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Understanding Skewed Bridge Behavior

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Skewed Bridge Behavior Out-of-plane effects occur in skewed bridges that cannot be predicted by one-dimensional (line girder) analysis methods.Out-of-plane effects occur in skewed bridges that cannot be predicted by one-dimensional (line girder) analysis methods. AASHTO/NSBA Guidelines for Design for Constructability identifies two separate issues:AASHTO/NSBA Guidelines for Design for Constructability identifies two separate issues: Intermediate Crossframe Effects Intermediate Crossframe Effects End Crossframe Effects End Crossframe Effects Both Intermediate and End Crossframe Effects will be examined using a test case.Both Intermediate and End Crossframe Effects will be examined using a test case.

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Test Case: 60° Skew, 150 ft Span FRAMING PLAN TRANSVERSE SECTION

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Analysis of Test Case, Line Girder Model: We will conduct an initial analysis of the test structure using a Line Girder Model. This is the most commonly used analysis method for non-complex bridges, and is used by many common software packages. (MDX, Merlin Dash, BARS-PC) Each girder is modeled independently, with crossframe effects ignored. Mz Line Girder Model:

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Test Structure, Deflection Due to Deck Weight Line Girder Analysis Results Crossframe Effects Ignored

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Line Girder Analysis Results Crossframe Effects Ignored Length (ft) Deflection (in) G2G1G3G4G5 Crossframe Locations Test Structure, Deflection Due to Deck Weight Results Show: Large differential deflections between interior and exterior girders Abrupt changes in differential deflection across the width of the bridge

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Line Girder Analysis Results Crossframe Effects Ignored Test Structure, Differential Deflections at Crossframe Locations:

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D D Section D-D Differential Deflection (in) Girder Deflection (in) Deflections Exaggerated x 12 Framing Plan Line Girder Analysis Results Crossframe Effects Ignored

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Problem: If the girders are assumed to stay vertical, the crossframes will not permit differential deflections of this magnitude.Problem: If the girders are assumed to stay vertical, the crossframes will not permit differential deflections of this magnitude. Conclusion: Crossframe interaction needs to be included to accurately model structure behavior.Conclusion: Crossframe interaction needs to be included to accurately model structure behavior. Line Girder Analysis Results Crossframe Effects Ignored Section A-A Differential Deflection (in) Girder Deflection (in) Deflections Exaggerated x 12

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We will now use a refined method to analyze the test structure with crossframe effects included. All intermediate crossframes are fully connected during the deck pour (no slotted holes). The end crossframes will be removed in order to isolate intermediate crossframe effects. The behavior of the bridge will be examined under wet concrete load only. FRAMING PLAN Intermediate Crossframe Effects

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ODOT Standard Crossframe: Typical crossframes restrain girders against differential deflection and differential twist.Typical crossframes restrain girders against differential deflection and differential twist.

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Differential vertical deflection causes crossframes to deform if the girders do not twist.Differential vertical deflection causes crossframes to deform if the girders do not twist. Large forces are needed to create axial deformations in the crossframe members, so resistance to this type of deflection is very high.Large forces are needed to create axial deformations in the crossframe members, so resistance to this type of deflection is very high. Lengthened Shortened

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Twisting of the girders allows differential deflection to occur without deforming the crossframe.Twisting of the girders allows differential deflection to occur without deforming the crossframe. Generally, the torsional stiffness of the girders is low compared to the stiffness of the crossframes, so this behavior is dominant.Generally, the torsional stiffness of the girders is low compared to the stiffness of the crossframes, so this behavior is dominant. Undeformed Undeformed

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Analysis of Test Case, Refined Model: In order to include crossframe effects in the analysis, we will need to use a Refined Model. Refined Model is a general term we will use to refer to any analysis that includes both the girders and the crossframes. Refined Models will be discussed in more detail in another presentation. Refined Model:

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Refined Analysis Results Intermediate Crossframe Effects Included Results Show: More uniform differential deflection across the width of the bridge at crossframe locations (compared to line girder analysis) Test Structure, Deflection Due to Deck Weight Crossframe Locations

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Refined Analysis Results Intermediate Crossframe Effects Included Test Structure, Deflection Due to Deck Weight Line Girder Analysis Results Crossframe Effects Ignored

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Refined Analysis Results Intermediate Crossframe Effects Included Test Structure, Differential Deflections at Crossframe Locations:

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D D Section D-D Differential Deflection (in) Girder Deflection (in) Deflections Exaggerated x 12 Framing Plan Refined Analysis Results Intermediate Crossframe Effects Included

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Section D-D Differential Deflection (in) Girder Deflection (in) Deflections Exaggerated x 12 Section D-D Differential Deflection (in) Girder Deflection (in) Line Girder Analysis Results Crossframe Effects Ignored

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The analysis results show that intermediate crossframe effects cause girder twist in skewed structures.The analysis results show that intermediate crossframe effects cause girder twist in skewed structures. The next several slides will step though the deflection of the test structure at each crossframe location.The next several slides will step though the deflection of the test structure at each crossframe location. Deflected Shape Due to Intermediate Crossframe Effects

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Deflected Shape Due to Intermediate Crossframe Effects (Refined Analysis): A A Deflections Exaggerated x 12 Section A-A Differential Vertical Deflection (inches)

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B B Deflections Exaggerated x 12 Deflected Shape Due to Intermediate Crossframe Effects (Refined Analysis): Section B-B Differential Vertical Deflection (inches)

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Deflections Exaggerated x 12 Section C-C C C Deflected Shape Due to Intermediate Crossframe Effects (Refined Analysis): Differential Vertical Deflection (inches)

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D D Deflections Exaggerated x 12 Section D-D Deflected Shape Due to Intermediate Crossframe Effects (Refined Analysis): Differential Vertical Deflection (inches)

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E E Deflections Exaggerated x 12 Section E-E Deflected Shape Due to Intermediate Crossframe Effects (Refined Analysis): Differential Vertical Deflection (inches)

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F F Deflections Exaggerated x 12 Section F-F Deflected Shape Due to Intermediate Crossframe Effects (Refined Analysis): Differential Vertical Deflection (inches)

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Deflections Exaggerated x 12 Section G-G G G Deflected Shape Due to Intermediate Crossframe Effects (Refined Analysis): Differential Vertical Deflection (inches)

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H H Deflections Exaggerated x 12 Section H-H Deflected Shape Due to Intermediate Crossframe Effects (Refined Analysis): Differential Vertical Deflection (inches)

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J J Deflections Exaggerated x 12 Deflected Shape Due to Intermediate Crossframe Effects (Refined Analysis): Section J-J Differential Vertical Deflection (inches)

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K K Deflections Exaggerated x 12 Deflected Shape Due to Intermediate Crossframe Effects (Refined Analysis): Section K-K Differential Vertical Deflection (inches)

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L L Deflections Exaggerated x 12 Section L-L Deflected Shape Due to Intermediate Crossframe Effects (Refined Analysis): Differential Vertical Deflection (inches)

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M M Deflections Exaggerated x 12 Section M-M Deflected Shape Due to Intermediate Crossframe Effects (Refined Analysis): Differential Vertical Deflection (inches)

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Animation of Deflection Under Wet Concrete Load with Intermediate Crossframe Effects Included (Exaggerated Scale):

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Deflected Shape Under Wet Concrete Load with Intermediate Crossframe Effects Included (Exaggerated Scale):

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Test Structure, Refined Analysis, Intermediate Crossframes Only: In a single span skewed structure, twist is generally highest at the supports.In a single span skewed structure, twist is generally highest at the supports. End twist for the test case is shown below.End twist for the test case is shown below. Definition of Girder Twist : Girder Twist due to Intermediate Crossframe Effects Sign Convention: (+ Clockwise, Looking Forward - Counterclockwise, Looking Forward) Forward

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Support Reactions due to Intermediate Crossframe Effects HIGH REACTIONS Intermediate crossframe effects cause vertical support reactions to be concentrated at the obtuse corners of a skewed structure.Intermediate crossframe effects cause vertical support reactions to be concentrated at the obtuse corners of a skewed structure. Significant redistribution of reactions occurs throughout the structure.Significant redistribution of reactions occurs throughout the structure.

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Support Reactions Due to Wet Concrete Weight, Refined Analysis: Rear Bearings (Fixed) Forward Bearings (Exp.) Rear Bearings (Fixed) Forward Bearings (Exp.)

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There are natural differences in dead load deflections at opposite ends of intermediate crossframes in skewed structures.There are natural differences in dead load deflections at opposite ends of intermediate crossframes in skewed structures. Differential deflections occurring at intermediate crossframe locations cause girders to twist.Differential deflections occurring at intermediate crossframe locations cause girders to twist. Intermediate crossframe effects must be included in analysis of highly skewed structures in order to accurately predict behavior.Intermediate crossframe effects must be included in analysis of highly skewed structures in order to accurately predict behavior. Conclusions for Intermediate Crossframe Effects: Undeformed Undeformed

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End Crossframe Effects End crossframes produce twisting effects that are independent of the intermediate crossframe behavior.End crossframes produce twisting effects that are independent of the intermediate crossframe behavior. End Armor Bottom Chord Diagonals End Crossframe End Crossframe:

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End Crossframe Effects To illustrate end crossframe behavior, we will examine a 2-girder structure with end crossframes only (no intermediate bracing). PLAN VIEW

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PLAN VIEW (PARTIAL) ISOMETRIC VIEW (PARTIAL) 2-Girder Structure: The end crossframe is oriented on the skew and connects the bearing points of the adjacent girders.

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The end diaphragm can be thought of as a pair of rigid links connecting the top flange of one girder to the bottom flange of the adjacent girders.The end diaphragm can be thought of as a pair of rigid links connecting the top flange of one girder to the bottom flange of the adjacent girders. 2-Girder Structure: ISOMETRIC VIEW (PARTIAL)

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Deflection of a Cambered Girder: When a girder deflects, the top flange moves longitudinally relative to the bottom flange at the beam ends. We will define this distance as.When a girder deflects, the top flange moves longitudinally relative to the bottom flange at the beam ends. We will define this distance as.

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The end crossframe of a skewed structure restrains the longitudinal translation of the top flange.The end crossframe of a skewed structure restrains the longitudinal translation of the top flange. 2-Girder Structure: PLAN VIEW (PARTIAL) x GIRDER A GIRDER B

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The end crossframe forces the top flange to move radially about the adjacent bearing point. The resulting motion produces twist in the girders.The end crossframe forces the top flange to move radially about the adjacent bearing point. The resulting motion produces twist in the girders. 2-Girder Structure: PLAN VIEW (PARTIAL) x y GIRDER A GIRDER B

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A similar effect occurs in the adjacent girderA similar effect occurs in the adjacent girder 2-Girder Structure: PLAN VIEW (PARTIAL) x y GIRDER B GIRDER A

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The movement of the top flange is approximately perpendicular to the centerline of bearings.The movement of the top flange is approximately perpendicular to the centerline of bearings. 2-Girder Structure: PLAN VIEW (PARTIAL) x y x y GIRDER B GIRDER A

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We will now perform a refined analysis of the test structure with end crossframe effects included. All end crossframes are fully connected during the deck pour (no slotted holes). The intermediate crossframes will be removed in order to isolate end crossframe effects. The behavior of the bridge will be examined under wet concrete load only. FRAMING PLAN End Crossframe Effects

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By cutting sections along the length of the bridge it can be shown that the twist caused by end crossframe effects is very similar to that caused by intermediate crossframe effects. Girder Twist Due to End Crossframe Effects:D D Framing Plan Section D-D

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By cutting sections along the length of the bridge it can be shown that the twist caused by end crossframe effects is very similar to that caused by intermediate crossframe effects. Girder Twist Due to End Crossframe Effects:J J Framing Plan Section J-J

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Animation of Deflection Under Wet Concrete Load with End Crossframe Effects Only (Exaggerated Scale):

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Deflected Shape Under Wet Concrete Load with End Crossframe Effects Only (Exaggerated Scale):

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Test Structure, Girder End Twist End Crossframes Only: Intermediate Crossframes Only: Sign Convention: (+ Clockwise, Looking Forward - Counterclockwise, Looking Forward) Forward Forward

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End crossframe effects do not cause redistribution of vertical reactions, but they do produce horizontal loads on restrained bearings.End crossframe effects do not cause redistribution of vertical reactions, but they do produce horizontal loads on restrained bearings. For the test case, the rear abutment bearings are fully restrained against translation, and the forward abutment bearings are free to move longitudinally but restrained laterally.For the test case, the rear abutment bearings are fully restrained against translation, and the forward abutment bearings are free to move longitudinally but restrained laterally. The bearing restraints result in axial forces in the girders and end crossframes due to differential movements caused by de-cambering of the beams (or differential lengthening of the bottom flanges).The bearing restraints result in axial forces in the girders and end crossframes due to differential movements caused by de-cambering of the beams (or differential lengthening of the bottom flanges). End Crossframe Support Reactions TEST CASE, MEMBER AXIAL FORCES: 6 T = 19 k C = 11 k T = 13 k C = 9 k C = 12 k T = 22 k T = 6 k C = 1 k C = 15 k

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Test Case, Support Reactions The resulting horizontal components of the support reactions for the test case are shown below.The resulting horizontal components of the support reactions for the test case are shown below. These forces need to be accounted for in the bearing design if end crossframes are left connected during the deck pour.These forces need to be accounted for in the bearing design if end crossframes are left connected during the deck pour. TEST CASE, HORIZONTAL BEARING LOADS: 11

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End crossframes in skewed structures cause girders to twist. The magnitude of the twist is similar to that caused by intermediate crossframes.End crossframes in skewed structures cause girders to twist. The magnitude of the twist is similar to that caused by intermediate crossframes. End crossframes in skewed structures produce longitudinal and lateral forces at restrained bearing locations.End crossframes in skewed structures produce longitudinal and lateral forces at restrained bearing locations. If end crossframes are fully connected prior to the deck pour, end crossframe effects must be considered in the design.If end crossframes are fully connected prior to the deck pour, end crossframe effects must be considered in the design. Conclusions for End Crossframe Effects:

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Combined Effects: Girder End Twist End Crossframes Only / Intermediate Crossframes Only: Combined effects: Sign Convention: (+ Clockwise, Looking Forward - Counterclockwise, Looking Forward) Forward Forward

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Combined Effects: Girder End Twist Conclusions: Intermediate and end effects are not additive.Intermediate and end effects are not additive. Interaction between effects redistributes twist slightly, but the overall magnitude remains about the same when effects are combined.Interaction between effects redistributes twist slightly, but the overall magnitude remains about the same when effects are combined. Sign Convention: (+ Clockwise, Looking Forward - Counterclockwise, Looking Forward) Forward

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Q: Will using skewed intermediate crossframes prevent girder twisting? Common Questions: A: No. Skewed intermediate crossframes behave like end crossframes. They will produce twist due to differential movements between the bottom and top flanges of adjacent girders.

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A: No. Tighter crossframe spacing does not address the basic problem, which is differential movement between adjacent girders. Adding crossframes may reduce crossframe member forces and increase girder stability, but twisting will still occur. Q: Will reducing crossframe spacing keep girders from twisting? Common Questions:

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Both intermediate and end crossframes produce twist in skewed bridges.Both intermediate and end crossframes produce twist in skewed bridges. Intermediate crossframes cause significant redistribution of support reactions and girder forces (shear and moment) in heavily skewed structures.Intermediate crossframes cause significant redistribution of support reactions and girder forces (shear and moment) in heavily skewed structures. End crossframes may cause significant lateral and longitudinal reactions to occur at restrained bearingsEnd crossframes may cause significant lateral and longitudinal reactions to occur at restrained bearings Both intermediate and end crossframe effects need to be accounted for in design of highly skewed bridges.Both intermediate and end crossframe effects need to be accounted for in design of highly skewed bridges. Summary:

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QUESTIONS ? questions to:

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