Exterior girder rotation of skew and non-skew bridges during construction

Abstract

In bridge design, bridge decks regularly overhang past the exterior girders in arrange to extend the width of the deck whereas constraining the specified number of girders. The overhanging part of the deck comes about in uneven eccentric loads to the exterior girders which are by and large most prominent. These eccentric loads are primarily a result of bridge construction operations as well as the weight of new concrete and other construction live loads. These unbalanced loads can lead to a differential edge deflection of overhang deck and a rotation of the exterior girders. The girder rotation or differential deck deflection can also affect local and global stability of the entire bridge. The objective of this study is to enhance the knowledge and understanding of external girder behavior due to unbalanced eccentric construction loads and to identify the critical factors affecting their rotation. In this article, field data obtained during the construction of two skewed (one with a small skew (3.8°) and the second with a severe skew (24°)) and one non-skewed steel girder bridges are described, and a detailed comparison is presented. The three bridges experienced maximum outward exterior girder rotation during construction which subsequently decreased following construction operations. The field results were used to validate and calibrate the finite element models. The numerical and field-monitored data showed good agreement and can be used to assist bridge designers and construction engineers to design appropriate systems to limit girder rotation during construction.

Keywords

deck differential deflection deck overhang girder rotation skewed and non-skewed bridge steel girder

Introduction

In composite bridge construction, operation loads for deck construction on the deck overhanging part is braced by triangular brackets which are placed at a maximum spacing of 1.83 m (6 ft.) along the length of the end girders. In bridge deck design, this deck overhang is kept structurally balanced to design same girder size for all the girders of the bridge. In one side, bridge deck overhang can bring an economical design, on the other side, the construction of these deck overhangs ends up bring severe rotation in the exterior girder. Excessive rotation of the girders leads to a deck with lesser thickness than the design, decreased concrete cover, uneven roadway, and local or global bridge failure during construction, to name a few, as shown in Figure 1(b) and (c).

Figure 1.

Exterior girder rotation due to unbalanced eccentric load on overhang deck. (a) Girders arrangement and deck formwork before placing concrete; (b) outward rotation at exterior girders; (c) calculation of girder rotation.

The deck overhang is usually formed by wood sheathing or corrugated metal sheets supported with triangular steel brackets spaced at a certain specified distance over the length of the bridge. The triangular brackets are connected to the top flange of the exterior girders and the diagonal leg of the bracket rests against the girder web. In few cases, these loads have brought about in bridges that were perilously near to collapse emerging from local and global instabilities (Fasl, 2008). Girder web buckling and other local issues are considered a specific fear for steel girder bridges due to the slenderness of the girder webs (Gupta et al., 2006; Shokouhian and Shi, 2015). On the other hand, global instability is concern for concrete girders that have a tendency to rotate as a rigid element (Haskett et al., 2009; Yang et al., 2010). There have been quite a few research results to assess commercially accessible triangular brackets and hangers (Ariyasajjakorn, 2006; Clifton and Bayrak, 2008; Grubb, 1990) in spite of the fact that the girder rotation proceeds to be a concern due to challenges with usage and analysis.

Steel girder rotation depends on bridge geometry including span length, overhang dimensions, bridge cross section details (Schilling, 1988) and the lateral bracing system and connection with the main girders (Helwig and Yura, 2012; Roddis et al., 2008). Specifically, exterior girder rotation (illustrated in Figure 1) basically affected by the size of overhang deck, overhang deck erection loads and on the efficacy of the girder rotation preventing bracing systems. Several types of erection loads are applied to the overhang deck which is transferred to the exterior girders through steel brackets placed along the span of the bridge. In general, quite a few types of erection load can be responsible for exterior girder rotation, which include weight of wet concrete, deck paving machine, deck overhang formwork, construction personnel, and other related construction live loads. It is conceivable to decrease the torsional moment created by these loads by setting the concrete paving machine directly on the centerline of the exterior girders instead of on the deck overhang. However, most contractors choose to set the concrete paving machine on the deck overhang since in this setup, the finishing machine can reach maximum percentage of the deck surface, and also, adjustment of the screed rails during placement is not required (Suprenant, 1994).

The overhang deck width and girder bracing system can vary significantly. Generally, an ultimate width for overhang can be determined based on the influencing factors including spacing of beam, depth of beam, and overall concrete deck thickness. To avoid exterior girder rotation due to all erection loads, it is indispensable to provide a suitable bracing system to transfer loads to the girders. Transverse tie bars are elements of bracing systems used to restrict girder rotation in the State of Illinois as shown in Figure 2(a). The tie bars consist of a No. 13 [metric] (No. 4 [imperial]) steel reinforcing bar connected to the top flanges of end girders transversely of the deck or to connect the end girder to the first interior girder. Transversely placed tie bars are difficult to install and tighten in the field primarily due to meddling with bridge deck reinforcement and difficulty of tightening the bars (shown in Figure 3(a)). These issues may reduce the effectiveness of tie bars during construction. An alternate bracing system is to use diagonal tie bars as shown in Figure 2(b). In this system, No. 13 (No. 4) bars are used as a diagonal link from the top flange of the exterior girder to the bottom flange of the first interior girder. These tie bars are typically spaced at 0.91 m (3 ft.) to 1.22 m (4 ft.) along the span of the bridge. Installation of the ties in this system is somewhat simplified as access to one end can be used for tightening. Tie bars in this system require adjustable hangers to account for the angle formed between adjacent girders. For the bridges considered in this study, non-adjustable hangers that form a 45° angle were repurposed (they were also used to set the overhang formwork) to set the diagonal ties as shown in Figure 2(b). In this case, the angle formed between the girders was not 45° and bending of the diagonal ties was required for installation. The resulting configuration is shown schematically in Figure 3(b). Effectiveness of these conventional systems (diagonal and transverse tie bars) as mentioned earlier relies on the axial stiffness of the tie bars which cannot be fully utilized until the bars are straightened through rotation of the girders during construction.

Figure 2.

Bracing systems: (a) transverse ties; (b) diagonal ties.

Figure 3.

Possible deviations in bracing systems that can introduce more girder rotation: (a) transverse tie bars; (b) diagonal tie bars.

Bridges with properly implemented bracing systems may still be subjected to rotation. This is especially true for bridges that have wide girder spacing, slender girders, or both. Precast concrete diaphragms or steel channel sections have also been used to limit rotation (Fasl, 2008). Throughout the construction of bridges, additional temporary lateral bracing is also provided with the use of 100 mm × 100 mm (4 in. × 4 in.) timber blocks which are located between the exterior and first interior girder at every 0.91 m (3 ft.) to 1.22 m (4 ft.) along the bridge (shown in Figure 2(b)). In addition, the tie bars (transverse and diagonal) as shown in Figure 2 are utilized to provide additional backing to the exterior girders to prevent rotation throughout the construction. The objectives of this research are investigating the installation flaws and performance of the temporary lateral bracing systems to avoid exterior girder rotation, and to determine the exterior girder rotation under bridge deck construction loads. The idea was to provide important field data to researchers to define effective bracing systems for overhang construction. In this article, primarily, the rotational response of the exterior girders due to eccentric loads occurring during bridge deck construction is presented.

Bridges description and instrumentation

Three steel girder bridges in the state of Illinois were selected for this study. The selected bridges have similar girder sizes (W762 (W30) steel sections) and three continuous spans. Basic information about these bridges is presented in Table 1. In each of the bridges, instrumentation was focused on the middle span assuming the maximum transverse rotation takes place in the longest span (span with longer unsupported length) for all three bridges. In each case, the middle span was divided into several different transverse sections for instrumentation. The first section (S1) was at mid-span, the second (S2) was at a diaphragm located near the mid-span, and the third section (S3) was toward the pier. Girder rotation and strains in tie bars were recorded using dual-axis tilt sensors and foil strain gages, respectively. The maximum allowable deflection (Δ) of the overhang deck is taken as 4.76 mm (3/16 in.), but the maximum allowable rotations were determined for different bridges based on the overhang length. The corresponding allowable maximum girder rotations (shown in Figure 1(c)) (θ) for different overhang widths are provided in Table 1 for all three bridges. The 4.76 mm (3/16 inch) was based on the standard specifications for road and bridge construction for Illinois Department of Transportation (IDOT, 2012).

Table 1.

Bridge descriptions.

	Bridge A	Bridge B	Bridge C
Beam type	W762 × 197 (W30 × 132)	W762 × 147 (W30 × 99)	W762 × 185 (W30 × 124)
Skewed/non-skewed	Non-skewed	24° skewed	3.8° skewed
No. of spans	3	3	3
Monitored span length	16.31 m (53 ft.-6 in.)	15.77 m (51 ft.-9 in.)	24.69 m (81.-0 in.)
Overhang width	1.054 m (3 ft.-5.5 in.)	0.97 m (3 ft.-2 in.)	0.94 m (3 ft.-1 in.)
Number of girders	3	7	3
Girder spacing	2.21 m (7 ft.-3 in.)	1.93 m (6 ft.-4 in.)	2.13 m (7 ft.-0 in.)
Tie type	Diagonal tie	Transverse tie	Transverse tie
Type of screed machine	Vibrating paving machine	Screed machine	Screed machine
Screed rails location	On the deck overhang	On the deck overhang	On the deck overhang
Rotation limit	0.26°	0.28°	0.29°

Instruments

Dual-axis tilt sensors (sensitivity: 0.01% per degree) were utilized to record girder rotations as illustrated in Figure 4(a). All tilt sensors were mounted on the top surface of the bottom flange and on the mid web location of the exterior and first interior girders at the predefined sections. The tilt sensors were used in agreement with manufacturer suggestions and the sensitivity check of the tilt sensors was performed before installation. An aluminum seat was used to place the tilt sensors as shown in Figure 4(a) and instant adhesive glue (Gorilla/Scotch Super Glue) was used to mount the chair to the girder. Same direction and pattern were maintained during installation of tilt sensor to keep the consistency in the data. The purpose of attaching tilt sensors to the web of the girders was to monitor the rotation induced by local web deformation during concrete placement. All rotations were measured in degrees.

Figure 4.

(a) Installed 2-axis tilt sensor on the bottom flange of the exterior girder; (b) installed strain gage in the transverse tie bar.

Foil strain gages were attached on the tie bars to measure the stresses during and after the concrete deck pouring, shown in Figure 4(b). All strain gages were calibrated (using a shunt calibration process) and protected according to manufacturer recommendations to ensure accuracy and linearity of the strain gages. Calibration was necessary to scale strain gage sensitivity (by adjusting the gage factor) to monitor the output strain conveniently and accurately with a predetermined input. A zero point was determined before recording data to nullify residual readings that may have occurred due to movement of the tie bars during concrete placement. Two strain gages were attached to each bracing bar.

Instrumentation plan

The instrumentation plan for the transverse sections is shown in Figure 5 for all three bridges. Figure 6 shows the locations of the tilt sensors and the strain gages at each section.

Figure 5.

Plan of bridges A, B, and C (top to down) and the chosen sections for instrumentation.

Figure 6.

Location of tilt sensors and strain gages: (a) bridge cross section with diagonal tie arrangement; (b) bridge cross section with transverse tie arrangement.

Results and discussions

Field data analysis

Transverse rotations in exterior girders may happen in both inward and outward directions as shown in Figure 1. To simplify, outward rotation is considered as positive rotation while inward rotation is considered negative rotation. Rotation data were collected every 30 s and recorded with respect to time. Simple exponential smoothing (SES) was utilized to remove higher-frequency noise and analyze the field data. The SES equation is shown in equation (1).

{\hat{x}}_{i + 1} = α x_{i} + (1 - α) {\hat{x}}_{i}

(1)

where ${\hat{x}}_{i}$ is the known series values for i time period, x_i is the predicted value for i time period, ${\hat{x}}_{i + 1}$ is the predicted value for i + 1 time period, and α (between 0 to 1; smaller α gives more smoothing, and larger α gives less smoothing) is the smoothing constant as per Brown and Meyer (1961). The α-value varies depending on the type of data series, and values of α were chosen for the data series based on diminishing the mean of the squared errors (MSE).

A sample time history data set is shown with the darker line representing forecasted data obtained using the SES method. Two different types of rotations are defined in Figure 7 including the maximum rotation and the residual rotation (i.e. permanent rotation). The “maximum rotation” at any section takes place when all construction loads are placed on that section. The “residual rotation” at any section was obtained after the construction of the entire bridge deck when all of the construction loads are removed except the unhardened concrete.

Figure 7.

Maximum and stable rotation by simple exponential smoothing.

Transverse rotation in exterior girders

Field-monitored results

Figure 8(a-i) depicts the measured rotation at mid-span (section S1) of bridges A, B, and C. It can be observed that the “maximum rotation” of the exterior girder for section S1 of bridges A, B, and C are 0.45°, 0.53°, and 0.44°, respectively. The corresponding residual rotations are 0.34°, 0.27°, and 0.30°. Figure 8(a-ii) also shows measured rotations of the exterior girder webs for bridges A and C. The maximum and residual rotations are 0.50° and 0.39° for bridge A and 0.46° and 0.31° for bridge C, respectively. It can be observed that both the construction loads and the weight of unhardened concrete action on the overhang deck have an important effect on the exterior girders leading to overhang deflections that exceed IDOT limits.

The “maximum and residual rotations” of the first interior girders for bridges A and B at mid-span (section S1) are small compared with that of the exterior girders as presented in Figure 8(a-iii). Bridge C showed higher rotation (maximum rotation of 0.19° and residual rotation of 0.083°) compared with bridges A and B. This increased rotation may be a result of misplaced or improperly shimmed timber blocks or ineffective transverse ties. Girder rotations at diaphragm locations (section S2) exhibit a different behavior. The bottom flange of exterior girders experiences relatively lesser rotations than the web of the girder at section S1. That behavior was expected due to the presence of a diaphragm at the section where the measurements were taken. In section S3, the exterior girder rotations at the web are similar to those taken at section S1. Rotations in S3 in exterior girders for bridges B and C are again larger than the values at section S2 due to the absence of diaphragms. In general, the bottom flange experiences higher rotation compared with the web at the same transverse section due to the restraint provided by the diaphragm. And, the exterior girder experienced the smallest rotation at the section neighboring to the pier.

Figure 8.

Field measurements of transverse rotations at sections (a) S1, (b) S2, and (c) S3.

In this article, bridge C was considered a non-skewed bridge since it had a very small skew angle (3.8°) as per the design drawings. The field data for the skewed bridge (B) are theoretically dissimilar than the data obtained for the non-skewed bridges. Bridge B has a 24° skew and showed some unusual behavior compared with the other two bridges. In this case, rotations of the exterior girder were larger than the corresponding values in the non-skewed bridges. It can be perceived from Figure 8 that the maximum rotation of bridge (B) at section S1 is larger than obtained for the non-skewed bridges, but in terms of the residual rotation, bridge B had smaller rotations compared with the other bridges at sections S1 and S2. This might be attributed to the spacing of girder and the girder number. In this case, bridge B has the smallest spacing between the girders, length of span, and the highest number of longitudinal girders. In other words, the torsional stiffness of its cross section is higher, thereby creating a lower residual rotation in bridge B compared with bridges A and C. In the case of skewed bridge, placing of tie bars on top of the deck and the concrete placement were perpendicular to the roadway, which may produce additional unbalanced construction loads on both sides of exterior girders at any particular section. As a conclusion from Figure 8, it can be observed that the maximum rotations in exterior girders (both flange and web) at all sections of all bridges exceeded the “limit for rotation” (bridge A: 0.26°, bridge B: 0.28°, bridge C: 0.29°) as shown in Table 1. For instance, a noticeable difference was found at mid-span (section S1) for all the bridges where the monitored exterior girder rotations (Figure 8) were 50%–90% larger than the limit prescribed by the department of transportation

Stresses/strains on tie bars

Strain gage installation and data recording

Diagonal and transverse tie bars were instrumented using strain gages to monitor strain during and after bridge deck placement. The installation of gages for bracing bars is provided in Figure 4. The gages were installed according to manufacturer recommendations and self-sealing (insulating) adhesive tape was used to wrap the strain gages after installation to protect them from moisture and mechanical damage.

Field results

The strain values in tie bars are recorded in micro-strain (µε) and were converted into stresses experienced by the tie bars through the whole construction. Figure 9 shows the average maximum and residual strain and stress in the tie bars at mid-span (section S1) for all bridges. The average maximum stress value obtained in the non-skewed bridge (A) is less than the related values for the skewed bridges (B and C). These differences might be a result of the type of finishing machine used for bridge A (lightweight vibrating screed) while a much heavier screed machine was used in bridges B and C. The maximum strain values in tie bars of the skewed bridges are 322 µε (bridge C) and 344 µε (bridge B) which is 2.4 times higher than the values obtained for the non-skewed bridge. Though multiple factors are responsible for this phenomenon, there is no question that the skew angle of the bridge plays an important role. After concrete placement, the strain values decreased to residual strains of 79, 142, and 44 µε for bridges A, B, and C, respectively, as shown in Figure 9.

Figure 9.

Field measurement of average tensile strains and stresses in tie bars.

Finite element (FE) analysis

FE modeling

FE models were created for all three bridges as shown in Figure 10 utilizing the comprehensive FE code ABAQUS/CAE 6.13. The FE model was conducted as a full-scale model using the available plan dimensions and manufacturer equipment information. The main girders and diaphragms were modeled using shell elements (S4R). S4R is a 4-node general purpose shell element with reduced integration option and hourglass control. More details about the description of the element could be found in ABAQUS. The No. 13 (No. 4) tie bars (diagonal and transverse) were modeled as truss elements (T3D2) and the overhang brackets were modeled using beam elements (B31). T3D2 elements have no resistance to bending and they are used for members subjected to tension or compression loads, while the beam element B31 offers flexibility with transverse shear deformation with linear interpolation. The considered mesh size was 50.8 mm (2 in.). For the analysis, interactive mode was used as the method of analysis in ABAQUS.

Figure 10.

Full-scale finite element model for the bridge C.

Boundary conditions were assigned to simulate a continuous (pinned–roller-roller) three-span bridge. The results of the FE model were compared with values measured at the same sections as those selected for field instrumentation (see Figure 5). Three different loading conditions were applied to the model for each of the three sections (S1, S2, and S3). A plastic concrete load from an 8-in. thick deck was distributed over the surface of the top flange of each girder based on the tributary area. For the exterior girders, the overhang concrete load was not considered as a distributed load on top of the flange of the girder but was calculated separately as a static line load distributed over the cantilever brackets. The weight of the consolidation and finishing equipment, as well as other construction live loads, were estimated as point loads and applied to the screed rail that extends over the entire portion of the bridge on that bracket.

Comparison of field-monitored rotation and FE results

Three separate cases were included in the FE modeling. In the first case, no bracing system was considered in the analysis of the bridges and rotation results were calculated at mid-span (section S1) of the exterior girder. In Figure 11, the FE results without any bracing systems showed approximately 1.5 times larger rotation than the measured field rotation and almost 2.5 times more than the maximum rotational limit.

Figure 11

Exterior girder rotation at bottom flange under different bracing conditions at section S1.

In the second case, rotation prevention systems (transverse tie bars and timber blocks) were assumed to be fully engaged. Fully engaged tie bars are modeled in their original and straight position without any sagging, bending, or loose transverse ties. The results obtained in the bottom flange of the exterior girder at section S1 (shown in Figure 11) showed that for all bridges, both the maximum and residual rotations were significantly smaller than the field measured rotations.

In the third case, to model actual conditions, tie bars and timber blocks were considered partially engaged by assuming that the tie bars have initial sagging, bending, and tightening issues prior to the application of external loads. It was difficult to measure the slack distance for the tie bars in the field, but the observed average slacked distance for tie bar and gap distance for timber blocks were 3.5 mm and 2.5 mm, respectively. These initial imperfections were modeled using non-linear “translator” connectors or “gap” elements that represent the connections between the girders and tie bars and timber blocks. Considering the slack (tie bars) and improper shimming (timber blocks) issues, the “gap” value is assigned to the “translator” connector on the basis of field observed slack and gap values for tie bars and timber blocks, respectively.

The FE results for section S1 are summarized for the bottom flange of the exterior girders, exterior girder webs, and at the bottom flange of the first interior girder as shown in Figure 12 where the maximum and residual rotation values are similar to field values for the bottom flange of the exterior girders but still higher than the allowable limit, as shown in Figure 12(a-i). The obtained residual rotations from the FE analysis of bridges A, B, and C were 11.1%, 9.4%, and 13.6% higher than the field data, respectively. At the web of the exterior girders, the FE results for bridges A and C (field data from bridge B was not collected) were in a good agreement with the field rotations both in terms of the maximum and residual rotations, but the maximum rotations were almost two times higher than the allowable rotations, as shown in Figure 12(a-ii). The FE results at the web of the exterior girders for bridges A and C are 2.0% higher and 4.3% smaller than the field data, respectively. The maximum and residual rotation in bridge B obtained from the FE analysis were 0.65° and 0.37°, respectively, which are higher than rotations calculated for the bridges A and C. For the bottom flange of the first interior girder, the FE results are in good agreement for all bridges except bridge C (the calculate FE rotation is quite a bit smaller than the field rotation) as shown in Figure 12(a-iii).

Figure 12.

Girder rotation with partially engaged bracing: FE results at sections (a) S1, (b) S2, and (c) S3.

Conceptually, the maximum and residual rotations for bridge C was expected to be similar to bridge A since both are straight (bridge A is non-skewed and bridge C has a mild skew of 3.8°) and they have the same number of girders. However, the calculated rotation in bridge C is much lower than the measured field rotation. At section S2, as shown in Figure 12(b), the FE results at the bottom flange of the girders were similar to the field-monitored data. The maximum rotation from the FE results for bridges A and B were 9.1% and 5.3% larger than the field data, respectively, but bridge C showed 20.0% smaller rotation compared with the field value. Also, it can be observed in Figure 12(b) that both the maximum and residual rotations were greater than the allowable rotation (listed in Table 1). Figure 12(c) shows good agreement between field and FE results for the acquired rotation at section S3. Maximum rotation at the web location of the girders obtained from the field for bridges A and B were 16.7% and 1.9% smaller than the FE analysis, respectively, whereas the FE results for bridge C was 4.4% smaller than the field value.

Comparison of field-monitored stresses and FE results

It can be seen from the FE analysis that in the case of partially engaged bracing system, the tie bar stresses at mid-span (section S1) for all bridges are in a good agreement (the percentage of error between the FE results and the field data are close to and within 20%) with the field data for bridges A and C, as shown in Figure 13. The maximum stresses from the FE analysis in bridges A and C for the partially engaged cases are 11.4% larger and 29.2% smaller than the field values. The calculated FE results for the maximum tie bar stress in bridge B is 49.9% smaller than the stress monitored in the tie bars in field. In the case of bridges A and C, the FE results, assuming that the bracing system is fully engaged, showed much higher maximum stresses than field values, whereas the FE result of bridge B showed lower maximum stresses than field rotation.

Figure 13.

Comparison of stresses at sections: S1 in tie bars between field data and FEA.

One more interesting point to be noticed in Figure 13 is that the stresses in fully engaged tie bars were larger than the stresses obtained from partially engaged tie bars. It happened in the fully engaged tie bars due to the immediate action of tie bars during the placement of the construction loads. On the other hand, in the case of the partially engaged tie bars, the tie bars could not respond immediately during placement of construction loads because of sagging, bending, and tightening issues and by this time, a large portion of the overhang construction loads were carried by other load carrying elements which results in comparatively smaller stresses in the partially engaged tie bars. Based on the stress values, it can be concluded that the tie bars and the timber block were not working effectively during construction based on the comparison of the measured rotations and the limit for rotation.

Conclusions

This article introduces a study on exterior steel girder rotations during construction of three bridge decks in the state of Illinois. The data were presented in terms of exterior girder rotations monitored in three transverse sections in the middle span of each bridge. The sections are located at the mid-span, near the mid-span (at diaphragm location), and near the pier for each bridge. The article also presents the results of a FE analysis conducted for the bridges. The results of this article were based on three data points, and further research is necessary to verify that the asserted correlations are consistent with the behavior exhibited with other bridge system properties. The following conclusions are based on the data and analysis presented in this article.

The mid-span location is the longest unbraced length from either side of the piers. Based on field-monitored data and FE analysis, it was found that the largest maximum and residual rotations for the exterior girders occurred at mid-span for all three bridges despite of the degree of skew angles in all of them.

Rotations in the first interior girders are negligible compared with the corresponding values in the exterior girders.

The bracing systems used to prevent exterior girder rotation were not properly installed and therefore at least partially ineffective in preventing rotation. Improper installation in the field was included in the FE analysis and rotations measured in the field were in reasonable agreement with that determined from the FE models. These partially engaged bracing systems resulted in rotations that exceeded limits set by the Illinois Department of Transportation (IDOT). Properly installed and tightened bracing bars are available to immediately engage themselves to prevent exterior girder rotation, and in this study, fully engaged tie bars showed excellent results and the exterior girder rotations were well below the allowable limit.

Rotation of exterior girders is affected by their torsional stiffness although additional work is recommended to further characterize the effect of torsional stiffness and skew angle on girder rotation during bridge deck construction.

Footnotes

Acknowledgements

The authors would also like to thank Mr. Darren Green, SLU, for his help throughout this research. The opinions and findings of this article are those of the authors.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This project was made possible through funding from the Illinois Department of Transportation (IDOT) through the Illinois Center of Transportation (ICT); this support is very much appreciated. Also, many thanks are extended to Saint Louis University (SLU) for financial assistance and operations support.

ORCID iD

Ahmed Ibrahim

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