Girder Distribution Factors Research Articles

Modeling and analysis of a prestressed girder bridge prior to diagnostic load testing

Progressive deterioration is a problem that affects road infrastructure, especially bridges. This requires the development of methods for its adequate detection and revision, one of them being load testing. Within load testing, finite element analysis (FEA) models provide initial information to understand the behavior of a structure and plan accordingly, which represents a fundamental step towards a precise structural evaluation of a bridge. This study focused on the modeling and analysis of the static response of the bridge over the river Lili in Cali, Colombia, a prestressed girder bridge programmed to undergo a diagnostic load test. A linear FEA model was created with information from a manual survey and from other bridges’ plans designed and built under the regulations in force at the time. Due to the absence of plans and design specifications for the bridge, variations were applied to certain model parameters (stiffness of diaphragms and elastomeric bearings), to quantify their effect on the overall behavior of the bridge. The analysis included obtaining the critical position for the design vehicles, the transversal distribution of stresses and determining the influence of the variation parameters in the response of the structure. Results showed that the critical combinations for bending moment and shear were when the loads were the closest to the exterior girders, being these elements the most affected. The variation on the modulus of elasticity for the diaphragms and the stiffness of the elastomeric bearings did not significantly influence the results for bending moment and shear, nor the critical position. Girder distribution factors (GDF) from the model were compared to previous research, finding similarities in shape and value with other FEA models and experimental results. Finally, an instrumentation plan focused on the girders of the bridge was proposed based on the zones where the maximum effects are expected. The findings in this study show how linear FEA models provide initial but relevant information regarding the critical position of design vehicles, the distribution of stresses and the expected values for bending moment and shear under design loads.

Girder distribution factors for steel bridges subjected to permit truck or super load

There are constraints on truck weight, axle configurations and size imposed by departments of transportation around the globe due to structural capacity limitations of highway pavements and bridges. In spite of that, freight movers demand some vehicles that surpass the maximum size and legal weight limits to use the transportation network. Oversized trucks serve the purpose of spreading the load on the bridge; thus, reducing the load effect on the superstructure. For such vehicles, often a quick structural analysis of the existing bridges along the traveled route is needed to ensure that the structural capacity is not exceeded. For a wide vehicle having wheel gage larger than the standard 1830 mm, the girder distribution factors in the design specifications cannot be directly used to estimate the live load in the supporting girders. In this study, a simple approach that is based on finite element analysis is developed by modifying the AASHTO LRFD's girder distribution factors for slab-on-steel-girder bridges to overcome this problem. The proposed factors allow for determining the oversized vehicle bending moment and shear force effect in the individual girders as a function of the gage width characteristics. Findings of the study showed that the relationship between the girder distribution factor and gage width is more nonlinear in shear than in flexure. The proposed factors yield reasonable results compared with the finite element analysis with adequate level of conservatism.

Experimental and numerical evaluation of a folded plate girder system for short-span bridges – A case study

Bridge owners and engineers focusing on bridge design, management and maintenance continue to search for more efficient ways to design, construct, and maintain their bridge inventory. Recently, a folded plate girder system has been promoted as a cost-effective alternative for the design and construction of bridge superstructures due to merits such as low cost and facilitation of accelerated bridge construction. The folded plate girder system has a structural shape strategically press-brake formed from a single sheet of plate steel and achieves composite action with a concrete deck utilizing shear studs in between. To further facilitate the development and adaptation of the system for bridge application, this paper presents a systematic performance evaluation of the folded plate girder system through experimental and numerical programs. To this end, a folded plated girder specimen was designed, fabricated, and tested to evaluate the constructability and capacity of the girder specimen. Finite Element (FE) Analysis was performed to understand the behavior of the girder specimen under different loading conditions. The predictions using traditional design calculations and FE analysis were compared with the test results. After the FE models were validated against the test data, a full bridge model was established to further investigate the behavior of the bridge under loading condition up to the ultimate load. It was found that the ultimate capacity of the bridge girders were much higher than the bridge demand and the bridge had good ductility until failure. The predictions using the design calculations based on the AASHTO LRFD Bridge Design Specifications were in reasonable agreement with the test results. The FE models showed better predictions since more sophisticated modeling techniques and material constitutive models were used. Results obtained from the sophisticated non-linear bridge model indicated that the girder distribution factors varied along with an increase of the truck loading and especially their change trend was gradually reversed after the yield of the girder steel. And according to the FE results, the distribution factor based on the AASHTO LRFD Bridge Design Specifications was sufficient for the design of the folded plate girder bridge investigated in this study.

Field Tests of Two Prestressed-Concrete Girder Bridges for Live-Load Distribution and Moment Continuity

AbstractTwo similar bridges constructed with a live-load continuous connection were tested for live-load distribution and joint continuity. Girder distribution factors (GDFs) were compared with AASHTO equivalent values. For positive moments on all girders as for negative moments on interior girders, results using AASHTO equivalent GDFs were found to be generally conservative. However, for negative moments on exterior girders, test results exceeded AASHTO values, significantly so with two-lane results. GDF results were verified with a finite-element analysis (FEA) model, which produced behavior similar to the field tests. With respect to joint continuity, it is estimated that a simple span would produce a maximum positive moment about 7% higher than the actual structure, whereas a completely continuous structure would produce a maximum positive moment about 16% lower than that of the actual structure. For negative moments, the actual structure experienced about 28% of that of a continuous structure. Shear ...

Statistical bridge damage detection using girder distribution factors

A hypothesis testing framework is introduced for bridge damage detection, which enables a rigorous, decision-oriented approach for detection of bridge damage when it exists. A bridge damage detection hypothesis test is developed using girder distribution factors (GDF) under operational, output-only strain monitoring. GDFs are calculated from measured strain data collected during traffic events at the Powder Mill Bridge in Barre, Massachusetts. A sample of GDFs is drawn to establish a baseline over the course of one week, representing the probabilistic behavior of a healthy bridge under normal operating conditions. A new sample can be compared with the baseline at the end of each day, providing a timely and effective operational damage detection method. A calibrated finite element model is used to simulate damaged bridge GDF samples under four damage scenarios. The damaged bridge GDF samples are compared with the healthy baseline sample using the rank-sum test, and the results are employed to develop a damage index capable of alerting bridge owners of potential damage. A simple bootstrap resampling scheme is used to evaluate the probability of issuing a false alarm (Type I error), as well as the likelihood of not issuing an alert when the bridge is damaged (Type II error). A three-dimensional statistical bridge signature is developed to aid damage localization and assessment. Nonparametric prediction intervals corresponding to a baseline signature are generated using the bootstrap method, creating an envelope of possible baseline bridge signatures. When a bridge signature falls outside the baseline bridge signature envelope, damage is detected. Damage was successfully identified for all four artificial damage cases considered. The overall damage detection method is designed to alert bridge owners when damage is detected and to provide a probabilistic tool to aid damage assessment and localization while controlling for both Type I and Type II errors.

Effect of measurement uncertainties on strain-based damage diagnostics for highway bridges

Diagnostic load rating of highway bridges using distributed strain transducers is one of the more prominent strategies applied for both periodic and continuous monitoring of highway bridges. Techniques for load rating structures using experimental measurements of neutral axis locations, girder distribution factors, and dynamic increase factors have been suggested for structural health monitoring and damage detection applications. However, practical considerations related to the influence of measurement uncertainties on the reliability of these diagnostic measures in the presence of damage have only been examined recently. This paper extends uncertainty propagation formulae previously derived for neutral axis measurements to girder distribution factors. The significance of measurement uncertainties on damage-sensitive features are then explored using experimental data from a real bridge subjected to progressive, prescribed damage. The experimental results suggest that both apparent neutral axis locations and girder distribution factors exhibit sensitivity to the damage mechanisms introduced that exceeds the measurement uncertainty. In addition, girder distribution factors are found to demonstrate the ability to locate the damage. Comparisons with finite element simulations underline the challenges associated with faithfully modeling the effects of structural damage and emphasize the need for continued full-scale validation of structural health monitoring approaches on real structures.

Influence of Atypical Vehicle Types on Girder Distribution Factors of Secondary Road Steel-Concrete Composite Bridges

This paper investigated the influence of atypical agricultural vehicle parameters on girder distribution factors (GDFs) for two simply supported steel-concrete composite bridges located on secondary roads in the United States. As part of the parametric investigation, field measurements were performed on the bridges under the passage of full-scale agricultural vehicles along each bridge centerline. Strain data obtained from field tests were used to determine field GDFs. Both field data and GDFs were used to calibrate a finite element model of the bridge. Data from over in-use one hundred agricultural vehicles were collected, and then each vehicle was applied to the model to compute analytical GDFs. These vehicles were analytically and statistically investigated to determine the sensitivity of GDFs to vehicle parameters, including maximum vehicle axle load, gage width, and spacing distributions. Based upon field strain investigation for the two bridges, the responses of the central girders were greater than those of the exterior girders, resulting in greater field GDFs for central girders than those of the exterior girders. Results also indicated from the sensitivity study that each girder had different levels of correlation between GDFs and single vehicle parameters.

Lateral Live-Load Distribution Characteristics of Simply Supported Steel Girder Bridges Loaded with Implements of Husbandry

This paper discusses the effect of agricultural live-loads on lateral load distribution characteristics of girder bridges on rural roadways in the United States. In this study, load distribution factors for bridges subjected to agricultural vehicles frequently used on rural roads are calculated based upon codified processes, field test results, and simulations. As part of this work, five simply supported steel girder bridges in Iowa were selected for field tests with four agricultural vehicles and a highway-type truck. Strain sensors were mounted on the bottom flanges of girders at midspan of all five bridges. Strain data resulting from the test vehicles were measured and used to determine girder distribution factors for each bridge. These strain data were also used to calibrate analytical models of the bridges. Over 120 agricultural vehicles were identified and used to analytically load the models. Girder distribution factors were then computed using responses from the vehicle-induced model simulations. Findings revealed that the analytical and field distribution factors were in most cases smaller than code-specified values, as has been observed by others. In some cases, however, these factors exceeded code values. Furthermore, the variability in agricultural vehicles’ characteristics had a significant impact on the live-load distribution factors for each bridge.

Spring analogy to predict the 3-D live load response of slab-on-girder bridges

In current bridge design methodology, beam line analysis and girder distribution factors are often used to compute the maximum live load demands on the girders. However, this method may not effectively predict the response of all girders under live load. Furthermore, it has been found to be conservative compared to 3-D analysis results and load tests of bridges. With the spring analogy, it is possible to closely approximate the 3-D live load response of bridges with accuracy comparable to that from a detailed finite element analysis. For a given truck position, the bending moment resisted by each girder and individual girder deflections can be computed easily. The live load demand imposed on the secondary members, such as diaphragms or cross-frames, can also be predicted using the results of the spring analogy. This analysis method can be used for any transverse truck location on the bridge, and should be useful for both the design and rating of bridges.

In-Service Shear and Moment Girder Distribution Factors in Simple-Span Prestressed Concrete Girder Bridge

An optical fiber monitoring system was designed and built into the I-25 bridge at the Dona Ana exit in Las Cruces, New Mexico. The bridge is a simple-span, high-performance prestressed concrete girder bridge. The girders are six BT-63 high-performance-concrete girders with a span length of 112.5 ft (34.2 m). Fiber Bragg grating optical fiber deformation sensors along with thermocouples were embedded in the girders during fabrication. Sensors were installed along the top and bottom flanges and at midspan and quarter spans. Pairs of crossed sensors in a rosette configuration were embedded in the webs at the supports. The bridge was monitored for 2 years, from transfer of the prestressing force through service. The sensor data were analyzed to evaluate shear and moment girder distribution factors, in situ material properties, pre-stress losses, camber, dynamic load allowance, and bridge performance under traffic loads. This study focuses on the lateral load distribution in the bridge. Shear and moment girder distribution factors are obtained from a finite element model, sensor measurements under a live load test, as well as regular traffic loading and compared with the values specified by the AASHTO standard specifications (2002) and the AASHTO load and resistance factor design specifications (2007).

Parapet Strength and Contribution to Live-Load Response for Superload Passages

The main objective of this study is to evaluate the effects of parapets on the live-load response of slab-on-girder steel bridges subjected to superload vehicles and the effects of these loads on the parapets. A superload is a special permit truck that exceeds the predefined weight limitation. The presence of parapets can result in reduced girder distribution factors (GDFs) for critical girders, and this reserve strength can be considered for passage of a superload truck. This reduction is investigated, as well as the effects of discontinuous parapets and the capacity of parapets. Two steel bridges with significantly different geometric proportions were analyzed to evaluate the sensitivity of the structure to the effects of parapets. It was found that the GDFs can be decreased by as much as 30%, depending on the stiffness of the girders and the transverse truck position if the parapets are included in the analysis. The axial forces and bending moments resisted by the parapets were compared with the capaci...

Live Load Radial Moment Distribution for Horizontally Curved Bridges

This study is designed to determine the effect of major parameters on maximum total bending moments of curved girders, establish the relationship between key parameters and girder distribution factors (GDFs), and develop new approximate distribution factor equations. A level of analysis study using 3 numerical models was performed to establish an appropriate numerical modeling method on the basis of field test results. 81, 2-traffic lane curved bridges were analyzed under HL-93 loading. Two approximate GDF equations were developed based on the data obtained in this study: 1) a single GDF based on total girder normal stress; and 2) a combined GDF treating bending and warping normal stress separately. The 2 equations were developed based on both an averaged coefficient method and regression analysis. A goodness-of-fit test revealed that the combined GDF model developed by regression analysis best predicted GDFs. This research study demonstrated that radius, span length, cross frame spacing, and girder spacing most significantly affect GDFs. The proposed GDF equations are expected to provide a more refined live load analysis for preliminary design.

Live-Load Distribution Factors for Prestressed Concrete, Spread Box-Girder Bridge

This study presents an evaluation of shear and moment live-load distribution factors for a new, prestressed concrete, spread box-girder bridge. The shear and moment distribution factors were measured under a live-load test using embedded fiber-optic sensors and used to verify a finite element model. The model was then loaded with the American Association of State Highway and Transportation (AASHTO) design truck. The resulting maximum girder distribution factors were compared to those calculated from both the AASHTO standard specifications and the AASHTO LRFD bridge design specifications. The LRFD specifications predictions of girder distribution factors were accurate to conservative when compared to the finite element model for all distribution factors. The standard specifications predictions of girder distribution factors ranged from highly unconservative to highly conservative when compared to the finite element model. For the study bridge, the LRFD specifications would result in a safe design, though exterior girders would be overdesigned. The standard Specifications, however, would result in an unsafe design for interior girders and overdesigned exterior girders.

Influence of Parapets and Aspect Ratio on Live-Load Distribution

Significant discrepancies in girder distribution factors have been observed between actual bridge field-testing results and AASHTO code predictions. One of the reasons for the discrepancies is that code methods fail to account for the existence of secondary members such as parapets in bridges. This research investigates the effects of parapets and bridge aspect ratio on live-load moment distribution for bridge girders. The influence on distribution factors of parapets with varying overhang lengths and of aspect ratio with varying roadway width is investigated. To study the effects of parapets and aspect ratios, 34 two-span continuous bridges with a 0° or a 45° skew angle and with varied structure parameters are analyzed using the finite element method. The distribution factors obtained from these analyses are compared with those from the AASHTO methods. The presence of parapets is shown to reduce distribution factors by as much as 36 and 13% for exterior and interior girders, respectively. The effect of parapets is slightly less for skewed bridges. Aspect ratio is shown to have very little effect on distribution factors until the ratio exceeds 1.8.

Analysis and Instrumentation of a Steel Bridge for Investigation of Superload Effects

The number of superload trucks, which often carry loads three to 15 times those of common design vehicles, has increased in recent years. The increased frequency of occurrence has prompted concerns about the ability of highway bridges to accommodate such loads and remain in serviceable condition. To address these concerns, an analysis of effects of superloads has been conducted for a case study bridge. A detailed finite element (FE) model of the bridge, including all primary and secondary members, was created to evaluate the behavior. The FE analysis results were compared with results from a controlled load test of the bridge. The girder distribution factors determined experimentally and analytically were found to be significantly lower than comparable design values. Furthermore, from the load tests, the rotational restraint at the girder ends due to the abutments was determined to be as high as a fixed support. The FE model was then used to predict the effects of various superload trucks. The analysis results and field data suggest that some of the stiffener plates and cross-frame members of the analyzed bridge would be overstressed by certain superload truck configurations.

Analysis and Instrumentation of a Steel Bridge for Investigation of Superload Effects

The number of superload trucks, which often carry loads three to 15 times those of common design vehicles, has increased in recent years. The increased frequency of occurrence has prompted concerns about the ability of highway bridges to accommodate such loads and remain in serviceable condition. To address these concerns, an analysis of effects of superloads has been conducted for a case study bridge. A detailed finite element (FE) model of the bridge, including all primary and secondary members, was created to evaluate the behavior. The FE analysis results were compared with results from a controlled load test of the bridge. The girder distribution factors determined experimentally and analytically were found to be significantly lower than comparable design values. Furthermore, from the load tests, the rotational restraint at the girder ends due to the abutments was determined to be as high as a fixed support. The FE model was then used to predict the effects of various superload trucks. The analysis results and field data suggest that some of the stiffener plates and cross-frame members of the analyzed bridge would be overstressed by certain superload truck configurations.

Performance Comparison of Four Fiber-Reinforced Polymer Deck Panels

In an effort to assess the constructability and performance of bridges with fiber-reinforced polymer ~FRP! composite decks, the short-term and long-term responses of a 207 m, five-span bridge retrofitted with four different FRP panel systems were monitored. The overall aspects of the panel systems, connection details, and construction techniques are presented prior to presentation of the observed and measured responses. Key design parameters ~impact factors, girder distribution factors, and level of composite action ! for FRP and reinforced concrete decks are evaluated. This paper demonstrates that FRP replacement decks are a viable alternative to reinforced concrete decks and identifies the differences in performances of various FRP deck systems. Two of the FRP panel systems were found to perform considerably better than the other deck systems. Issues that may reduce the service life of FRP deck systems are presented and discussed.

Live-Load Response of Alabama’s High-Performance Concrete Bridge

Results are reported from live-load tests performed on Alabama’s high-performance concrete (HPC) showcase bridge. Load distribution factors, deflections, and stresses measured during the tests are compared with values calculated using the provisions of the AASHTO LRFD Bridge Design Specifications and AASHTO Standard Specifications for Highway Bridges. Measured dynamic amplification of load effects was approximately equal to or less than predicted by both specifications. Distribution factors from both specifications were found to be conservative. Deflections computed according to AASHTO LRFD Bridge Design Specifications suggestions matched best with the measured deflections — overestimating the maximum deflections by 20% or less. Bottom flange stresses computed with AASHTO distribution factors were significantly larger than measured values. AASHTO LRFD Bridge Design Specifications provisions suggest a special procedure for computing exterior girder distribution factors in bridges with diaphragms. When two or more lanes were loaded, this special procedure did not reflect the actual behavior of the bridge and resulted in very conservative distribution factors for exterior girders. Further research is recommended to correct this deficiency.

Effects of Edge-Stiffening Elements and Diaphragms on Bridge Resistance and Load Distribution

This research investigates the effects of barriers, sidewalks, and diaphragms (secondary elements) on bridge structure ultimate capacity and load distribution. Simple-span, two-lane highway girder bridges with composite steel and prestressed concrete girders are considered. The finite-element method is used for structural analysis. For the elastic range, typical secondary elements can reduce girder distribution factors (GDF) between 10 and 40%, depending on stiffness and bridge geometry. For the inelastic response, steel is modeled using von Mises yield criterion and isotropic (work) hardening. Concrete is modeled with a softening curve in compression with the ability to crack in tension. At ultimate capacity, typical secondary elements can reduce GDF an additional 5 to 20%, and bridge system ultimate capacity can be increased from 1.1 to 2.2 times that of the base bridge without secondary elements, depending on bridge geometry and secondary-element dimensions.

Live Load Distribution for Steel Girder Bridges

This paper deals with distribution of truck load on girder bridges. Previous analytical studies based on finite-element method indicated that AASHTO code-specified girder distribution factors (GDFs) are inaccurate. In particular, GDFs appear to be conservative for longer spans and larger girder spacing, but too permissive for short spans and girder spacings. Therefore, a field testing program was carried out including about 20 steel girder bridges with spans up to 45 m. For each tested structure, GDFs were determined by measuring strains in the girders under heavy trucks. Test trucks were 11-axle vehicles, loaded to the legal limit in Michigan (over 650 kN). The strains were recorded for a single truck and for two trucks side-by-side. The tests were repeated for crawling speed and normal traffic speed for the location. In all tested bridges, the GDFs determined from the field measurements are lower than code-specified values. In addition, the considered bridges were analyzed using a commercial finite-element software package, ABAQUS. The analytical results were compared with those from field tests. It was observed that the maximum values of the strain and corresponding stress are lower than analytical values obtained using ABAQUS. The reason for this discrepancy is unintended composite action and partial fixity of supports (rather than simple supports).