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).     

Effect of Multilanes on Wheel Load Distribution in Steel Girder Bridges

This paper presents the results of a parametric study that investigated the effect of multilanes and continuity on wheel load distribution in steel girder bridges. Typical one- and two-span, two-, three-, and four-lane, straight, composite steel girder bridges were selected for this study. The major bridge parameters chosen for this study were the span length, girder spacing, one- versus two-spans, and the number of lanes. These parameters were varied within practical ranges to study their influence on the wheel load distribution factors. A total of 144 bridges were analyzed using the finite-element method. The computer program, SAP90, was used to model the concrete slab as quadrilateral shell elements and the steel girders as space frame members. Simple supports were used to model the boundary conditions. AASHTO HS20 design trucks were positioned in all lanes of the one- and two-span bridges to produce the maximum bending moments. The calculated finite-element wheel load distribution factors were compared with the AASHTO and the National Cooperative Highway Research Program (NCHRP) 12-26 formulas. The results of this parametric study agree with the newly developed NCHRP 12-26 formula and both were, in general, less than the empirical AASHTO formula (S∕5.5) for longer span lengths [>15.25 m (50 ft)] and girder spacing >1.8 m (6 ft). This paper demonstrates that the multiple lane reduction factors are built into the newly developed distribution factors for steel girder bridges that were presented in the NCHRP 12-26 final report. It should be noted that AASHTO LRFD contains a similar expression that results in a value that is 50% of the value in the equations developed as a part of NCHRP 12-26. This is due to the fact that AASHTO LRFD consider the entire design truck instead of half-truck (wheel loads) as the case in the NCHRP 12-26 report and the AASHTO Standard Specifications for Highway Bridges. Therefore, this paper supports the use of the new distribution factors for steel girder bridges developed as a part of NCHRP 12-26 and consequently the distribution factors presented in the AASHTO LRFD Bridge Design Specifications.     

Effect of Changing Truck Weight Regulations on U.S. Bridge Network

Historically, truck weight regulations have maintained controls on axle and gross weights with legal load formulas based on limiting allowable stresses in certain types of bridges. These stress limitations do not usually lead to consistent or defensible reliability levels and also ignore the impact of the weight regulation on the existing highway bridge network. This paper is the second part of a two-paper series. The companion paper by the first writer illustrated how new truck weight regulations can be developed to provide an acceptable reliability level. The target reliability level was derived from bridge structures designed to satisfy AASHTO standard design specifications that showed safe and adequate performance levels under current truck loading conditions. In this part of the two-paper series, a deterministic load capacity evaluation as well as a reliability assessment are performed to review the consequences of adapting such regulations on the existing U.S. bridge network. A sensitivity analysis shows how changes in the safety criteria used to develop the truck weight regulations would affect the existing bridge network. Detailed load capacity evaluations and reliability analyses also are performed on a representative sample of bridges to provide specific examples of expected changes in rating and safety levels if the proposed truck weight regulation is to be adopted.     

Load Configuration and Lateral Distribution of NATO Wheeled Military Trucks for Steel I-Girder Bridges

This paper presents the lateral load distribution of various North Atlantic Treaty Organization (NATO) wheeled military trucks on a simple-span steel I-girder bridge (L = 36?m). The military trucks are classified into the military load classification (MLC) system. The MLC trucks demonstrate different load configurations when compared to the standard HS20 truck in terms of wheel-line spacing, number of axles, and weight. A calibrated three-dimensional finite-element analysis is conducted to examine the MLC load effects. The applicability of the AASHTO LRFD provisions is evaluated using 72 different load models. The wheel-line spacing and weight of the MLC trucks cause different flexural behavior and load distributions of the bridge when compared to those of HS20. The current AASHTO LRFD approach to determine live load distribution factors may be reasonably applicable to the MLC trucks, including approximately 20% of conservative predictions.     

Effects of State Legal Loads on Bridge Rating Results Using the LRFR Procedure

The main objective of this research was to study the effects of different specified trucks on bridge rating with the load and resistance and factor rating (LRFR) procedure. Twelve specified trucks were selected for this study, which include one AASHTO design truck, three AASHTO legal trucks, and eight state legal trucks. These rating trucks were applied on 16 selected Tennessee Dept. of Transportation bridges to obtain the LRFR ratings. The selected bridges covered four commonly used bridge types, including prestressed I-beam bridges; prestressed box beam bridges; cast-in-place T-beam bridges; and steel I-beam bridges. The research results revealed that (1) LRFR AASHTO legal load ratings factors were enveloped by the LRFR HL-93 truck ratings factors, thereby confirming the validity of the LRFR tiered approach with regard to AASHTO legal loads; (2) the lighter state legal trucks were enveloped by the HL-93 loads, whereas the heavier state trucks with closer axle spacing typically resulted in load ratings that governed over the HL-93 loads; and (3) the bridges with both high average daily truck traffic and short spans were more likely to be governed by state legal load ratings instead of HL-93 load ratings.     

Reliability Analysis of Plank Decks

The objective of this study is to summarize the load and resistance criteria for highway bridge plank decks, and to estimate the reliability of plank decks designed by the AASHTO Code. Both transverse and longitudinal planks for a variety of typical stringer spacings and plank sizes are considered. Truck traffic load data are based on the model used to calibrate the 1994 AASHTO LRFD Code. However, for plank decks, wheel load rather than whole vehicle weight is most important, and these statistics are developed for this study. For wood planks, dead load and dynamic load are not significant. The limit state considered is flexural strength, and resistance statistics are presented for wood planks in terms of modulus of rupture. Special flat-wise use data are presented to account for section aspect ratio as well as edge of load application. The reliability analysis is carried out using the procedure developed for calibration of AASHTO LRFD. Reliability indices for both the AASHTO Standard and AASHTO LRFD Code are presented for plank decks. The results indicate that there are considerable differences in plank reliability indices. Causes of inconsistencies in safety are identified.     

Truck Models for Improved Fatigue Life Predictions of Steel Bridges

A new fatigue load model has been developed based on weigh-in-motion (WIM) data collected from three different sites in Indiana. The recorded truck traffic was simulated over analytical bridge models to investigate moment range responses of bridge structures under truck traffic loadings. The bridge models included simple and two?equally continuous spans. Based on Miner’s hypothesis, fatigue damage accumulations were computed for details at various locations on the bridge models and compared with the damage predicted for the 240-kN (54-kip) American Association of State Highway and Transportation Officials (AASHTO) fatigue truck, a modified AASHTO fatigue truck with an equivalent effective gross weight, and other fatigue truck models. The results indicate that fatigue damage can be notably overestimated in short-span girders. Accordingly, two new fatigue trucks are developed in the present study. A new three-axle fatigue truck can be used to represent truck traffic on typical highways, while a four-axle fatigue truck can better represent truck traffic on heavy duty highways with a significant percentage of the fatigue damage dominated by eight- to 11-axle trucks.     

Wheel Load Distribution in Simply Supported Concrete Slab Bridges

This paper presents the results of a parametric study related to the wheel load distribution in one-span, simply supported, multilane, reinforced concrete slab bridges. The finite-element method was used to investigate the effect of span length, slab width with and without shoulders, and wheel load conditions on typical bridges. A total of 112 highway bridge case studies were analyzed. It was assumed that the bridges were stand-alone structures carrying one-way traffic. The finite-element analysis (FEA) results of one-, two-, three-, and four-lane bridges are presented in combination with four typical span lengths. Bridges were loaded with highway design truck HS20 placed at critical locations in the longitudinal direction of each lane. Two possible transverse truck positions were considered: (1) Centered loading condition where design trucks are assumed to be traveling in the center of each lane; and (2) edge loading condition where the design trucks are placed close to one edge of the slab with the absolute minimum spacing between adjacent trucks. FEA results for bridges subjected to edge loading showed that the AASHTO standard specifications procedure overestimates the bending moment by 30% for one lane and a span length less than 7.5 m (25 ft) but agrees with FEA bending moments for longer spans. The AASHTO bending moment gave results similar to those of the FEA when considering two or more lanes and a span length less than 10.5 m (35 ft). However, as the span length increases, AASHTO underestimates the FEA bending moment by 15 to 30%. It was shown that the presence of shoulders on both sides of the bridge increases the load-carrying capacity of the bridge due to the increase in slab width. An extreme loading scenario was created by introducing a disabled truck near the edge in addition to design trucks in other lanes placed as close as possible to the disabled truck. For this extreme loading condition, AASHTO procedure gave similar results to the FEA longitudinal bending moments for spans up to 7.5 m (25 ft) and underestimated the FEA (20 to 40%) for spans between 9 and 16.5 m (30 and 55 ft), regardless of the number of lanes. The new AASHTO load and resistance factor design (LRFD) bridge design specifications overestimate the bending moments for normal traffic on bridges. However, LRFD procedure gives results similar to those of the FEA edge+truck loading condition. Furthermore, the FEA results showed that edge beams must be considered in multilane slab bridges with a span length ranging between 6 and 16.5 m (20 and 55 ft). This paper will assist bridge engineers in performing realistic designs of simply supported, multilane, reinforced concrete slab bridges as well as evaluating the load-carrying capacity of existing highway bridges.     

Assessment of Load Transfer and Load Distribution in Bridges Utilizing FRP Panels

A primary means of demonstrating the feasibility and effectiveness of fiber-reinforced polymer (FRP) composite bridge materials is via in situ bridge load testing. For this study, the prescribed or assumed design factors for each of the study bridges were compared to those exhibited by the performance of the bridge. Specifically, the wheel load distribution factors and impact factors as defined by AASHTO were considered in order to assess the load transfer and distribution in structures utilizing FRP panels. The in situ testing configurations for the study bridges are outlined, including the truck and instrumentation placement to obtain the desired information. Furthermore, comparisons were drawn between the design values for deflection and those experienced by the structures during testing. It was found that although the deflections exhibited by the bridges were well within the design limits, further research is needed to be able to prescribe bridge design factors for FRP panels.     

Predicting Truck Load Spectra under Weight Limit Changes and Its Application to Steel Bridge Fatigue Assessment

Truck weight-limit regulations have significant influence on truck operating weights. These regulations directly influence loads applied to highway facilities, such as bridges and pavements. “Truck weight” herein collectively refers to a vehicle’s gross weight, axle weights, and axle configuration. Truck load spectra as a result of truck weight limits are important to bridge engineering in many respects, such as that of determining requirements for evaluation and design of bridges for both strength and fatigue. This paper’s objective is to present a new method for predicting truck weight spectra resulting from a change in truck weight limits. This method is needed to estimate impacts of the change on highway bridges such as accelerated fatigue accumulation. Historical and recent truck weight data are used to test and illustrate the proposed method, and the results show its good prediction capability. This method is also applied here to an example of estimating the impact on steel bridge fatigue due to a possible increase in the gross-vehicle-weight limit from 356 kN (80 kips) on five axles to 431 kN (97 kips) on six axles. Also included is an investigation of the AASHTO fatigue truck model for steel bridge evaluation. Results show that the current fatigue truck model may become invalid under the studied scenario of truck weight-limit increase.     

The beta-adrenomimetic effect of human and animal blood serum

The conventional analysis and design of highway bridges ignore the contribution of sidewalks and∕or railings in a bridge deck when calculating the flexural strength of superstructures. The presence of sidewalks and railings or parapets acting integrally with the bridge deck have the effect of stiffening the outside girders and attracting more load while reducing the load effects in the interior girders. This paper presents the results of a parametric study showing the influence of typical sidewalks and railings on wheel load distribution as well as on the load-carrying capacity of highway bridges. A typical one-span, two-lane, simply supported, composite steel girder bridge was selected in order to investigate the influence of various parameters such as: span length, girder spacing, sidewalks, and railings. A total of 120 bridges were analyzed using three-dimensional finite-element analysis. American Association of State Highway and Transportation Officials (AASHTO) HS20 design trucks were positioned in both lanes to produce the maximum moments. The finite-element analysis results were also compared with AASHTO wheel load distribution factors. The AASHTO load and resistance factor design (LRFD) wheel load distribution formula correlated conservatively with the finite-element results and all were less than the typical empirical formula (S∕5.5). The presence of sidewalks and railings were shown to increase the load-carrying capacity by as much as 30% if they were included in the strength evaluation of highway bridges.     

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 capacity of the parapets. The parapets and their connection with the deck were found to have adequate strength to accommodate the demand imposed by the superload trucks included in the study. For the discontinuous parapets, the open joint was determined to be acting like a notch, which increases the bottom flange stresses in the positive moment region and the tensile deck stresses in the negative moment region.     

Shear Behavior and Mode of Failure for ASTM C1433 Precast Box Culverts

This study evaluates the shear behavior and capacity of the precast concrete box culverts subjected to HS 20 truck wheel load. The most critical culvert behavior was considered by studying culverts subjected to zero depth of the fill and placed on a rigid bedding material. Full-scale experimental tests, with wheel load placed at the distance d from the tip of the haunch to the edge of the load plate, were conducted on 24 typical precast concrete box culverts designated as per ASTM C1433-05. The test results further indicated that flexure governed the behavior up to and beyond AASHTO 2005 factored load. Three-dimensional nonlinear finite-element models (FEMs) of the test specimens were developed and verified with the experimental results. The three-dimensional volumetric shear force distributions on the top slab of the 42 ASTM C1433-05 boxes were obtained by using the FEM from which the distribution width for each box was calculated. This was used to obtain the critical factored shear force for all the boxes which were then compared with the American Concrete Institute shear capacity equations. It was shown that the shear capacity exceeded the factored critical shear force for all the ASTM C1433-05 boxes. This study shows that the AASHTO 2005 provision with regard to the shear transfer device across the joint is unsupported.     

Vehicle Induced Dynamic Behavior of Short-Span Slab Bridges Considering Effect of Approach Slab Condition

In this paper the vehicle induced dynamic bridge responses are calculated by modeling the bridge and vehicle as one coupled system. The dynamic behavior of short slab bridges with different span lengths induced by the AASHTO HS20 truck is investigated. A parametric study is conducted to analyze the effects of different truck speeds and different road surface conditions. Critical truck speeds that result in peaks of dynamic response are found to follow the rule that describes the resonant vibration of bridges due to train loading. The approach slab condition that consists of faulting at the ends and deformation along the span is considered in the analysis. Although the effect of the along-span deformation on the dynamic response of bridges is trivial, the faulting condition of the approach slab is found to cause significantly large dynamic responses in short-span slab bridges. Impact factors obtained from numerical analyses are compared with those values specified in the AASHTO codes.     

Equivalent Wheel Load Approach for Slender Cable-Stayed Bridge Fatigue Assessment under Traffic and Wind: Feasibility Study

In the current AASHTO LRFD specifications, the fatigue design considers only one design truck per bridge with 15% dynamic allowance. While this empirical approach may be practical for regular short and medium span bridges, it may not be rational for long-span bridges (e.g., span length >152.4?m or 500?ft) that may carry many heavy trucks simultaneously. Some existent studies suggested that fatigue may not control the design for many small and medium bridges. However, little research on the fatigue performance of long-span bridges subjected to both wind and traffic has been reported and if fatigue could become a dominant issue for such a long-span bridge design is still not clear. Regardless if the current fatigue design specifications are sufficient or not, a real understanding of the traffic effects on bridge performance including fatigue is desirable since the one truck per bridge for fatigue design does not represent the actual traffic condition. As the first step toward the study of fatigue performance of long-span cable-stayed bridges under both busy traffic and wind, the equivalent dynamic wheel load approach is proposed in the current study to simplify the analysis procedure. Based on full interaction analyses of a single-vehicle–bridge–wind system, the dynamic wheel load of the vehicle acting on the bridge can be obtained for a given vehicle type, wind, and driving condition. As a result, the dimension of the coupled equations is independent of the number of vehicles, through which the analyses can be significantly simplified. Such simplification is the key step toward the future fatigue analysis of long-span bridges under a combined action of wind and actual traffic conditions.     

Simplified Method of Lateral Distribution of Live Load Moment

This paper introduces a simplified method, known as Henry’s method, for the calculation of distribution factors of the live load moment. Using the simplified method, the live load effects are equally distributed in all beams, including interior and exterior beams. This method has been used in Tennessee for nearly four decades. It offers advantages in simplicity of calculation and flexibility in application. To carefully examine the simplified method, 24 actual bridges of six different types of superstructures were selected for the study. The distribution factors of actual bridges using Henry’s method were compared with the ones from the AASHTO LRFD, the AASHTO standard, and finite-element analysis. In the comparison study, the effects of bridge superstructure types and key parameters that significantly affected the calculation of distribution factors are discussed. Based on the results of the comparison and evaluation, a modified Henry’s method was proposed by introducing modification factors to Henry’s method. With proper modification, the simplified method can be used to determine reasonable and reliable distribution factors of the live load moment.     

Response of Prestressed Concrete I-Girder Bridges to Live Load

Design and evaluation of prestressed concrete I-girder bridges is in large part dependent on the transverse load distribution characteristics and the dynamic load amplification, as well as service level, live load, and tensile stresses induced in the girders. This study presents the results of field tests conducted on three prestressed concrete I-girder bridges to obtain dynamic load allowance statistics, girder distribution factors (GDF), and service level stress statistics. The field-based data are also compared to approximate and numerical model results. Bridge response was measured at each girder for the passage of test trucks and normal truck traffic. The dynamic amplification is observed to be a strong function of peak static stress and a weak function of vehicle speed and is independent of span length, number of axles, and configuration. GDFs for one- and two-lanes are less than code specified GDFs. Results from the numerical grillage models agree closely with experimentally derived results for transverse distribution.     

Load Distribution and Impact Factors for I-Girder Bridges

This paper presents the procedure and results of field tests that were performed on two simply supported steel I-girder bridges to assess girder distribution and impact factors. The measurements were performed under normal truck traffic. Strain data were taken from bottom flanges of girders in the middle of a span. Additional strain data were obtained under passes of a control truck with known weight and configuration. A computerized data acquisition technique enabled selective recording of the significant blocks of the strain data under normal traffic. Strains were measured for two consecutive days on each bridge. Measured data consist of strain blocks from approximately 900 trucks. The strain records were filtered with a lowpass digital filter to remove the dynamic components and to obtain an equivalent static strain. The data were further processed to obtain statistical parameters (mean and standard deviation) of the girder distribution and impact factors. The results were compared with the values calculated according to American Association of State Highway and Transportation (AASHTO) methods. Measured girder distribution factors are lower than AASHTO values. Measured impact factors are well below AASHTO values.     

Behavior of Reinforced Concrete Bridge Decks on Skewed Steel Superstructure under Truck Wheel Loads

This paper focuses on the behavior of skewed concrete bridge decks on steel superstructure subjected to truck wheel loads. It was initiated to meet the need for investigating the role of truck loads in observed skewed deck cracking, which may interest bridge owners and engineers. Finite-element analysis was performed for typical skewed concrete decks, verified using in?situ deck strain measurement during load testing of a bridge skewed at 49.1°. The analysis results show that service truck loads induce low strains/stresses in the decks, unlikely to initiate concrete cracking alone. Nevertheless, repeated truck wheel load application may cause cracks to become wider, longer, and more visible. The local effect of wheel load significantly contributes to the total strain/stress response, and the global effect may be negligible or significant, depending on the location. The current design approach estimates the local effect but ignores the global effect. It therefore does not model the situation satisfactorily. In addition, total strain/stress effects due to truck load increase slightly because of skew angle.     

Field Investigation of a Sandwich Plate System Bridge Deck

This paper presents the results of a live-load test of the Shenley Bridge, the first bridge application of the sandwich plate system technology in North America. The investigation focused on the evaluation of in-service performance including lateral load distribution behavior and dynamic load allowance. Real-time midspan deflections and strain values were measured under both static and dynamic conditions and under various loading configurations to assess the in-service performance. Distribution factors were determined for interior and exterior girders subjected to single and paired truck loadings. In addition, dynamic load allowance was determined from a comparison of the bridge’s response under static conditions to the response under dynamic conditions. From a comparison of measured results to AASHTO LRFD, AASHTO standard, and CHBDC provisions, it was determined that the current provisions tend to produce conservative predictions for lateral load distribution, but can be unconservative for dynamic load allowance. As a result of the testing program containing a single field test, a finite-element model was also used for determination of lateral load distribution and yielded predictions similar to measured results. The results from the finite-element models were often less conservative than the code provisions.