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Federal Highway Administration Research and Technology
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 Public Roads This magazine is an archived publication and may contain dated technical, contact, and link information.
 Publication Number:  FHWA-HRT-08-006    Date:  Sept/Oct 2008
 Publication Number: FHWA-HRT-08-006 Issue No: Vol. 72 No. 2 Date: Sept/Oct 2008

# Using Supercomputers to Determine Bridge Loads

Drawing. This definition sketch shows a cross-section of the model six-girder bridge deck tested during the study. It defines the direction of the hydrodynamic forces and flow acting on the flooded bridge deck model. The sketch defines the positive direction of drag force, lift force, and turning moment. At the bottom of the sketch, in a box, the Froude number, Fr, is defined as upstream velocity, V, divided by the square root of the product of gravitational acceleration, g, and upstream flow depth, hu. To the right of this, the Reynolds number, Re, is defined as the product of upstream velocity, V, and deck height, s, divided by the kinematic viscosity of water, v. To the right of this, the inundation ratio, h*, is defined as upstream flow, hu, minus inundation depth, hb, divided by deck height, s. Above the equations is the sketch of the six-girder bridge deck. To the far left of the deck, near the margin, is a vertical double-headed arrow labeled, "hu," upstream flow depth, that is both deeper and higher than the deck. An arrow, "V" for velocity, points rightward toward the deck. To the right of this and beside the left end of the deck is a vertical double-headed arrow labeled "s" for deck height. Below the deck is a horizontal double-headed arrow labeled "W" indicating the deck width. To the right of the deck and below it is a vertical double-sided arrow labeled "hb" for inundation depth. At the center of the deck is a point labeled "cg" for center of gravity, with arrows representing the three forces emanating from it. The lift force, FL, points straight up. The drag force, FD, points straight rightward (downstream). The moment around the bridge deck's center of gravity, MCG, pivots counterclockwise.

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Graph. The graph shows experimentally determined and computer simulated drag coefficients versus inundation ratio for the six-girder bridge deck model. This graph compares the simulated drag coefficients, derived from Fluent and STAR-CD, and the experimentally observed drag coefficients, derived from the Froude numbers. The x-axis is the dimensionless inundation ratio, h*, and ranges from 0.0 to 3.5 at 0.5 intervals. The y-axis is the dimensionless drag coefficient, CD, and ranges from 0.0 to 3.5 at 0.5 intervals. Five sets of data points are plotted, one each for measured drag forces using Froude numbers, Fr, 0.22 and 0.32; and one each for simulated drag forces using Fluent with the LES model, Fluent with the k-(epsilon) model, and STAR-CD. In addition, two regression lines, or fitting equations, are plotted through the measured and simulated data points. In the upper left corner of the graph is an equation: The drag coefficient, CD, equals 1.7681 divided by the inundation ratio, h*, minus 8.2816 multiplied by exponential of -1.3268 and the inundation ratio, plus the product of 3.4868 and the Froude number, Fr, plus 0.6303. In the lower right corner of the graph is a key: Hollow triangles represent data points for Froude Number 0.22 and Reynolds Number 20292, black triangles represent data points for Froude Number 0.32 and Reynolds Number 28965; a blue line represents a regression line, or fitting equation; pink filled circles represent data points for STAR-CD; red squares represent data points for Fluent-LES, and yellow diamonds represent data points for Fluent-K(epsilon). Beginning with Froude Number 0.22 and Reynolds Number 20292, hollow triangles appear on the graph at x-y coordinates of 0.3-1.3, 0.5-1.3, 0.8-0.8, 1.0-0.8, 1.2-1.1, 1.4-1.3, 1.6-1.5, 1.7-1.6, 1.9-1.7, 2.1-1.8, 2.2-1.8, 2.4-1.8, 2.6-1.8, 2.7-1.9, 2.9-1.9, 3.1-1.9, and 3.3-1.9. For Froude Number 0.32 and Reynolds Number 28965, black triangles appear on the graph at x-y coordinates of 0.3-1.8, 0.5-1.5, 0.8-1.2, 1.0-1.2, 1.2-1.4, 1.4-1.6, 1.6-1.8, 1.7-2.0, 1.9-2.0, 2.1-2.2, 2.2-2.2, 2.4-2.1, 2.6-2.1, 2.7-2.1, 2.9-2.1, 3.1-2.1, and 3.3-2.1. For Star-CD, pink circles appear at x-y coordinates of 1.2-1.6, 1.6-1.7, 2.2-1.8, 2.7-1.8, and 3.2-1.8. For Fluent-LES, red squares appear at x-y coordinates of 1.6-1.6, 2.1-1.7, 2.6-1.8, and 3.3-1.9. For Fluent-K(epsilon), yellow diamonds appear at x-y coordinates of 1.6-1.6, 2.1-1.7, 2.6-1.8, and 3.3-1.9. One blue line roughly tracks with the Froude Number 0.22, Reynolds Number 20292 data points (hollow triangles), and the other roughly tracks with the Froude Number 0.32 and Reynolds Number 28965 data points (black triangles). The plot shows that the drag coefficient is constant for higher inundation ratios.

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Graph. The graph shows experimentally determined and computer simulated lift coefficients versus inundation ratio for the six-girder bridge deck model. This graph compares the simulated lift coefficients, derived from Fluent and STAR-CD, and the experimentally observed lift coefficients, derived from the Froude numbers. The lift coefficient is negative for all tested inundation ratios. This observation corresponds to a down-pull force. The x-axis is the dimensionless inundation ratio, h*, and ranges from 0.0 to 3.5 at 0.5 intervals. The y-axis is the dimensionless lift coefficient, CL, and ranges from -2.0 to 0.4 at 0.2 intervals. Five sets of data points are plotted, one each for measured drag forces using Froude numbers, Fr, 0.22 and 0.32; and one each for simulated drag forces using Fluent with the LES model, Fluent with the k-(epsilon) model, and STAR-CD. In addition, two regression lines, or fitting equations, are plotted through the measured and simulated data points. In the upper left corner of the graph is an equation: The lift coefficient, CL, equals 1.8427 divided by the inundation ratio, h*, plus the product of 15 and the Froude number, Fr, minus 11.6, all multiplied by exponential -1.0333 and the inundation ratio, h*, minus 0.34. In the lower right corner of the graph is a key: Hollow triangles represent data points for Froude Number 0.22 and Reynolds Number 20292, black triangles represent data points for Froude Number 0.32 and Reynolds Number 28965; a blue line represents a regression line, or fitting equation; pink circles represent data points for STAR-CD; red squares represent data points for Fluent-LES, and yellow diamonds represent data points for Fluent-K(epsilon). Beginning with Froude Number 0.22 and Reynolds Number 20292, hollow triangles appear on the graph at x-y coordinates of 0.3--0.1, 0.5-0.0, 0.7--1.7, 1.0--1.5, 1.2--1.3, 1.4--1.1, 1.5--0.8, 1.7--0.6, 1.8--0.5, 2.1--0.4, 2.2--0.3, 2.4--0.2, 2.6--0.2, 2.7--0.1, 2.9--0.1, 3.2--0.1, and 3.3-0.0. For Froude Number 0.32 and Reynolds Number 28965, black triangles appear on the graph at x-y coordinates of 0.3--0.1, 0.5--0.4, 0.7--1.1, 1.0--1.0, 1.3--0.9, 1.4--0.8, 1.6--0.5, 1.7--0.4, 1.9--0.3, 2.1--0.2, 2.2--0.2, 2.4--0.2, 2.6--0.2, 2.7--0.2, 2.9--0.2, 3.1--0.2, and 3.3--0.1. For Star-CD, pink circles appear at x-y coordinates of 1.1--1.2, 1.5--0.8, 2.1--0.5, 2.6--0.3, and 3.2-0.1. For Fluent-LES, red squares appear at x-y coordinates of 1.5--0.7, 2.1--0.6, 2.6--0.6, and 3.3--0.2. For Fluent-K(epsilon), yellow diamonds appear at x-y coordinates of 1.5--0.5, 2.1--0.5, 2.6--0.6, and 3.3--0.3. One blue line roughly tracks with the Froude Number 0.22 and Reynolds Number 20292 data points (hollow triangles), and the other roughly tracks with the Froude Number 0.32 and Reynolds Number 28965 data points (black triangles).

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Graph. The graph shows experimentally determined and computer simulated moment coefficients versus inundation ratio for the six-girder bridge deck model. This graph compares the simulated moment coefficients, derived from Fluent and STAR-CD, and the experimentally observed moment coefficients, derived from the Froude numbers. The moment coefficients have a maximum when the girders of the bridge deck are inundated. The x-axis is the dimensionless inundation ratio, h*, and ranges from 0.0 to 3.5 at 0.5 intervals. The y-axis is the dimensionless lift coefficient, CM, and ranges from -0.2 to 0.4 at 0.1 intervals. Five sets of data points are plotted, one each for measured drag forces using Froude numbers, Fr, 0.22 and 0.32; and one each for simulated drag forces using Fluent with the LES model, Fluent with the k-(epsilon) model, and STAR-CD. In addition, two regression lines, or fitting equations, are plotted through the measured and simulated data points. In the upper right corner of the graph is an equation: The moment coefficient, CM, equals, expressed negatively, 1 divided by the product of 4 and the inundation ration, h*, plus the product of 1.84 minus 2 multiplied by the Froude number, Fr, all multiplied by exponential of -1.15 and the inundation ratio, minus the product of 0.9 and the Froude number plus 0.258. In the lower left corner of the graph is a key: Hollow triangles represent data points for Froude Number 0.22 and Reynolds Number 20292; black triangles represent data points for Froude Number 0.32 and Reynolds Number 28965; a blue line represents a regression line, or fitting equation; red squares represent data points for Fluent-LES; yellow diamonds represent data points for Fluent-K(epsilon); and pink circles represent data points for STAR-CD. Beginning with Froude Number 0.22 and Reynolds Number 20292, hollow triangles appear on the graph at x-y coordinates of 0.3-0.1, 0.7-0.3, 1.0-0.26, 1.2-0.23, 1.4-0.19, 1.5-0.12, 1.7-0.1, 1.9-0.07, 2.1-0.04, 2.2-0.03, 2.4-0.2, 2.6-0.02, 2.7-0.0, 2.9-0.0, 3.1-0.0, 3.3--0.02. For Froude Number 0.32 and Reynolds Number 28965, black triangles appear on the graph at x-y coordinates of 0.3-0.03, 0.5-0.03, 0.7-0.1, 1.0-0.09, 1.2-0.06, 1.4-0.02, 1.6--0.03, 1.7--0.04, 1.9--0.06, 2.1--0.06, 2.2--0.07, 2.4--0.08, 2.6--0.07, 2.7--0.07, 2.9--0.07, 3.1--0.07, and 3.3--0.07. For STAR-CD, pink circles appear at x-y coordinates of 1.1-0.04, 1.6-0.02, 2.1-0.0, 2.6--0.03, and 3.1--0.06. For Fluent-LES, red squares appear at x-y coordinates of 1.2-0.02, 1.6--0.08, 2.6--0.09, and 3.3--0.1. For Fluent-K(epsilon), yellow diamonds appear at x-y coordinates of 1.2--0.02, 1.6-0.0, 2.6--0.03, and 3.3--0.07. One blue line, or fitting equation, roughly tracks with the Froude Number 0.22 and Reynolds Number 20292 data points (hollow triangles), and the other roughly tracks with the Froude Number 0.32 and Reynolds Number 28965 data points (black triangles).

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Diagram. This gray silhouette of a tanker truck shows elements of an onboard communications system that transmits real-time data. In the upper left corner are the phrases "Hours of Service (HOS)," "Commercial Driver's License (CDL) Number," and "Other Driver Monitoring Data." An arrow points from the phrases down and to the right, to the truck's cab, where a driver is silhouetted in black. In the lower left corner are the phrases "Vehicle Identification (VIN)" and "USDOT Number (Carrier ID)." An arrow points from these phrases up and to the right, to two black boxes under the truck's hood. Above the tank trailer is the phrase "Other Fault Code Information," and under this are the phrases "Fuel System," "Transmission," "Air System," and "Electrical/Electronic Systems." An arrow points from these phrases down to the tank trailer. To the right is the phrase "Lighting System Performance," and an arrow points down to a red box at the rear bottom of the trailer. At the bottom and left of center of the vehicle is the phrase "Brake System Performance," and an arrow points to the rear wheels of the truck cab. To the right of the phrase is a close-up of a wheel braking mechanism. At the bottom and rear of the vehicle is the phrase "Tire Condition Monitoring," and an arrow points to the rear wheels of the trailer. To the right of the phrase is a closeup of a tire displayed in cutaway.

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Graph. This diagram consists of an oval, elongated horizontally, with a crescent to the left and one to the right, the inner curves of both abutting the oval. The title at the bottom reads "Advanced Quality System," with the subtitle "Fulfilling and Raising Pavement Performance Expectations." In the lower left corner is a legend: A dotted line with arrows on either end depicts "flow of information," while a solid line with an arrow on just one end depicts "value-adding activities." At the center of the oval is a large dollar sign. Within the oval and depicted with arrows as moving counterclockwise around the dollar sign are four terms: "Top Management Commitment" at the top, "Resource Management" to the left, "Product Realization" at the bottom, and "Assessment & Improvement" at the right. The left-hand crescent is labeled "Database." The top of the crescent has the term "Agency," and a double-arrow dotted line connects it to "Top Management Commitment" in the oval. Toward the bottom of the crescent, in an oval, is the term "Requirements." A solid arrow, labeled "Input," points from here into the bigger, central oval toward "Product Realization." Another solid arrow, labeled "Output," points from "Product Realization" to the right-hand crescent. The top of this crescent is labeled "Customer." In the middle of the crescent in an oval is the term "Satisfaction," and a double-arrow dotted line connects this with "Assessment & Improvement" within the bigger, central oval.

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Diagram. This diagram/flowchart, within a horizontal rectangle, depicts the information and connections that comprise the AQS database setup. Below the diagram is a legend. According to the legend, the letter "A" denotes "data input by project management staff from the Maryland State Highway Administration's central or district office"; "C" denotes "data input by contractor, may be input using stand-alone input interface"; "F" denotes "data input by agency field personnel and may be input using stand-alone input interface"; an asterisk denotes "information common to the entire system and entered by the agency"; and a number sign denotes "analysis and calculations performed for specific needs, may require data integration with other databases." Inside the framing rectangle, at the top, is a narrow rectangle labeled "3. QA Management Module (DOT) [Department of Transportation]." Within this rectangle are five more labeled "Acceptance System," footnoted with an asterisk; "Specification System," with an asterisk; "Pay System," with a number sign; "Analysis System," with an asterisk and a number sign; and "System Information" (no footnote). Vertical lines from the bottom of each rectangle are connected by a single horizontal line. Below this rectangle are four figures. To the left is a small rectangle labeled "1. Database Server Module." A double-arrow line connects the rectangle to a small planet earth illustration, labeled "Internet." Another double-arrow line connects the earth illustration to the large rectangle above labeled "3. QA Management Module (DOT)." A double-arrow line to the right of the earth illustration connects the earth to another rectangle on the right (the third figure in this row), labeled "4. Data Translation Module." Another double-arrow line connects this rectangle to a box on the right, the fourth figure. This box is labeled "Other Databases" and holds the bulleted items "Contracts," "Inventory," "PMS," "Cost," and "Safety, etc." An arrow points down from the earth to a big rectangle (still within the first, framing rectangle). This rectangle is labeled at the bottom with "2. QA Data Input Module (DOT & Contractor)." Seven smaller rectangles are within this rectangle near its top, labeled as follows from left to right: "Contract Information," footnoted with an "A"; "Material Design," with an "A"; "QC Testing," with a "C"; "Acceptance Testing," with an "F" and a "C"; "Construction Records," with an "F"; "Checklist," with an "F"; and "Independent Assurance (IA) Evaluation," with an "F." Below that line of rectangles on the left-hand side is an eighth rectangle, "Certification/Qualification," footnoted with an "A." Vertical lines sprout upward from all eight boxes and are joined by one horizontal line. Still within this big, lower rectangle, and bigger than the eight rectangles, is another rectangle on the lower left labeled "Contractor" and with graphic representations of a computer. Lines sprout up from this box and connect to the "QC Testing" and "Acceptance Testing" rectangles. Similarly, another rectangle labeled "State Users" and with graphic representations of a computer appears on the lower right. This rectangle is connected by lines to the "Acceptance Testing," "Construction Records," "Checklist," and "IA Evaluation" rectangles.

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Graph. This diagram shows an oval elongated horizontally in the middle and a crescent to the left and one to the right, the inner curves of both abutting the oval. The title at the bottom reads "Advanced Quality System," with the subtitle "Fulfilling and Raising Pavement Performance Expectations." In the lower left corner is a legend: A dotted line with arrows on either end depicts "flow of information," while a solid line with an arrow on just one end depicts "value-adding activities." At the center of the oval is a large dollar sign. Within the oval and around the dollar sign, with a single arrow indicating counterclockwise movement, are 12 terms; from the top and going counterclockwise: "Top Management Commitment," "Resource Management," "Project Planning"-wedged in here is a box labeled "QA/PRS/Warranty Specification"-"Design," "Verification," "Adjustment," "Construction," "Process Control," "Acceptance"-to the right here is a box labeled "Product"-"Monitoring," "Assessment," and "Improvement." The left-hand crescent is labeled "Database." The top of the crescent has the term "Agency." Between these terms is a small oval labeled "Requirements," and a single-arrow solid line connects it to the big, central oval at the term Project Planning. A double-arrow dotted line connects the crescent to the central oval at "Top Management Commitment." The top of the right-hand crescent is labeled "Customer." Within the crescent is a small oval labeled "Satisfaction," and there is a double-arrow dotted line connecting this to "Assessment" in the big, central oval. A single-arrow solid line extends from the oval to the crescent.

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