Design for Shear in Curved Composite Multiple Steel Box Girder Bridges

Modern highway bridges are often subject to tight geometric restrictions and, in many cases, must be built in curved alignment. These bridges may have a cross section in the form of a multiple steel box girder composite with a concrete deck slab. This type of cross section is one of the most suitable for resisting the torsional, distortional, and warping effects induced by the bridge’s curvature. Current design practice in North America does not specifically deal with shear distribution in horizontally curved composite multiple steel box girder bridges. In this paper an extensive parametric study, using an experimentally calibrated finite-element model, is presented, in which simply supported straight and curved prototype bridges are analyzed to determine their shear distribution characteristics under dead load and under AASHTO live loadings. The parameters considered in this study are span length, number of steel boxes, number of traffic lanes, bridge aspect ratio, degree of curvature, and number and stiffness of cross bracings and of top-chord systems. Results from tests on five box girder bridge models verify the finite-element model. Based on the results from the parametric study simple empirical formulas for maximum shears (reactions) are developed that are suitable for the design office. A comparison is made with AASHTO and CHBDC formulas for straight bridges. An illustrative example of the design is presented.     

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.     

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.     

Model Validation for Bridge-Road-Vehicle Dynamic Interaction System

The dynamic response of highway bridges subjected to moving truckloads has been observed to be dependent on (1) dynamic characteristics of the bridge; (2) truck configuration, speed, and lane position on the bridge; and (3) road surface roughness profile of the bridge and its approach. Historically, truckloads were measured to determine the load spectra for girder bridges. However, truckload measurements are either made for a short period of time [for example, weigh-in-motion (WIM) data] or are statistically biased (for example, weigh stations) and cost prohibitive. The objective of this paper is to present results of a 3D computer-based model for the simulation of multiple trucks on girder bridges. The model is based on the grillage approach and is applied to four steel girder bridges tested under normal truck traffic. Actual truckload data collected using a discrete bridge WIM system are used in the model. The data include axle loads, truck gross weight, axle configuration, and statistical data on multiple presence (side by side or following). The results are presented as a function of the static and dynamic stresses in each girder and compared with code provisions for dynamic load factor. The study provides an alternate method for the development of live-load models for bridge design and evaluation.     

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.     

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).     

Live Load Distribution Formulas for Single-Span Prestressed Concrete Integral Abutment Bridge Girders

In this study, live load distribution formulas for the girders of single-span integral abutment bridges (IABs) are developed. For this purpose, two and three dimensional finite-element models (FEMs) of several IABs are built and analyzed. In the analyses, the effects of various superstructure properties such as span length, number of design lanes, prestressed concrete girder size, and spacing as well as slab thickness are considered. The results from the analyses of two and three dimensional FEMs are then used to calculate the live load distribution factors (LLDFs) for the girders of IABs as a function of the above mentioned parameters. The LLDFs for the girders are also calculated using the AASHTO formulas developed for simply supported bridges (SSBs). The comparison of the analyses results revealed that LLDFs for girder moments and exterior girder shear of IABs are generally smaller than those calculated for SSBs using AASHTO formulas especially for short spans. However, AASHTO LLDFs for interior girder shear are found to be in good agreement with those obtained for IABs. Consequently, direct live load distribution formulas and correction factors to the current AASHTO live load distribution equations are developed to estimate the girder live load moments and exterior girder live load shear for IABs with prestressed concrete girders. It is observed that the developed formulas yield a reasonably good estimate of live load effects in prestressed concrete IAB girders.     

Impact Factors for Horizontally Curved Composite Box Girder Bridges

This paper presents a method for determining the dynamic impact factors for horizontally curved composite single- or multicell box girder bridges under AASHTO truck loading. The bridges are modeled as three-dimensional structures using commercially available software. The vehicle is idealized as a pair of concentrated forces, with no mass, traveling in two circumferential paths parallel to the curved centerline of bridges. An extensive parametric study is conducted, in which over 215 curved composite box girder bridge prototypes are analyzed. The key parameters considered in this study are: Number of cells, number of lanes, degree of curvature, arc span length, slope of the outer steel webs, number and area of bracing and top chord systems, and truck(s) speed and truck(s) positioning. Based on the data generated from the parametric study, expressions for dynamic impact factors for longitudinal moment, reaction, and deflection are proposed as function of the ratio of the arc span length to the radius of curvature. The results from this study would enable bridge engineers to design horizontally curved composite box girder bridges more reliably and economically. Furthermore, the results can be used to potentially increase the live-load capacity of existing bridges to prevent posting or closing of the bridge.     

Strength of Stiffened Flanges in Horizontally Curved Box Girders

Longitudinal stiffeners are often attached to increase the buckling strength of thin-walled box girder flanges. The minimum required rigidity for longitudinal stiffeners for curved box girder flanges is given by the AASHTO “Guide specifications for horizontally curved steel girder highway bridges.” However, this requirement is simply adopted from the current AASHTO specifications for straight stiffened flanges. The validity of this requirement has been questioned in a series of recent studies. The effect of important design parameters on the minimum required stiffener rigidity is investigated numerically in this study by examining the prebuckling stress distribution and elastic and inelastic buckling stresses of horizontally curved stiffened flanges. In order to characterize and quantify the analytically collected data, a series of parametric studies were performed. A new equation for the minimum required rigidity for the longitudinal stiffeners is derived from regression analyses. Through the evaluation of a few selected case studies and a design example, the validity and reliability of the proposed new equation is demonstrated.     

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.     

Distribution Factors for Curved Continuous Composite Box-Girder Bridges

The use of horizontally curved composite box-girder bridges in modern highway systems has become increasingly popular for economic as well as for aesthetic considerations. Based on a recent literature review on the design of box-girder bridges, it was observed that a simple design method for curved bridges, based on load distribution factors for stresses and shears, is as yet unavailable. This paper presents the results of an extensive parametric study, using a finite element method, in which the structural responses of 240 two-equal-span continuous curved box-girder bridges of various geometries were investigated. The parameters considered in this study included span-to-radius of curvature ratio, span length, number of lanes, number of boxes, web slope, number of bracings, and truck loading type. Based on the data generated from this study, empirical formulas for load distribution factors for maximum longitudinal flexural stresses and maximum deflection due to dead load as well as AASHTO live loading were deduced. An illustrative design example is presented.     

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.     

Impact Factors for Curved Continuous Composite Multiple-Box Girder Bridges

The results from a parametric study on the impact factors for 180 curved continuous composite multiple-box girder bridges are presented. Expressions for the impact factors for tangential flexural stresses, deflection, shear forces and reactions are deduced for AASHTO truck loading. The finite-element method was utilized to model the bridges as three-dimensional structures. The vehicle axle used in the analysis was simulated as a pair of concentrated forces moving along the concrete deck in a circumferential path with a constant speed. The effects of bridge configurations, loading positions, and vehicle speed on the impact factors were examined. Bridge configurations included span length, span-to-radius of curvature ratio, number of lanes, and number of boxes. The effect of the mass of the vehicle on the dynamic response of the bridges is also investigated. The data generated from the parametric study and the deduced expressions for the impact factors would enable bridge engineers to design curved continuous composite multiple-box girder bridges more reliably and economically.     

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.     

Experimental Verification of Horizontally Curved I-Girder Bridge Behavior

Past research has been conducted on the behavior of horizontally curved girders by testing scaled models and full-scale laboratory bridges and by analyzing numerical models. Current design specifications are based on this past research; however, little field data of in-service bridges exist to support the findings of the past research on which the current design criteria are based. The purpose of the present study was to gather field response data from three in-service, curved, steel I-girder bridges to determine behavior when subjected to a test truck and normal truck traffic. Transverse bending distribution factors and dynamic load allowance were calculated from the data collected. Numerical grillage models of the three bridges were developed to determine if a simple numerical model will accurately predict actual field measured transverse bending distribution, deflections, and cross-frame and diaphragm shear forces. The present study found that AASHTO specifications are conservative for both dynamic load allowance and transverse bending moment distribution. The grillage models were found to predict with reasonable accuracy the behavior of a curved I-girder bridge.     

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.     

Ambient Vibration Monitoring of a Highway Bridge Undergoing a Destructive Test

Developing a technique to continuously monitor in-service highway bridges is one of the major research focuses at the Connecticut Department of Transportation and the University of Connecticut. The goal has been to use ambient traffic loading as the force to excite a measurable parameter that is sensitive to overall structural integrity. In this study, the dynamic responses of a full-scale steel-girder highway bridge during the passage of a small truck were measured using a number of sensors that could be reasonably implemented on a network of in-service bridges. Measurements were taken before and during the staged introduction of a simulated crack in one of the main supporting girders. The crack was introduced in five stages until it extended through two-thirds of the depth of the girder. Accelerometers were placed at various locations on each girder. Frequency spectra for each stage of the testing were compared to those recorded before the introduction of the crack to determine which aspects of the spectra were sensitive to the change in stiffness. The results indicate that monitoring the amplitudes at the natural frequencies and the frequency response spectrum using the cross signature assurance criterion can be used as an indicator that significant cracks have developed in a multigirder highway bridge.     

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.     

High-Cycle Fatigue of Diagonally Cracked Reinforced Concrete Bridge Girders: Field Tests

Large numbers of conventionally reinforced concrete deck–girder (RCDG) bridges remain in-service in the national highway system. Diagonal cracks have been identified in many of these bridges, which are exposed to millions of load cycles during service life. The anticipated life of these bridges in the cracked condition under repeated service loads is uncertain. RCDG bridges with diagonal cracks were inspected and instrumented. Strain and crack displacement data were collected under ambient traffic conditions and controlled test trucks. Results indicated relatively small stirrup stresses and diagonal cracks exhibited opening and closing under truck loading.     

Truck Loading and Fatigue Damage Analysis for Girder Bridges Based on Weigh-in-Motion Data

Based on data collected by weigh-in-motion (WIM) measurements, truck traffic is synthesized by type and loading condition. Three-dimensional nonlinear models for the trucks with significant counts are developed from the measured data. Six simply supported multigirder steel bridges with spans ranging from 10.67 m (35 ft) to 42.67 m (140 ft) are analyzed using the proposed method. Road surface roughness is generated as transversely correlated random processes using the autoregressive and moving average model. The dynamic impact factor is taken as the average of 20 simulations of good road roughness. Live-load spectra are obtained by combining static responses with the calculated impact factors. A case study of the normal traffic from a specific site on the interstate highway I-75 is illustrated. Static loading of the heaviest in each truck type is compared with that of the American Association of State Highway and Transportation Officials standard design truck HS20-44. Several important trucks causing fatigue damage are found.