Load Distribution Factors Research Articles

Reliability of Girder Bridge System under Lateral Uneven Vehicular Overloads

Truck presence on bridges is random. Trucks may centrically or eccentrically appear on a bridge span in one or more lanes, which will cause extra load effects on girder components and eventually influence structural performance. Especially when trucks are heavily loaded, their eccentric passage is possible to induce damage in components, and, thus, the prescribed load- delivery path will be changed among components within the system. Therefore, component- and system-level structural performance of bridges subjected to aggressive vehicular overloads need to be thoroughly addressed. In this study, a WIM-based 5-axle overloaded truck model is chosen, and it is gradually applied to the finite element models of two girder bridges with different eccentric distance, considering two loading scenarios of single truck and multiple trucks. In detail, trucks are transversely loaded with an incremental eccentric distance, to investigate the impacts of eccentric loadings on structural performance, including failure sequences of components, load distribution factors among components, as well as system redundancy, as structures entering nonlinear stage. Finally, the reliability indices of the two bridges under uneven overloads are assessed at the component level and system level, respectively. The results of this study were beneficial to structural evaluation bridges subjected to overloads to ensure their serviceability and integrity.

Load Distribution Factors of Simply Supported Concrete T-beam Bridges under Typical Freight Vehicle Loads

Load Distribution Factors of Simply Supported Concrete T-beam Bridges under Typical Freight Vehicle Loads

Primary frequency control optimization of coal-fired power plants with high-low position shafts: Employing a revised strategy with power-decoupling and feedforward-compensating

Coal-fired units play a critical role in peak-shaving and frequency regulation with high penetration of renewable energy. The coal-fired unit arranged by high-low position shafts applied in power stations will participate in these regulation processes. In this study, the dynamic model of the 1100 MW supercritical coal-fired unit is built and verified, dynamic characteristics of the primary frequency regulation process are analyzed and a poor control effect of the original control strategy is illustrated. Then, the dynamic coupling relationship between high and low-level units is obtained, and there is a 14-s time delay between the two power outputs, and a revised regulation strategy that employs load distribution factor and flow-rate feedforward-compensating is proposed. Compared with the original control strategy, the revised control strategy can effectively lower fluctuations of the steam parameters by approximately 50%, and the corrective regulation time decreases from 25.1 s and 15.8 s to 6.9 s and 12.1 s under positive and negative load disturbance, respectively. Moreover, it can improve the control effect of low-level unit, whose regulation time under positive and negative load disturbance decreases from 45.7 s and 27.7 s to 9.4 and 20.6 s, respectively. This research can provide technical guidance for the operation of coal-fired units.

Experimental study on the aerodynamic characteristics of combined angle transmission tower subject to skew wind

The transmission towers served as crucial carriers in the process of power transmission. The combined angle transmission tower of dual-angle steel with cruciform section are relatively a novel type of angle tower, which is being more widely used in transmission lines. The studies on aerodynamic characteristics of combined angle tower in skewed wind are limited. In this paper, the wind tunnel tests are conducted to investigate the aerodynamic characteristics of the combined angle tower, and the high frequency force balance (HFFB) test is introduced to obtain the transverse and longitudinal forces on the tower using the direct force measurement (DFM) method. The drag coefficients and wind load-distribution factors of the combined angle tower are obtained from the wind tunnel tests, and the effects of interference and tower leg spacing on the wind loads of the tower legs are fully explored. It can be found that the aerodynamic coefficients and drag coefficients of the combined angle steel tower leg tend to decrease with the increase of interference members and it also decreases with the decrease of the tower leg spacing. The test wind load-distribution factors of the isolated leg are generally larger than those defined by seven typical codes (e.g., US, EU, Japanese, and Chinese codes) and significantly exceed the code-specified values under partial wind angles. The observations obtained from this study may provide helpful guidance on the wind-resistant design of this relatively novel type of combined angle tower.

Axial live load distribution among single row of piles of integral bridges

This study investigates the axial live load distribution among steel H-piles in single-span integral bridges. To achieve this, two- and three-dimensional finite-element models for various integral bridges are conducted and analysed using the structural analysis software SAP2000, to determine the maximum axial loads in steel H-piles within two- and three-dimensional models. Subsequently, axial live load distribution factors from the ratio of axial loads calculated from these models are derived. The parametric study reveals that girder spacing and pile spacing exert notable influences on the axial live load distribution among the steel H-piles in integral bridges. Then, non-linear regression analysis is employed to formulate practical equations as functions of these two parameters. These equations can effectively calculate the live load distribution factors for the piles in integral bridges. To validate the accuracy of the live load distribution factors calculated from the proposed formulae, a comparative analysis is performed with results obtained from structural analysis. The standard deviations of the ratios between these two results are found to be a mere 2%. This clearly demonstrates that the developed formulae yield highly precise estimates of axial live load effects in integral bridge piles.

Investigation on mechanical performance of prestressed concrete box‐girder bridge strengthened using composite trusses with different shapes

AbstractIn this study, a finite element (FE) model of an existing prestressed concrete box‐girder (PCB) bridge is developed using Abaqus/Explicit (2022), and a series of FE simulations are conducted to examine the results of composite trusses (CTs) in strengthening PCB bridges with different shapes. A concrete damage plastic model of concrete is used to predict the nonlinear behavior of concrete. Field tests and theoretical calculations are performed to verify the rationality of the model. Three CTs of different shapes, that is, a K‐shaped composite truss (KCT), an X‐shaped composite truss (XCT), and a triangle‐shaped composite truss (TCT), are used to strengthen the PCB bridge models. The deflection, load distribution, distortion, and surface connection forces under two types of lane loads (European code [EU] and Chinese code [CC]) are discussed. The results show that the CT can reduce the deflection and distortion of the PCB bridge and improve the load distribution. However, the different CT shapes offer other strengthening effects. Among them, the XCT reduces deflection the most significantly, that is, by 8.9% and 17.1% under the two load modes, separately. In addition, the XCT improves the load distribution of the PCB bridge the most significantly. The KCT reduces the distortion of the PCB bridge the most significantly and decreases the stress ratio by 75.36%. Moreover, the deflection of the PCB bridge under the EC is more significant, indicating that the lane load defined by the EC is larger than that by the CC. The maximum surface connection forces are different under the same load mode for the different CTs. However, in all the models, the bending moment at surface‐2 is insignificant. Based on the analysis results, five assumptions are introduced. Using the KCT as an example, the plane model of the reinforced section is simplified, and a canonical equation is established to calculate the load distribution factor. The 324 coefficients and 18 free terms in this canonical equation are deduced, which provides a theoretical basis for strengthening PCB bridges using CTs.

Structural Behavior and Load Distribution Factor of a T-Girder Bridge with Various Truss Diaphragms

Structural Behavior and Load Distribution Factor of a T-Girder Bridge with Various Truss Diaphragms

Load distribution factors for quick design and assessment in typical Australian bridges

ABSTRACT The increase in freight productivity in Australia is pressuring Australian bridge infrastructure. Bridge assessment is crucial to ensure the safety of bridges to accommodate heavier vehicles. Load distribution factor (LDF) has been widely used for bridge design and evaluation in the preliminary stage, but it is not specified in the Australian standard code. This study aims to develop the LDFs for typical Australian bridges with the most adverse load effects of single- and two-lane loads. Later, the LDFs were compared with the LDF equations in the different standards, including National Association of Australian State Road Authorities (National Association of Australian State Road Authorities, 1976), American Association of Highway and Transportation Officials: Load and Resistance Factor Design (AASHTO (2017), Henry’s and modified Henry’s methods. It can be concluded that the AASHTO (2017) LDF equations provide very good correlations with typical Australian bridges. It is possible to use the AASHTO LRFD LDF equations for assessing and designing in Australian concrete I-girder and Super-T girder bridges. However, most AASHTO LFRD provides conservative results of LDFs compared with LDFs of Australian bridges. It is recommended that LDFs of Australian bridges should be developed for bridge design and assessment.

Development of Improved Equations for Live Load Moment Distribution in Interior Girders of Shallow Steel Tub Girder Bridges

AbstractThe focus of this paper is the development of improved live load distribution factor (LLDF) prediction equations for interior beams of press‐brake‐formed tub girder (PBFTG) bridges. PBFTGs consist of cold‐bent standard plate widths and thicknesses to form a trapezoidal box girder. Based on a survey of literature and field testing performed on PBFTG bridges across multiple states in the United States, the empirical equations found in the American Association of State Highway and Transportation Officials Load Resistance and Factor Design Bridge Design Specifications (AASHTO LRFD BDS) have been found to be conservatively applicable to shallow steel tub girder bridges. Improvements can be made to AASHTO LRFD BDS provisions relating to shallow steel tub girders and their respective live load distribution factors (LLDFs). To overcome this gap in design and analysis, rigorous three‐dimensional finite element analysis tools were developed and benchmarked against field implementations. The tools were used to analyze the live load distribution behavior of an interior girder of a matrix of approximately 18,000 PBFTG bridges. From the result of the analysis, statistical methods were employed to produce simplified empirical equations to better predict live load moment distribution in PBFTGs. The simplified equations are to be used in conjunction with line girder analysis to further simplify the design of shallow steel tub girder bridges and expand their application in the short‐span bridge market.

Refined analysis of steel girder bridges for computation of live load distribution factors considering effects of freight and emergency vehicles

Recent revisions to federal guidelines require state departments of transportation (DOTs) to rate bridges in their inventory with special hauling vehicles (SHVs) and emergency vehicles (EVs). In this research, refined analysis method was used to compute live load distribution factors of steel girder bridges considering the impacts of SHVs and EVs on the live load distribution behavior. To determine the live load distribution factors for interior and exterior girders under different lane loading conditions, finite element models of twenty-one steel girder bridges from the state of Virginia were developed and then analyzed. The effects of vehicle type and transverse position on the results of the refined analysis were evaluated. The results were comparatively evaluated with those obtained using AASHTO LRFD equations. The live load distribution factor of steel girder bridges with various geometrical parameters were predicted using a series of linear regression models that were built using the data from the numerical simulations. The developed models can be used to identify bridges whose rating factors will be improved through refined analysis when these bridges are susceptible to posting.

Load Distribution Factors For Horizontally Curved Composite Concrete-Steel Girder Bridges

This paper focuses on Load distribution factors for horizontally curved composite concrete-steel girder bridges. The finite-element analysis software“SAP2000” is used to examine the key parameters that can influence the distribution factors for horizontally curved composite steelgirders. A parametric study is conducted to study the load distribution characteristics of such bridge system due to dead loading and AASHTO truck loading using finite elements method. The key parameters considered in this study are: span-to-radius of curvature ratio, span length, number of girders, girders spacing, number of lanes, and truck loading conditions. The results have shown that the curvature is the most critical factor which plays an important role in the design of curved girders in horizontally curved composite bridges. Span length, number of girders and girder spacing generally affect the values of the moment distribution factors. Moreover, present study reveals that AASHTO Guide criterion to treat curved bridges with limited curvature as straight one is conservative. Based on the data generated from the parametric study, sets of empirical equations are developed for the moment distribution factors for straight and curved steel I-girder bridges when subjected to the AASHTO truck loading and due to dead loading.

Structural strengthening of a constructed timber bridge: Field application and numerical modeling

This paper presents the behavior of a timber bridge strengthened with lag bolts, carbon fiber reinforced polymer (CFRP) sheets, and hollow structural sections (HSS). The 83-old bridge is composed of three spans, supported by 14 Douglas Fir girders, and is tested employing truck loadings of 120 kN and 267 kN. Three-dimensional finite element models are formulated to study the flexural response of the bridge with and without the retrofit options. The magnitude of the truck load dominates the degree of dispersion in girder deflections and alters the shape of probability density functions, which are associated with behavioral uncertainty. The effectiveness of strengthening is apparent in terms of reducing the exceedance probability of deflection limits and increasing reliability indices above the design threshold of β = 3.5, stipulated in bridge specifications. Among the three methods, the stiffening efficiency of the HSS option is higher at the system level; however, the use of CFRP is most efficient at the member level. Live load distribution factors are examined and implementable recommendations are provided for practice. Parametric investigations clarify the efficacy of variable HSS sizes and the ramifications of a permit truck weighing 445 kN.

Assessment of web shear stresses and shear capacity of FRP composite tub girders for highway bridges

Reinforced polymer composite tub (CT) girders are a novel solution as the main structural element of short to medium span highway bridges. These girders are lightweight and more durable than the steel and concrete bridges they are designed to replace. Although CT girders have been shown to behave well in flexure, significant questions remain as to the shear strength and buckling resistance provided by their foam-core sandwich webs, and regarding the distribution of shears under traffic live-load. Current practice is expected to provide conservative designs but could lead to inefficient material utilization, and few bridges have been placed in service to-date. In this study, CT girder sandwich web specimens were tested in near-pure shear in an attempt to assess their ultimate shear strength. The test results justify significant increases to the current web design strengths. A comprehensive suite of finite element analyses of typical girder webs was then analyzed to assess their shear buckling capacity. The analysis results were used to create design charts that provide critical web shear buckling loads for a range of web face sheet thicknesses, web foam core thicknesses, and web depths. Finally, a diagnostic field live load test of the first CT girder highway bridge placed in service is described, which focused on examining shear live load distribution. The results of this test indicate that the original design was reasonably conservative but demonstrate the need for live load distribution factors specifically tailored to the behavior of CT girders.

Experimental Study of Wind Loads on Tubular Crossarms of Transmission Towers

The actions exerted by yawed wind on the crossarm substantially differ from those on the tower body due to the presence of the angle between the crossarm’s cross-section and the incoming flow, and this phenomenon deserves a better understanding. Focusing on the tubular crossarms with round-section members, this paper aims to determine insights into wind actions, as affected by various factors, such as the tower type, the mean width to mean height ratio, the solidity ratio, and the wind incidence angle, and thereby derive the wind loads for design. Accordingly, a succession of wind tunnel tests was conducted by using quadrilateral and triangular crossarm models with various solidity ratios and mean width to mean height ratios. The method of direct force measurement (DFM) is employed for the high frequency force balance (HFFB) test to attain the transverse and longitudinal forces on the crossarm simultaneously. It was found that the wind load coefficients increase with increases of the mean width to mean height ratio and decreases of the solidity ratio. Moreover, in the case of the incoming flow perpendicular to the crossarm face, it is concluded that compared to the quadrilateral crossarm, the triangular crossarm possesses a relatively smaller drag coefficient, provided a moderate mean width to mean height ratio of 1.19. Furthermore, an analysis of the experimental results shows that the skewed wind load factor specified in the relevant codes would overestimate the effects of the wind incidence angle and the variations in mean width to mean height ratio, which is evident in the tests but not considered in the codes. It is worth noting that the experimental results show that the crosswind force is pronounced, which is usually ignored in the skewed wind load factor-based approach. Comparatively, using wind load distribution factors seems to be more rational. Thus, the corresponding estimating equations are proposed for the wind load-distribution factors of the crossarms, which agree well with the experimental results. The developed equations would greatly facilitate the determination of wind loads on tubular crossarms.

Pavement Evaluation of Kampi Ya Moto - Eldama Ravine - Kamwosor B77 Road

Assessment of pavement performance is essential in determining the serviceability and structural state of the pavement structure. Pavement failure and deterioration always commence immediately after the road has been opened to traffic. Several factors contributing to pavement failure and damage include traffic load, soil, environmental, economic, and stress distribution factor. Therefore, flexible pavement failure and deterioration are well-defined by alligator cracks, concentrated potholes, ruts, settlement, and localised depression. Pavement evaluation determines highway sections' functional and structural conditions for frequent monitoring or planning for maintenance. Kampi ya Moto-Eldama Ravine- Kamwasor (B77) road is a Kenya National Highways, Authority (KeNHA) class B road constructed in 2008. The length of the road is approximately 79.5 Km. However, the pavement had numerous distress features which developed even before the design life of the pavement was attained. The study, therefore, concentrated on evaluating the performance of the pavement to identify the type and level of severity of pavement distress; to establish a surface condition by measuring the level of roughness and rut depth and to perform a visual evaluation survey of the existing flexible pavement distresses; to identify the reason of structural and functional failures on Eldama Ravine-Kamwosor, and finally, to establish the residual structural strength of the existing flexible pavement and suggests the most viable maintenance intervention measures.

Field Test of a Shear Force Measurement Technique Using Fiber Optic Sensing under Variable Speed Truck Loading

The measurement of reaction forces at bridge bearings would enable engineers tasked with maintaining bridges to detect potential damage to the bearing and bridge by detecting changes in the load distribution at the supports with time. Currently, measuring the load in the bearing requires sensors built into the bearing, which means that they are hard to repair when damaged and cannot be installed after the bridge is built (unless the bearings are replaced). A potential alternative is the use of distributed fiber optic sensors (DFOS) that could be used to measure curvature in the beams of a bridge, which can then be used to calculate the moment, shear, and ultimately reaction force due to live loading. To investigate this, a DFOS system was installed on a newly built steel girder bridge on a single beam near one of the piers. A series of load tests were undertaken using a truck with a known load and driving along the bridge directly over the instrumented beam at speeds ranging from pseudo-static up to 30 km/h. The maximum measured strain in the bridge beam was 15 microstrain, which was lower than can be measured with certain DFOS systems, and highlighted the need to select a system with appropriate accuracy and precision. The measured strains were used to calculate the beam shear at the pier as the truck moved across the bridge. These results were compared with a continuous beam and two grillage analyses, and it was found that, based on the continuous beam model, about 25% of the total truck load was being carried by the beam, which was lower than the code live load distribution factor suggested. The grillage models provided better estimates of load spreading but were still conservative and dependent on the choice of transverse stiffness.

Low-Cost Assessment Method for Existing Adjacent Beam Bridges

Damage in grouted joints is an unavoidable early disease in adjacent box beam bridges and hollow-core slab bridges. Joint damage will lead to degradation of the transverse load transmission capacity of the bridge, causing beams of the bridge superstructure to bear loads higher than the designed value, and eventually fail prematurely. Precise assessment of bearing--capacity degradation degree of adjacent box beam bridges and hollow-core slab bridges that are of great number is the keypoint to maintaining the serviceability of traffic network. The current specifications regard grouted joints as individual components and cannot correctly assess the degradation degree of bearing capacity caused by joint damage. In this paper, the traditional hinge connected beam method is improved by modifying deformation compatibility conditions at grouted joints. By using a modified hinge connected beam method, the relationship of joints at different locations with the lateral load distribution factor (LLDF) is analyzed. Based on analysis results, this paper proposes a new low-cost assessment method and a new assessment index that can utilize visual inspection results. Based on the concept of standard deviation, the proposed method assesses the degradation degree of the lateral load transmission performance of bridge superstructures by calculating the variation in LLDFs of beams, which is expressed by the lateral load distribution performance rating number LDN. The proposed method is applied to three real bridges. The accuracy of the calculation results is verified by comparing the ranking of LDNs of three bridges with the ranking of the variation degrees of lateral deflection influence lines of three bridges obtained from static-load test results.

Displacement-function analysis of local stresses in thick beams on simple supports

A new boundary modeling scheme is introduced for the solution of thick beams on simple supports using the displacement-function elasticity approach. The performance of two sets of mixed boundary conditions at the opposing lateral ends of a quasi-infinitely long beam is investigated for the analytical solution of the thick beam. In this approach, a cropped solution strategy is implemented to obtain the elastic field from the central region of the long beam, in which the solution of the beam is obtained in terms of a single scalar function in the form of infinite trigonometric series. The appropriateness and accuracy of the solutions is verified through the comparison with corresponding solutions obtained by FEM and classical beam theory. The convergence characteristics of the series solution are analyzed in the perspective of required computational effort with varying load distribution factor, beam aspect ratio and far-field span ratio. Finally, the method is applied to analyze the local stress and displacement fields, especially in the immediate neighborhood of the discretely applied loads and supports of thick beams. Significant concentrations of bending and shear stresses are observed, especially at the terminal regions of the discrete loading, which are captured in details and verified to be highly sensitive to the loading span and beam aspect-ratio.

Comparative study on overall and local static performance of steel open‐web girders

SummaryTo quantify the mechanical properties of five types of steel open‐web girders that have been tested or applied in practical engineering, a systematic study of the overall and local mechanical properties of steel open‐web girders based on the same dimensions and material conditions was presented. An overall study of the quasi‐intersection beam method for shear deformation was introduced for 8 × 8 grid open‐web girders to derive the determinants of the load distribution factor. Based on the load distribution factors, the essence and formula of any shear key node domain (SKND) were derived theoretically. The reliability of the numerical model was verified by tests on the H‐type unidirectional SKNDs, which led to a comparative load–displacement study of unidirectional and bidirectional SKNDs. Quantitative results of the overall flexural capacity and SKND load capacity of the H‐type, TH‐type, TS‐type, T‐type, and DT‐type open‐web girders were obtained. The maximum shear deformation in the elastic phase of the five open‐web girders accounted for 39.04% to 54.76% of the overall deformation. In this study, the adjustment factors of the modeling analysis based on the current practical design of equivalent dense‐ribbed solid beams (DRSBs) were revised. A method of SKND's design load capacity under the action of bidirectional forces was put forward for the first time.

Field Testing and Refined Load Rating of a Load-Posted Continuous Steel Girder Bridge

Load-posted bridges have potential effects on traffic, commerce, and emergency egress due to detours in routes between origins and destinations. Posted bridges can also be problematic for state departments of transportation from a management standpoint because they may call for more frequent maintenance, monitoring, and inspection. For these reasons, it is beneficial for states to minimize the number of load-posted bridges. This study investigates a continuous steel plate girder bridge superstructure and proposes a methodology for exploring the refined load rating of this bridge type in a safe manner through refined modeling and load testing. Load test results were used to examine live load distribution factors, and finite-element models were developed to refine load ratings. It was determined that the refined load-rating factors for the bridge are significantly higher than the currently posted limits, and therefore, the posting could be removed. The methodology presented in this paper can potentially be used to increase the load-rating factors for similar continuous steel girder bridges.