STUDY ON THE SEISMIC BEHAVIOR OF SELF-ANCHORED SUSPENSION BRIDGES

Transcription

1 384 Journal of Marine Siene and Tehnology, Vol., No. 4, pp () DOI:.69/JMST--34- STUDY ON THE SEISMIC BEHAVIOR OF SELF-ANCHORED SUSPENSION BRIDGES Wen-Liang Qiu, Chang-Huan Kou, Chin-Sheng Kao 3, Shih-Wei Ma, and Jiun Yang Key words: self-anhored suspension bridge, seismi behavior, dutility seismi response analysis, metal damper seismi response analysis. ABSTRACT The suspension bridge has a beautiful strutural shape and an exellent spanning ability. The self-anhored suspension bridge has its main ables anhored diretly on the two ends of the main girders, saving onstrution osts and time inurred during the anhorage onstrution of an earth-anhored suspension bridge. However, the feasibility of a self-anhored suspension bridge in a strong earthquake zone and the use of dampers to redue seismi responses have yet to be fully investigated. Using the Yellow-River Road Bridge in Mainland as an example, this study sets out to analyze and investigate a series of seismi responses of a self-anhored suspension bridge, with the purpose of understanding its seismi responses in a strong earthquake zone and the effetiveness of metal dampers in reduing the seismi response. In this paper, in addition to performing a linearly elasti seismi analysis, the dutility seismi response was also analyzed. Additionally, metal dampers were installed at the joints of main girders and towers so that the energy damping effet an be investigated. The results of this researh will be useful to the aademi researh ommunity and for pratial engineering appliations. I. INTRODUCTION Paper submitted 3//; revised /4/; aepted 3/4/. Author for orrespondene: Chang-Huan Kou ( hkou@hu.edu.tw). Shool of Civil Engineering, Dalian University of Tehnology, Dalian City, Liaoning Provine, China, P.R.C. Department of Civil Engineering, Chunghua University, Hsinhu City, Taiwan, R.O.C. 3 Department of Civil Engineering, Tamkang University, Tamsui, Taipei County, Taiwan, R.O.C. The suspension bridge is a flexural bridge struture omposed of main ables, hangers, bridge towers and main girders. Due to the beautiful strutural shape and its spanning apability, the suspension bridge is often seen as a landmark struture rossing a river. Beause its main ables are anhored diretly on the two ends of the main girders, the self-anhored suspension bridge an save muh osts and time spent on onstruting the anhorages of an earth-anhored suspension bridge. In addition, the axial ompressive fores exerted by the main ables on the main girders may be used as prestressed fores for the girders whih an inrease the bending resistane apaity of the reinfored onrete main girders. Thus, the self-anhored suspension bridge is an eonomial suspension bridge. Due to the differenes in anhorage, the seismi response of a self-anhored suspension bridge is different from that of an earth-anhored suspension bridge. It has its own harateristis. Beause the main ables are anhored on the two ends of the main girders, the anhors move together with the girders and the tops of the towers also move with the main girders due to the linking of the ables, whih makes of the self-anhored suspension bridge to be a longitudinal floating system. Under the longitudinal seismi fore, the displaements of the main girders and the top of the towers, and the bending moments at the tower bottoms are all very large. Thus, the most important part of the seismi design for this type of bridge is to ontrol the fores and displaements of the bridge by use of damping devies. The early onstruted self-anhored suspension bridges with short span all use steel main girders [7], so the seismi responses do not ontrol the bridge design and few studies on the seismi response of self-anhored suspension bridges were arried out. However, with some long-span self-anhored suspension bridges building in reent years, seismi ation often ontrols the fores and displaements of the design espeially for self-anhored suspension bridges with reinfored onrete main girders. Investigators have started to pay attention to the seismi resistane of the self-anhored suspension bridge. Liu et al. [4, 5] derived the governing differential equations for determining the natural vibration of a self-anhored suspension bridge. He onsidered the dynami seismi spae effet and applied the pseudo-exiting method to study the longitudinal seismi response of a self-anhored suspension bridge subjeted to random exitations at various points along the bridge. On the other hand, Yang et al. [8] performed a nonlin-

2 W.-L. Qiu et al.: Study on the Seismi Behavior of Self-Anhored Suspension Bridges Fig.. The layout of the main Yellow River Road Bridge in Mainland (unit: m). ear time-history analysis and investigated the seismi harateristis of a single tower self-anhored suspension bridge. MDaniel et al. [6] used inelasti tower links to edue the seismi responses of tower of the new San Franiso-Oakland Bay Bridge East Span self-anhored suspension bridge with global seismi time history analyses. Fang et al. [] studied the energy and vibration redution designs by installing visous damper and lead extrusion damper between the main girder and tower while Jiang et al. [3] performed a parametri analysis for the self-anhored suspension bridge based on dissipation due to elasti ollision and visous damper between the tower and girder. Gao et al. [] studied the optimization of seismi resistane design of the tower and the loation of dampers for a self-anhored suspension bridge. This paper presents a nonlinear time-history method to investigate the seismi response of a self-anhored suspension bridge, onsidering the geometri nonlinearity of the struture and the material nonlinearity of the tower. Also investigated herein is the damping effet of the metal damper whih is stable and easily maintained. II. ANALYSIS OF BRIDGE STRUCTURE AND ITS SEISMIC RESPONSE. The Bridge Struture The Yellow River Road Bridge is a three-span selfanhored suspension bridge. The main span is 8 m and the side spans are 73 m eah with a total length of 36 m. The main ables have a rise-span ratio of /5.5. The general layout of the bridge is shown in Fig.. Longitudinal movable supports are used under the main bridge at the towers and side piers. Transverse displaement-limiting bearings are installed at the main piers and the gaps between the bearings and the main girders are. m. The main girder is a pre-stressed onrete box girder with two pre-stressed main able anhorage at the both ends. The tower has the shape of a gate and the olumn of the tower has a solid ross setion of 3.5 m 5.5 m at the bottom of tower, gradually hanged to.5 m 4.5 m just under the girder, and.5 m 4.5 m for the upper part of the olumn. Pile groups are used for the foundations of the towers. There are nine.8 m-diameter drilled piles underneath eah olumn. The bridge has two main ables and eah able is made of 4699 paralleled, 5 mm in diameter, high strength galvanized steel wires. The hangers are also made of parallel high strength galvanized steel wires. Fig.. The finite element model of the Yellow River Road Bridge.. Method of Analysis The ANSYS finite element software and a spae element model are used to investigate the dynami harateristis and seismi response of the Yellow River Road Bridge. In the seismi response analysis, time-history analysis was onduted to onsider the geometrial and material nonlinearity of the struture. The finite element model is shown in Fig.. Beam element was used for the tower olumns, the piers, the piles, the main girders and the ross beams. The foundations were simplified as a spring models. The main ables and hangers were modeled as a truss element. The analysis onsidered the effets of large displaement in the main ables and hangers and the rigidity at initial loading. In ANSYS, the 3D elasti Beam 4 element was used to model the tower and the bridge dek system (main girders and ross beams); while truss element Link was used to model the main ables and hangers. 3. Seismi Wave Used for Analysis and Artifiial Seismi Waves For the seismi response time-history strutural analysis, the seismi wave used in the analysis an either be an atual seismi wave with some adjustments or an artifiial seismi wave. The methods for generating the artifiial seismi waves inlude ode response spetrum simulated by the trigonometri series, diretly simulated ode response spetrum, superposition method in the time domain to simulate the ode response spetrum, semi-empirial iteration to simulate the ode response spetrum, an artifiial seismi wave based on the power spetrum, and the ARMA model. The following equation based on Kaul s relation between the response spetrum and the power spetrum is adopted to obtain the artifiial seismi wave by simulating the ode response spetrum: ξ T π Sx( ωk) = Sa ( ωk) ln ln p πω k ωktd ()

3 386 Journal of Marine Siene and Tehnology, Vol., No. 4 () Aeleration (m/s ) Fig. 3. Artifiial seismi wave. f f onfined onrete unonfined onrete first stirrup broken Aeleration (m/s ) Aeleration (m/s ) Fig. 4. Taft seismi wave Fig. 5. El Centro seismi wave T where Sa ( ω k ) is a given ode response spetrum, ξ is the damping ratio, T d is the time duration of the seismi wave; and p is the probability of not exeeding the response spetrum value. (Usually p.85) Calulation using the following two equations led to a stable Gaussian proess A(t) with a zero mean value: N At () = Ck os( ωkt+ ϕk) () k= / Ck = 4 Sx( ωk) ω ω = ( ωu ωl)/ N ωk = ωl + ( k /) ω where ω k and C k are the frequeny and amplitude of the kth Fourier omponent respetively; ϕ k is the initial phase angle with the probability funtion of an uniform distribution between (, π), ω u and ω l are the upper and lower bounds in the positive ω region respetively; and N is a positive number dividing (ω u, ω l ) into N number of equal divisions. The nonstationary Gaussian proess was alulated by where the envelope funtion f(t) is: (3) xt () = f() t At () (4) E ε so E se ε so ε sp over onrete ε Fig. 6. Stress-strain relationship urve of onfined onrete. (/ t t ) t t f() t = t t t t ( t ) e t t t 3 where is the attenuation onstant with value between.~., t, t and t 3 are onstants related to the intensity of earthquake and soil ondition. The artifiial seismi wave reated from the above proedure is shown in Fig. 3. This artifiial seismi wave is generated based on the design response spetrum of the Seismi Design Speifiation for Highway Bridges of China. The site lassifiation belongs to the II ategory, whih is onsistent with the analyzed Huanghe Road Bridge. The upper limit adopted by this researh during the generation of artifiial seismi waves is 5 Hz, the lower limit.5 Hz, and the interval.5 Hz. In addition to using this artifiial seismi wave in the time-history analysis, two frequently used seismi aeleration reords (Taft and El Centro seismi wave) were used as shown in Figs. 4 and 5. The aeleration peak values were all adjusted to. g for onsideration of frequently ourred earthquake. 4. The Material Nonlinearity of Reinfored Conrete ) Constitutive Relation for Conrete The Mander stress-strain model was used for onfined onrete in this paper, as shown in Fig. 6. The equations are: f ε u (5) f xr = (6) r r + x x = ε / ε (7) f ε = 5 + εo f where f is the peak ompressive strength of onfined on- (8)

4 W.-L. Qiu et al.: Study on the Seismi Behavior of Self-Anhored Suspension Bridges 387 f s f y B C θ ε y ε s, u ε s Fig. 7. Stress-strain relationship urve of reinforing steel. Moment (N.m) 3.E+8.E+8.E+8.E Rotation angle (Rad) Fig. 8. Moment-rotation angle relationship urve of plasti hinge. rete, ε is the ompressive strain of onrete; ε is the ompressive strain orresponding to f, f and ε o are the nononfined ompressive strength of onrete and its orresponding ompressive strain respetively (usually ε o =.). r = E /( E E ) (9) E = 5 f (Unit for f and E is MPa) () se P P y d d y d d d y E = f ε () se / ) Constitutive Relation for Reinforing Steel The stress-strain relation for reinforing steel used in this paper was a perfetly elasto-plasti model with a bi-linear stress-strain urve as shown in Fig. 7. Its equations are: f y When εs εy, σs = Esεs ( E = ), () ε When ε ε ε,, σ = f, (3) y s s h s y 3) A Plasti Hinge Method for the Reinfored Conrete Tower Based on elasti analysis, the bottom of the tower of Yellow River Road Bridge is the first part entering its elasto-plasti stage under longitudinal earthquake. Therefore, in the dutility analysis, the plasti hinge was loated at the bottom of tower. The dutility apaity of the plasti hinge was very important in the assessment of the seismi resistane of the struture through seismi energy absorption and dutility index. The dutility apaity of a plasti hinge was determined by the length of the hinge and by the moment-urvature relation of the reinfored onrete omponent. The Euroode 8 was used to determine the length of the plasti hinge. The length of the plasti hinge, L p is L =.8L+.d f (4) P s y or L = (.4/.6) H (5) P where L is the height of the pier, H is the height of the ross y P y Fig. 9. Moment-rotation angle relationship urve of plasti hinge. setion, d s and f y are the diameter of the longitudinal reinforing steel and yield stress respetively. Based on the atual dimensions of the tower ross setion of Yellow River Road Bridge and the reinforing steel used, the length of the plasti hinge was alulated to be L P = 3.33 m. Using the aforementioned onstitutive relations for onrete and reinforing steel, the Ufyber software was used to alulate the moment-urvature relation at the bottom of the tower of Yellow River Road Bridge, whih led to the relationship of moment and angular displaement at plasti hinge as shown in Fig. 8. The ANSYS finite element software was used in this study to perform a dutility seismi response analysis of the Yellow River Road Bridge. The ombin 39 spring element was used to simulate the plasti hinge. 4) Mehanial Model for Metal Damper The most ommonly used restoring fore models for a metal damper inlude perfetly elasto-plasti model and bilinear model. Here, the perfetly elasto-plasti model was used as shown in Fig. 9. The initial elasti stiffness ould be alulated from the equation below: k = ε Py / d (6) y

5 388 Journal of Marine Siene and Tehnology, Vol., No. 4 () Table. Summary of the natural frequeny and vibration mode. No Frequeny (Hz) Vibration mode.387 longitudinal floating mode of main girder first symmetrial vertial bending mode of main girder first unsymmetrial vertial bending mode of main girder symmetrial lateral bending mode of main girder seond symmetrial vertial bending mode of main girder seond unsymmetrial vertial bending mode of main girder When displaement of the devie exeeded d y, the restoring fore was P y. The dissipated energy for eah yle, W d was equal to the area of hysteresis loop between point (P y, d ) and point (-P y, -d ), i.e.: W = 4 P ( d d )( d > d ) (7) d y y y 4 Py ( d d ) βε = (8) π kd y ε III. ELASTIC SEISMIC RESPONSE ANALYSIS OF SELF-ANCHORED SUSPENSION BRIDGE. Dynami Charateristis Analysis In order to understand the dynami harateristis and the regularities of seismi response of a self-anhored suspension bridge, the spae element model of Fig. was first used to alulate the dynami properties of the Yellow River Road Bridge. The natural frequeny and mode shape were obtained. Table shows the first six modes of vibration. It an be seen from the natural frequeny and mode shape that the first mode of the self-anhored suspension bridge was a longitudinal floating mode with a longer period. This mode diretly affeted the internal fore and displaement of the bridge subjeted to longitudinal seismi ation.. Seismi Response Time-History Analysis Referring to the measured damping ratio of.5%~.5% for the two suspension bridges, i.e. Hu-men Bridge and Jiang-In Bridge, the damping ratio of the bridge studied in this paper was taken as %. The analysis showed that when the bridge was subjeted to a transverse seismi wave, the seismi response did not ontrol the design of the bridge. However, when subjeted to a longitudinal seismi wave, the seismi response was very notieable, and the main responses were the longitudinal floating of main girder and longitudinal vibration of the tower. The response analysis results produed by the three seismi waves Fig.. Longitudinal displaement time-history response of the main girder under longitudinal exitation. Displaement (m) Displaement (m) Fig.. Longitudinal displaement time-history response at tower top under longitudinal exitation. Moment (N.m).E+8.E+8.E+ -.E E+8 Fig.. Longitudinal bending moment time-history response at tower bottom under longitudinal exitation were quite different. The responses produed by the artifiial seismi wave were larger than that produed by Taft seismi wave and El Centro seismi wave. So the following studies were all based on the artifiial wave. Under the longitudinal exitation of artifiial seismi wave, the maximum longitudinal displaement of the main girder was.83 m, the maximum longitudinal displaement at the tower top was.65 m, and the maximum bending moment along the longitudinal diretion at the base of the tower was.65 8 N-m. At this point of time, the time histories of the longitudinal displaement of the girder, the displaement of the top of the tower, and the bending moment are shown in Figs. -. IV. DUCTILITY SEISMIC RESPONSE ANALYSIS OF SELF-ANCHORED SUSPENSION BRIDGE. Analysis Results of Dutility Seismi Response The finite element model used in the dutility seismi response analysis is the same as that used in the elasti seismi response analysis. Nevertheless, sine there was a plasti hinge at the tower base, the material nonlinearity was onsidered for the tower in the dutility analysis. In the time-history analysis, the effet of geometri nonlinearity was onsidered.

6 W.-L. Qiu et al.: Study on the Seismi Behavior of Self-Anhored Suspension Bridges 389 Table. Comparison of seismi response. Seismi Analysis Seismi intensity Displaement of Girder Displaement at Tower Top Moment at Tower Bottom (m) (m) (N-m) Elasti analysis VII Elasti analysis VIII Dutility analysis VIII Displaement (m) Elasto-plasti Elasti Fig. 3. Longitudinal displaement time-history response of the main girder under longitudinal exitation. Displaement (m) Elasto-plasti Elasti Fig. 4. Longitudinal displaement time-history response at tower top under longitudinal exitation. Moment (N.m) 6.E+8 4.E+8 Elasto-plasti Elasti.E+8.E+ -.E E+8-6.E+8 Fig. 5. Longitudinal bending moment time-history response of the plasti hinge under longitudinal exitation. The artifiial seismi wave was inputted into the model to perform dutility time-history analysis, and the peak value of the aeleration of seismi wave was adjusted to.5 g for onsideration of rarely ourred earthquake. Under exitation of artifiial longitudinal seismi wave, the maximum longitudinal displaement of the main girder was.6 m, the maximum longitudinal displaement at the tower top was.599 m, the maximum bending moment in the longitudinal diretion of the plasti hinge at the tower bottom was.55 8 N-m, and the maximum angular displaement of the plasti hinge was.789 rad. The seismi time-history responses of longitudinal displaement of the girder, the displaement of the tower top, the bending moment of the plasti hinge, and the angular displaement are shown in Figs. 3-6 and Table. Rotation angle (rad) Fig. 6. Longitudinal rotation angle time-history response of the plasti hinge under longitudinal exitation. The results of the elasti analysis are also shown in the same figures. V. SEISMIC RESPONSE REDUCTION ANALYSIS OF SELF-ANCHORED SUSPENSION BRIDGE WITH METAL DAMPERS Through the previous analysis, the Yellow River Road Bridge was found to have exessive displaement in the girder when subjeted to seismi loading. Thus, a damping devie was neessary to satisfy the safety requirement of the struture. Due to the advantages of using metal dampers, they were seleted as the damping devie for this bridge. The metal dampers were installed to onnet the tower and the girder. Here, two metal dampers were installed for eah tower. In total, four dampers were used for the bridge. The metal dampers of this bridge satisfy the perfetly elasto-plasti model shown in Fig. 9. The hoie of damper must satisfy the following requirement: the damper must be in the elasti stage under temperature loads and it must enter the plasti stage under seismi loads. Due to the hysteresis loop, energy was dissipated and d y was taken to be 5 m. For the rarely ourred earthquake, the displaement of the girder and the top of the towers were ontrolled. The displaement of the girder was ontrolled to within 5 m to protet the expansion joints and to ontrol bending moment of the bottom of the tower. In the onstrution of a model for energy dissipation and seismi mitigation analysis, the metal damper was simulated by spring elements, i.e. four springs were plaed along the longitudinal diretion of the bridge. The mehanial model of the damper is shown in Fig. 7 where k ε denotes the elasti stiffness. In the ase of the rarely ourred artifiial longitudinal seismi wave, different parameters were used in the alulation (P y or k ε ), and the hysteresis loops of the metal dampers are shown in Fig. 7. The results of the alulation are shown in Table 3.

7 39 Journal of Marine Siene and Tehnology, Vol., No. 4 () Table 3. Effets of metal damper with different k ε parameter. Parameter of Damper k e (N/m) Displaement of The Girder (m) Displaement at Tower Top (m) Moment at Tower Bottom (N-m) No damper E+6 3.5E+6 Load (N).E Load (N).E E+6 Defletion (m) -3.5E+6 Defletion (m) (a) k e = 5.5e7 (b) k e = 6.e7 Fig. 7. Load-defletion relationship of metal damper. Displaement (m) Fig. 8. Longitudinal displaement time-history response of the main girder under longitudinal exitation. Displaement (m) Fig. 9. Longitudinal displaement time-history response at tower top under longitudinal exitation. It an be seen from the above analysis that the metal damper was quite sensitive to the hoie of parameters. The metal damper was quite effetive in the hystereti energy dissipation and it ould effetively redue the longitudinal displaement of the main girder and the horizontal displaement at the tower top. Besides, it ould effetively protet the struture and redued the bending moment of the tower. For the rare Moment (N.m) E+8 E+8 -E+8 -E+8-3E Fig.. Longitudinal bending moment time-history response at tower bottom under longitudinal exitation. Fore (N) 4E+6 E+6 -E+6-4E Fig.. Restoring fore time-history response of the metal damper under longitudinal exitation. earthquake of intensity VIII, when the damper parameter was k ε = (N/m), the displaement of the main girder redued from.464 m to.47 m, the displaement at the tower top redued from.4 m to.46 m, and the bending moment at the tower bottom redued from 4. 8 N-m to.85 8 N-m. Time-histories for the displaement of the girder, the displaement at the tower top, the moment at the tower bottom and the restoring fore for the damper are shown in Figs. 8-.

8 W.-L. Qiu et al.: Study on the Seismi Behavior of Self-Anhored Suspension Bridges 39 VI. CONCLUSIONS Using the Yellow River Road Bridge in China as an example, the present paper investigated the dynami harateristis, elasti seismi response, dutility seismi response, and energy dissipation and seismi response redution effet of the metal dampers for the self-anhored suspension bridge. The main onlusions are:. From the dynami harateristis analysis, it was found that the self-anhored suspension bridge retains two speifi features similar to the earth-anhored suspension bridge. One is the low mode has a longer period, the other is the onentration of vibration modes. Due to the free motion of the main girder along the longitudinal diretion, the first vibration mode is longitudinal floating, whih is similar to the able-stayed bridge of the floating system. It is benefiial to the strutural seismi response, but leads to large longitudinal displaement thus resulting in a seismi disaster of dropping girder or damaging expansion joints of the bridge.. Sine earthquake is a random proess, several seismi waves must be onsidered and ompared in the seismi time-history analysis. In this paper, two reorded seismi waves and an artifiial wave were used to analyze the time-history of the frequent earthquake. It an be dedued from the results that for the self-anhored suspension bridge with a longitudinal floating first mode, displaements are large for the main girders and the tower top, and the bending moment is large at the bottom of the tower. 3. Comparing with elasti response analysis for the Yellow River Road Bridge, the moment of the bottom of the tower was drastially redued when using dutility analysis. Therefore, in the dutility design, the seismi resistane of a suspension bridge is greatly inreased, while displaements of the main girder and the tower top are apparently inreased. These fators should be arefully onsidered in the design. 4. After installation of the metal dampers along the longitudinal diretion, longitudinal displaements of the girder and tower an be well ontrolled when subjeted to the ation of longitudinal earthquake, and bending moment of the bottom of the tower an also be redued largely. Bridge omponents, suh as expansion joints, were well proteted and the girder was prevented from dropping. REFERENCES. Fang, H., Liu, W. Q., and Wang, R. G., Design method of energydissipating earthquake redution along longitudinal diretion of selfanhored suspension bridge, Earthquake Engineering and Engineering Vibration, Vol. 6, No. 3, pp. -5 (6).. Gao, Y., Yuan, W. C., Zhou, M., and Cao, X. J., Seismi analysis and design optimization of a self-anhored suspension bridge, Lifeline Earthquake Engineering in a Multihazard Environment (TCLEE9), ASCE, Oakland, California, United States, pp (9). 3. Jiang, M., Qiu, W. L., and Yu, B. C., Researh on seismi response redution of self-anhored suspension bridge, Proeedings of the International symposium on Computational and Strutural Engineering (CSE9), Shanghai, China, pp. 9-6 (9). 4. Liu, C. C., Zhang, Z., and Shi, L., Analysis of longitudinal seismal response for self-anhored suspension bridges, Journal of Wuhan University of Tehnology, Vol. 6, No. 5, pp (). 5. Liu, C. C., Zhang, Z., Shi, L., and Du, P. J., Theoretial study of vertial free vibrations of onrete self-anhored suspension bridges, Engineering Mehanis, Vol., No. 4, pp. 6-3 (5). 6. MDaniel, C. C. and Seible, F., Influene of inelasti tower links on ablesupported bridge response, Journal of Bridge Engineering, Vol., No. 3, pp. 7-8 (5). 7. Ohsendorf, J. A. and Billington, D. P., Self-anhored suspension bridges, Journal of Bridge Engineering, ASCE, Vol. 4, No. 3, pp (999). 8. Yang, M. G., Hu, J. H., and Chen, Z. Q., Seismi response analysis of self-anhored suspension bridge with single-tower, Journal Centeral South University, Vol. 36, No., pp (5).