Behavior & Design. Curved Girder. Curved Steel Girder Bridges. PDF Created with deskpdf PDF Writer - Trial ::
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1 Curved Steel Girder Bridges Curved Girder Behavior & Design
2 Curved Steel Girder Design L1 L2 OUTSIDE GIRDER CROSS FRAME d C L PIER C L ABUT CL ABUT RADIUS INSIDE GIRDER CURVED BRIDGE - PLAN VIEW
3 Crossframe Spacing Centerline Radius Max. Diaphragm Spacing R < < R < < R < R >
4 Curved Steel Girder Design Design Forces (per specification) Primary Bending Forces Secondary Bending Forces Lateral Flange Moments Cross Frame Forces (Primary Members)
5 Curved Steel Girder Design Top Flange Cross frame Compression Tension Bottom Flange Unrestrained by Cross Frame Compression Tension
6 Curved Steel Girder Design Top Flange Cross frame Compression Tension Bottom Flange Compression Tension
7 Curved Steel Girder Design
8 Curved Steel Girder Design
9 Curved Steel Girder Design
10 Curved Steel Girder Bridges What Has Changed over the Years? Analysis Methods Yield Strengths Frequency of highly curved and/or skewed bridges
11 Curved Steel Girder Bridges But there is still a key aspect of curved girder behavior that an engineer must understand
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14 Curved Steel Girder Bridges The V-Load Method (Analysis)
15 Curved Steel Girder Design
16 Curved Steel Girder Design
17 Curved Steel Girder Design Central Angle Limit Primary Force Secondary Forces Lateral Flange Moments When Subtended Angle ( ) is Less Than Code Limit θ Secondary Forces Neglected Span X θ Span Y R Bridge Centerline
18 Behavior and Analysis of Curved and Skewed Steel Girder Bridges Domenic Coletti, PE John Yadlosky, PE World Steel Bridge Symposium 2005 Orlando, FL
19 Levels of Analysis Three Levels of Analysis Approximate Analysis 2D ( Grid ) Analysis 3D Analysis
20 Levels of Analysis Issues Level of modeling detail / accuracy Level of modeling effort Amount of output Live load modeling
21 Levels of Analysis Live Load Modeling Multiple live load cases ( live load generator ) Influence line approach Influence surface approach
22 Levels of Analysis Influence Surface Examples BSDI, Ltd.
23 Levels of Analysis Influence Surface Examples BSDI, Ltd.
24 Levels of Analysis Approximate Analysis Approximate Analysis Methods Line Girder + Factors V-Load Method: I -Girders M/R Method: Tub Girders
25 Levels of Analysis Approximate Analysis Line Girder + Factors Any line girder analysis tool can be used Factors from FHWA Curved Girder Workshop Approximate! Good for preliminary design FHWA Curved Girder Workshop Manual, 1976
26 Levels 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 available FHWA Curved Girder Workshop Manual, 1976 FHWA Curved Girder Workshop Manual, 1976
27 Levels 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 systems Tung and Fountain, 1970
28 Levels of Analysis 2D Grid Analysis What is a 2D Grid Analysis? Girders modeled as line elements Diaphragms modeled as line elements Deck modeled in strips as line elements
29 Levels of Analysis 2D Grid Analysis Grid Analysis Computer Tools MDX DESCUS I & II General FEM programs Others?
30 Levels 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 available
31 Levels of Analysis 2D Grid Analysis Disadvantages of Grid Analysis Diaphragm modeling Deck modeling Load Distribution In sum: Accuracy questions?
32 Levels of Analysis 2D Grid Analysis Grid Analysis is Not Recommended for Severe curvature and/or skew Deep girders Long spans Variable depth girders
33 Levels 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 elements
34 Levels of Analysis 3D Analysis 3D Analysis Computer Tools BSDI 3D System (limited LRFD capabilities) General FEM programs Others?
35 Levels 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 (?)
36 Levels 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?
37 Levels 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 money
38 Curved Steel Girder Design Design Process 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 elements
39 Curved Steel Girder Bridges Detailing & Construction
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41 Construction Issues Horizontal, Vertical and Rotational Camber Single I Girder Stability Erecting Curved Girders Shipping and Handling Heat - Curving
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44 Curved Steel Girder Bridges Say No to Oversized Holes in Main (Geometry Controlling) Load Carrying Members!
45 Girder 3 Girder 2 Girder 1 3/4" 3/8" Maximum Horizontal Displacement 3/8" : (1 1/16" - 7/8") 3/16" : (1/2" Hole) x (4 Holes)
46 Girder 3 Girder 2 Girder 1 3/4" 3/8" Maximum Vertical Displacement
47 Girder 3 Girder 2 Girder 1 See Detail 1 See Detail 2 See Detail 3 DWG. CT-010 See Detail 4 Maximum Displacement with Rotation
48 2.302 " Left Outside Top Flange (Detail 1) Girder 3 Girder 2 8'-9" 0.371" (Not to Scale) 0.191" Original Location of Girder Original Location of Bolt Holes 7/8" Dia. Bolt Displaced & Rotated Position Center Girder Top Flange (Detail 2) " (See Note)
49 Curved Steel Girder Bridges Consider Warping Stresses and Associated Deflections During Lifting and Handling.
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53 Curved Steel Girder Bridges Bearing Orientation
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55 Before Expansion Radial Line Tangent After Expansion Bearings A & C B All Other Pier End Support Pier End Support DIRECTION OF MOVEMENT Lineal in Horizontal Plane Tangential Radial Any Movements Arrested Radially Tangentially Tangent Radial Line Suggested Support Arrangement for Curved Girder Spans Minimize Number of Total Fixed Points Adjust for Longer Structures
56 Bearing Design Tips Use multi-rotational bearings Pot/spherical bearings Round laminated neoprene pads Restrain as few bearings as possible Restraint costs more Minimizes bearings locking up Minimizes concern over lateral restraint forces
57 Curved Steel Girder Bridges Some Thoughts on Cut Curving & Heat Curving
58 Curved Steel Girder Bridges Cut Curving
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62 Curved Steel Girder Bridges Heat Curving
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64 Curved Steel Girder Bridges FHWA/NCHRP Documents FHWA-IF Heat-Straightening Repairs of Damaged Steel Bridges (A Technical Guide and Manual of Practice) NCHRP Report 271 Guidelines for Evaluation and Repair of Damaged Steel Bridge Members
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68 Curved Steel Girder Bridges Review - Parts I & II: Cross Frames are Primary Members Lateral Flange Bending (Warping) / Wind Analysis Methods Holistic Approach Consider Construction During Design Account for ROTATIONS and Deflections No Oversized Holes
69 Curved Steel Girder Bridges Closing
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