Dynamic Response Impact of Vehicle Braking on Simply Supported Beam Bridges with Corrugated Steel Webs Based on Vehicle-Bridge Coupled Vibration Analysis

A novel approach for analyzing coupled vibrations between vehicles and bridges is presented,taking into account spatiotemporal effects and mechanical phenomena resulting fromvehicle braking.Efficient modeling and solution of bridge vibrations induced by vehicle deceleration are realized using this method.The method’s validity and reliability are substantiated through numerical examples.A simply supported beam bridge with a corrugated steel web is taken as an example and the effects of parameters such as the initial vehicle speed,braking acceleration,braking location,and road surface roughness on the mid-span displacement and impact factor of the bridge are analyzed.The results show that vehicle braking significantly amplifies mid-span displacement and impact factor responses in comparison to uniform vehicular motion across the bridge.Notably,the influence of wheelto-bridge friction forces is of particular significance and cannot be overlooked.When the vehicle initiates braking near the middle of the span,both the mid-span displacement and impact factor of the bridge exhibit substantial increases,further escalating with higher braking acceleration.Under favorable road surface conditions,the midspan displacement and the impact factor during vehicle braking may exceed the design values stipulated by codes.It is important to note that road surface roughness exerts a more pronounced effect on the impact factor of the bridge in comparison to the effects of vehicle braking.

Discussion on Detection and Evaluation of Simply Supported Prestressed Concrete Small Box Girder Bridge After a Fire

The article takes a simply supported prestressed concrete small box girder bridge project as an example for inspection and evaluation after a fire incident.This includes appearance detection,concrete color hardness detection,concrete strength detection,concrete surface damage layer detection,reinforcement protective layer detection,and concrete carbonation detection.It is hoped that this analysis can be used as a reference for the detection and evaluation of future bridge projects with fire incidents to smoothen its subsequent repair and maintenance.

Damage Identification in Simply Supported Bridge Based on Rotational-Angle Influence Lines Method

To locate and quantify local damage in a simply supported bridge, in this study, we derived a rotational-angle influence line equation of a simply supported beam model with local damage. Using the diagram multiplication method, we introduce an analytical formula for a novel damage-identification indicator, namely the diff erence of rotational-angle influence linescurvature(DRAIL-C). If the initial stiff ness of the simply supported beam is known, the analytical formula can be effectively used to determine the extent of damage under certain circumstances. We determined the effectiveness and anti-noise performance of this new damage-identification method using numerical examples of a simply supported beam, a simply supported hollow-slab bridge, and a simply supported truss bridge. The results show that the DRAIL-C is directly proportional to the moving concentrated load and inversely proportional to the distance between the bridge support and the concentrated load and the distance between the damaged truss girder and the angle measuring points. The DRAIL-C indicator is more sensitive to the damage in a steel-truss-bridge bottom chord than it is to the other elements.

Pure bending of simply supported circular plate of transversely isotropic functionally graded material

This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM).

Analytical solutions of simply supported magnetoelectroelastic circular plate under uniform loads

In this paper, the axisymmetric general solutions of transversely isotropic magnetoelectroelastic media are expressed with four harmonic displacement functions at first. Then, based on the solutions, the analytical three-dimensional solutions are provided for a simply supported magnetoelectroelastic circular plate subjected to uniform loads. Finally, the example of circular plate is presented.

Wind tunnel measurement of aerodynamic characteristics of trains passing each other on a simply supported box girder bridge

The aerodynamic performance of high-speed trains passing each other was investigated on a simply supported box girder bridge,with a span of 32 m,under crosswinds.The bridge and train models,modeled at a geometric scale ratio of 1:30,were used to test the aerodynamic forces of the train,with the help of a designed moving test rig in the XNJD-3 wind tunnel.The effects of wind speed,train speed,and yaw angle on the aerodynamic coefficients of the train were analyzed.The static and moving model tests were compared to demonstrate how the movement of the train influences its aerodynamic characteristics.The results show that the sheltering effect introduced by trains passing each other can cause a sudden change in force on the leeward train,which is further influenced by the wind and running speeds.Detailed analyses related to the effect of wind and train speeds on the aerodynamic coefficients were conducted.The relationship between the change in aerodynamic coefficients and yaw angle was finally described by a series of proposed fitting formulas.

Effect of temperature difference load of 32 m simply supported box beam bridge on track vertical irregularity

In order to study the effect of temperature difference load （TDL） along the vertical direction of a simply supported beam bridge section on the vertical irregularity, a rail-bridge-piers calculation model was established. Taking 32 m simply supported box beam bridge which is widely used in the construction of pas- senger dedicated line in China as an example, influences of the temperature variation between the bottom and top of the bridge, temperature curve index, type of temperature gradient, and beam height on track vertical irregularity were analyzed with the model. The results show that TDL has more effects on long wave track irregularity than on short one, and the wavelength mainly affected is approxi- mately equal to the beam span. The amplitude of irregu- larity caused by TDL is largely affected by the temperature variation, temperature curve index, and type of temperature gradient, so it is necessary to monitor the temperaturedistribution of bridges in different regions to provide accurate calculation parameters. In order to avoid the irregularity exceeding the limit values, the height of 32, 48, and 64 m simply supported box beam bridges must not be less than 2.15, 3.2, and 4.05 m, respectively.

Influence of key factors on deflection of bonded prestressed concrete simply supported slabs subjected to fire

In order to validate the accuracy of nonlinear fire simulation programs,comparison analysis is carried out between simulation and experiment induced from small-scale specimens,and then fire resistance of large-scale prestressed concrete slabs is further investigated through parameter expansion.The influences on fire resistance ratings controlled by deflection are explored and discussed,including effective span,concrete cover thickness,load level,prestress degree,effective prestress,composite reinforcement index and other factors.The calculated results indicate that fire resistance ratings of large-scale bonded prestressed concrete simply supported slabs are bigger than those of small-scale ones.Finally,the calculation formulas of fire resistance ratings controlled by deflection are established,which rationally consider the influence of effective span,concrete cover thickness,load level,composite reinforcement index and so on key factors.

ANALYTICAL SOLUTION OF A SIMPLY SUPPORTED PIEZOELECTRIC BEAM SUBJECTED TO A UNIFORMLY DISTRIBUTED LOADING

Using the inverse method, the analytical solution of a simply supported piezoelectric beam subjected to a uniformly distributed loading has been studied.First,the polynomials of stress function and induction function are given.Then, considering the gradient properties of the elastic parameter and the potential funciton as well as the piezoelectric parameter,the analytical solution of a simply supported beam subjected to a uniformly distributed loading is obtained and discussed.

Analytical Solutions to Strain Rates of Reinforced Concrete Simply Supported Slabs under Blast Loads

Based on the Duhamel integral, a couple of analytical solutions are derived to predict the strain rates of concrete and steel reinforcement in reinforced concrete slabs under blast loads and to estimate their variation over depth of a cross-section along the entire length of the member. The analytical approach utilizes the single-degree-of-freedom mode for the analysis of reinforced concrete simply supported one-way panels subjected to blast loads. These analytical solutions can give the strain rate profile for any cross-section at any time and permit variations of strain rate in each time step of numerical iteration method, thus making it possible to directly incorporate strain rate effects into non-linear dynamic response analysis of structural members subjected to blast loads.

THE DYNAMIC PLASTIC BEHAVIOR OF A SIMPLY SUPPORTED CIRCULAR PLATE IN A DAMPING MEDIUM WITH FINITE-DEFLECTIONS

A theoretical analysis is presented for the dynamic plastic behavior of a simply supported rigid, perfectly plastic circular plate in damping medium with finite-deflections subjected to a rectangular pressure pulse. Analytical solutions of every moving stage under both medium and high loads are developed.

BENDING OF UNIFORMLY LOADED RECTANGULAR PLATES WITH TWO ADJACENT EDGES CLAMPED, ONE EDGE SIMPLY SUPPORTED AND THE OTHER EDGE FREE

In this paper, an exact solution for an uniformly loaded rectangular plate with two adjacent edges clamped, one edge simply supported and the other edge free, was given by using the concept of generalized simply supported edges and superposition method. The numerical results were given for the deflections along the free edge and bending moments along the clamped edges of a square plate.

THE APPLICATION OF WEINSTEIN-CHIEN′S METHOD——THE UPPER AND LOWER LIMITS OF FUNDAMENTAL FREQUENCY OF RECTANGULAR PLATES WITH EDGES ARE THE MIXTURE OF SIMPLY SUPPORTED PORTIONS AND CLAMPED PORTIONS

In this paper, the method of relaxed boundary conditions is applied to rectangular plates with edges which are a sort of the mixture of simply supported portions and clamped portions, so that the lower limit of fundamental frequency of such plates is evaluated. A kind of polynomial satisfying the displacement boundary conditions is designed, os that it is enabled to evaluate the upper limit of fundamental frequency by Ritz' method. The practical calculation examples solved by these methods have given satisfactory results. At the end of this paper, it is pointed out that the socalled exact solution of such plates usually evaluated by the force superposition method is essentially a kind of lower limit of solution, if the truncated error of series which occurs in actual calculation is considered.

Effect of Web Opening on Buckling Instability of Simply Supported Steel I-Beam

The lateral torsional buckling phenomenon often governs design of steel I-beams. Although web opening is often used to accommodate the required mechanical and piping works in buildings, its effect on the buckling instability is not considered in the design codes. In this paper, the effect of web opening on both lateral torsional buckling and local buckling behaviors has been investigated. A simply supported steel I-beam has been studied under uniform bending moment around the major axis. Buckling analysis has been performed using the finite element method. Linear regression analysis has been conducted for output data to formulate an equation for the critical moment including web opening effect. The results have shown a limited reduction in the lateral torsional buckling capacity and a significant reduction in the local buckling capacity.

Damage Detection for Simply Supported Bridge with Bending Fuzzy Stiffness Consideration

The benchmark of a simply supported beam with damage and bending fuzzy stiffness consideration is established to be utilized for damage detection. The explicit expression describing the Rotational Angle Influence Lines(RAIL) of the arbitrary section in the benchmark is presented as the nonlinear relation between the moving load and the RAIL appeared, when the moving load is located on the damage area. The damage detection method is derived based on the Difference of the RAIL Curvature(DRAIL-C) prior to and following arbitrarily section damage in a simply supported beam with bending fuzzy stiffness consideration. The results demonstrate that the damage position can be located by the DRAIL-C graph and the damage extent can be calculated by the DRAIL-C curve peak. The simply supported box girder as a one-dimensional model and the simply supported truss bridge as a three-dimensional model with the bending fuzzy stiffness are simulated for the validity of the proposed method to be verified. The measuring point position and noise intensity effects are discussed in the simply supported box girder example. This paper provides a new consideration and technique for the damage detection of a simply supported bridge with bending fuzzy stiffness consideration.

THE EFFECT OF BOUNDARY SHAPE ON BOUNDARY LAYER OF P-MODEL PLATE PROBLEMS WITH HARD SIMPLY SUPPORT

The paper shows that, for a unit circular plate, Reissner-Mindlin plate model with hard simply support does not capture the boundary layer behaviour for the bending moment when the load is independent of θ, where (r,θ) is the polar coordinates in plane. In contrast p-model shows this boundary layer, which is proved theoretically and numerically. But for the case when the boundary is a straight line, the boundary layer for p-model is weak and disappears as the plate thickness tends to zero.

Probability-based practice-oriented seismic behaviour assessment of simply supported RC bridges considering the variation and correlation in pier performance

Probability-based seismic performance assessment of in-service bridges has gained much attention in the scientific community during the past decades. The nonlinear static pushover analysis is critical for describing the seismic behaviour of bridges subjected to moderate to high seismicity due to its simplicity. However, in existing analysis methods,the generation of pushover curve needs tremendous amount of computational costs and requires skills, which may halter its application in practice, implying the importance of developing practice-oriented analysis method with improved efficiency. Moreover, the bridge pier performance has been modelled as deterministic, indicating that the variation associated with the pier material and mechanical properties remains unaddressed. The correlation in the performance of different piers also exists due to the common design provisions and construction conditions but has neither been taken into account. This paper develops a simplified pushover analysis procedure for the seismic assessment of simply supported RC bridges. With the proposed method, the pushover curve of the bridge can be obtained explicitly without complex finite element modelling. A random factor is introduced to reflect the uncertainty in relation to the pushover curve. The correlation in the pier performance is considered by employing the Gaussian copula function to construct the joint probability distribution. Illustrative examples are presented to demonstrate theapplicability of the method and to investigate the impact of variation and correlation in bridge pier behaviour on the seismic performance assessment.

Quality evaluation of layerlike backfilling and flow pattern of backfill slurry in stope

Stability condition and quality evaluation formula of layerlike backfilling roof,Q≥C,where Q denotes is quality index depending on allowable compressive or tensile strength and integrity of backfilling,and C is the technical index depending on mining method and backfilling technology,were inferred according to simply supported beam theorem.Technical treatment measures for instable backfilling roof,including optimum of appropriate filling materials and dosage for excellent flow property and reduction of backfill cost.It is proved that slope equation of backfill slurry in a stope to be filled is y=hexp[x2/(2σ)2)],where h is height of cone and σ2 is mean square,and that optimum drainage point of backfill slurry can be determined by the equation and sizes of stope.Case study indicates that the results can give a theoretical support for quality evaluation and control of layerlike backfilling.

Three-dimensional analysis of a thick FGM rectangular plate in thermal environment

The thermal behavior of a thick transversely isotropic FGM rectangular plate was investigated within the scope of three-dimensional elasticity. Noticing many FGMs may have temperature-dependent properties, the material constants were further considered as functions of temperature. A solution method based on state-space formulations with a laminate approximate model was proposed. For a thin plate, the method was clarified by comparison with the thin plate theory. The influences of material inhomogeneity and temperature-dependent characteristics were finally discussed through numerical examples.

Seismic analysis of high-speed railway irregular bridge–track system considering V-shaped canyon effect

To explore the effect of canyon topography on the seismic response of railway irregular bridge-track system that crosses a V-shaped canyon, seismic ground motions of the horizontal site and V-shaped canyon site were simulated through theoretical analysis with 12 earthquake records selected from the Pacific Earthquake Engineering Research Center(PEER) Strong Ground Motion Database matching the site condition of the bridge.Nonlinear seismic response analyses of an existing 11-span irregular simply supported railway bridge-track system were performed under the simulated spatially varying ground motions. The effects of the V-shaped canyon topography on the peak ground acceleration at bridge foundations and seismic responses of the bridge-track system were analyzed. Comparisons between the results of horizontal and V-shaped canyon sites show that the top relative displacement between adjacent piers at the junction of the incident side and the back side of the V-shaped site is almost two times that of the horizontal site, which also determines the seismic response of the fastener. The maximum displacement of the fastener occurs in the V-shaped canyon site and is 1.4 times larger than that in the horizontal site. Neglecting the effect of V-shaped canyon leads to the inappropriate assessment of the maximum seismic response of the irregular high-speed railway bridge-track system. Moreover, engineers should focus on the girder end to the left or right of the two fasteners within the distance of track seismic damage.