Optimization of Rib-to-Deck Welds for Steel Orthotropic Bridge Decks

508 Captions

Figure 1. Illustration. Typical closed-rib steel orthotropic deck panel. This illustration shows a hypothetical isometric view of an orthotropic deck system. The roadway is shown at a prospective with direction of traffic running from the lower left to upper right; two parallel lines denote the traffic lane markings. Beneath the deck and oriented in the direction of traffic are the ribs. There are six ribs that are trapezoidal in shape, and they are distributed across the width of the roadway (though oriented upside down).

Figure 2. Illustration. Type 1 rib geometry. This illustration shows an elevation view of the type 1 specimen. The deck plate is 0.75 inch thick, 26 inches wide, and horizontally oriented. Atop the deck plate is a trapezoidal-shaped rib. The two legs of the rib are 14 inches apart at the deck plate, and the rib is overall centered on the deck plate. The rib stands 14 inches tall and is 0.3125-inch thick. The sides of the trapezoid are inclined with a rise of 14 over a run of 3.

Figure 3. Illustration. Type 2 rib geometry. This illustration shows an elevation view of the type 2 specimen. The deck plate is 0.75 inch thick, 26 inches wide, and horizontally oriented. Atop the deck plate is a trapezoidal-shaped rib. The two legs of the rib are 14 inches apart at the deck plate, and the rib is overall centered on the deck plate. The rib stands 12 inches tall and is 0.3125 inch thick. The sides of the trapezoid are inclined with a rise of 12 over a run of 3.

Figure 4. Illustration. Type 3 rib geometry. This illustration shows an elevation view of the type 3 specimen. The deck plate is 0.625 inch thick, 26 inches wide, and horizontally oriented. Atop the deck plate is a trapezoidal-shaped rib. The two legs of the rib are 14 inches apart at the deck plate, and the rib is overall centered on the deck plate. The rib stands 12 inches tall and is 0.3125 inch thick. The sides of the trapezoid are inclined with a rise of 12 over a run of 3.

Figure 5. Illustration. Comparison of rib edge preparation: beveled (left) and no preparation (right). The figure shows two illustrations that provide a comparison of rib edge preparation. The illustration on the left shows a close-up of the rib-to-deck weld joint. The rib has been machined with a bevel so that it can fully bear on the deck plate. However, to account for tolerances, the rib is elevated a small distance above the deck plate. The gap is uniform across the width of the rib from the inside of the joint (root gap) to the outside of the joint (face gap). The illustration on the right shows the same setup except that the rib is not prepared. In this case, the rib does not completely bear on the deck plate, and only the inside corner of the rib touches the deck plate. A small root gap is provided for tolerances, but, in the absence of preparation, the face gap is larger than the root gap.

Figure 6. Illustration. Overbeveled (left) and underbeveled (right) edge preparation. This figure shows two illustrations that provide a close-up of the rib-to-deck weld joint for overbeveled and underbeveled edge preparation. For both illustrations, the rib has been machined with a bevel almost matching that of the deck plate so that it can almost fully bear on the deck plate. In the case of the overbeveled preparation, the outside edge of the rib contacts the deck plate, but there is a small gap at the root. For the underbeveled scenario, the inside corner of the rib contacts the deck plate, and there is a small gap at the face of the weld.

Figure 7. Photo. Typical saw cuts introduced at the weld roots on the OB and UB series specimens. This photo shows a macro of a rib-to-deck weld joint. A saw blade has introduced a notch at the weld root paralleling the deck plate and extends across approximately 40 percent of the rib thickness.

Figure 8. Illustration. Intentional fit-up gaps in OG1 panel (left) and OG2 panel (right). This figure shows two illustrations of a close-up of the rib-to-deck weld joint. The rib has not been prepared so that the face gap is larger than the root gap. The illustration on the left shows the OG1 geometry where the root gap was set at 0.020 inch. The illustration on the right shows the OG2 geometry where the root gap was set at 0.031 inch.

Figure 9. Illustration. Fit-up gap and edge preparation for W series. The illustration shows a close-up of the rib-to-deck weld joint. The rib has been machined with a bevel so that it can fully bear on the deck plate. The root and face gap have been set at 0.020 inch.

Figure 10. Illustration. Test setup. The lower left part of this illustration shows an elevation view of the test fixture with the specimen installed. A 5-inch square steel tube with a thickness of 0.5 inch is bolted to an actuator at the midpoint of the tube. On each end of the tube are four steel bars rectangular in cross section sticking up from the tube and screwed to the tube with three fasteners each. These bars are tracks for pillow blocks that can freely slide up and down. There are upper and lower pillow block assemblies, and each holds a 4-inch diameter roller. The upper and lower rollers are aligned vertically, and the left and right rollers on each side of the tube are spaced 24 inches apart. The test specimen is mounted into the fixture so that the deck plate is parallel with the tube. Each end of the deck plate is sandwiched between the upper and lower rollers. The rib of the specimen attaches to the load cell of the test machine with a spherical washer in between. One-inch-thick plates sandwich the top of the rib.

Figure 11. Photo. Test setup at VT. This photo shows the test fixture described in figure 10 mounted into the testing machine at Virginia Tech. The fixture is mounted upside down from that shown in figure 10, where the tube is bolted to the load cell and the rib is mounted to the actuator.

Figure 12. Photo. Test setup at TFHRC. This photo shows the test fixture described in figure 10 mounted into the testing machine at the Turner–Fairbank Highway Research Center (TFHRC). The fixture is mounted as shown in figure 10 where the tube is bolted to the actuator cylinder and the rib is mounted to the load cell. Two load cells are shown; the larger diameter blue one was not used in testing, though the smaller diameter green one was used for feedback.

Figure 13. Illustration. Partitioning of specimen. This illustration shows an isometric view of a test specimen. The deck plate runs from the upper left to the lower right, and this direction defines the x-axis. The width of the specimen defines the z-axis, and the height of the specimen defines the y-axis. A line is shown across the width of the deck plate on the right end of the specimen with a callout of “Translation Y restrained.” A line is shown across the width of the deck plate on the left end of the specimen with a callout of “Translation X and Y restrained.” The distance between these two lines is 24 inches. The flat portion at the top of the rib is hatched across the width of the specimen, though, in terms of length in the X direction, the callout indicates “Either 3.5 or 5.0 inch.” The junction between the rib and deck is a line in the Z direction. Two lines parallel to this are shown on the deck plate spaced “t subscript deck” from each other. Two similar parallel lines are drawn up the rib spaced “t subscript rib” away from each other.

Figure 14. Illustration. Meshed specimen. This illustration shows the finite element mesh on a specimen with the same isometric view as described in figure 13. The entire deck plate has a grid of 6 elements across the width and 44 across the length. There are 12 elements on the rib across the width of the specimen and approximately the same size in the direction around the rib perimeter.

Figure 15. Illustration. Membrane stress in specimen under unit load. This illustration shows an isometric view of the entire specimen model shown deformed. The deck plate is oriented upper left to lower right and is arched upward in the deformed shape. The trapezoidal-shaped rib is atop the deck plate, and the rib legs are bent outward from the center of the specimen as displacement compatibility is enforced at the plate intersections. A rainbow-colored scale is used to show stress in the model, with blue representing the lowest stress and red representing the highest stress. The highest stresses are at the plate intersection at the midwidth of the specimen.

Figure 16. Illustration. Extrapolation points from rib and deck plate. This illustration shows a close-up view of the finite element model mesh near the rib and deck plate intersection. The intersection runs diagonally across the illustration from lower left to upper right. The mesh on the deck plate is 6 elements wide across the intersection and 12 elements wide for the rib plate. All elements are approximately square to indicate mesh size along the length of each plate. Four black points are shown at the midpoint of four elements and are all at the midwidth of the specimen. One point on the second deck element away from the plate intersection is labeled “open parenthesis f subscript 1.5 closed parenthesis times deck.” The second point is the first deck element away from the plate intersection labeled “open parenthesis f subscript 0.5 closed parenthesis times deck.” The third point is the first rib element away from the plate intersection labeled “open parenthesis f subscript 0.5 closed parenthesis rib.” The fourth point is the second rib element away from the plate intersection labeled “open parenthesis f subscript 1.5 closed parenthesis deck.” The mesh is overlaid with membrane stress contours using a rainbow color palette ranging from 0.0 ksi represented by blue transitioning to green, to yellow, to orange, and ending at red representing 9.0 ksi. The areas around the extrapolations points have stress ranging from 3.75 to 8.25 ksi.

Figure 17. Photo. Macro of specimen SA4-2 (example of open root condition). This photo shows a macro of specimen SA4-2. The rib-to-deck weld is centered in the photo. The deck plate is running horizontally across the bottom, though only about half of the thickness is shown. The rib plate runs from the upper right to the center of the deck plate. The rib plate edge was not prepared before welding. The weld has approximately 70 percent penetration, and there is a large gap between the inside corner of the rib plate and the deck plate.

Figure 18. Photo. Macro of specimen SA6-1 (example of closed root condition). This photo shows a macro of specimen SA6-1. The rib-to-deck weld is centered in the photo. The deck plate is running horizontally across the bottom, though only about half the thickness is shown. The rib plate runs from the upper right to the center of the deck plate. The rib plate edge was not prepared before welding. The weld has approximately 70 percent penetration, and while the inside corner of the rib plate is unfused, it has clearly been compressed into the deck plate from weld shrinkage.

Figure 19. Photo. Macro of specimen W-1. This photo shows a macro of specimen W-1. The rib-to-deck weld is centered in the photo. The deck plate is running horizontally across the bottom, though only about half the thickness is shown. The rib plate runs from the upper right to the center of the deck plate. The rib plate edge is beveled to sit flat on the deck plate. The weld has approximately 30 percent penetration, and while the rib plate is beveled, the unfused area between the two plates can only be seen as a thin line, which indicates that the two plates are likely in contact.

Figure 20. Photo. Macro of specimen W-11. This photo shows a macro of specimen W-11. The rib-to-deck weld is centered in the photo. The deck plate is running horizontally across the bottom, though only about half the thickness is shown. The rib plate runs from the upper left to the center of the deck plate. The rib plate edge is beveled to sit flat on the deck plate. The weld has approximately 30 percent penetration, and while the rib plate is beveled, there is a gap between the unfused area of the rib and deck plate.

Figure 21. Graph. Plot of all R = −1 data. This graph shows a plot of all R = −1 data. It has a logarithmic x-axis that shows cycles to failure that ranges from 0.1 to 100 in millions. The logarithmic y-axis shows local structural stress (LSS) range that ranges from 1 to 100 ksi. The American Association of State and Highway Transportation Officials fatigue resistance categories B, C, and D are solid black lines sloping downward from left to right. All data points except one are banded horizontally across the graph between 20,000 and 10 million on the x-axis and between 20 and 60 ksi on the y-axis. Most important in the figure is a heavy solid line indicating that the lower bound resistance is just above category B. In the legend, the boxes represent R = −1, the solid line represents R = −1 (95 percent confidence), and the arrow lines represent runout.

Figure 22. Graph. Plot of all R = 0 data. This graph shows a plot of all R = 0 data. It has a logarithmic x-axis that shows cycles to failure that ranges from 0.1 to 100 in millions. The logarithmic y-axis shows local structural stress (LSS) range that ranges from 1 to 100 ksi. The American Association of State and Highway Transportation Officials fatigue resistance categories B, C, and D are solid black lines sloping downward from left to right. All data points except one are banded horizontally across the graph between 15,000 and 2 million on the x-axis and between 25 and 45 ksi on the y-axis. One runout data point is at 20 million on the y-axis and 40 ksi on the y-axis. Most important in the figure is a heavy solid line indicating that the lower bound resistance is just below category C. In the legend, the circles represent R = 0, the solid line represents R = 0 (95 percent confidence), and the arrow lines represent runout.

Figure 23. Graph. Plot of all root failure (R = −1). This graph shows a plot of all root failure where R = −1. It has a logarithmic x-axis that shows cycles to failure that ranges from 0.1 to 100 in millions. The logarithmic y-axis shows local structural stress (LSS) range at weld root that ranges from 1 to 100 ksi. The American Association of State and Highway Transportation Officials fatigue resistance categories B, C, and D are solid black lines sloping downward from left to right. All data points are banded horizontally across the graph between 50,000 and 7 million on the x-axis and between 30 and 40 ksi on the y-axis. Most important in the figure is a heavy solid line indicating that the lower bound resistance is just above category B. In the legend, the triangles represent root failures (R = −1) and the solid line represents root failure (95 percent confidence).

Figure 24. Graph. Plot of all R = 0 data sorted by penetration. This graph shows a plot of all R = 0 data sorted by penetration. It has a logarithmic x-axis that shows cycles to failure that ranges from 0.1 to 100 in millions. The logarithmic y-axis shows local structural stress (LSS) range that ranges from 1 to 100 ksi. The American Association of State and Highway Transportation Officials fatigue resistance categories B, C, and D are solid black lines sloping downward from left to right. All data points are banded horizontally across the graph between 10,000 and 20 million on the x-axis and between 20 and 40 ksi on the y-axis. Most important in the figure are heavy solid lines indicating the lower bound resistance for each of the three datasets: penetration less than 60 percent, penetration between 60 and 80 percent, and penetration greater than 80 percent. For the penetration less than 60 percent data, the line is just above category B. For the other two datasets, the lines are almost on top of each other at approximately one-third of the way between categories C and B. In the legend, the squares represent penetration < 60 percent, the circles represent 60 percent ≤ penetration < 80 percent, the triangles represent penetration ≥ 80 percent, and the arrow lines represent runout.

Figure 25. Graph. Plot of all fatigue data differentiated by welding process. This graph shows a plot of all fatigue data differentiated by welding process. It has a logarithmic x-axis that shows cycles to failure that ranges from 0.1 to 100 in millions. The logarithmic y-axis shows local structural stress (LSS) range that ranges from 1 to 100 ksi. The American Association of State and Highway Transportation Officials fatigue resistance categories B, C, and D are solid black lines sloping downward from left to right. All data points are banded horizontally across the graph between 10,000 and 20 million on the x-axis and between 20 and 45 ksi on the y-axis. Most important in the figure are heavy solid lines indicating the lower bound resistance of the laser welded specimens and all other specimens. The laser specimen line is one-third of the way between categories C and B, and the line for the rest of the data is slightly less than category B. In the legend, the squares represent HLAW specimens, the circles represent all other specimens, and the arrow lines represent runout.

Figure 26. Graph. Relation between rib and deck plate leg sizes at R = −1. This graph shows the relation between the rib and deck plate leg sizes at R = −1. The x-axis shows normalized leg dimension on deck plate that ranges from 0.0 to 1.8. The y-axis shows normalized leg dimension on the rib plate that ranges from 0.0 to 1.8. All data are evenly distributed through the central part of the graph between the bounds of 0.3 and 1.3 on the x-axis and 0.5 and 1.3 on the y-axis. In the legend, the largest circle represents A = 2,000 ksi³, the second-largest circle represents A = 1,000 ksi³, the third-largest circle represents A = 500 ksi³, and the smallest circle represents A = 250 ksi³.

Figure 27. Graph. Relation between rib and deck plate leg sizes at R = 0. This graph shows the relation between the rib and deck plate leg sizes at R = 0. The x-axis shows normalized leg dimension on deck plate that ranges from 0.0 to 1.8. The y-axis shows normalized leg dimension on the rib plate that ranges from 0.0 to 1.8. All but three data points are clustered between the bounds of 0.4 and 1.2 on the x-axis and 0.8 and 1.2 on the y-axis. Three data points away from the major population are clustered around 0.35 on the x-axis and 0.6 on the y-axis. In the legend, the largest circle represents A = 1,500 ksi³, the second-largest circle represents A = 750 ksi³, the third-largest circle represents A = 375 ksi³, and the smallest circle represents A = 188 ksi³.

Figure 28. Graph. Relation between weld penetration and deck plate leg size at R = −1. This graph shows the relation between weld penetration and deck plate leg size at R = −1. The x-axis shows normalized leg dimension on deck plate that ranges from 0.0 to 1.8. The y-axis shows normalized weld penetration that ranges from 0.0 to 1.8. The data follow a downward left-to-right band bounded by values of 1.5 and 1.8 on each of the two axes. In the legend, the largest circle represents A = 2,000 ksi³, the second-largest circle represents A = 1,000 ksi³, the third-largest circle represents A = 500 ksi³, and the smallest circle represents A = 250 ksi³.

Figure 29. Graph. Relation between weld penetration and deck plate leg size at R = 0. This graph shows the relation between weld penetration and deck plate leg size at R = 0. The x-axis shows normalized leg dimension on deck plate that ranges from 0.0 to 1.8. The y-axis shows normalized weld penetration that ranges from 0.0 to 1.8. All but three data points are clustered between the bounds of 0.3 and 0.9 on the x-axis and 0.8 and 1.2 on the y-axis. Three data points away from the major population are evenly distributed between 1.1 and 1.4 on the x-axis and all around 0.6 on the y-axis. In the legend, the largest circle represents A = 1,500 ksi³, the second-largest circle represents A = 750 ksi³, the third-largest circle represents A = 375 ksi³, and the smallest circle represents A = 188 ksi³.

Figure 30. Graph. Relation between throat and deck plate leg sizes at R = −1. This graph shows the relation between throat and deck plate leg sizes at R = −1. The x-axis shows normalized leg dimension on deck plate that ranges from 0.0 to 1.8. The y-axis shows normalized throat and ranges from 0.0 to 1.8. The majority of the data is banded between values of 0.5 and 1.3 on the x-axis and 0.7 and 1.2 on the y-axis. A smaller population of eight data points is clustered around 0.4 on the x-axis and 1.5 on the y-axis. In the legend, the largest circle represents A = 2,000 ksi³, the second-largest circle represents A = 1,000 ksi³, the third-largest circle represents A = 500 ksi³, and the smallest circle represents A = 250 ksi³.

Figure 31. Graph. Relation between throat and deck plate leg sizes at R = 0. This graph shows the relation between throat and deck plate leg sizes at R = 0. The x-axis shows normalized leg dimension on deck plate that ranges from 0.0 to 1.8. The y-axis shows normalized throat that ranges from 0.0 to 1.8. All but three data points are clustered in a circle in the middle of the graph between the bounds of 0.6 and 1.2 on each axis. Three outlier data points are at approximately 0.6 on the y-axis and distributed evenly between 1.4 and 1.7 on the x-axis. In the legend, the largest circle represents A = 1,500 ksi³, the second-largest circle represents A = 750 ksi³, the third-largest circle represents A = 375 ksi³, and the smallest circle represents A = 188 ksi³.

Figure 32. Graph. Relation between weld penetration and throat at R = −1. This graph shows the relation between weld penetration and throat at R = −1. The x-axis shows normalized throat that ranges from 0.0 to 1.8. The y-axis shows normalized weld penetration that ranges from 0.0 to 1.8. Data points are open circles clustered along a line anchored by point coordinates of normalized throat equal to 0.7 and normalized weld penetration of 0.3 and on the other end by normalized throat equal to 1.7 and normalized weld penetration of 1.4. In the legend, the largest circle represents A = 2,000 ksi³, the second-largest circle represents A = 1,000 ksi³, the third-largest circle represents A = 500 ksi³, and the smallest circle represents A = 250 ksi³.

Figure 33. Graph. Relation between weld penetration and throat at R = 0. This graph shows the relation between weld penetration and throat at R = 0. The x-axis shows normalized throat that ranges from 0.0 to 1.8. The y-axis shows normalized weld penetration that ranges from 0.0 to 1.8. Data points are open circles clustered along a line anchored by point coordinates of normalized throat equal to 0.3 and normalized weld penetration of 0.8 and on the other end by normalized throat equal to 1.4 and normalized weld penetration of 1.7. In the legend, the largest circle represents A = 1,500 ksi³, the second-largest circle represents A = 750 ksi³, the third-largest circle represents A = 375 ksi³, and the smallest circle represents A = 188 ksi³.

Figure 34. Equation. General regression function. A subscript i equals open parenthesis quantity A tilde times product from j equals 1 to p of x subscript ij superscript beta subscript j times closed parenthesis times epsilon subscript i.

Figure 35. Equation. Linear regression function. Log base 10 of A subscript i equals log base 10 of A tilde plus the summation from j equals 1 to p of beta subscript j times log base 10 of x subscript ij plus log base 10 of epsilon subscript i.

Figure 36. Equation. Standard least squares regression error function. E subscript LS equals the summation of the entire squared quantity of open parenthesis log base 10 of A subscript i minus log base 10 of A tilde minus summation from j equals 1 to p of beta subscript j times log base 10 of x subscript ij closed parenthesis.

Figure 37. Graph. Standard regression cross-validation error. This graph shows the standard regression cross-validation error. The x-axis shows number of model variables that ranges from 0 to 20. The y-axis shows cross-validation mean square error and ranges from 0.03 to 0.13. The graph starts near the upper left and quickly drops to a value of 0.04 for a six-parameter model. The graph stays fairly flat from the 6- to 19-parameter model.

Figure 38. Equation. Least squares regression final predictive model. Log base 10 of A equals 11.2 minus 0.513 times alpha subscript 1 plus 1.44 times log base 10 times the quantity open parenthesis d subscript 1 divided by d subscript 4 closed parenthesis minus 0.414 times alpha subscript 2 plus 0.960 log base 10 times the quantity of open parenthesis d subscript 2 divided by d subscript 4 closed parenthesis.

Figure 39. Equation. Simplified least squares regression final predictive model. A equals 1585e8 ksi cubed times 0.307 raised to the alpha subscript 1 power times 0.385 raised to the alpha subscript 2 power times the quantity of open parenthesis d subscript 1 divided by d subscript 4 closed parenthesis raised to the 1.44 power times the quantity of open parenthesis d subscript 2 divided by d subscript 4 closed parenthesis raised to the 0.960 power.

Figure 40. Graph. Normal probability plot of standard regression studentized residuals. This graph shows a normal probability plot of standard regression studentized residuals. The x-axis shows theoretical quantiles that ranges from −3 to 3. The y-axis shows sample quantiles that ranges from −3 to 3. A solid data black line is drawn from the lower left to the upper right. There are two datasets: square data points for load reversal data and circles for tension only data. Data points from both sets closely follow the solid black line.

Figure 41. Histogram. Distribution of model residuals. This bar chart histogram shows the distribution of model residuals. The x-axis shows residual in log space that ranges from −0.6 to 0.6. The y-axis shows probability density that ranges from 0.0 to 2.5. The bars look normally distributed between −0.3 and 0.3 on the x-axis and a peak frequency of about 2.5. A solid red line shows the fitted normal distribution, and a dashed green line shows the fitted cross-validation mean square error fit, both which are a smoothed symmetric function between −0.6 and 0.6 on the x-axis with a peak of 2.0.

Figure 42. Equation. Design fatigue resistance coefficient. Log base 10 of A subscript D is less than or equal to 11.2 minus 0.513 times alpha subscript 1 minus 0.414 times alpha subscript 2 plus 1.44 times log base 10 of open parenthesis d subscript 1 divided by d subscript 4 closed parenthesis plus 0.960 times log base 10 of open parenthesis d subscript 2 divided by d subscript 4 closed parenthesis minus 2 times 0.207.

Figure 43. Equation. Simplified design fatigue resistance coefficient. A subscript D is less than or equal to open parenthesis 187e08 ksi cubed closed parenthesis times 0.385 raised to the alpha subscript 2 power times the quantity of open parenthesis d subscript 1 divided d subscript 4 closed parenthesis raised to the 1.44 power times the quantity of open parenthesis d subscript 2 divided d subscript 4 closed parenthesis raised to the 0.960 power.

Figure 44. Equation. Design weld-dimension inequality. The quantity of open parenthesis A subscript D divided by 187e08 ksi cubed closed parenthesis raised to the 1.04 power times the quantity of open parenthesis d subscript 1 divided by d subscript 4 closed parenthesis raised to the −1.5 power is less than or equal to the quantity of open parenthesis d subscript 2 divided by d subscript 4 closed parenthesis.

Figure 45. Equation. Final design weld-dimension inequality. k times the quantity of open parenthesis d subscript 1 divided by d subscript 4 closed parenthesis raised to the −1.5 power is less than or equal to the quantity of open parenthesis d subscript 2 divided by d subscript 4 closed parenthesis.

Figure 46. Scatterplot. Weld design inequality. This graph shows weld design inequality. The x-axis shows d sub 1 slash d sub 4 that ranges from 0.2 to 1.3. The y-axis shows weld penetration that ranges from 0.3 to 1.0. Solid data points represent zero load ratio data, and open data points represent a load ratio of −1 data. Both datasets are lumped together on a band from the upper left to lower right of the plot. There are two legends. In the first legend, the load ratio equals 0, the large solid circle represents category A, the medium solid circle represents category B, and the small solid circle represents category C. In the second legend, the load ratio equals −1, the large hollow circle represents category A, and the small hollow circle represents category B.

Figure 47. Histogram. Frequency of h‑to‑d₁ ratio in experimental specimens. This bar chart histogram shows the frequency of h-to-d subscript 1 ratio in experimental specimens. The x-axis shows h slash d sub 1 that ranges from 0.0 to 3.5. The y-axis shows frequency that ranges from 0 to 40. The data are normally distributed between 0.5 and 2.0 on the x-axis and reach a peak frequency of about 30. The exception is one large bar with a frequency of about 35 at an h/d₁ of 1.7.

Figure 48. Illustration. Comparison of minimum weld dimensions for categories C or B fatigue design. This figure shows two illustrations that depict close-up views of a rib-to-deck joint. Each joint shows hypothetical weld volumes where the cross-hatched area defines the minimum weld size, and the hatched area is the maximum weld size. The joint on the left is labeled “Category C,” and the joint on the right is labeled “Category B.” Comparing the left and right joints, the left joint has a leg length on the deck plate roughly equal to the penetration distance and roughly double the penetration distance on the right joint. In terms of leg length on the rib, the left joint is approximately one rib thickness, and the right joint is approximately 2.5 rib thicknesses.

Figure 49. Illustration. GM8 series panel. This illustration shows a cross sectional view of the GM8 panel geometry on the left of the illustration. Callouts are provided on the cross section indicating that the rib thickness is 0.3125 inch, the deck plate thickness is 0.75 inch, and the type 1 rib geometry is used. The right side of the illustration shows an elevation of the panel with the labeling of the specimens that were cut out. The overall panel was saw-cut 32.5 inches from the left edge, creating a left and right section. The left section was further cut every 4.25 inches from its right edge, defining specimens labeled sequentially (left to right) GM8-2 through GM8-14 in increments of two. The right section was further cut every 4.25 inches from its left edge defining specimens labeled sequentially (right to left) GM8-1 through GM8-15 in increments of two. The last specimen, GM8-16, was to the right of GM8-15.

Figure 50. Illustration. SA8 series panel. This illustration shows a cross sectional view of the SA8 panel geometry on the left of the illustration. Callouts are provided on the cross section indicating that the rib thickness is 0.3125 inch, the deck plate thickness is 0.75 inch, and the type 1 rib geometry is used. The right side of the illustration shows an elevation of the panel with the labeling of the specimens that were cut out. The overall panel width was thermally cut in half. The left side of the elevation view is labeled “south,” and the first cut is 4.25 inches from the left edge. The remaining cuts are spaced every 4.25 inches to the right, and the specimens are labeled sequentially (left to right) starting with SA8-1 through SA8-7 in increments of one. The right side of the elevation view is labeled “north,” and the first cut is 4.25 inches from the right edge. The remaining cuts are spaced every 4.25 inches to the left, and the specimens are labeled sequentially (right to left) starting with SA8-9 through SA8-16 in increments of one.

Figure 51. Illustration. SA6 series panel. This illustration shows a cross sectional view of the SA6 panel geometry on the left of the illustration. Callouts are provided on the cross section indicating that the rib thickness is 0.3125 inch, the deck plate thickness is 0.75 inch, and the type 1 rib geometry is used. The right side of the illustration shows an elevation of the panel with the labeling of the specimens that were cut out. The first cut is 2 inches from the right edge, and the remaining cuts are spaced every 4.25 inches to the left. Specimens are labeled sequentially (right to left) as SA6-8, SA6-6, SA6-4, SA6-2, SA6-1, SA6-3, SA6-5, and SA6-7.

Figure 52. Illustration. SA4 series panel. This illustration shows a cross sectional view of the SA4 panel geometry on the left of the illustration. Callouts are provided on the cross section indicating that the rib thickness is 0.3125 inch, the deck plate thickness is 0.75 inch, and the type 1 rib geometry is used. The right side of the illustration shows an elevation of the panel with the labeling of the specimens that were cut out. The first cut is 2 inches from the left edge, and the remaining cuts are spaced every 4.25 inches to the right. Specimens are labeled sequentially (left to right) as SA4-7, SA4-5, SA4-3, SA4-1, SA4-2, SA4-4, SA4-6, and SA2-8.

Figure 53. Illustration. SA2 series panel. This illustration shows a cross sectional view of the SA2 panel geometry on the left of the illustration. Callouts are provided on the cross section indicating that the rib thickness is 0.3125 inch, the deck plate thickness is 0.75 inch, and the type 1 rib geometry is used. The right side of the illustration shows an elevation of the panel with the labeling of the specimens that were cut out. The first cut is 2 inches from the right edge, and the remaining cuts are spaced every 4.25 inches to the left. Specimens are labeled sequentially (right to left) as SA2-8, SA2-6, SA2-4, SA2-2, SA2-1, SA2-3, SA2-5, and SA2-7.

Figure 54. Illustration. FIL series panel. This illustration shows a cross sectional view of the FIL panel geometry on the left of the illustration. Callouts are provided on the cross section indicating that the rib thickness is 0.3125 inch, the deck plate thickness is 0.75 inch, and the type 1 rib geometry is used. The right side of the illustration shows an elevation of the panel with the labeling of the specimens that were cut out. The first cut is 2 inches from the right edge, and the remaining cuts are spaced every 4.25 inches to the left. Specimens are labeled sequentially (right to left) as FIL-8, FIL-6, FIL-4, FIL-2, FIL-1, FIL-3, FIL-5, and FIL-7.

Figure 55. Illustration. LP1 series panel. This illustration shows a cross sectional view of the LP1 panel geometry on the left of the illustration. Callouts are provided on the cross section indicating the rib thickness is 0.3125 inch, the deck plate thickness is 0.75 inch, and the type 1 rib geometry is used. The right side of the illustration shows an elevation of the panel with the labeling of the specimens that were cut out. The overall panel width was thermally cut in half. The left side of the elevation view is labeled “south,” and the first cut is 3.25 inches from the left edge. The remaining cuts are spaced every 4.25 inches to the right, and the specimens are labeled sequentially (left to right) starting with LP1-1 through LP1-7 in increments of one. The right side of the elevation view is labeled “north,” and the first cut is 3.25 inches from the right edge. The remaining cuts are spaced every 4.25 inches to the left, and the specimens are labeled sequentially (right to left) starting with LP1-15 down through LP1-8 in increments of one. A plan view of the panel of the illustration shows that specimen LP1-1 has excess penetration on both rib legs, specimen LP1-7 has excess penetration on one leg, specimen LP1-8 has excess penetration on both legs, and specimens LP1-14 and LP1-15 have insufficient penetration on one rib leg.

Figure 56. Illustration. LP2 series panel. This illustration shows a cross sectional view of the LP2 panel geometry on the left of the illustration. Callouts are provided on the cross section indicating that the rib thickness is 0.3125 inch, the deck plate thickness is 0.75 inch, and the type 1 rib geometry is used. The right side of the illustration shows an elevation of the panel with the labeling of the specimens that were cut out. The overall panel width was thermally cut in half. The left side of the elevation view is labeled “south,” and the first cut is 3.25 inches from the left edge. The remaining cuts are spaced every 4.25 inches to the right, and the specimens are labeled sequentially (left to right) starting with LP2-1 through LP2-7 in increments of one. The right side of the elevation view is labeled “north,” and the first cut is 4.25 inches from the right edge. The remaining cuts are spaced every 4.25 inches to the left, and the specimens are labeled sequentially (right to left) starting with LP2-13 through LP2-8 in increments of one. A plan view of the panel shows that specimen LP2-1 has insufficient penetration on one leg and excess penetration on the other, specimen LP2-7 has excess penetration on one leg, and specimen LP2-13 has excess penetration on one leg.

Figure 57. Illustration. LP3 series panel. This illustration shows a cross sectional view of the LP3 panel geometry on the left of the illustration. Callouts are provided on the cross section indicating that the rib thickness is 0.3125 inch, the deck plate thickness is 0.75 inch, and the type 1 rib geometry is used. The right side of the illustration shows an elevation of the panel with the labeling of the specimens that are cut out. The overall panel width is thermally cut in half into two pieces. The left side of the elevation view is labeled “south,” and the first cut is 4.25 inches from the left edge. The remaining cuts are spaced every 4.25 inches to the right, and the specimens are labeled sequentially (left to right) starting with LP3-0 through LP3-6 in increments of one. The right side of the elevation view is labeled “north,” and the first cut is 4.25 inches from the right edge. The remaining cuts are spaced every 4.25 inches to the left, and the specimens are labeled sequentially (right to left) starting with LP3-13 through LP3-7 in increments of one. A plan view of the panel shows that specimens LP3-0 and LP3-13 are considered scrap sections because they represent the beginning and termination of welding. One side of LP3-7 and LP3-8 have insufficient penetration.

Figure 58. Illustration. OB series panel. This illustration shows a cross sectional view of the OB panel geometry on the left of the illustration. Callouts are provided on the cross section indicating that the rib thickness is 0.3125 inch, the deck plate thickness is 0.75 inch, and the type 2 rib geometry is used. The right side of the illustration shows an elevation of the panel with the labeling of the specimen that is cut out. The overall panel length is 72 inches, and the first cut is 1.5 inches from the left edge. The remaining cuts are spaced every 4.25 inches, and the specimens are labeled sequentially (left to right) starting with OB-1 through OB-16 in increments of one.

Figure 59. Illustration. UB series panel. This illustration shows a cross sectional view of the UB panel geometry on the left of the illustration. Callouts are provided on the cross section indicating that the rib thickness is 0.3125 inch, the deck plate thickness is 0.75 inch, and the type 2 rib geometry is used. The right side of the illustration shows an elevation of the panel with the labeling of the specimen that is cut out. The overall panel length is 72 inches, and the first cut is 1.5 inches from the left edge. The remaining cuts are spaced every 4.25 inches, and the specimens are labeled sequentially (left to right) starting with UB-1 through UB-16 in increments of one.

Figure 60. Illustration. OG1 series panel. This illustration shows a cross sectional view of the OG1 panel geometry on the left of the illustration. Callouts are provided on the cross section indicating that the rib thickness is 0.3125 inch, the deck plate thickness is 0.625 inch, and the type 3 rib geometry is used. The right side of the illustration shows an elevation of the panel with the labeling of the specimen that was cut out. The overall panel length is 72 inches, and the first cut is 1.5 inches from the left edge. The remaining cuts are spaced every 4.25 inches, and the specimens are labeled sequentially (left to right) starting with OG-1 through OG-16 in increments of one.

Figure 61. Illustration. OG2 series panel. This illustration shows a cross sectional view of the OG2 panel geometry on the left of the illustration. Callouts are provided on the cross section indicating that the rib thickness is 0.3125 inch, the deck plate thickness is 0.625 inch, and the type 3 rib geometry is used. The right side of the illustration shows an elevation of the panel with the labeling of the specimen that was cut out. The overall panel length is 2 inches, and the first cut is 1.5 inches from the left edge. The remaining cuts are spaced every 4.25 inches, and the specimens are labeled sequentially (left to right) starting with OG-17 through OG-32 in increments of one.

Figure 62. Illustration. W series panel. This illustration shows a cross sectional view of the W series panel geometry on the left of the illustration. Callouts are provided on the cross section indicating that the rib thickness is 0.3125 inch, the deck plate thickness is 0.625 inch, and the type 3 rib geometry is used. The right side of the illustration shows an elevation of the panel with the labeling of the specimen that is cut out. The overall panel length is 72 inches, and the first cut is 1.5 inches from the left edge. The remaining cuts are spaced every 4.25 inches, and the specimens are labeled sequentially (left to right) starting with W-1 through W-16 in increments of one.

Figure 63. Schematic. Denotation of weld locations. This illustration shows an isometric view of a test specimen. The deck plate is horizontal and projected inward. The rib is trapezoidal in shape and is centered on the deck plate with the larger width of the trapezoid against the deck plate. The near right intersection of the rib and deck plate is labeled “1,” and the far right intersection of the rib and deck plate is labeled “3.” The near left intersection of the rib and deck plate is labeled “2,” and the far left intersection of the rib and deck plate is labeled “4.” A callout to the right intersection of the deck plate between 1 and 3 is labeled “fatigue crack.”

Figure 64. Schematic. Measured dimensions. This illustration shows a close-up elevation view of the rib-to-deck weld cross section. The deck plate is oriented horizontally, and the rib plate is inclined off the deck plate to the upper left. Nine dimensions are shown in the illustration relating to the weld size. The dimension d sub 1 is shown as the hypothetical intersection of the outer rib face on the deck and the outer weld toe on the deck. The dimension d sub 2 is shown as the hypothetical intersection of the outer rib face on the deck and the weld root. The dimension d sub 3 is the distance between the weld root and the shown as the hypothetical intersection of the inner rib face on the deck. The dimension d sub 4 is shown as the hypothetical horizontal projection distance of the rib plate thickness on the deck plate. The dimension d sub 5 is shown as the hypothetical intersection of the inner rib face on the deck to the outer weld toe on the deck. The dimension h is the distance between the hypothetical intersection of the outer rib plate surface with the deck plate and the weld toe on the rib. The dimension h sub 1 is the distance between the rib weld toe and the original end of the outer rib surface. The dimension h sub 2 is shown as the hypothetical original face gap. Finally, the dimension t is shown at the minimized distance between the real weld root and the curved face of the weld.

Figure 65. Schematic. Denotation of weld locations for laser panel specimens. This illustration shows an isometric view of a test specimen. The deck plate is horizontal and projected inward. The rib is trapezoidal in shape and is centered on the deck plate with the larger width of the trapezoid against the deck plate. The right intersection of the rib and deck plate is labeled “1,” and the left intersection of the rib and deck plate is labeled “2.” A callout to the right intersection of the deck plate is labeled “fatigue crack.”

Figure 66. Schematic. Measured dimensions for laser panel specimens. This illustration shows a close-up elevation view of the rib-to-deck weld cross section. The deck plate is oriented horizontally, and the rib plate is inclined off the deck plate to the upper left. Five dimensions are shown in the drawing. The dimension d sub 2 is shown as the distance between the inner and outer weld toes on the deck plate. The dimension d sub 4 is shown as the hypothetical horizontal projection distance of the rib plate thickness on the deck plate. The dimension d sub 1 is the distance between the hypothetical intersection of the outer rib plate surface with the deck plate and out weld toe on the deck plate. The dimension h is the distance between the hypothetical intersection of the outer rib plate surface with the deck plate and the weld toe on the rib. Finally, the dimension t is shown at the minimized distance between the inner weld toe on the deck plate and the curve face of the weld.