Out-of-Plane Buckling Mechanism and Enhancing Method of Stiff Skeleton Arch Bridge When Wrapping Surrounding Concrete

Arch bridges with vertical suspended deck systems have been constructed during the last 30 years, different from the existing arch bridges with longitudinal beams or panel beams. The latter have better the seismic inertia forces can be transmitted to the piers or foundations through both the arch rib and the longitudinal beam. However, for arch bridges with vertical suspended deck systems, seismic inertia forces produced by deck systems are transmitted to arch ribs by the geometric nonlinearity of suspenders firstly, and then further transmitted through the arch ribs to the piers or foundations, resulting in greater seismic demands on the arch ribs. In this paper, the seismic performance and weak structural elements of the half-through concrete-filled steel tubular (CFST) arch bridge with a vertical suspension deck system under tri-directional ground motions were studied by numerical simulation, and the bridge model was primarily verified by a static loading test conducted in situ. Moreover, Buckling-Restrained Braces (BRBs) were strategically placed to optimize their seismic mitigation effects by systematically analyzing the bridge’s seismic response. The results identify the arch foot, the 1/8 point of the arch rib, the arch crown, and the transverse bracing as weak structural elements for seismic resistance of the half-through concrete-filled steel tubular (CFST) arch bridge with a vertical suspension deck system. Therefore, a thoughtfully designed arrangement of BRBs targeting the seismic weak structural elements can significantly increase the values of capacity demand ratio (CDR) for weak structural element, thereby strengthening the seismic safety margin of the bridge.

With the increasing span of steel box-section arch bridges, the stability and ultimate strength of arch ribs under horizontal loading become crucial for earthquake resistance. This paper presents a numerical study on the cyclic behavior of steel box-section twin arch ribs under out-of-plane horizontal cyclic loading to assess the seismic performance of steel box-section twin arch ribs. Seventy-two finite element (FE) models of arch ribs were established and validated based on previous experimental studies. An pseudo static elasto-plastic numerical analysis was conducted to investigate the influence of the inclination angle, rise-span ratio, and width-span ratio on the cyclic behavior of the arch ribs. The results indicate that as the angle of inclination and width-span ratio increase, or as the rise-span ratio decreases, the initial stiffness and ultimate strength of the arch ribs improve. However, this also leads to an increase in internal forces within the transverse brace, resulting in local instability and damage. In addition, the inclination angle of the arch rib and the span-to-rise ratio may influence the yielding sequence of the components. Therefore, while increasing the angle of inclination of the arch rib can enhance the transverse cyclic behavior of the steel box-section twin arch ribs, it is important to consider the potential adverse effects caused by the increased internal forces on the transverse brace.

In order to obtain the natural frequency and vibration mode of concrete-filled steel tube (CFST) arch bridge with different parameters, the modal analysis of a double-span arch bridge with a total length of 257.4 meters and a full width of 31.8 meters is carried out. By controlling the three variables of concrete strength, steel tube thickness and the number of transverse braces in arch ribs, the regularity of the natural frequency and vibration mode of CFST arch bridge with different variables is discussed. The results show that with the increasing of the strength of concrete-filled steel tube in arch ribs, the fundamental frequency increases gradually. The vertical stiffness of the arch bridge is positively related to the thickness of the arch rib steel pipe. The fundamental frequency of the arch bridge can be improved by setting transverse brace, and the change of the number of transverse braces has a significant effect on the sixth-order natural frequency. It is limited for the arch bridge to improve the stiffness by changing the number of transverse braces. These can lay the foundation for the dynamic response analysis of the CFST arch bridge.

In recent years, the construction of a CFST arch bridge has developed rapidly; however, as a kind of structural system dominated by compression, with the increase of material strength and span, the stability of the main arch of the CFST arch bridge has become more and more important. In this paper, the finite element method is used to analyze the hanger force and the main arch stability of the long-span CFST arch bridge. Combined with the Shenzhen Rainbow Bridge project, the axial force of the hanger, the internal force, and stability of the main arch of the arch bridge are studied. In the establishment of the finite element model, considering the actual operation of the arch bridge, the model simulates the interaction between steel pipe and concrete, it studies the large deformation of CFST arch bridges, and the stress distribution and overall stability of the arch bridge are analyzed. The results show that the main deformation of the CFST arch bridge is the vertical displacement of the deck, and the axial force of most members of the upper arch ribs is greater than that of the lower arch ribs. The axial force and bending moment of the lower arch rib near the arch foot are larger, and the compressive stress of the arch foot is greater than that of other positions. The axial force of the suspender of the arch bridge is the largest at both ends of the hanger and the middle hanger, and the axial force of the other hanger is close to each other, and the axial force changes little under the same case. The buckling modes of the arch are mainly the lateral buckling or flexural buckling of the arch rib outside the plane, which indicates that the vertical stiffness of the arch bridge structure is larger than that of the transverse stiffness. The research results make the load-bearing mechanism of the CFST arch bridge more clear and also provide a certain reference for the design and construction of the CFST arch bridge.

In the present study, multiscale finite element (FE) models of half-through steel basket-handle arch bridges were established. The eigenvalue analyses were conducted to explore the dynamic characteristics of the arch bridges based on the FE models. In addition, a parametric analysis was carried out to investigate the impact of the inclination angle of the arch rib (0°, 4°, and 7°) on the longitudinal and transverse seismic performances of arch bridges. The results show that with the increase in inclination angle, the out-of-plane stiffness of half-through steel basket-handle arch bridges increases, resulting in the natural period of the structure becoming shorter from 3.09 s to 2.93 s. Adjusting the inclination angle appropriately has a beneficial impact on the overall seismic performance of the structures, affecting both displacement and internal forces, in which the most significant improvements include a 42.8% decrease in displacement and a 62.6% reduction in internal forces. Adjusting the inclination angle can cause the arch springing and transverse brace to undergo larger plastic deformation. It is advisable to judiciously enlarge the sectional dimensions and enhance the material strength of both the arch springing and the transverse bracing in seismic designs.

Design and stability analysis of a special concrete-filled steel tubular arch bridge

When the arch rib of the mid-bearing through and lower-bearing through arch bridges undergoes out-of-plane deformation, it is usually subject to the resilience force provided by the flexible hanger, which is known as the “non-conservative force effect” of the suspender. In contrast to the static condition, in the dynamic scenario, the time-varying non-conservative force exerted by the flexible suspender becomes more complex due to dynamic changes in external load. Moreover, the difference in fundamental frequency and vibration period between the bridge system and arch rib may influence the stress distribution within the arch rib during ground motion. This paper investigates the impact of time-varying non-conservative forces on the dynamic stability of arch ribs in concrete-filled steel tube (CFST) bridges under seismic loads. Specifically, it examines the influence of different seismic waveforms, frequency disparities between bridge slabs and arch ribs, and suspender stiffness on the non-conservative effect. The results reveal significant disparities in the impact of non-conservative forces exerted by the suspender during seismic events with identical intensity but varying frequency characteristics. The influence of non-conservative forces on the dynamic stability of bridges escalates as deck stiffness increases, while it remains relatively unaffected by changes in suspender stiffness.

The provisions for out-of-plane stability of steel arch bridges in three major design codes are presented in this paper. By employing an existing steel arch bridge as a model, the influence of bridge type, arch rib to lateral bracing stiffness ratio, rise-to-span ratio, arch rib spacing, and range of lateral bracing arrangements on the out-of-plane critical axial force of the arch rib is studied using FE analysis. The accuracy of the critical axial force provisions is then evaluated against the FE analysis. The results show that the influence of the rise-to-span ratio on critical axial force is generally small. The critical axial force decreases with increasing arch rib spacing when the stiffness ratio is relatively large. A smaller ratio of arch rib length provided with lateral bracing (γ-value) significantly reduces the critical axial force and normalized critical axial force decreases with increasing stiffness ratio. The critical axial force of half-through type arch bridges is lowest when the stiffness ratio is relatively small. A deck-type bridge has a larger critical axial force than a through-type bridge when the stiffness ratio is relatively large, while the results are the opposite when the ratio is small. The different assumptions made in the provisions result in the various parameters having different impacts on the out-of-plane critical axial force in each code, thus affecting code accuracy. Considering the influence of the rise-to-span ratio, ratio of lateral bracing, and arch rib spacing with different stiffness ratios, factors to improve the accuracy of the critical axial force obtained by the three codes are proposed for a practical design process.

<p> Three new types of continuous steel arch bridges are proposed and the structural characteristics are studied: the continuous arch bridge (model-A), the S-shaped arch bridge (model-B), and the double arch bridge (model-C). The continuous arch bridge has upward arch ribs. The S-shaped arch bridge has upward and downward arch robs. The double arch bridge has both upward and downward arch ribs. The arch ribs and the girders are all continuous on these bridges, which improves seismic resistance. It also eliminates expansion joints which improves drivability and reduces noises and vibrations. These three continuous arch bridges are studied in two stages. First, the member cross sections are determined for the dead and design live loads by the allowable stress method, and then the structural characteristics are studied. The S-shaped arch bridge has a larger vertical displacement than the other bridges. The vertical displacement and bending moment of the arch ribs and the girder of the double arch bridge are smaller than the others. Second, elastic plastic large deformation analysis is conducted to find the ultimate strength of the new arch bridges. It is found that the lateral buckling is critical in all the models. The initial imperfection is also considered by inclining the arch planes. This non-linear analysis shows that the proposed bridges have sufficient ultimate strength. Finally, the construction cost of these new arch bridges is estimated, finding that model-C requires more steel by 15% than model-A and model-B. In conclusion, the proposed new bridges are found to be feasible.</p>

An analytical solution for lateral buckling critical load of leaning‐type arch bridge was presented in this paper. New tangential and radial buckling models of the transverse brace between the main and stable arch ribs are established. Based on the Ritz method, the analytical solution for lateral buckling critical load of the leaning‐type arch bridge with different central angles of main arch ribs and leaning arch ribs under different boundary conditions is derived for the first time. Comparison between the analytical results and the FEM calculated results shows that the analytical solution presented in this paper is sufficiently accurate. The parametric analysis results show that the lateral buckling critical load of the arch bridge with fixed boundary conditions is about 1.14 to 1.16 times as large as that of the arch bridge with hinged boundary condition. The lateral buckling critical load increases by approximately 31.5% to 41.2% when stable arch ribs are added, and the critical load increases as the inclined angle of stable arch rib increases. The differences in the center angles of the main arch rib and the stable arch rib have little effect on the lateral buckling critical load.

To investigate the reasonable range of the inclination angle of arch ribs, a spatial finite element method was employed based on a concrete-filled steel tube (CFST) basket-handle through an arch bridge with a span of 360 m. A spatial finite element model was established using Midas/Civil software, which was verified with actual bridge data. The effects of different arch rib inclination angles were investigated under static loads. The structural natural frequencies, linear elastic stability coefficients, internal forces, and displacements were comprehensively considered to determine the reasonable range of the inclination angle. The results show that when the inclination angle ranges between 8° and 10°, the first, third, and sixth natural frequencies of the structure are increased. It effectively improves the lateral and torsional stiffness of the arch ribs while ensuring optimal out-of-plane stability of the arch ribs. Compared with the parallel arch, the stability is improved by 20.2%. The effects of angle variation on displacement and internal force of the arch ribs were not significant. Considering all indicators, the optimal range of the inclination angle for the arch ribs of 300-m-level highway CFST arch bridges is suggested to be 8~10°.

Large-diameter concrete-filled steel tube (CFST) arch bridge transverse braces adopt self-compacting concrete to avoid laitance and air void defects. However, several old CFST arch bridges in China use ordinary concrete, whose fluidity before initial setting produces cap gaps at the top of the transverse brace. Furthermore, harsh environments and concrete dry shrinkage enlarge the gaps, producing composite defects. Hence, using ultrasonic scanning, this study performs a scale-model experiment and finite-element analysis to determine the bearing capacity of a serviced CFST arch bridge transverse brace with cap gap and air void defects in the concrete core column under small eccentric axial compression. Parametric analyses were conducted to investigate the influence of the composite defects on the bearing capacity of the transverse brace. A new ultimate strength index of the brace with composite defects was proposed, including a simplified formula for estimating the effects of cap gap and air void defects on the ultimate strength of the CFST arch bridge transverse brace. Thus, this study can provide a strong foundation for the construction of reliable CFST arch bridges.

Due to their excellent thermal conductivity and sensitivity to temperature changes, special attention should be paid to the influence of temperature on steel-structure bridges. The temperature effect is complex, especially for unstable steel arch bridges with complex structural forms. This paper proposes an approximate method that measures the three-dimensional temperature field of the symmetrical arch rib with the two-dimensional temperature field of multiple sections. In addition, it converts the complex radiant intensity calculation of the special-shaped steel box arch rib into the calculation of numerous planar radiant intensities. It uses the ANSYS Workbench to establish the three-dimensional transient thermal analysis finite element model of the No. 2 steel box arch rib. The influence of seasons and arch rib direction on the temperature field of steel box arch ribs and the stress and deformation of steel box arch ribs under non-linear temperature effects were analyzed. The results show that the temperature changes in different seasons significantly impact the temperature changes in the arch ribs. The change in the azimuth angle of the arch rib has a significant impact on the temperature difference between the web plates on both sides of the arch rib; under the influence of the temperature field at the most unfavorable time in summer and winter, symmetrical stress concentration occurs in the arch foot area. Furthermore, the maximum vertical displacement is 13.9 mm and 10.8 mm, respectively. Finally, when the angle is 40°, the maximum temperature difference between the web plates on both sides is 6.9 °C.

As one of the most common failure types of arch bridges, stability is one of the critical aspects for the design of arch bridges. Using 3D finite element model in ABAQUS, this paper has studied the stability performance of an arch bridge with inclined arch ribs and hangers, and the analysis also took the effects of geometrical and material nonlinearity into account. The impact of local buckling and residual stress of steel plates on global stability and the applicability of fiber model in stability analysis for steel arch bridges were also investigated. The results demonstrate an excellent stability of the arch bridge because of the transverse constraint provided by transversely-inclined hangers. The distortion of cross section, local buckling and residual stress of ribs has an insignificant effect on the stability of the structure, and the accurate ultimate strength may be obtained from a fiber model analysis. This study also shows that the yielding of the arch ribs has a significant impact on the ultimate capacity of the structure, and the bearing capacity may also be approximately estimated by the initial yield strength of the arch rib.

To explore the different influence of traveling wave effect on the isolated and non-isolated arch bridge, the isolated and non-isolated multi-span arch bridges models are established respectively, three measured seismic waves were selected, and under the eight kinds of apparent wave velocities and multi-point consistent excitations, the structural responses of the two models, including the internal force response, the arch rib velocity, the pier’s internal force response, the bridge deck acceleration, and the shear force and displacement of isolation support of different arch ribs position in two models, were compared and analyzed. The results show that the isolation effect of the isolation structure is obvious; the wave effect of the isolated structure is significant, the two structures show different internal force response curves in different positions of the arch ribs under the influence of different seismic waves; the influence of the apparent wave velocity on the force and shock reduction rate of the arch ribs is complex; the vertical acceleration of the arch ribs and bridge deck of the isolated structure is reduced significantly; and the shear force and displacement of the isolation bearing increase with the increase of the apparent wave velocity. The study shows the traveling wave effect of multi-span through a concrete-filled steel tubular arch bridge with and without isolation, and the results will be used for the seismic design and analysis of structural diseases caused by the wave effect.