Island, 1994 [2] Abbas S., Scordelis A., ‘Nonlinear Analysis **of** Cable-Stayed Bridges’, Proc Int Conference on Cable-Stayed **and** Suspension Bridges, Vol 2, Deauville, France, Oct 1994, pp 195-210 [3] Abdel-Ghaffar A.M., Khalifa M.A., ‘Importance **of** **Cable** Vibration in Dynamics **of** Cable-Stayed Bridges’, J Eng Mechanics, ASCE, 117, 1991, pp 2571-2589 [4] Abdel-Ghaffar A.M., Nazmy A.S., ‘3-D Nonlinear Seismic Behavior **of** CableStayed Bridges’, J Struct Eng., ASCE, 117, 1991, pp 3456-3476 [5] Adeli H., Saleh A., ‘Optimal Control **of** Adaptive/Smart **Bridge** Structures’, J Struct Eng., ASCE, 123, 1997, pp 218-226 [6] Adeli H., Zhang J., ‘Fully Nonlinear Analysis **of** Composite Girder CableStayed Bridges’, Computers **and** Structures, 54, 1995, pp 267-277 [7] Ali H.M., Abdel-Ghaffar A.M., ‘Modeling the Nonlinear Seismic Behavior **of** Cable-Stayed Bridges with Passive Control Bearings’, Computers **and** Structures, 54, 1995, pp 461-492 [8] Argyris J., Mlejnek H.P., Dynamics **of** Structures, North-Holland, Amsterdam, 1991 [9] Aurell J., Edlund S., ‘Vehicle Dyamics **of** Commercial Vehicles’, Volvo Technology Report, 1990, pp 20-35 [10] Bachmann H., Weber B., ‘Tuned Vibration Absorbers for “Lively” Structures’, Struct Eng Int., Vol 5, No 1, 1995, pp 31-36 – 189 – [11] Bathe K.J., Finite Element Procedures, Prentice Hall, New Jersey, 1996 [12] Boonyapinyo V., Yamada H., Miyata T., ‘Wind-Induced Nonlinear LateralTorsional Buckling **of** Cable-Stayed Bridges’, J Struct Eng., ASCE, 120, 1994, pp 486-506 [13] Bruno D., Grimaldi A., ‘Nonlinear Behaviour **of** Long-Span Cable-Stayed Bridges’, Meccanica, 20, 1985, pp 303-313 [14] Buchholdt H.A., An Introduction **to** **Cable** Roof Structures, Cambridge University Press, Cambridge, 1985 [15] Buchholdt H.A., Structural Dynamics for Engineers, Thomas Telford, London, 1997 [16] Conti E., Grillaud G., Jacob J., Cohen N., ‘Wind Effects on the Normandie Cable-Stayed Bridge: Comparison Between Full Aeroelastic Model Tests **and** Quasi-Steady Analytical Approach’, Proc Int Conference on Cable-Stayed **and** Suspension Bridges, Vol 2, Deauville, France, Oct 1994, pp 81-90 [17] Crisfield M.A., Non-linear Finite Element Analysis **of** Solids **and** Structures, Wiley, Chichester, 1991 [18] Das A.K., Dey S.S., ‘Effect **of** Tuned Mass Dampers on Random **Response** **of** Bridges’, Computer & Structures, Vol 43, No 4, 1992, pp 745-750 [19] Davenport A., Larose G., ‘The Structural Damping **of** Long Span Bridges: An Interpretation **of** Observations’, Canada-Japan Workshop on Aerodynamics, Ottawa, Sept 1989 [20] Dean D.L., ‘Static **and** Dynamic Analysis **of** Guy Cables’, J Struct Division, ASCE, 87, 1961, pp 1-21 [21] Den Hartog J.P., Mechanical Vibrations, 4th edition, McGraw-Hill, New York, 1956 [22] Fleming J.F., Egeseli E.A., ‘Dynamic Behaviour **of** a Cable-Stayed Bridge’, Earthquake Eng **and** Struct Dynamics, 8, 1980, pp 1-16 – 190 – [23] Forsell K., ‘Dynamic Analyses **of** Static Instability Phenomena’, Licentiate Thesis, TRITA-BKN Bulletin 34, Dept **of** Struct Eng., Royal Institute **of** Technology, Stockholm, 1997 [24] Frýba L., Vibration **of** Solids **and** Structures under Moving Loads, Noordhoff International Publishing, Groningen, 1972 [25] Gambhir M.L., Batchelor B., ‘A Finite Element for 3-D Prestressed Cablenets’, Int J Numer Methods in Eng., 11, 1977, pp 1699-1718 [26] Géradin M., Rixen D., Mechanical Vibrations, Wiley, Chichester, 1994 [27] Gimsing N.J., **Cable** Supported Bridges, second edition, Wiley, Chichester, 1997 [28] Gimsing N.J., Technical University **of** Denmark, Tanaka H., Danish Maritime Institute, **and** Esdahl S., COWIconsult A/S, Personal communication, 1997 [29] Green M.F., Cebon D., ‘Dynamic Interaction Between Heavy **Vehicles** **and** Highway Bridges’, Computer & Structures, Vol 62, No 2, 1997, pp 253-264 [30] Housner G.W., Bergman L.A., Gaughey T.K., Chassiakos A.G., Claus R.O., Masri S.F., Skelton R.E., Soong T.T., Spencer B.F., Yao J.T.P., ‘Structural Control: Past, Present, **and** Future’, J Eng Mechanics, ASCE, 123, 1997, pp 897-971 [31] Huddleston J.V., ‘Computer Analysis **of** Extensible Cables’, J Eng Mechanics Div., ASCE, 107, 1981, pp 27-37 [32] Huddleston J.V., Ham H.J., ‘Poisson Effect in Extensible Cables with Both Ends Fixed’, J Eng Mechanics Div., ASCE, 120, 1994, pp 1590-1595 [33] Indrawan B., ‘Vibrations **of** a Cable-Stayed **Bridge** due **to** Vehicle Moving over Rough Surface’, Master Thesis, Asian Institute **of** Technology, Bangkok, March 1989 [34] Irvine H.M., **Cable** Structures, MIT Press, Cambridge, 1992 [35] Jayaraman H.B., Knudson W.C., ‘A Curved Element for the Analysis **of** **Cable** Structures’, Computers **and** Structures, 14, 1981, pp 325-333 – 191 – [36] Jensen G., Petersen A., ‘Erection **of** Suspension Bridges’, Proc Int Conference on Cable-Stayed **and** Suspension Bridges, Vol 2, Deauville, France, Oct 1994, pp 351-362 [37] Johnson R., Larose G., ‘Field Measurements **of** the Dynamic **Response** **of** the Höga Kusten **Bridge** During Construction’, TRITA-BKN Report 49, Dept **of** Struct Eng., Royal Institute **of** Technology, Stockholm, 1998 [38] Jones R.T., Pretlove A.J., ‘Vibration Absorbers **and** Bridges’, The Highway Engineer, 26, No 1, 1979, pp 2-9 [39] Judd B.J., Wheen R.J., ‘Nonlinear **Cable** Behavior’, J Struct Division, ASCE, 104, 1978, pp 567-575 [40] Kanok-Nukulchai W., Hong G., ‘Nonlinear Modelling **of** Cable-Stayed Bridges’, J Construct Steel Research, 26, 1993, pp 249-266 [41] Kanok-Nukulchai W., Yiu P.K.A., Brotton D.M., ‘Mathamatical Modelling **of** Cable-Stayed Bridges’, Struct Eng Int., 2, 1992, pp 108-113 [42] Karoumi R., ‘Dynamic **Response** **of** Cable-Stayed Bridges Subjected **to** Moving Vehicles’, IABSE 15th Congress, Denmark, 1996, pp 87-92 [43] Kawashima K., Unjoh S., Tsunomoto M., ‘Damping Characteristics **of** **Cable** **Stayed** Bridges for Seismic Design’, J Res Public Works Res Inst., Vol 27, Dec 1991 [44] Kawashima K., Unjoh S., Tsunomoto M., ‘Estimation **of** Damping Ratio **of** Cable-Stayed Bridges for Seismic Design’, J Struct Eng., ASCE, Vol 119, No 4, April 1993, pp 1015-1031 [45] Kwon H.C., Kim M.C., Lee I.W., ‘Vibration Control **of** Bridges Under Moving Loads’, Computer & Structures, Vol 66, No 4, 1998, pp 473-480 [46] Larose G.L., Zasso A., Melelli S., Casanova D., ‘Field Measurements **of** the Wind-Induced **Response** **of** a 254 m High Free-Standing **Bridge** Pylon’, Proc **of** the 2nd European African Conference on Wind Engineering, Genova, Italy, June 1997, pp 1-8 – 192 – [47] Larsen A., Jacobsen A.S., ‘Aerodynamic Design **of** the Great Belt East Bridge’, Proc 1st Int Symposium on Aerodynamics **of** Large Bridges, Copenhagen, Denmark, Feb 1992, pp 269-283 [48] Larsen A., ‘Aerodynamic Aspects **of** the Final Design **of** the 1624 m Suspension **Bridge** Across the Great Belt’, J Wind Eng **and** Industrial Aerodynamics, Elsevier, 48, 1993, pp 261-285 [49] Leonard J.W., Tension Structures, McGraw-Hill, New York, 1988 [50] Luft R.W., ‘Optimal Tuned Mass Dampers for Buildings’, J Struct Division, ASCE, Vol 105, No ST12, Dec 1979, pp 2766-2772 [51] Madsen B.S., Sorensen L.T., ‘Manufacture **and** Erection **of** the Steel Main Span’, Proc Int Conference on Cable-Stayed **and** Suspension Bridges, Vol 1, Deauville, France, Oct 1994, pp 691-697 [52] MAPLE V Language Reference Manual, Springer-Verlag, New York, 1991 [53] MATLAB Using Matlab Version 5, The MathWorks Inc., Natick, 1996 [54] McNamara R.J., ‘Tuned Mass Dampers for Buildings’, J Struct Division, ASCE, Vol 103, No ST9, Feb 1977, pp 1785-1798 [55] Nazmy A.S., Abdel-Ghaffar A.M., ‘Three-Dimensional Nonlinear Static Analysis **of** Cable-Stayed Bridges’, Computers **and** Structures, 34, 1990, pp 257-271 [56] O'Brien T., Francis A.J., ‘Cable Movements Under Two-Dimensional Loads’, J Struct Division, ASCE, 90, 1964, pp 89-123 [57] O'Brien T., ‘General Solution **of** Suspended **Cable** Problems’, J Struct Division, ASCE, 93, 1967, pp 1-26 [58] Ostenfeld K.H., Larsen A., ‘Bridge Engineering **and** Aerodynamics’, Proc 1st Int Symposium on Aerodynamics **of** Large Bridges, Copenhagen, Denmark, Feb 1992, pp 3-22 [59] Ostenfeld K.H., ‘Long Span Bridges: State-of-the-art’, Väg- och Vattenbyggaren, J Swedish Society **of** Civil Eng., 6·97, pp 26-31 – 193 – [60] Ozdemir H., ‘A Finite Element Approach for **Cable** Problems’, Int J Solids Structures, 15, 1979, pp 427-437 [61] Pacoste C., Eriksson A., ‘Beam Elements in Instability Problems’, Comput Methods Appl Mech Eng., 144, 1997, pp 163-197 [62] Patten W.N., Sack R.L., He Q., ‘Controlled Semiactive Hydraulic Vibration Absorber for Bridges’, J Struct Eng., ASCE, Vol 122, No 2, Feb 1996, pp 187-192 [63] Peyrot A.H., Goulois A.M., ‘Analysis **of** **Cable** Structures’, Computers **and** Structures, 10, 1979, pp 805-813 [64] Peyrot A.H., Goulois A.M., ‘Analysis **of** Flexible Transmission Lines’, J Struct Division, ASCE, 104, 1978, pp 763-779 [65] Raoof M., ‘Estimation **of** Damping Ratio **of** Cable-Stayed Bridges for Seismic Design’, J Struct Eng., ASCE, Vol 120, No 8, Aug 1994, pp 2548-2550 [66] Setareh M., Hanson R.D., ‘Tuned Mass Dampers **to** Control Floor Vibration from Humans’, J Struct Eng., ASCE, Vol 118, No 3, March 1992, pp 741762 [67] Soong T.T., ‘State-of-the-art Review: Active Structural Control in Civil Engineering ’, Eng Struct., 10, 1988, pp 74-84 [68] Walther R., Houriet B., Isler W., Moïa P., **Cable** **Stayed** Bridges, Thomas Telford, London, 1988 [69] Wells M., ‘Active Structural Control: an Appraisal for a Practical Application The Royal Victoria Footbridge London Docklands’, J Constructional Steel Research, 46:1-3, 1998, paper no 59 – 194 – ... moving load problem of cable- stayed and suspension bridges The first approach uses a simplified analysis method to study the dynamic response of simple cable- stayed bridge models The bridge is idealized... predict their response due to moving vehicles Not only the dynamic behavior of new bridges need to be studied and understood but also the response of existing bridges, as governments and the industry... 1.1 and Figure 1.2 The first modern cable- stayed bridge was the Strömsund Bridge in Sweden opened to traffic in 1956 For the study of the concept, design and construction of cable- stayed bridges,

- Xem thêm - Xem thêm: Response of cable stayed and susspension bridge to moviing vehicles , Response of cable stayed and susspension bridge to moviing vehicles

- xác định các mục tiêu của chương trình
- khảo sát chương trình đào tạo của các đơn vị đào tạo tại nhật bản
- mở máy động cơ lồng sóc
- mở máy động cơ rôto dây quấn
- các đặc tính của động cơ điện không đồng bộ
- hệ số công suất cosp fi p2
- đặc tuyến mômen quay m fi p2
- sự cần thiết phải đầu tư xây dựng nhà máy
- từ bảng 3 1 ta thấy ngoài hai thành phần chủ yếu và chiếm tỷ lệ cao nhất là tinh bột và cacbonhydrat trong hạt gạo tẻ còn chứa đường cellulose hemicellulose
- chỉ tiêu chất lượng 9 tr 25