Journal of Bridge Engineering

Cable-stayed bridges with long spans are excited by different support vibrations on both sides of the main span. Therefore, a realistic seismic structural analysis of the bridge must involve multiple-support excitation. The dynamic equation of motion, in which all degrees of freedom are solved at once, can be solved directly. A modal analysis might also be possible, but care must be taken with the number of modes used in the analysis. If the ground motion is described in terms of displacement and velocity, which is referred to as displacement loading, then a static correction that will account for the unconsidered higher modes must be performed. In this study, the procedure of multiple-support excitation through the use of modal transformation is explained in detail. The effects of changes in damping levels that affect the analysis results are investigated by using the static correction method in displacement loading. An example is given to illustrate the mentioned problem by using a finite-element model of the cable-stayed Bill Emerson Memorial Bridge.

This paper derives simplified differential displacement loading patterns, in lieu of spatially variable seismic excitations, for use in the seismic design of bridges, based on the displacement sets originally presented in the European seismic design codes. The most significant difference between the patterns derived herein and those of the European seismic design codes is that the patterns derived in this work have a clear physical interpretation. First, the relationship between the space and time derivatives of ground motions in the free field is discussed, and an estimate for the differential ground motions at different locations on the ground surface with respect to a reference point is derived. Second, a deterministic methodology is developed to produce simplified displacement loading patterns, consistent with the propagation characteristics of seismic waves, for the evaluation of the nonuniform excitation of bridge supports when the soil properties along the structure do not vary significantly. The proposed displacement loading patterns are compared with the ones recommended by the European seismic design codes for the consideration of the multisupport excitation of long-span bridges. The numerical results of this study indicate that the displacement loading pattern proposed by the European seismic design codes for the case in which the adjacent bridge supports move in opposite directions may provide unrealistic values for the differential ground motions.

The development of the Chinese economy is associated with many changes in vehicle loads, particularly the increasing numbers of heavy trucks and other types of vehicles. However, currently, no standard vehicle has been identified for studying the fatigue design of highway bridges in China. Using the weigh-in-motion system, the authors obtained vehicle loads of 23 Chinese provinces. Miner’s rule for cumulative fatigue damage was then used to categorize each vehicle as one of eight representative types according to load. From these types, five equivalent vehicle models were found. Subsequently, simplified fatigue load spectra for highway bridges were obtained for each province. The six-axle vehicle can be used as the standard fatigue vehicle for most provinces, except in Zhejiang and Guizhou, in which three- and four-axle vehicles are most representative. Also, a standard fatigue vehicle for China is proposed.

The basic mechanical behavior of a nonprismatic concrete-encased beam with corrugated steel webs (CSWs) was investigated through a scale model experiment and finite-element model analysis. Because of the influence of variable cross sections and the concrete encasement, results of this study contradicted the assumption that CSWs bear all of the shear force in a nonprismatic beam. The inclined bottom flange resisted a significant portion of the shear force in the section under longitudinal bending moment. Shear stress in the CSW was uniformly distributed through the cross section when the CSWs were encased in concrete. In addition, the authors made the counterintuitive finding that the average shear stress in the CSW decreased gradually from the free end to the middle support. In other words, the root section near the support did not exhibit the greatest stress concentration, even though this region had the maximum vertical shear force and the largest hogging bending moment. Last, normal strain in concrete flanges and the concrete web approximately obeyed the plane section assumption. The longitudinal bending moment was mainly balanced by the moment from coupled axial forces in the concrete flanges. In general, the CSWs encased in concrete were unable to provide sufficient bending strength.

Earthquake ground motions may vary significantly at multiple supports of long-span bridges, such as cable-stayed bridges, due to the incoherence, wave-passage, and site-response effects. To investigate the seismic vulnerability of these bridges, fragility analysis is performed using spatially variable ground motions. To achieve this aim, this study chooses a cable-stayed bridge with the most common configuration in China and creates a numerical model of the bridge, which can account for the inelastic response of its multiple components. Using the conditional simulation method, a set of unknown ground motions are simulated on the basis of a set of prescribed ground motions and characteristics of the target random field. The simulated acceleration time histories are then converted into the associated displacement time-histories to perform multisupport excitation analysis. Using the displacement time histories, a set of nonlinear time-history analyses are performed to generate demand models. The demand models are convolved with limit-state models to develop fragility curves. Moreover, the influence of spatial variability parameters associated with the incoherence, wave-passage, and site-response effects on the vulnerability of multiple components is examined in terms of damage-exceedance probability. The results indicate that the incoherency and site-response effects significantly affect the demands and corresponding component fragilities. The worst case corresponds to the combination of a firm-soft soil site and the largest incoherency drop parameter. The section ductility demands at the base of the pylon are significantly affected by the spatial variability of ground motions. However, it does not appear to produce obvious changes in the cable, the abutment, or the bearing displacement.

The expressions of hydrodynamic pressure based on the radiation wave theory are too complex to be conveniently utilized in engineering applications; therefore, a simplified extraction that is accurate and concise for calculating the hydrodynamic effect on deepwater bridge piers is highly desirable for seismic analyses. With a further comparison between the elastic vibration and rigid motion of cylindrical piers submerged in water, the hydrodynamic pressure of the cylindrical piers can be approximately acquired in terms of the added mass caused by rigid motion based on the linear radiation wave theory. A simplified formula for the hydrodynamic pressure is proposed by elaborate data fitting, in which the section radius of the pier and the water height are the main parameters. The accuracy of the proposed formula is validated by the radiation wave theory and the potential-based fluid-element method. Results prove that the simplified expressions are not only accurate but also convenient in calculating the hydrodynamic pressure of cylindrical piers with a wide range of geometries. The applicability of the Morison equation and the Goto-Toki formula is also presented.

Two types of damage—numerous cracks in the main girder and excessive midspan deflections—are sometimes observed in conventional long-span prestressed concrete box-girder bridges. To this end, a new box-girder bridge structure is proposed based on the superior properties of the reactive powder concrete (RPC). Diaphragms are densely distributed in the proposed structure to reduce the torsional warping stresses of the box girder and the local stresses of the deck slabs under wheel loads, as well as to improve the shear performance of the webs and the compression stability of the bottom slabs. Moreover, compared to the conventional box-girder bridge, the proposed structure is characterized by unidirectional (longitudinal) and partial external prestressing, as well as thinner slabs. According to the aforementioned characteristics of the proposed structure, the experimental model of the RPC box girder was designed and fabricated to explore its feasibility and mechanical performance. Tests on the deck slabs of the experimental model were first carried out to investigate the load path in deck slabs and evaluate the effect of diaphragm spacing. Results show that it is feasible to remove the transverse prestressing tendons in the deck slabs of the proposed box-girder structure. Subsequently, the shear failure test on the new box-girder structure was conducted. It was found that the postcracking shear performance of the proposed structure is improved due to the presence of the ribbed structures consisting of diaphragms and webs. Combined with the finite-element (FE) analyses, the safety factor of the shear cracking resistance of the web was calculated, up to 1.844 for a 400-m RPC box-girder bridge. Thus, it is feasible to remove the vertical prestressing tendons in this new structure. In addition, the shear capacity of the tested box girder was predicted by using the related design recommendations. Comparisons were performed among these predicted values and the test results. Although the feasibility of the proposed bridge structure is clearly demonstrated in this paper, further studies prior to its practical applications are being extensively performed to clarify its flexural capacity, shear behavior of webs, torsional behavior, fatigue behavior of deck slabs, seismic behavior, dynamic behavior under wind loads, prestressing optimization, and anchor details.

Forty specimens were tested under different stress amplitudes to study the roof and U-rib weld fatigue performances of orthotropic steel bridge decks, considering different penetration rates and thicknesses. Nominal and hot-spot stresses were measured. The crack propagation and microstructure were analyzed, and the cracked sections were cut out to observe the metallographic means. On the basis of test results, the fatigue life and strength were investigated. In addition, crack-propagation processes and stress-intensity factors were analyzed by the finite-element method (FEM). The results reveal that an increased penetration rate can decrease the crack-propagation rate and enhance fatigue life. An increase in deck thickness can cause a more obvious improvement in slowing the rate of crack propagation and the fatigue life under high-stress amplitudes. A lower penetration rate resulted in a larger decrease in bearing capacity after cracking, especially in a thicker deck. The increased penetration rate contributed to a decrease in the local stress-intensity factor but had little effect on crack angle and path. The fatigue strengths of nominal and hot-spot stress methods were suggested to be 70 and 75 MPa, respectively.

In this paper, an effective simulation technology was proposed for finely predicting the temperature effect of bridges. Based on the ray tracing method, a three-dimensional (3D) sunlight-sheltering algorithm was developed to predict the temperature field more precisely. To improve the computational efficiency, the substructure method was applied in mechanical or coupled thermomechanical analysis. The effects of wind speed, atmospheric environment, and thermal properties of ground surface were also included. The proposed technology was verified by comparing the measured data (temperature on a rigid-frame concrete bridge) with the predicted values and was applied to analyze the seasonal temperature effect of a cable-stayed bridge thoroughly. In the analysis, a girder-pylon-cable system was finely established, and nonuniform distribution of temperature and stress were shown as well. The results show that the maximum thermal stress was 30 MPa on the steel girder in summer, and the deflection reached a maximum value of 22 mm. Moreover, the different effect of heat flux intensity received by horizontal and vertical surfaces was identified. Also, temperature variations in cables were found to play a significant role in the vertical and longitudinal deformation. As a result the computing time was saved up to 83%, and this study provided a comprehensive reference for designs of bridges.

The vehicles moving on a bridge excite bridge vibration and can also serve as response receivers because the vehicle dynamic response contains the vibration information of the bridge. A methodology was proposed in a previous study for extracting bridge modal properties, such as natural frequencies and modal shapes, from the vehicle dynamic responses. A specialized test vehicle consisting of a tractor and two following trailers was developed in which the two trailers towed by the tractor moving along the bridge were used as the dynamic response receivers. The responses of one trailer with a time shift were subtracted from the responses of the other to obtain the residual responses that were then processed with fast Fourier transformation (FFT) and short-time Fourier transformation (STFT) to extract the bridge modal properties. In the present paper, field test data of an existing bridge were adopted to verify the proposed methodology. In the vehicle and bridge system, a bridge finite-element (FE) model was updated using the measured accelerations and strains of the bridge; two types of test vehicle models were proposed for use in simulations of the tractor–trailer test system; and the measured surface-roughness profile was used in the numerical simulation. Parametric studies have been conducted to determine the trailer mass and stiffness. Vehicle Model I shows a good capacity for extracting bridge frequencies and the first two modal shapes with a dominant vertical component. However, Vehicle Model II performed better than Vehicle Model I on the extraction of bridge modal shapes that are dominant in lateral bending.

In recent years, particularly after the occurrence of strong earthquakes, there is an increased need for seismic retrofit of present bridges and changes in the design of new bridges. A method for retrofitting concrete bents in bridges involves the use of steel sheets or profiles to apply the confinement force. In this study, two specimens were analyzed in the laboratory at the scale of 30% under constant gravity and lateral cyclic loading. Also, a finite-element model was used to compare the behavior of experimental specimens. The first specimen was a model of a typical as-built bridge in Iran as generally designed by the common regulations of the 2000s, and the other specimen was a retrofitted model of the same frame in which transverse and longitudinal confinement in the connection region was used. The results show that the retrofit method will improve most of the frame seismic behavior indices, such as the performance level, absorbing energy in hysteresis curves, ductility, modification of failure propagation, and formation priority of plastic hinges.