Live Load Distribution for Reactions at Piers of Continuous Prestressed Concrete Skewed Bridges

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Live Load Distribution for Reactions at Piers of
Continuous Prestressed Concrete Skewed Bridges
Presented at the ASCE Structures Congress
X. Sharon Huo, Ph.D., P.E. Qinghe Zhang, MS,
Tennessee Technological University May 17, 2007
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Outline

• Introduction
• Objectives
• Information on selected bridges
• Bridge analysis and results
• Comparison study
• Conclusions

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Introduction

• Using a live load distribution factor, bridge
  engineers can simply decouple the lateral effect
  from the longitudinal effect on a bridge beam.
• It has been observed in some studies that the
  reactions at piers in a skewed continuous bridge
  are amplified.
• Skew correction factors for reactions are unique
  from those for beam shear.

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Introduction (cont.)

• The current AASHTO Specifications do not address
  any specific modification for live load reactions
  in skewed continuous bridges.
• Use of inaccurate estimation of live load
  reactions would lead to incorrect design for
  bridge substructures

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Objectives

• To investigate the effect of bridge skewness on
  live load reactions at the supports of continuous
  bridges.
• To understand the differences between skew
  corrections for shear and reaction.
• To compare the results from the study and current
  procedures.

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Selected Bridges
BRIDGE 1 - Two Span Bridge
TYPICAL CROSS-SECTION
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SKEWED BRIDGES STUDIED
BRIDGE 1 - Two Span Bridge
PLANE VIEW of BRIDGE WITH VARIED SKEW ANGLE
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BRIDGE 2 - Four Span Bridge
TYPICAL CROSS-SECTION
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SKEWED BRIDGES STUDIED
BRIDGE 2 - Four Span Bridge
PLANE VIEW OF BRIDGE WITH VARIED SKEW ANGLE
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Finite Element Modeling

• Frame elements were used to model composite beam
  sections in bridge superstructure.
• Shell elements were used to model transverse
  members for the formation of an integrated
  superstructure.

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Finite Element Modeling
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Bridge Loading
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DISTRIBUTION FACTOR OF REACTION AT SUPPORTS
BRIDGE 1
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DISTRIBUTION FACTORS OF SHEAR AT BEAM ENDS
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DISTRIBUTION FACTOR OF REACTION AT SUPPORTS
BRIDGE 2
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Distribution Factors of Shear at Beam Ends
Bridge 2 (Exterior Beam Line)
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Comparison of Reaction and Shear
Ratios of reaction distribution factor vs. shear
distribution factor
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Current Practice in Live Load Reaction
Distribution

• Lever Rule method
• The statical summation of moments about one point
  to calculate the reaction at a second point.
• LRFD Shear distribution factor
• Shear distribution equations
• Skew correction factor specified

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Lever Rule Sample Loading Cases(Exterior beam)
Distribution Factor
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Lever Rule Sample Loading Cases(Interior beam)
Distribution Factor




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LRFD Shear Equations
Interior beam One Design Lane loaded Two or
More Design Lanes loaded Range of
Applicability
Exterior beam One Design Lane loaded Two or
More Design Lanes loaded Range of
Applicability
Lever Rule
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LRFD Skew Correction for Shear
Skew Correction Factor
Range of Applicability
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Comparison to Current Procedures
Reaction Distribution Factor from Various Methods
Bridge 1
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Reaction Distribution Factor from Various Methods
Bridge 2
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Comparison to Current Procedures (Bridge 1)
(a) At support of exterior beam line
(b) At support of interior beam line
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Comparison to Current Procedures (Bridge 2)
(a) At supports of exterior beam line
(b) At supports of interior beam line
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Conclusions

• The distribution factor of reaction at a support
  is higher than that of shear at beam end near the
  same support.
• The increase in reaction distribution factor on
  the interior beam line is more significant than
  that in shear distribution factor when skew angle
  is greater than 30 degrees.
• The LRFD shear equations and the Lever Rule
  method conservatively predict live load reaction
  distribution at piers on exterior beam lines but
  underestimate the reaction distribution at piers
  on interior beam lines.

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Questions ?