Live Load Distribution Factors Research Articles

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.

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.

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.

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.

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.

Shear design of precast prestressed concrete NEXT beam bridges: A critical assessment

Northeast extreme tee (NEXT) precast prestressed concrete beams have recently emerged as a promising solution to accelerate bridge construction and enhance the sustainability of bridges. To date, several studies on the live load distribution factor (LLDF) for moment and shear in NEXT F beam bridges have been reported, which indicated that using the AASHTO LRFD LLDF for moment in NEXT F beam bridges could provide a sufficient safety margin; however, a 20% increase in the LRFD LLDF for shear was recommended for the safety of shear design. This paper intended to investigate the required transverse shear reinforcements in NEXT F beam bridges by using a factor of 1.2 for the LRFD LLDF for shear. A comprehensive study was carried out by considering various parameters, including concrete strength, beam section, bridge section, and span length. Results from this study showed that providing the minimum transverse shear reinforcement could offer a sufficient safety margin for the shear design of NEXT F beam bridges, even with an increase of 20% on the LRFD LLDF for shear. It is recommended that a factor of 1.2 be used for the LRFD LLDF for shear to ensure a safe design of NEXT F beam bridges, though the minimum transverse reinforcements will be likely to control the shear design.

A New Proposal for Live Load Distribution Factors of Bridges with Transverse Beams

Many bridge superstructures use transverse beams as load carrying components. In these systems, usually the transverse beams are connected to the main longitudinal girders or trusses on the two sides of the bridge. Such systems are commonly used in plate girder, box girder, cable-stayed and truss bridges. The live load distribution factor (LLDF) for bridge superstructures with transverse beams in AASHTO-LRFD bridge design specification has remained unchanged for decades and is prescribed as a function of the distance between the transverse beams. However, for slab-beam superstructures in which longitudinal beams at close spacing carry the loads to the substructure, the LLDFs have gone through many changes throughout the years and in their current forms depend on many parameters such as concrete slab thickness, beam span, longitudinal beam stiffness as well as the distance between the longitudinal beams. This study investigates the factors affecting the LLDF for transverse beams and intends to obtain new equations similar to AASHTO’s longitudinal beam equations. For this purpose, 3D finite element models of different sample bridges were developed and critical parameters affecting the LLDF were identified and varied. Accordingly, the LLDFs for moment and shear forces of transverse beams were obtained through regression analyses. The proposed equations have less than 3.1% of average error for the cases considered.

Construction and Live Load Behavior of a Skewed Steel I-Girder Bridge

As part of a long-term monitoring project, a two-span continuous steel I-girder bridge (skewed 41° with seat-type abutments) was instrumented and evaluated in the field during construction and after the bridge was in service. This paper discusses data from when the first stage (of a three-stage sequence) was constructed and initially opened to traffic. Girders and cross-frames were instrumented with strain gauges using a data acquisition system with a high sampling frequency (up to 20 Hz). Data collection began just before deck placement, and a series of live load tests was then conducted on the completed Stage I (half of the bridge) using a loaded truck. Three-dimensional finite element analyses were carried out to provide enhanced understanding of bridge behavior. Good agreement was observed between the numerical simulation results and the field monitoring data for both deck placement and live load testing. A slight inconsistency between numerical simulation and field measurement data at one girder section and an adjacent cross-frame indicated an unexpected local site condition, which was confirmed through a targeted field inspection. Live load distribution factors used during design conservatively overestimate bridge girder strong-axis bending response under live load (by around 50%). Maximum flange lateral bending stresses of 6.3 MPa (0.9 kips per square inch [ksi]) and 2.5 MPa (0.4 ksi) were observed during deck placement and truck tests, respectively. In addition, out-of-plane response of 10.6 MPa (1.5 ksi) was observed at girder web plates under concrete dead load.

Development of Applicability of Distribution Factor for Single Cell Box Girder Bridges by Modifying Bakht and Mufti Method

Live load distribution factors for simply supported single cell box girder by manual method has been studied. The distribution factor allows the designer to consider the transverse effect of wheel loads in determining the shear and moments of each beam for live load. The increased need of transporting very heavy loads by road haulage has given rise to the need for an easily applied and accurate method of calculating the division of loads between the main girders of highway bridge decks. The bridge is loaded with IRC 70 R and Class A loading so as to obtain maximum bending moment. Bakht and Mufti is close representation of semi-continuum idealization to obtain distribution factors for slab on girder bridges where shear deformation or more correctly cell distortion is neglected. An attempt is made to obtain distribution factor for single cell box girders by modifying the formula of Bakht and Mufti method with Cusens and Pama formula to consider distortional effects. Results are compared with spine beam method using Midas Civil Software which shows good agreement between both the methods.

Theoretical and computational simulation of the effect of the number of intermediate diaphragms on the live load distribution factors and structural response of a precast girder bridge

Intermediate diaphragms (ID) in bridges with precast girders are intended to improve load distribution among girders. Despite this, their efficacy has been doubted recently due to the complex construction tasks needed to join them to the girders. Accordingly, this work aimed to determine the effect of the number of IDs on the distribution of vertical loads and girders response of a simply supported bridge. Four bridge layouts (0, 1, 2, and 3 IDs) were analyzed using 3D computational grillage models. The load distribution factors from the models were compared to those calculated using the Engesser-Courbon and Fauchart methods to determine the latter’s accuracy in capturing the effect of the number of IDs. Moreover, the girders responses under the live loads in the current Colombian and Brazilian bridge design codes were assessed. The results show that the IDs have a more significant effect on the load distribution and deflection of interior girders than the exterior girders. Additionally, increasing the number of IDs reduced the maximum shear and torque while the bending moment and deflections remained nearly constant.

Shear live load analysis of NEXT beam bridges for accelerated bridge construction

Using precast concrete elements in bridge structures has emerged as an economic and durable solution to enhance the sustainability of bridges. The northeast extreme tee (NEXT) beams were recently developed for accelerated bridge construction by the Precast/Prestressed Concrete Institute (PCI). To date, several studies on the live load distribution factor (LLDF) for moment in NEXT F beam bridges have been reported. However, the LLDFs for shear in NEXT F beam bridges are still unclear. In this paper, the lateral distributions of live load shear in NEXT F beam bridges were examined through a comprehensive parametric study. The parameters covered in this study included bridge section, span length, beam section, number of beams, and number of lanes loaded. A validated finite element (FE) modeling technique was employed to analyze the shear behavior of NEXT F beam bridges under the AASHTO HL-93 loading and to determine the LLDFs for shear in NEXT beam bridges. A method for computing the FE-LLDF for shear was proposed for NEXT beam bridges. Results from this study showed that the FE-LLDFs have a similar trend as the AASHTO LFRD-LLDFs. However, it was observed that some LRFD-LLDFs are lower than the FE-LLDFs by up to 14.1%, which implied using the LRFD-LLDFs for shear could result in an unsafe shear design for NEXT beam bridges. It is recommended that a factor of 1.2 be applied to the LRFD-LLDF for shear in NEXT F beam bridges for structural safety and design simplicity.

Estimation of Live Load Distribution Factor for a PSC I Girder Bridge in an Ambient Vibration Test

Maintenance of bridges in use is essential and measuring the live load distribution factor (LLDF) of a bridge to examine bridge integrity and safety is important. A vehicle loading test has been used to measure the LLDF of a bridge. To carry this out on a bridge in use, traffic control is required because loading must be performed at designated positions using vehicles whose details are known. This makes it difficult to measure LLDF. This study proposed a method of estimating the LLDF of a bridge using the vertical displacement response caused by traveling vehicles under ambient vibration conditions in the absence of vehicle control. Since the displacement response measured from a bridge included both static and dynamic components, the static component required for the estimation of LLDF was extracted using empirical mode decomposition (EMD). The vehicle loading and ambient vibration tests were conducted to verify the validity of the proposed method. It was confirmed that the proposed method can effectively estimate the LLDF of a bridge if the vehicle type and driving lane on the bridge are identified in the ambient vibration test.

Live load distribution factors for simply-supported composite steel I-girder bridges

The Canadian Highway Bridge Design Code (CHBDC) provides formulas for determining the live load distribution factors for composite slab-on-girder bridges. These formulas were developed by neglecting the contribution of secondary elements such as lateral bracing in bridges, leading to conservative design in some cases and unsafe design in others. This paper presents a practical-design-oriented parametric study, using three-dimensional (3D) finite-element modeling, to investigate the live load distribution factors of composite braces steel I-girder bridges under CHBDC truck loading conditions at ultimate, serviceability and fatigue limit states. The key parameters considered in this study included girder stiffness and spacing, span length, number of girders, and number of design lanes. The comparison of results suggested that the CHBDC equations underestimate the girder moments for the 15 m spans and overestimates the response for greater spans. On the other hand, CHBDC generally overestimates the shear distribution factors, with significant difference observed at fatigue limit state. Based on the database generated from this study, a set of empirical expressions were developed for the moment and shear distribution factors for rational prediction of the girder design moment and shear force. A design example is presented to illustrate the use of the developed equations.

Parametric study of deteriorating precast concrete double-tee girder bridges using computational models

This paper aims to study the effects of different parameters of precast concrete double-tee (DT) girder bridges on the live-load distribution factors (LLDFs) using 3D computational models. The models were created for two DT girder bridges (including 584 mm deep and 762 mm deep bridges) tested with a rating truck using solid and shell elements in CSi Bridge. From the field tests, LLDFs were initially calculated. The models were calibrated with the field LLDFs and then different parameters, encompassing span length, concrete strength, deck width, diaphragm usage, and width to length ratio, were adjusted individually to explore the variation in LLDFs. Each of the parameters was investigated in this study for DT girder bridges. The AASHTO LRFD interior LLDFs were generally accurate for the DT girder bridges with significant joint damage. It was demonstrated that the deck width, concrete strength, and diaphragm location had very little influence on the LLDFs, whereas the span length and width to length ratio had significantly affected the LLDFs. Strictly speaking, the exterior and interior LLDFs decreased as the span length increased. The pattern for the interior LLDFs is only in agreement with the AASHTO LRFD specifications, while the pattern for the exterior LLDFs is not consistent with the AASHTO LRFD LLDFs calculated using the lever rule without consideration of span length. As a final point, as the width to length ratio increased, the LLDFs increased.

Obtaining Live Load Distribution Factors Equations for Simply Supported Bridges Using Neural Networks

Yapay zekâ konusunda kaydedilen ilerlemeler günümüzde her alanda çok önemli dönüşümlere neden olmaktadır. İnşaat mühendisliği alanında da yapay zekâ, makine öğrenmesi ve yapay sinir ağları uygulamaları ve kullanımı her geçen gün artmakta ve çeşitlenmektedir. Bu gelişmelere paralel olarak, bu çalışmada, yapay sinir ağları kullanılarak köprü tasarımında kullanılan hareketli yüklerin köprü kirişlerine dağılımı için kapalı formüller elde edilmiştir. Bu formüllerde, farklı yapısal köprü parametrelerinin yanı sıra, AASHTO LRFD’de verilen denklemlerde dahil edilmemiş olan kiriş sayısı parametresi de eklenmiştir. Bu amaçla, birçok verevsiz basit mesnetli köprü modeli hazırlanarak olası tüm kamyon yükleri altında sonlu elemanlar analizleri yapılmış ve hareketli yük dağılım katsayıları elde edilmiştir. Yapay sinir ağları ile elde edilen hareketli yük dağılım faktörleri, sonlu elemanlar analiz sonuçları ile ve AASHTO LRFD’de verilmiş olan hareketli yük dağılım katsayıları ile karşılaştırılmıştır. Bu karşılaştırmalar göstermektedir ki, sinir ağları ile elde edilen formüller dağılım faktörlerini oldukça iyi tahmin edebilmektedir.

A portable monitoring approach using cameras and computer vision for bridge load rating in smart cities

Smart structures require novel, efficient, and effective technologies for their safe operation and serviceability. This paper presents a novel, practical, cost-effective, and field test-based methodology using portable cameras and computer vision technologies to identify the lateral live load distribution factors for the existing highway bridges to perform load rating. By using a computer vision-based measurement method and traffic recognition, the girder deflection under live load can be monitored in a noncontact way and can be utilized to derive the load distribution. To verify the feasibility of the proposed approach, a comparative experimental study is conducted on a real-life pre-stressed concrete bridge with a set of conventional load tests and experiments in normal traffic. The results are compared with the conventional approach, such as simplified formulations recommended by AASHTO specifications, and the experimental method using the data from strain gauges and a calibrated finite element model (FEM). The comparative results show that the proposed approach can obtain very similar load distribution factors and bridge load rating factors both in a conventional load test and normal traffic. In comparison to the simplified formulation recommended by AASHTO specifications, the proposed approach can reflect the real-life structural properties and improve the load rating factor of AASHTO specifications by around 12%. In addition, as compared to the load-test-based approaches, such as using strain data and calibrated FEM, the proposed approach does not require traffic closure and a large amount of effort to deal with the load test and model updating. The bridge studied in this paper represents a very typical one from a large population of bridges that are part of the smart infrastructure. Such a practical approach will be practical and cost-effective for bridge load rating in smart cities.

Bridge Load Testing for Identifying Live Load Distribution, Load Rating, Serviceability and Dynamic Response

In this article, dynamic and static load tests of a concrete highway bridge, which is a deteriorated and repaired, are presented depending on displacement and strain data for engineering decision making about the operation of a critical bridge. Static load test was carried out to determine the live load distribution factor (DF) and load-rating (RF) as well as serviceability by means of deflection limits. Modal characteristics in terms of structural frequencies and mode shapes and impact factor (IM) were identified from the dynamic load test for different truck-load and speed cases, and FE model. The distribution factor (DF) and load rating factor (RF) were also compared with those calculated according to AASHTO standard and FE model. The results showed that the distribution factor (DF) calculated by AASHTO standard gave more conservative results when compared with the experimental and FEM approaches. Similarly, the load-rating factor (RF) calculated by AASHTO standard yielded to more conservative results comparing with the experimental FEM approaches using practical distribution factors. Maximum deflections in static cases and dynamic cases were found to be within the limit calculated by (L/800) given in the AASHTO code. Impact factors among all the cases were obtained much smaller than the one recommended by AASHTO standard (33%). The modal properties were obtained to track changes in dynamic behavior due to stiffness and boundary effects as well as for finite element model calibration. The calibrated FE model of the bridge also indicated that the load carrying capacity of the bridge is adequate after repair. Finally, the results from the current study reveal that use of experimental data can be utilized to obtain load rating with minimum interruption to bridge operations through computer vision technology and methods.

Evaluation of live-load distribution factors for high-performance prestressed concrete girder bridges

Evaluation of live-load distribution factors for high-performance prestressed concrete girder bridges