Laser-Based Field Measurement for a Bridge Finite ...

Laser-Based Field Measurement for a Bridge Finite-Element Model Validation

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Kaoshan Dai, Ph.D., A.M.ASCE 1; David Boyajian, Ph.D., A.M.ASCE 2; Wanqiu Liu, Ph.D. 3; Shen-En Chen, Ph.D., M.ASCE 4; Jeremy Scott 5; and Marcus Schmieder 6 Abstract: In bridge engineering, laser-based measurement techniques show promise in assisting field tests due to their noncontact features. A case study of using laser-based remote sensing to help collect data during in situ testing for a bridge finite-element (FE) model validation is reported in this paper. The skewed two-span bridge in this study was constructed with nine high performance steel girders in two phases. A three-dimensional (3D) FE model of the bridge superstructure was developed based on the information provided by the design files. Various field tests were performed to validate the model: (1) light detection and ranging (LiDAR) scanning, (2) static truck load tests, and (3) laser Doppler vibrometer testing. The LiDAR scanner collected geometrical information of the actual bridge. It was also used to measure girder deflections during load testing. The fundamental frequency of the bridge vibration was obtained by using a laser Doppler vibrometer (LDV). In situ dynamic and static measurements were compared to the FE model results, thus offering validation of the analytical predictions. Such analysis of the bridge superstructure serves as a baseline for post construction investigations, with important implications especially for the long-term structural health monitoring of the system as a whole. DOI: 10.1061/(ASCE)CF.1943-5509.0000484. © 2014 American Society of Civil Engineers. Author keywords: Finite-element model; Steel bridge; Remote sensing; Light detection and ranging (LiDAR); Laser vibrometer; Load testing; Structural vibration; Model validation.

Introduction Recent developments in laser-based remote sensing technology offer rapid and high quality data collection options for field testing. Laser scanning devices commonly use interferometric wave manipulation to measure spatial distance, motion, reflectivity, and other physical parameters of a subject. Such measuring techniques have widespread usefulness in engineering and industrial applications. The range finding laser, also called light detection and ranging (LiDAR), has been integrated into the geographic information systems (GIS) toolset to model infrastructure, monitor erosion, map terrain, and other geometric tasks (Palmer and Shan 2002; Loudermilk et al. 2009; Perroy et al. 2010). The laser Doppler vibrometer (LDV), developed based on the Doppler effects 1 Associate Professor, College of Civil Engineering, Tongji Univ., 1239 Siping Rd., Shanghai 200092, China (corresponding author). E-mail: [email protected]; [email protected] 2 Associate Professor, Dept. of Physics and Engineering, Taylor Univ., 236 West Reade Ave., Upland, IN 46989. E-mail: [email protected] 3 Assistant Professor, Dept. of Transportation, Dalian Univ. of Technology, No. 2 Linggong Rd., Dalian, Liaoning 116024, China. E-mail: [email protected] 4 Associate Professor, Dept. of Civil and Environmental Engineering, Univ. of North Carolina, Charlotte, 9201 University City Blvd., Charlotte, NC 28223. E-mail: [email protected] 5 Former Graduate Student, Dept. of Civil and Environmental Engineering, Univ. of North Carolina, Charlotte, 9201 University City Blvd., Charlotte, NC 28223. E-mail: [email protected] 6 Principal, IE-Consulting, 1589 Bramble Ln., Coquitlam, BC, Canada V3E2T5. E-mail: [email protected] Note. This manuscript was submitted on January 8, 2013; approved on June 4, 2013; published online on June 6, 2013. Discussion period open until November 4, 2014; separate discussions must be submitted for individual papers. This paper is part of the Journal of Performance of Constructed Facilities, © ASCE, ISSN 0887-3828/04014024(11)/$25.00.

© ASCE

of a laser beam, has been used for micro-system monitoring of precision devices (Castellini et al. 2006) and for quality control in high fidelity fabrication settings (Paone et al. 1999). Using laser device techniques as these have likewise been explored for sensing applications in civil structures (e.g., bridges). However, there are different sensing requirements for monitoring physical structures, and engineers must be familiar with such specifications (e.g., bridge inspections) in order to develop proper laser-based measurement devices for use in monitoring civil infrastructure. For conventional bridge measurement methods, sensors need to be mounted onto the target in order to obtain structural responses. Accelerometers, strain gages, linear variable differential transformers (LVDTs), and cable extension transducers, are all commonly used devices during in situ experiments. The measurement setup requires access to bridges and can often involve heavy equipment and machinery, typically leading to the disruption of normal traffic flow patterns. Therefore, several nonconventional measurement methods have been investigated in bridge testing, including techniques involving microwave and radar interferometry (Farrar et al. 1999; Gentile and Bernardini 2008, respectively) and digital imaging analyses (Lee and Shinozuka 2006). A laser system was developed and used to measure bridge deflections under static loading by Fuchs et al. (2004a, b), with a resolution of
0.76 mm. A drawback of this approach, however, is that the system must be manually relocated to different places when scanning multiple locations along the bridge. Based on a commercially available LiDAR technique, researchers from the University of North Carolina at Charlotte have also utilized the remote sensing technique when performing field inspections of bridges (Chen et al. 2010; Liu et al. 2010; Dai et al. 2011). In this context, the distance measuring capabilities of the LiDAR scanner is achieved through algorithms designed for detecting shifts in the geometry of the structure, as in the case of geometric disparities due to damage or the amount by which a girder deflects. Bridges are common

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LDV study subjects because of their dynamic vibration behaviors (Chen et al. 2000). Nassif et al. (2005) compared LDV measurements of bridge deflections and vibrations with the more conventional results as collected by use of linear variable differential transducers (LVDTs) and geophone sensor techniques during field testing; they concluded that the LDV can effectively achieve valid measurements. Vibration frequencies of a bridge or its structural elements can also be readily obtained through LDV measurements thus enabling the investigations into the health conditions of bridges as a whole or its members at a component level (Chen and Petro 2005). One approach for structural health monitoring is achieved through the use of analytical models. Baseline finite-element (FE) analyses have been established for different types of bridges (Feng et al. 2004; Ren and Peng 2005; Liu et al. 2009), in conjunction with field test validations (Schlune et al. 2009). Application of laser technologies for field measurements has been demonstrated to greatly enhance testing efficiency and accuracy. In this paper, a description of the full-scale three-dimensional (3D) finite-element (FE) model that was first developed for the superstructure of a two span continuous steel girder bridge is discussed together with the corresponding validations as achieved by actual laser aided tests that were conducted on the site. Both LiDAR and LDV systems were used for in situ testing. The validated baseline FE model presented herein is shown to be a useful tool for structural analysis purposes as well as for long-term health monitoring of such complex structures. Laser-Based Field Measurement Methods Laser devices used in this study involved a terrestrial-based LiDAR scanner and a scanning LDV system. The former technique utilizes a static laser to generate spatial data with respect to a conventional XYZ-coordinate reference frame. Laser beam phase shift (or timeof-flight) measurements enable distance information to be gathered from a plane of data points referred to as a point cloud. The latter LDV approach involves a dynamic laser system to measure motions at a specific location. Built-in mechanical, electrical, and optical mechanisms allow the laser to provide imagery from the vibration data gathered. The vibrations are typically reported in terms of wavelengths or frequencies from which differential data may be converted to analog voltages or digitized directly to obtain velocity and displacement measurements of an object. The LiDAR scanner used for this study is the Faro LS 880 HE model (Faro Technology 2007). It is a phase-based laser system with an operating fields of view 320 and 360° for the vertical direction and the horizontal direction, respectively. The measurement range is from 0.6 to 76 m with the resolution of
3 mm at 25 m. The LDV system used for obtaining the vibration measurements involved the Ometron Laser Doppler Vibrometer (Type 8330) (Brüel & Kjær, Nærum, Denmark). It is a portable, compact unit with a scan angle of 25 × 25°. The lenses range for the LDV system is from 1 to 200 m and the spatial resolution is 1 mm at 20 m. Technical specifications of these two commercially available laser systems can be referred to the corresponding datasheets (Faro Technology 2007; Brüel & Kjær 2012). Generally, application of laser-based measurement techniques for bridge inspections involves both the gathering and analyses of field data. In the field measurement and gathering phase, the scanning LiDAR unit usually collects millions of data points in terms of the XYZ positions of each scanned point; the LDV, on the other hand, is able to obtain single and/or multiple point vibration data from which position and velocity information can be determined. In analyzing the information gathered, the processing © ASCE

of data can be tedious as it involves not only noise filtering and coordinate transformations, but extensive analyses on the streams of numbers amassed. Since the scanning measurement alone cannot provide the direct information associated with bridge inspection, additional evaluation methods are usually needed. Various algorithms can be used for this purpose. For example, a pseudo reference plan method (Liu et al. 2010) can obtain differences between different LiDAR scans of the same subject, which yield deformation information. The fast Fourier transformation (FFT) and modal analysis methods are used to process LDV measurements to detect vibration frequencies and to separate the different vibration mode shapes of the subject. It should be noted that laser-based measurements represent results relative to the XYZ-reference frame for the LiDAR scanner, or relative to velocity-time histories for the LDV. Coordinate transformations are therefore essential for LiDAR scanning result analyses; LDV-head vibrations must be taken into account for vibrations of the subject being studied relative to the ground or to other frames of reference. Finite-Element Model Development of a Steel Girder Bridge Bridge Description The present model considered a continuous two-span steel girder bridge constructed with a skew angle of 47° 37′ 30″ (Fig. 1). Before being fully opened to traffic, a series of laser-aided field test measurements were taken from which a baseline FE model of the bridge was devised. This bridge was constructed in two stages due to the presence of an existing bridge at the site that had to be removed. Stage I, approximately 40% of the total width of the finished structure, was constructed beside the existing bridge. Once stage I was completed and opened to traffic, the existing bridge was removed. Stage II, approximately 60% of the total width, was then constructed where the existing bridge used to stand. After the completion of stage II, the concrete deck between the two stages was joined with a two-foot wide longitudinal construction joint. A plan view of the steel framing of the bridge superstructure is shown in Fig. 2, with the supports being labeled as A, B, and C, from left to right. Supports A and C are elastomeric expansion bearings with slotted holes for the anchor bolts. The middle support, Support B, is a fixed pot bearing located on the intermediate pier. The total bridge length is 91.32 m from the bridge abutments and the total out-to-out width of the bridge is 27.61 m. Each clear span length between the centerline of the bearings is 44.79 m. There are nine girders: the spacing for Girder 1 through Girder 4

Fig. 1. A two-span steel girder bridge (image by Shen-En Chen’s research group; modified by Kaoshan Dai)

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Fig. 2. Steel girder layout plan

(Bay 1—Bay 3) is 3.51 m and the spacing for Girders 5 through Girder 9 (Bay 4—Bay 7) is 3.39 m. Each bridge girder consists of three different sections: Section A, Section AB, and Section B. Sections A and B, designed mainly for the positive moment regions, have the same cross-sectional dimensions, while Section AB, operating in the negative moment location, has different geometric dimensions. Sections A and B have a top flange that is 3.18 cm thick and a bottom flange that is 3.81 cm thick; for girder Section AB, the top and bottom flanges are both slightly thicker at 4.45 cm. As for width dimensions, all three sections are identical with the top flanges at a width of 43.18 cm and the bottom flanges at a width of 48.26 cm. Also, all three girder sections have the same web dimensions: 1.43 cm thick and a depth of 162.56 cm. Sections A and B are composed entirely of high performance steel (HPS) 70W; while Section AB has a HPS 70W web plate but flanges composed of HPS 100W steel. In Bays 1, 2, and 3 there are intermediate cross frames spaced at 7.62 m on the first span and at 6.71 m on the second span. The same spacing was used in Bays 5 through 7. There are no cross frames between Girders 4 and 5, with the only connection being the concrete deck at a width of 1.21 m. The intermediate cross frames are constructed of three L5 × 5 × 3=8 steel angles; also, the end bent diaphragms are fabricated in one piece consisting of a MC 18 × 42.7 channel and three WT 5 × 13 steel members using AASHTO M270 (AASHTO 2008) Gr. 50W steel. Stay-in-place (SIP) corrugated metal formwork was used for casting the 24.13 cm thick concrete deck and shear studs were used to connect the top flange of the girders with the overlying slab. The spacing of the shear studs on different girder sections varied. Only girder Sections A and B were considered to act compositely with the concrete deck for live load considerations in the design. Some studs were placed on girder Section AB, though this section was designed without the assumption of composite action due to the low tensile strength of the concrete in this region (AASHTO 2000). The concrete parapet wall is 0.76 m high and 0.36 m wide and is outfitted with a two bar aluminum railing on the top. © ASCE

FE Model Construction A 3D FE model of the bridge superstructure was developed by using ANSYS (ANSYS 2007) which considered all of the following elements: steel bridge girders, concrete deck, intermediate cross frames, end bent diaphragms, elastomeric expansion bearings, fixed pot bearings, and nonstructural components, e.g., the concrete parapet walls and concrete block. The bridge abutments, intermediate column bent, and substructure were excluded from the model. The hybrid design of the steel plate girders and the composite action between the girders and the deck posed special modeling challenges. Beam elements are by far the most widely used class in modeling homogeneous, regular cross sectioned bridge girders (Chan and Chan 1999; Shahaway and Huang 2001). Concrete deck slabs are usually modeled with shell elements (Wang et al. 1997; Brown et al. 2000; Barth and Wu 2006), and shells can be used to model girder webs and flanges separately (Thevendran et al. 1999; Fu and Lu 2003; Barth and Wu 2006). Two approaches are reported in the literature to simulate the interaction between the deck and girders: the first uses rigid links to connect the centroids of the concrete slab and the steel girders (Mabsout et al. 1996; Thevendran et al. 1999); the second uses contact elements (Lin et al. 1991). In this paper, two different elements were used to model the girders to account for the hybrid characteristics of the steel girders and the flange thickness variations. The top and bottom flanges were modeled conventionally using beam elements, while the web and also the concrete deck were modeled using SHELL63 elements, which are elastic shell elements with six degrees of freedom at each of the four nodes. To avoid overlapping between the flange and web elements, the section-offset technique was used, and the BEAM188 element, a 3D linear beam element following the Timoshenko beam theory, was selected to prevent compatibility issues that may arise when prescribing a combination of beam and shell elements in the model (ANSYS 2007; Chung and Sotelino 2006). The composite action between the bridge deck and girders as induced by the shear stud connectors is a complex phenomenon to model. In the positive moment region, the concrete deck and

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girder act compositely if an adequate number of shear studs are provided. To simplify the model in the negative moment region, the concrete slab over the column bent is commonly assumed as not exhibiting composite action with the bridge girders; only the reinforcing steel in the deck is considered to resist tensile stresses (AASHTO 2000; Taly 1998). The basis behind this assumption is that the deck may become susceptible to cracking if too many shear studs are prescribed for achieving full composite action, due to the low tensile capacity of the concrete. Therefore, only a few shear studs are provided in the negative moment area in a bridge design. In this case, the longitudinal steel reinforcement in the deck can be assumed to act compositely with the girder but not with the concrete. According to the design documents, only 8% of the shear studs on each girder are located on Section AB, which undergoes negative bending; 92% of the studs are located on Sections A and B of the bridge girders, which undergo positive bending. Therefore, in the FE model, the number of rigid links on Section AB to Section A or Section B reflects the same ratio of shear studs on these girder sections as pertaining to those of the actual bridge. The shear studs were modeled using the multipoint constraint element, MPC184 (ANSYS 2007), to simulate these structural protrusions as rigid links, analytically. The intermediate cross frames of the bridge were designed using steel angles connected to intermediate stiffeners, and were therefore modeled with the LINK8 element, a uniaxial tension-compression 3D truss element with three degrees of freedom at each node (ANSYS 2007); the stiffeners, were modeled with BEAM188 elements (ANSYS 2007), together with the offset technique mentioned previously. Since the connections of the angles to the stiffeners only consisted of a pair of bolts, it was reasonable to model them as pin connections to allow for some rotational degree of freedom. For simplicity, the cross frames were connected between the flange nodes on the girders, and to regulate a large number of local modes from arising, each cross frame member was modeled with only one truss element. To form a more rigid member for the bridge endbent diaphragms, three T-sections and a channel were welded together in the actual design and modeled using LINK8 elements. Also, the channel in the diaphragm had shear studs welded to the top for composite action with the concrete edge beam at the end of the deck, the models of which used BEAM188 elements. The concrete parapets on the bridge deck were modeled using BEAM188 elements, and though the aluminum railing was not modeled per se, its mass was accounted for. Since at the time that field testing was being conducted, a series of precast concrete jersey barriers were placed centrally that spanned the bridge deck longitudinally, concentrated mass elements defined by single nodes (MASS21) (ANSYS 2007) were used to model these incidental features at existing nodes along the bridge deck. The bridge elastomeric/pot bearing supports were modeled using LINK10 elements with compression only properties and the anchor bolts in these supports were modeled with LINK10 elements, too (ANSYS 2007). The compressive modulus Em of the elastomeric bearing was calculated according to the AASHTO Standard Specifications for Highway Bridges 16th Ed. (AASHTO 2000) as ¯ 2Þ Em ¼ 3Gð1 þ 2ks

Table 1. Parameters Used in the FE Model Parameter

Value

Modulus of elasticity steel (GPa) Density of steel (kg=mm3 ) Estimated concrete modulus of elasticity (GPa) Density of concrete (kg=mm3 ) Estimated modulus of elasticity for end bearing support (MPa) Estimated modulus of elasticity for middle pot support (MPa) Estimated rotational stiffness for the end support-X direction (MPa) Estimated rotational stiffness for the end support-Y direction (MPa) Estimated rotational stiffness for the middle support-both X and Y directions (MPa)

200 7.85 28.5 2.4 263.79

4,250.78 2,550.47 29.37

The rotation effect of bridge supports was simulated with the rotational spring element (COMBIN14) (ANSYS 2000), which was tailored to have only torsional properties using the stiffness value as calculated from Eq. (2) in accordance to the AASHTO specifications M ¼ ð0.5Ec IθTL;X Þ Hrt

ð2Þ

where Ec = compressive modulus; I = moment of inertia about the transverse axis; θTL;X = relative rotation of the bearing under total moment M; and Hrt = total elastomer thickness. All parameters used in the FE model are listed in Table 1, and the 3D model for the bridge superstructure developed is shown in Fig. 3. FE Model Validation through Field Testing Field Tests A series of field tests were conducted to validate the developed FE model. A full scan of the bridge superstructure was first implemented by the LiDAR system in the absence of traffic loads. The laser system recorded the coordinates of the points into images that were then processed to retrieve the geometry of the bridge, such as bridge elevation, span length, girder spacing, bottom flange width, and web height. A filter was used to deal with any noise encountered during the measurements of the scan, and coordinate transformation matrices were applied to switch between the space information relative to the LiDAR instrument into a local coordination established upon the bridge member of interest. This enabled direct measurements of the dimensions of interest

ð1Þ

where G ¼ 0.74 ðMPaÞ is the shear modulus obtained from the lab testing following the ASTM D4014 (ASTM 2007); the elastomer hardness constant k¯ ¼ 0.75 was obtained from Table 14.3.1 of the AASHTO Standard Specifications; the shape factor, s, for one layer of elastomer was calculated to be 8.88 in accordance to the Standard Specifications of Section 14.2 (AASHTO 2000). © ASCE

47.79

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Fig. 3. Bridge superstructure FE model J. Perform. Constr. Facil.

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Fig. 4. Truck configurations during load testing

to be made to reflect actual geometrical information that was used to construct the FE model developed based on the design drawings. Load tests were performed with two dump trucks being placed either back-to-back (Positions 1 and 3 in Fig. 4) or in parallel (Position 2 in Fig. 4). The weights of these two fully loaded dump trucks were measured during the tests and are listed in Table 2. All the truck loading configurations were designed on Span B because the bridge is symmetric about the intermediate support in the horizontal plane. Each truck position was located approximately 18.81 m from the centerline of the middle support to create a maximum negative moment effect in the girders over the intermediate pieras preliminarily determined by influence line analyses. Girder deflections under the truck loads were obtained through a two-step LiDAR scan: (1) A baseline value in the absence of any truck loads; and (2) A subsequent rescanned result under the weight of the dump trucks. An algorithm was developed to compare these two sets of scanned data to obtain girder deflections based on the 3D coordinate information renderings. Three cable extension transducers placed on Girders 1, 2, and 9, were individually used to measure deflections to verify the LiDAR scan results. These are the three girders that were directly located under at least one of the truck positions during testing. Measurements were taken near the ends of the girders to avoid interruptions to motorists. The transducer was placed on the ground and the end of the extension cable was attached to the bottom flange of the target girder (Fig. 5). By so doing, the ground could be taken as the datum, which, incidentally, doubled as the reference for the ground-based LiDAR scanner as well as the LDV. Another noteworthy detail concerning setup of instrumentation was the use of magnets for keeping the cable extension transducers securely fixed to the bottom flange of the steel girder (Fig. 5). A LDV was used to scan the bridge to obtain vibration frequencies. To reduce the influence of LDV vibrations from background traffic patterns on the quality of the target bridge vibration data, the LDV head was placed atop a temporary vibration isolator rather than on a tripod in direct contact with the ground. From the ground position beneath the bridge, the LDV setup could send a laser beam directed to the bottom flange of the girder overhead. The focus in this present study was the first bending mode of the bridge girder as

measured close to the middle of Span B, where the probability of obtaining the vibration frequency would be substantial. The vibration time history measurement for Girder 8 under ambient (traffic) excitation is shown in Fig. 6(a), and the first bending mode of the girder vibration as achieved through FFT analyses using the peak pick method is shown in Fig. 6(b). FE Model Validation The FE model developed in this study is based on the design calculations and shop drawings, and was validated by comparisons made to the field testing results. Span length, bridge width, girder web- and bottom flange-dimensions, and cross frame member lengths used in the FE model were validated by using the geometrical information derived from the LiDAR scan of the bridge without vehicle loads (Fig. 7). The girder elevation was calculated based on the images from the LiDAR scans, which show curves representing the actual girder elevations. Static analysis under the self-weight of the bridge was performed using the FE model, and the deformed shapes of the girders were derived by subtracting girder deflections from the original, unloaded girder elevations. Comparison was made between the girder elevation curves from the field LiDAR scan and those from the FE analysis. A typical girder elevation curve comparison is shown in Fig. 8, with the middle support of the bridge (support B) normalized to be zero,

Table 2. Truck Wheel Loads Front axle (kN) Truck A B © ASCE

First rear axle (kN)

Second rear axle (kN)

Left

Right

Left

Right

Left

Right

34.79 33.45

34.34 34.61

41.90 41.81

47.24 46.71

42.88 39.32

45.19 47.86

Fig. 5. Details of measurement setups during the truck load testing (images by Kaoshan Dai and Jeremy Scott; modified by Kaoshan Dai)

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Fig. 6. Vibration measurements: (a) girder ambient vibration time history; (b) girder vibration frequency analyses

Fig. 7. LiDAR scanned image of the underside of the bridge (image by Wanqiu Liu; modified by Kaoshan Dai)

Fig. 8. Comparison of Girder 8 elevation curves under static loading

revealing a good correlation between the LiDAR scan and FE analysis results. The FE model was further validated with truck load testing results. Girder deflections under the truck load were obtained

both from LiDAR scans and from direct transducer measurements. To obtain girder deflection calculations based on LiDAR scans, comparisons were made between girder elevation coordinates of the scans with and without the presence of truck loads. Using such a method enables the entire bottom girder deformation to be ascertained, whereas the placement of traditional transducers can only measure girder deflections at certain points. From a proper LiDAR reading, point cloud data collected from a two-step scan provides deformation information for all nine girders during field testing [Figs. 9–11(a)]. In these figures, the points shown are relative to the bottom flanges of the girders. Only the middle of Span B is shown because the trucks were positioned atop this location. The lighter colors of these images represent downward deflections toward the ground of larger magnitudes whereas the darker colors represent lower magnitude deflections, or in a few cases, upward deflections (i.e., negative values). Truck load analyses were conducted using the bridge FE model with the assumption that the steel girders and concrete deck behave compositely. In the FE analysis figures [Figs. 9–11(b)], the darker colors are downward deflections and have negative values. It can be seen that the maximum girder deflections occurred near the locations at which the trucks were placed, as evidenced by both the LiDAR scans and the modeled FE analyses. Consider the following observations, for example: (1) in Fig. 9, Girder 1, which is directly under the pair of tandem dump trucks, yields the greatest deflection; (2) in Fig. 10, the maximum downward deflection due to load case two occurs on both Girders 7 and 8, as anticipated; and, also as expected, (3) in Fig. 11, Girder 9 had the greatest deflection. The most significant difference (46%) for the maximum girder deflection amplitude throughout

Fig. 9. Comparison of girder deflections (cm) under the truck position 1 load case: (a) LiDAR scan; (b) FE analysis © ASCE

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Fig. 10. Comparison of girder deflections (cm) under the truck position 2 load case: (a) LiDAR scan; (b) FE analysis

Fig. 11. Comparison of girder deflections (cm) under the truck position 3 load case: (a) LiDAR scan; (b) FE analysis

the bridge between the LiDAR scan results and the FE analysis predictions, were found to occur at the Truck Position 2 (LiDAR scan result: maximum deflection ¼ 16 mm; FE analysis result: maximum deflection ¼ 8.5 mm). Noisy LiDAR data collected under this scenario incurred difficulties in precisely quantifying the maximum girder deflection. Please also note that the measurement error of the LiDAR scanner is
3 mm at 25 m due to its hardware resolution. The difference between the LiDAR scan and the FE analysis is expected to decrease if the measurement noise can be reduced and the higher resolution LiDAR scanner can be used.

Remaining comparisons for other load cases, however, offered closer correlations, which in general indicate the viability of the developed FE model for the prediction of bridge deformations as subjected to static loads. Additionally, in particular, deflections of Girders 1, 7, and 9 at the locations where the cable extension transducers were attached, were examined. Deflection values obtained here were compared with those calculated from the LiDAR scanned images and the FE analyses. Table 3 summarizes the girder deflections under the three different truck loading cases. The values in Table 3 are

Table 3. Comparison of Girder Deflection Results from FE, Transducer, and LiDAR Scan Girder 1 (cm) Load

FE

LiDAR

Truck position 1 Truck position 2 Truck position 3

1.12 0.08 0.05

1.50 0.41 −0.58

© ASCE

Girder 7 (cm) Transducer 1.37 −0.20 0

FE

LiDAR

0.08 0.81 0.51

0.10 0.91 −0.28

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Girder 9 (cm) Transducer 0 1.12 −0.03

FE

LiDAR

Transducer

0.05 0.58 1.24

0.15 0.74 1.60

0.03 0.58 0.86

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not the maximum deflections of each girder, but rather the deflections at the location where the transducers were mounted during testing. The FE model predicts slightly lower deflection values for each load case as compared to the LiDAR scans and transducer measurements. Out of nine comparisons, a group of four deflection values are very close: Girder 1’s deflection under the Truck Position 1 loading case; the deflections of Girders 7 and 9 under the Truck Position 2 loading case; and Girder 9’s deflection under the Truck Position 3 loading case. For other cases, due to instrumentation resolution limitations, values were found to differ somewhat from those as predicted from the FE analysis. Here, it should be pointed out that some deflections were so small, that the resolution limit of the LiDAR scanner was insufficient to render meaningful readings (e.g., the deflection of Girder 7 under the Truck Position 3 loading case and Girder 7 and Girder 9 deflections under the Truck Position 1 loading case). Among the four valid measurements, the maximum and minimum differences between the different methods were calculated as: (1) 33.93 and 12.35%, respectively, for LiDAR scan and FE analysis comparisons; (2) 38.27 and 0%, respectively, for transducer measurement and FE analysis comparisons; and (3) 46.25 and 8.67%, respectively, for LiDAR scan and transducer measurement comparisons. As being mentioned before, the FARO LiDAR scanner used in the testing has the measurement resolution of
3 mm at 25 m itself. The distance between the scanner head and the transducer installation point is around 18 m, the LiDAR measurement errors was not able to be completely eliminated at this measurement range. There is also the possibility that differences in some of the measurements may be due to measurement inaccuracies of the transducers, e.g., Girder 7 deflection under the Truck Position 3. Such measurement discrepancies may arise from the influence of wind currents on the extension cables and/or mechanical issues with the transducers themselves. Deflection values obtained from three different approaches revealed similar trends, with four of the measurements correlating closely to those of the FE results. Overall, the FE model did reliably predict girder deflections at the points where the transducers were mounted, which suggests validity of the FE model. In addition to static testing and analyses, modal analyses were also conducted from the developed FE model. The Block Lanczos solver (ANSYS 2007), suited to find mode shapes for large models having irregularly shaped shell elements, was used in this context. The first six bridge vibration modes from the numerical analysis are shown in Fig. 12. The first mode is a bending mode, showing a twowave curve feature for this two-span bridge. The natural frequency of the first mode is 1.98 Hz based on the numerical analysis, which

is close to the field test results of 1.88 Hz as obtained directly from use of the LDV. Although mode shapes are not obtained from field testing, the frequency comparison together with comparisons from the other efforts mentioned previously (e.g., LiDAR scanning and truck load testing), strongly indicate the validity of the FE model developed and used for the bridge in this study. Comparison with the Bridge Design The maximum dead load deflections obtained from the validated FE model and the design calculations were also compared. From the FE analysis, it was found that the exterior girders had the highest deflections and the maximum dead deflection of each girder varied somewhat between the different spans (Spans A and B). In the bridge design, it was assumed that the maximum noncomposite dead load deflections were the same for all nine girders on the bridge with a simplified structural analysis of a single girder being made by considering it as a two-dimensional (2D) beam, while more detailed information was furnished by the results of the 3D FE model analyses. The maximum dead load deflections as well as the location of the maximum deflection from the FE analyses are summarized in Table 4. Based on these analytical results, the average distance of the nine girders from the end of the bridge girders to the location of the maximum deflection, was found to be approximately 20.63 m for Span A and 19.54 m for Span B. The design calculations predicted that the maximum noncomposite dead load deflection of 10.77 cm would occur at a location of 17.92 m from each girder end. At a location of 20.16 m, the deflection as predicted by the design calculations was 10.69 cm. Since the deflections were only calculated in the design at approximately every 2.24 m, the maximum deflection may occur in between 17.92 and 20.16 m from the end of the bridge girders, which, from Table 4, is seen that the FE model predicted lower noncomposite dead load deflections over the design calculations. FE analyses for the dead load cases indicated that the maximum tensile and compressive stresses in the direction along the girders would occur at the intermediate pier, which is in good agreement with the design calculations, as the magnitudes of these stresses differed slightly. From the design predictions, the maximum tensile and compressive stresses were found to be 203.67 and 190.09 MPa, respectively, for Section AB. For Sections A or B, the maximum tensile and compressive stresses were, respectively, predicted to be 111.76 and 131.71 MPa. The maximum stresses in girder Section AB and in girder Sections A or B obtained from FE analysis are summarized in Table 5, revealing once again, that the model predictions resulted in lower stresses than those arising from the design calculations. According to the FE model, the exterior girders are found to be carrying more load than their interior counterparts.

Table 4. Max Noncomposite Dead Load Deflections from FE Analysis

Girder

Fig. 12. The first six bridge vibration modes obtained from FE modal analyses © ASCE

Span A maximum deflection (cm)

Distance from support A (m)

Span B maximum deflection (cm)

Distance from support C (m)

7.77 7.24 6.81 6.55 6.55 6.91 7.39 7.85 8.23

18.63 20.1 21.17 21.17 21.13 20.1 20.1 21.13 22.17

7.8 7.26 6.65 5.97 5.77 5.51 5.59 5.97 6.45

22.18 19.79 19.79 18.73 19.73 19.72 18.69 19.72 17.66

1 2 3 4 5 6 7 8 9

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Table 5. Maximum Noncomposite Dead Load Stresses from FE Analysis Section AB

Section A (B)

Tensile Compressive Tensile Compressive (top flange) (bottom flange) (bottom flange) (bottom flange) Girder (MPa) (MPa) (MPa) (MPa)

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1 2 3 4 5 6 7 8 9

150.31 149.62 140.65 120.66 117.21 134.45 136.52 142.03 162.72

155.82 155.82 155.82 148.93 145.48 145.48 155.13 166.85 182.71

76.53 75.15 75.84 62.05 62.74 71.02 77.22 75.84 73.08

93.08 91.70 91.70 71.02 72.39 84.81 94.46 91.70 84.81

Apart from the weight-induced loadings of the parapets upon the exterior girders, the 3D FE model also suggests that the skeweddesign of the bridge and its curvature affect the overall distribution of stresses throughout, as elaborated upon next. The 3D FE model took into account the vertical curvature and skew-geometry of the bridge, though the design was initiated by considering a 2D idealized, straight girder orientation. This is one of reasons for differences existing between the noncomposite dead load results of the FE model and those of the design. The deformed shapes of the girders from the FE model also revealed the presence of small torsional and axial effects in addition to those of flexure and shear. It is also noteworthy here that the robustness of the FE model also takes into account the various types of interactions, leading to lower deflections and predictions overall. Other researchers have also found that skewed bridges tend to have lower deflections and bending moments than nonskewed bridges (Choo et al. 2005). Given the fact that the dead load stresses predicted by the FE analysis were lower than those provided by the design calculations, the results from the model were found to render a more robust, and ultimately, accurate design of the skew bridge that was under investigation in this study.

Discussion The accuracy of the LiDAR-based girder deflection measurements were validated through both transducer readings as well as analytical FE model results. It was demonstrated that the scanner used in this study can provide useful bridge dimension and deformation information. Structural vibration responses collected by using the LDV system also yielded valid modal frequencies of the bridge structure in this research. Unlike traditional structural health monitoring systems, which usually involve a number of contact sensors or a sensor network, a single laser-based method was herein shown to be capable of providing the necessary structural response data for a very densely populated target region, as with the underside of a highway bridge. Another advantage of using the LiDAR and LDV systems is that normal traffic patterns can continue without undue interruptions. Compared to the conventional contact sensors, the proposed laser-based measurement strategies also offer a significant savings in time for field testing of civil infrastructure. The total time per LiDAR scan, including the setup and data collection, ranged between 15 and 25 min for the static load testing; in contrast, each transducer more than half an hour, rendering a total time that becomes a function of the number of transducers required. An obvious hindrance to the use of LiDAR and LDV systems is the up-front heightened costs associated with such expensive © ASCE

equipment. Of course, initial equipment costs can be offset in the long run when applying this technology to numerous projects. It should also be noted that, since the LiDAR and LDV systems collect data from the surface of the structure, these methods are incapable of furnishing interior characterizations of the members being studied, which is often the thrust of other nondestructive approaches. The LiDAR scanner is also limited in its shooting distance and the field of view that it is to capture. Obstructions to the target area also pose challenges for testing, e.g., if covered by shadows, or if the area is too wide or too far away, then only partial or obscured scan images may be achievable. The quality of scan cloud point data for a certain scanner partially depends on the scan resolution, which can be selected during testing. Obviously, higher resolution scans will require a greater commitment in both time and digital storage capacity. The LDV system measures the object motion along the laser beam axis. In other words, only out-of-plane vibrations are measurable. The quality of the laser focus for the LDV system is also dependent on both the distance and the reflectivity of the object being studied. If the LDV system is set at too great a distance from the object, and/or if the object possesses a less reflective surface, the focus may then be inadequate to yield a meaningful measurement. The position of the laser should be carefully designed to achieve a suitable scan angle for purposes of obtaining accurate measurements. Usually the increase in scan angle has the trade-off of heightening the error of the target dimensions under consideration (Liu and Chen 2013). A suitable angle is also important for ensuring that an adequate amount of the reflected energy be received by the LDV system. This is especially important if the object surface is not a flat plate. Another critical factor for ensuring that reliable measurements are being obtained involves the allowance of adequate in situ laser equipment manipulation. Barring the rotating head of the LiDAR scanner, the remainder of the instrument should be placed in such a manner to keep it stationary for the duration of testing. Carelessness in this aspect could otherwise introduce vibration noise into the data that would then have to be considered during post processing analyses. Only bridge vibration frequencies were obtained in this study. Usually, to construct vibration mode shapes of an object, multiple point scans will be required. However, the assumption for this measurement strategy is that the object be in a steady state with regard to vibrations. Since this assumption is not readily satisfied during field testing, bridge vibration mode shape data was not obtained. In such a scenario, alternative testing schemes must be used, e.g., implementation of two LDV systems. One can then serve as the single-point laser to provide the necessary reference vibration data of the object, while the other scans the structure to collect the relative vibration response values. Some aspects requiring further research are, finally, mentioned here. The impact of certain environmental factors, such as temperature, humidity, ambient light, object surface reflectivity, etc., should be studied to determine the role and the extent of influence these play on measurement accuracy. A suitable testing design methodology should therefore be developed to address these potential issues for heightened reliability of the data. Some initial research conducted in this vein can be found in the works of Watson et al. (2012) and Liu and Chen (2013).

Conclusion A full 3D FE model was constructed for a newly constructed, skewed, two-span steel girder bridge. Efforts were spent on modeling the hybrid features of these steel girders by beam elements

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for the flanges, and shell elements for the webs. The composite action between the steel girders and the concrete deck was captured by using rigid link elements. The bridge supports, such as the elastomeric bearings or the pot bearings, were also carefully modeled by using a combination of compression-only link elements (for the elastomeric pads/layers), tension link elements (for the anchor bolts), and springs (to capture the rotational constraint effects). Both the girder-deck system and nonstructural members for this bridge were included in this developed bridge superstructure FE model. A series of laser-aided field tests were performed in order to validate the FE model which was developed based on the design specifications and calculations. A LiDAR system was used to scan the entire underside of the bridge. From such images, pertinent information about the actual bridge in the field was obtained. A twostep method was designed based on the LiDAR scans to calculate girder deflections under the imposed truck loadings. This method proved to be effective for acquiring deflections of the bottom flange surfaces of the beams, continuously, for each of the nine girders via a noncontact measuring technique. This approach was found to be superior to the more traditional contact-method involving transducers placed at only discrete locations along the bridge. A series of three different truck load cases were used in the field tests from which LiDAR scans could be recorded to compare against the FE model results. Basic bridge vibration frequency information was also obtained by analyzing velocity-time history data as collected by using the LDV. The fundamental frequency from the field measurements was found to be close to the modal analysis as derived from the developed FE model. The FE model was also used to draw comparisons between the forerunning, simplified structural analysis that was used by engineers in the actual design of the bridge. The former approach proved to yield lower maximum stresses and deformations than those arising from the actual design. Since the 3D FE model considered the skewed geometry of the bridge and the variety of complex interactions possible while the design was based only on individual structural members, the results obtained from the elaborate model were found to more closely represent the performance of the actual structure as corroborated by field tests. Given the fact that the FE model yielded lower values as compared to those arising from the structural analysis of the design, it is concluded that the bridge design under the simplified structural analysis can result in an overall more conservative structure. The FE model developed from this study can also be used to establishing baseline information for future bridge inspections and long-term health monitoring protocol.

Acknowledgments Special thanks to the North Carolina Department of Transportation (NCDOT) for funding this research project and for providing traffic control and the tandem dump trucks for the static load testing. The authors would like to acknowledge the support of Dr. Moy Biswas. The views, opinions, findings, and conclusions reflected in this presentation or publication are the responsibility of the authors only and do not represent the official policy or position of the NCDOT. The research team would like to acknowledge the support from Rea Contracting for allowing the research team to conduct field tests on the bridge before construction was completed. The research team at UNC Charlotte would also like to acknowledge the help of Structural Steel Products, Inc. and DS Brown for providing documentation relating to the manufacturing of the bridge girders and the pot bearings, respectively. Kaoshan © ASCE

Dai would like to acknowledge the support offered by the following programs for his research at Tongji University: Shanghai Science Foundation (12ZR1433500), National Natural Science Foundation of China (51208382), and the Specialized Research Fund for the Doctoral Program of Higher Education (20120072120001).

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