Dynamic Response of RCC Curve-Skew Bridge Deck Supported by Steel Multi-Girders

Transcription

1 Paper ID: SE International Conference on Recent Innovation in Civil Engineering for Sustainable Development () Department of Civil Engineering DUET - Gazipur, Bangladesh Dynamic Response of RCC Curve-Skew Bridge Deck Supported by Steel Multi-Girders Md Basir Zisan 1*, Toshiro Hayashikawa 2, M. Z. Mousumi 3, Md Naimul Haque 4 Abstract The objective of this paper is to evaluate the dynamic responses of a curve-skew bridge deck supported by multi girders. The parameters influencing the deck behavior considered are transverse vehicle position, skew angle and curvatures. The numerical transient dynamic analysis is performed using a threedimensional (3-D) finite element (FE) model of bridge-vehicle-interaction (BVI). The BVI model consists of a spaced bridge-vehicle system and a contact model whose are modeled using ANSYS. Inertia and horizontal force, friction and road roughness are taken into account for the reality of the problem. The analysis results show the deck displacement ratio of the curve-skewed bridge is significant along the transverse radial direction and especially maximum at the corner region of a skew deck. The torsion and deformation flexibility of the bridge caused by curvature and skew angle are key factors for higher displacement ratios which may induce cracking within the concrete. Hence special care needs to be taken for the curve-skewed deck especially at the bridge end location. Keywords: ANSYS, 3D-BVI, curve-skewed bridge, displacement ratio, transient dynamic analysis 1. Introduction A bridge defined as a skew bridge when the normal of bridge centerline makes an angle with the support centerline. In non-skew bridge, the load path is straight toward the support along the direction of span. But in skew bridge, the direction of load path changed which significantly increase the torsional moment of the skewed-deck. The skew angle decreases the longitudinal moment while increases the transverse moment illustrated by Nouri, G. and Ahmadi [1]. Similarly, curvature yields significant differences in deflection for inside and outside girder described by Awall [2]. Also the outplane distortions and large deformation of the bridge are resulting from skew angle described by Zisan et al. [3]. Besides, high skewness arise difficulties in developing full reinforcing action within the concrete deck, especially for orthogonal bar on acute corners, which causes spalling and chipping. As a result, a deck is susceptible to faster mechanical degradation and local damage in those locations. AASHTO [4] specified to consider a bridge as a straight one when skew angle less is than or equal to 20 with no modifications and suggests to use of an alternate superstructure configuration for skew angle more than 20. But there is no calculation procedure or guidelines given in the specifications. Therefore, for decades, skewed bridges were analyzed and designed in the same way as straight ones regardless of the skew angle. Several researches say Menassa et al. [5] and Qaqish [6] are focusing the dynamic behavior and load distribution of skew slab bridge. However, no references have been found dealing with the curved or curve-skewed concrete deck supported by composite steel girder. Broquet et al. [7~8] studied the dynamic amplification factors (DAF) of concrete deck slabs and suggested road roughness as an important parameters effecting the DAFs. Buckler et al. [9] studied the effect of girder spacing on dynamic response of bridge deck. However, there is no information found in literature that studies the dynamic behavior of curved-skew concrete deck supported by steel girders. 1 Department of Civil Engineering, CUET, Chittagong-4349, Bangladesh, basirzisan@gmail.com 2 Faculty of Eng., Hokkaido University, Sapporo, , Japan, toshiroh@eng.hokudai.ac.jp 3 Department of Civil and Environmental Engineering, SUST, Sylhet-3114, Bangladesh, mzmzisan@gmail.com 4 Department of Civil Engineering, CUET, Chittagong-4349, Bangladesh, naimulce@gmail.com

2 585 The purpose of paper is to evaluate the use of commercial FE code, ANSYS for the analysis of composite curve-skewed concrete deck supported by multi steel I-girder and employ this analysis to investigate the effect of curvature and skew angle on the dynamic behavior of curved-skew bridge deck under moving vehicle. Because of the large skew angle, the bridge deck, especially on corner region undergoes twisting as well as large deformation and susceptible to local damage. Therefore, this study covers the dynamic magnification of skewed-deck for deflection. 2 Finite Element Modeling 2.1 Bridge modeling The finite element (FE) model of the bridge consists of five main I-girders, each of 2.8 m deep and equally spaced by 2.1 m, which are bonded with overlaying reinforced concrete slab and tied together with 10 equally spaced diaphragms. Table 1 describes the basic geometric properties of the original bridge has radius of 1000 m and skew angle 0 as shown in Fig. 1(a~b). The Fig. 1(d) shows the FE model for the bridge with right-angle diaphragm modeled by ANSYS in which, the skew angle varies from 0 to 45 and radii from 100 m to 1000 m. The bridge is modeled by using 8-noded SOLID45 hexagonal elements for concrete deck and 4-noded quadrilateral SHELL63 element for all steel members. SOLID 45 and SHELL 63 elements has 3 & 6 DOFs in each node and both elements have large deflection capability to perform nonlinear analysis [10]. Cylindrical coordinate system having the origin at center of the bridge curvature was used to define all geometric properties of FE models. Simply supported boundary conditions, roller and hinge supports are used at the bottom flange node of each girder ends. Table 2 shows the boundary conditions for bridge end. The moduli of elasticity and the mass density of steel and concrete are taken as 210 GPa & 7850 kg/m 3 and GPa & 2500 kg/m 3, respectively. The Poisson ratios of steel and concrete are assumed 0.3 and 0.2, respectively. The non-skew and skew angle 45 are taken to illustrate the effect of the skew angle on deck behavior and curvature 100 m, 400 m and 1000 m were considered to find out the effect of curvature. All displacements components for bridge deck were computed on the top face of the deck just above the diaphragm and girder meeting stations whose locations are marked by the alphabetic letter from A to T as shown in Fig. 1(c). The diaphragms were leveled by D1, D2, D3 and D4 where D1 indicates diaphragm 1 and same definition for others. The girder s mid-span locations are independent of skew angle in all cases. Table-1: Basic geometric property of Kita-go bridge Span length [mm] Deck width*thickness [mm] 11000*20 Web of main girder [mm] WEB 2800*10 Flange of main girder [mm] FLGG1 FLGG2 FLGG 3&4 FLGG5 540*25 350*16 370*14 510*25 Vertical Stiffener of main girder [mm] 145*12 Horizontal Stiffener of main girder [mm] 115*11 Flange and Web of Intermediate Diaphragm [mm] IFLG 100*8 and IWEB *8 Vertical Stiffener of Intermediate Diaphragm [mm] 145*12 Flange and Web of End Diaphragm [mm] EFLG 250*10 and EWEB 2400*9 Vertical Stiffener of End Diaphragm [mm] 145*22 Flange and Web of Lateral Bracing LWEB 150*10 and LFLG 150*12 Skew angle 0 and 45 Radius [m] 100, 400 and 1000 Table-2: Boundary conditions Support condition u 1 u 2 u 3 θ 1 θ 2 θ 3 Roller Fix Free Fix Free Free Free Hinged Fix Fix Fix Free Free Free u 1, u 2, u 3 are translations in R, θ, Z directions θ 1, θ 2, θ 3 are rotations in R, θ, Z directions

3 586 Fix Mov Mov Mov Diapghram 1 Diapghram @ @ @ Diapghram 3 Diapghram 4 G st End Hinged Support G2 (a) Pan view G G4 G5 P Q R S T Sup. 2% K L M N O F G H I J (b) Cross section A B C D E Mid span point 2nd End Roller Support G1 G2 G3 G4 G5 (c) Diaphragm arrangement in skew-unstaggered bridge (d) FE model of bridge with 30 0 skew angle Fig. 1 Geometric properties of Kita-go bridge and FE models of bridge Lump mass Hinged Z Y X Gap element Actuator (a) AASHTO HS20-44 truck (b) FE model of HS20-44 TRUCK Fig. 2 AASHTO HS20-44 design vehicle L 15 L 08 L 01 S= - 3.3m S= m S=3.3m Fig. 3 Trsnaverse vehicle positions Table-3: Stiffness coefficient of HS20-44 Design truck [11] Front axle (kn/cm) Drive axle (kn/cm) Semi-trailer axle (kn/cm) Tire Suspension spring Vehicle modeling The FE model of HS20-44 design truck, specified by AASHTO, consists of six wheels and three-axle tractor-trailer as shown in Fig. 2(a). A 3-D nonlinear FE model of HS20-44 truck is developed using ANSYS, which consists of five lump-masses representing tractor, semi-trailer and three axle sets as shown in Fig. 2(b). All masses are connected with rigid beam and supported by linear spring-dampers forming the vehicle body were modeled using MASS21 and BEAM4 elements, respectively. The upper and lower spring damper representing suspension of the vehicle body and tires are modeled by COMBIN40 element consists of parallel spring-slider and damper coupled with a gap in the series. The separation between tire and road is integrated using gap element at the lower spring-damper. The tire stiffness and spring suspension values are found from Wang et al. [11] as shown in Table 3. To simulate the road roughness, an actuator modeled by LINK11 element is connected with gap element. The suspension force consists of linear elastic spring force and constant interleaf friction force. Three vehicle position named outside (L01), central (L08) and inside (L15) are considered as shown in Fig. 3.

4 Roughness (m) Left Track Right Track GOOD Moving distance (m) Fig. 4 Road roughness profile for wheel track 2.3 Road roughness modeling Dodds et al. [12] assumed road surface roughness as a periodically modulated random process derived from Power Spectral Density (PSD) function expressed exponentially using Eq.(1). S(n) = S(n 0 ) ( n w ).. (1) n 0 Where S(n) = PSD (m 2 /cycle/m); n = wave number (cycle/m); S(n 0 )=roughness coefficient (m 2 /cycle/m); n 0 = discontinuity frequency = 1/(2π); Based on Motor Industry Research Association specification [13], w = 2 (1.36 ~2.28) for principle road and roughness coefficient is 20*10-6 for good surface. For vehicle bouncing, pitching and rolling effect, different roughness profiles for both tracks as shown in Fig. 4 are derived from PSD and cross spectral density functions considering the road surface as a homogenous and isotropic random process using Eq.(2) and Eq.(3)[2]. N y(x)= [ n i S(n i ). cos(2πn i x+φ i )]... (2) i=1 N n i.s x (n i ). cos(2πn i x+φ y R (x)= ( i )+ n i.(s(n i )-S x (n i )). cos (2πn i x+θ i ) )..(3) i=1 Where S x (n) = cross spectral density, Φ i, θ i = 1 st and 2 nd random phase angle, x = longitudinal distance, N=number of sinusoidal components, Δn i = bandwidth. 2.4 Bridge vehicle interaction modeling The VBI problem consists of two separate bridge and vehicle systems in which contact point and contact force is a function of time. Contact elements set the interaction between these two subsystems. Most of the BVI problems developed and solved the motion of the equation. Here, node to surface contact algorithm supported by ANSYS has been used to develop the VBI. The contact element establishes the equilibrium condition between moving vehicles and bridge deck. CONTA174 and TARGE170 are used to generate node to contact surface and target surface, respectively. CONTA174 supports sliding, large deformation, Coulomb friction and provides better contact result [10]. Augmented Lagrangian method is used to solve the contact problems. 3 Transient Dynamic Analyses The Rayleigh damping and lumped-mass are assumed and 1% critical damping is assumed for 1 st and 2 nd natural mode. Newmark s β and Newton-Raphson methods with transient option [10] are used to calculate the structural response. The friction force between tires and pavement mainly depends on the types of pavement surface and tire characteristics. A frictional coefficient of value 0.18 is used in all cases [14]. The vehicle is assumed to run at a constant speed 105 km/hr along different periphery and to obtain the initial conditions of the vehicle; it is subjected to run an approach road of 45 m length having surface roughness same as that of bridge deck before entering the bridge. In all cases, good surface roughness condition is considered. The dynamic behavior of curved-skew bridge is invested for differential deflection, distortion-stress and bearing force.

5 588 LOADING L01, RADIUS 100 m LOADING L01, RADIUS 400 m LOADING L01, RADIUS 1000 m D1,0 0 D1,45 0 D2,0 0 D2,45 0 D3,0 0 D3,45 0 D4,0 0 D4,45 0 D1 D2 D3 D4 D1 D2 D3 D4 (a) Displacement ratio for outside vehicle position (L01) LOADING L08, RADIUS 100m LOADING L08, RADIUS 400m LOADING L08, RADIUS 1000m (b) The displacement ratio for the central vehicle position (L08) LOADING L15, RADIUS 100m D1 D2 D3 D4 D1 D2 D3 D4 LOADING L15, RADIUS 400m LOADING L15, RADIUS 1000m (c) Displacement ratio for inside vehicle position (L15) Fig. 5 Maximum displacement ratio for concrete deck 3.1 Maximum deck displacement ratio Fig. 5 describes the displacement ratio Δ α /Δ 0 along the transverse direction of curve-skewed deck at different diaphragm and three loading conditions. The solid line and dotted line indicates Δ α /Δ 0 ratio for non-skew and 45 skewed bridge, respectively. The ratio Δ α /Δ 0, for non-skew curved deck increase along the transverse direction for any position of the vehicle and the highest value is found on deck outer side locations. In addition, for small radius of curvature, especially 100 m, the ratio Δ α /Δ 0 increases rapidly when the vehicle moves inside along the transverse direction. The ratio, Δ α /Δ 0 along the longitudinal direction for non-skew bridge is constant. The ratio Δ α /Δ 0 for curve-skewed bridge differs significantly with non-skew bridge both for transverse and longitudinal direction. In all cases, the Δ α /Δ 0 ratios for inside locations is higher and for outside locations are lower as compared with non-skew bridge and remains same at the midsection. Inside and outside locations have opposite relation on Δ α /Δ 0 because of wheel load distribution by concrete deck. Vehicle load on acute corner transfer through the deck to girder whereas on the obtuse corner major portion of load is carried by deck itself to the bridge supports. Hence, deck on acute corner subject to large deformation that yields higher value for Δ α /Δ 0 ratio. In all cases, it found a maximum change of Δ α /Δ 0 ratios for diaphragm 1 at location P (Fig.1 (c)) is 2.40 and minimum 0.30 for same diaphragm at location T. Again major difference of Δ α /Δ 0 found between diaphragm 1 and 2 for both inside and outside location, which indicates twisting, or torsion of deck between diaphragm 1 and 2.

6 589 4 Conclusions The displacement ratio of non-skew bridge increases along transverse direction while constant along the longitudinal direction. The displacement ratio decreases for skew angle and highly remarkable for diaphragm near to the bridge end and subject to extreme torsional and vertical displacement. For skew bridge the Δ α /Δ 0 ratio abruptly change along both direction with minimum value 0.30 on obtuse corners while maximum value 2.40 found for acute corner. For highly curved bridge Δ α /Δ 0 increases abruptly for torsion, which is about 0.90 to 2.25 for 100 m bridge. The acute region skewed deck subjected to higher vertical and torsional deformation provides abrupt increase of displacement ratio along the transverse deck direction. Since high skewness in acute region arise difficulties in reinforcing of concrete, especially for orthogonal, hence special care needs to be taken for this region. References [1] Nouri, G. and Ahmadi, Z., Influence of Skew Angle on Continuous Composite Girder Bridge. Journal of Bridge Engineering, Vol. 17(4), pp , [2] Awall, M. R., Dynamic behavior f horizontally curved twin I-girder bridge under moving vehicle, PhD Thesis, Hokkaido University, [3] ZISAN M. B, HAYASHIKAWA T., MATSUMOTO T. and He X., Dynamic response and distortion-stress in curved multi-girder bridges subjected to high-speed moving vehicles, Journal of Structural Engineering, JSCE, Vol.61 (A), pp , [4] AASHTO, Standard specifications for highway bridges. Washington, D.C. 2. [5] Menassa, C., Mabsout, M., and Tarhini, K., Influence of Skew Angle on Reinforced Concrete Slab Bridges. Journal of Bridge Engineering, Vol. 12(2), pp , 7 [6] Qaqish, M. S., Effect of skew angle on distribution of bending moment in bridge slabs, Journal of Applied Science, Vol. 6 (2), pp , 6. [7] Broquet, C., Bailey, S. F., Fafard, M., Brühwiler, E. and Fafard, Dynamic amplification factors in deck slabs of concrete road bridges. Proceeding, 4 th European Conference on Structural Dynamics (EURODYN), L. Fryba and J. Naprstek, eds., Balkema, Rotterdam, Netherland, pp , [8] Broquet, C., Bailey, S., Fafard, M., and Brühwiler, E., Dynamic Behavior of Deck Slabs of Concrete Road Bridges. Journal of Bridge Engineering, Vol. 9(2), pp , 4. [9] Buckler, J. G., Barton, F. W., Gomez, J. P., Massarelli, P. J. and McKeel, W. T., Effect of girder spacing on bridge deck response, Final report, Virginia Transportation Research Council, Charlottesville, Virginia, 0. [10] ANSYS Inc., Release 13.0 Documentation, Theory References, [11] Wang T. L., Li H., and Huang, D.(1992). Computer modeling analysis in bridge evaluation, Final Report-Highway Planning and Research Program, Florida. [12] Dodds C. J. and Robson J. D., The description of road surface roughness, Journal of Sound and Vibration, Vol. 31(2), pp , [13] Labarre, R. P., Forbes, R. T. and Andrew, S., The measurement and analysis of road surface roughness, Motor Industry Research Association Report No. 1970/5, [14] Samaan M., Kennedy J. B. and Sennah K., Impact factors for curve continuous composite multiple-box girder bridges, Journal of Bridge Engineering, ASCE, Vol. 12(1), pp , 7.