Curved Girder Behavior & Design - H-B-S.org

1 Curved Girder Behavior & DesignCurved Steel Girder BridgesPDF Created with deskPDF PDF Writer - Trial :: Steel Girder DesignL1L2 OUTSIDEGIRDERL ABUTL PIERL ABUTCCCINSIDEGIRDERCROSSFRAMERADIUSCURVE D BRIDGE - PLAN VIEWdPDF Created with deskPDF PDF Writer - Trial :: R > 1000 20 500 < R < 1000 17 200 < R < 500 15 R < 200 Max. Diaphragm SpacingCenterline RadiusCrossframe SpacingPDF Created with deskPDF PDF Writer - Trial :: Steel Girder DesignDesign Forces (per specification) Primary Bending Forces Cross Frame Forces (Primary Members) Lateral Flange Moments Secondary Bending ForcesPDF Created with deskPDF PDF Writer - Trial :: by Cross FrameTop FlangeCross frameCompressionCompressionTensionTensio nBottom FlangeCurved Steel Girder DesignPDF Created with deskPDF PDF Writer - Trial :: FlangeTop FlangeCross frameCurved Steel Girder DesignPDF Created with deskPDF PDF Writer - Trial :: Steel Girder DesignPDF Created with deskPDF PDF Writer - Trial.

2 Steel Girder DesignPDF Created with deskPDF PDF Writer - Trial :: Steel Girder DesignPDF Created with deskPDF PDF Writer - Trial :: Has Changed over the Years?What Has Changed over What Has Changed over the Years?the Years? Curved Steel Girder Bridges Analysis MethodsAnalysis Methods Yield StrengthsYield Strengths Frequency of highly Curved Frequency of highly Curved and/or skewed bridgesand/or skewed bridgesPDF Created with deskPDF PDF Writer - Trial :: there is still a key aspect of Curved Girder Behavior that an engineer must understandBut there is still a key But there is still a key aspect of Curved aspect of Curved Girder Behavior that Girder Behavior that an engineer must an engineer must understandunderstandCurved Steel Girder BridgesPDF Created with deskPDF PDF Writer - Trial :: Created with deskPDF PDF Writer - Trial :: Created with deskPDF PDF Writer - Trial.

3 V-Load Method (Analysis) Curved Steel Girder BridgesPDF Created with deskPDF PDF Writer - Trial :: Steel Girder DesignPDF Created with deskPDF PDF Writer - Trial :: Steel Girder DesignPDF Created with deskPDF PDF Writer - Trial :: Steel Girder DesignCentral Angle Limit Primary Force Secondary Forces Lateral Flange MomentsSpan XSpan YBridge CenterlineWhen Subtended Angle ( ) is Less Than Code LimitSecondary Forces Neglected RPDF Created with deskPDF PDF Writer - Trial :: and Analysis of Curved and SkewedSteel Girder BridgesBehavior and Analysis of Curved and SkewedSteel Girder BridgesDomenic Coletti, PEJohn Yadlosky, PEDomenic Coletti, PEJohn Yadlosky, PEWorld Steel Bridge Symposium 2005 Orlando, FLWorld Steel Bridge Symposium 2005 Orlando, FLPDF Created with deskPDF PDF Writer - Trial :: of Analysis Three Levels of Analysis Approximate Analysis 2D ( Grid ) Analysis 3D AnalysisPDF Created with deskPDF PDF Writer - Trial :: of Analysis Issues Level of modeling detail / accuracy Level of modeling effort Amount of output Live load modelingPDF Created with deskPDF PDF Writer - Trial.

4 Of Analysis Live Load Modeling Multiple live load cases ( live load generator ) Influence line approach Influence surface approachPDF Created with deskPDF PDF Writer - Trial :: of Analysis Influence Surface ExamplesBSDI, Created with deskPDF PDF Writer - Trial :: of Analysis Influence Surface ExamplesBSDI, Created with deskPDF PDF Writer - Trial :: of Analysis Approximate Analysis Approximate Analysis Methods Line Girder + Factors V-Load Method: I - girders M/R Method: Tub GirdersPDF Created with deskPDF PDF Writer - Trial :: of Analysis Approximate Analysis Line Girder + Factors Any line Girder analysis tool can be used Factors from FHWA Curved Girder Workshop Approximate!

5 Good for preliminary Design FHWA Curved Girder Workshop Manual, 1976 PDF Created with deskPDF PDF Writer - Trial :: of Analysis Approximate Analysis V-Load Method For Curved I- girders Developed by USS in 1960s V-Loads are the shears in diaphragms Computer tools availableFHWA Curved Girder Workshop Manual, 1976 FHWA Curved Girder Workshop Manual, 1976 PDF Created with deskPDF PDF Writer - Trial :: of Analysis Approximate Analysis M/R Method For Curved Tub girders Developed by Tung and Fountain in 1970 Analogous to V-Load Very cumbersome for multiple Girder systemsTung and Fountain, 1970 PDF Created with deskPDF PDF Writer - Trial :: of Analysis 2D Grid Analysis What is a 2D Grid Analysis?

6 girders modeled as line elements Diaphragms modeled as line elements Deck modeled in strips as line elementsPDF Created with deskPDF PDF Writer - Trial :: of Analysis 2D Grid Analysis Grid Analysis Computer Tools MDX DESCUS I & II General FEM programs Others?PDF Created with deskPDF PDF Writer - Trial :: of Analysis 2D Grid Analysis Advantages of Grid Analysis Simple modeling Efficient (level of modeling effort) Some find it easier to understand Computer tools readily availablePDF Created with deskPDF PDF Writer - Trial :: of Analysis 2D Grid Analysis Disadvantages of Grid Analysis Diaphragm modeling Deck modeling Load Distribution In sum: Accuracy questions?

7 PDF Created with deskPDF PDF Writer - Trial :: of Analysis 2D Grid Analysis Grid Analysis is Not Recommended Severe curvature and/or skew Deep girders Long spans Variable depth girdersPDF Created with deskPDF PDF Writer - Trial :: of Analysis 3D Analysis What is a 3D Analysis? Flanges: beam or plate elements Webs: plate elements Diaphragms, bracing: truss or plate elements Deck: solid or plate elementsPDF Created with deskPDF PDF Writer - Trial :: of Analysis 3D Analysis 3D Analysis Computer Tools BSDI 3D System (limited LRFD capabilities) General FEM programs Others?PDF Created with deskPDF PDF Writer - Trial :: of Analysis 3D Analysis Advantages of 3D Analysis All pieces and parts modeled - rigorous Direct analysis results for all pieces and parts Greater refinement Greater accuracy (?)

8 PDF Created with deskPDF PDF Writer - Trial :: of Analysis 3D Analysis Disadvantages of 3D Analysis Greater modeling effort More complicated model Results less intuitive In sum: Is the refinement worth the effort?PDF Created with deskPDF PDF Writer - Trial :: of Analysis 3D Analysis Limitations of 3D Analysis Virtually no limitations on type or complexity of structures that can be modeled Limitations come down to time and moneyPDF Created with deskPDF PDF Writer - Trial :: Steel Girder Design Lay out framing plan Establish initial plate sizing philosophy Run line Girder Adjust plates for 3D Model Run 3D Model Resize plates Rerun 3D Model Design remaining Girder elementsDesign ProcessPDF Created with deskPDF PDF Writer - Trial :: & ConstructionDetailing & Detailing & ConstructionConstructionCurved Steel Girder BridgesPDF Created with deskPDF PDF Writer - Trial.

9 Created with deskPDF PDF Writer - Trial :: Issues Horizontal, Vertical and Rotational Camber Single I Girder Stability Erecting Curved girders Shipping and Handling Heat - CurvingPDF Created with deskPDF PDF Writer - Trial :: Created with deskPDF PDF Writer - Trial :: Created with deskPDF PDF Writer - Trial :: No toOversized Holes in Main (Geometry Controlling)Load Carrying Members!Say Say NoNo totoOversized Holes in Oversized Holes in Main Main (Geometry Controlling)(Geometry Controlling)Load Carrying Members!Load Carrying Members! Curved Steel Girder BridgesPDF Created with deskPDF PDF Writer - Trial :: 3 Girder 2 Girder 13/4"3/8"Maximum Horizontal Displacement3/8" : (1 1/16" - 7/8") 3/16" (1/2" Hole) x (4 Holes):PDF Created with deskPDF PDF Writer - Trial :: 3 Girder 2 Girder 13/4"3/8"Maximum Vertical DisplacementPDF Created with deskPDF PDF Writer - Trial :: 3 Girder 2 Girder 1 See Detail 1 See Detail 2 See Detail 3 DWG.

10 CT-010 See Detail 4 Maximum Displacement with RotationPDF Created with deskPDF PDF Writer - Trial :: OutsideTop Flange(Detail 1)Center GirderTop Flange(Detail 2) Girder 3 Girder " " Original Locationof Girder Original Locationof Bolt Holes7/8" Dia. BoltDisplaced & RotatedPosition8'-9" (Not to Scale) " " (See Note)PDF Created with deskPDF PDF Writer - Trial :: Warping Stresses and Associated Deflections During Lifting and Warping Consider Warping Stresses and Associated Stresses and Associated Deflections During Lifting Deflections During Lifting and Steel Girder BridgesPDF Created with deskPDF PDF Writer - Trial :: Created with deskPDF PDF Writer - Trial :: Created with deskPDF PDF Writer - Trial :: Created with deskPDF PDF Writer - Trial :: OrientationBearing OrientationBearing OrientationCurved Steel Girder BridgesPDF Created with deskPDF PDF Writer - Trial :: Created with deskPDF PDF Writer - Trial.