Analysis of PostTensioned,

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• Analysis of Post-Tensioned,
• Continuous Span Bridges With GTSTRUDL

Abhijit Naik Jay A. Quiogue Chuong V. Ho Li-Hong
Sheng Office of Earthquake Engineering California
Department of Transportation
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Background
The majority of bridges in California are
post-tensioned, box-girder bridges and are,
therefore, of great interest to the California
Department of Transportation (Caltrans).

• Caltrans design engineers currently use Bridge
  Design System (BDS) which is based on Plane Frame
  Analysis using Moment Distribution.

BDS is the main tool for the design and analysis
of typical post-tensioned bridges. However,
extending its application to complex structures
requires considerable engineering judgement and
experience.
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Research Project

• Project Objectives
• To determine methods that accurately model the
  effects of post-tensioning on continuous span
  bridges and compare them with BDS.
• To provide bridge engineers with an alternative
  tool for analysis of these types of bridges using
  GTSTRUDL.
• To compare results from these models with the
  readings from bridge instrumentation.

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Overview of Prestress
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Overview of Prestress
Effects of Prestress on a Simply-Supported Member
The support reactions are only due to the
self-weight of the member. There are no
reactions due to prestress since the member is
statically determinate.
C.G
Prestressing Cable
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Overview of Prestress
Effects of Prestress on a Continuous Member
For a continuous member, which is statically
indeterminate, support reactions depend on the
member deformation.
The continuous ends are restrained against free
rotation and the support reactions due to
post-tensioning may be associated with additional
moments that are required to enforce
compatibility of slopes. These moments are
generally called Secondary Moments.
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Overview of Prestress
Effects of Prestress on a Continuous Member
Total Moment Primary Moment Secondary Moment
Total Moments are used in Working Stress Design
to check service stresses.
For Ultimate Strength Design, the Secondary
Moment is treated as an external load with a load
factor of 1.0 in addition to the other applied
factored loads.
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Overview of Prestress
Concept of Secondary Moments
Secondary Moments should vary linearly between
the supports because the restraint forces causing
these moments occur only at supports.
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Research Project
Methods to Model Post-Tensioning Effects

• Method I
• The post-tensioning tendon (prestress) is not
  explicitly modeled.
• Instead the post-tensioning in the tendon is
  converted to an equivalent distributed loading
  acting directly on the superstructure.

• Method II
• The post-tensioning tendon (prestress) is
  explicitly modeled.
• The post-tensioning effect is imparted to the
  superstructure through thermal loads that are
  applied to the tendon elements.

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Input From BDS
Bridge Design System (BDS) Data

• Design prestress jacking force, Pjack
• Force coefficients, fci, based on friction losses
  due to profile curvature and anchor set loss
• Member eccentricities, ei

All the above data is based on a given cable
profile.
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Method I Equivalent Distributed Loading
Equivalent Distributed Loading

• Topics
• Assumptions
• Sign Conventions
• Concept

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Equivalent Distributed Loading

• Assumptions
• Concrete is assumed to remain elastic and
  uncracked.
• Post-tensioning tendons are assumed to be fully
  grouted and bonded to ducts so that the
  post-tensioning force is completely transferred
  to the concrete.
• Since the post-tensioning tendons are not
  explicitly modeled the prestressing forces are
  directly applied to the center of gravity of the
  superstructure.

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Equivalent Distributed Loading
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Equivalent Distributed Loading

• Concept
• The structure is discretized into series of frame
  elements.

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Equivalent Distributed Loading

• Assuming prestressing forces to act only
  horizontally throughout the structure the
• post-tensioning force acting along each element
  is approximated by converting
• it into a series of equivalent uniformly
  distributed axial and moment loads.

• From equilibrium equations, the distributed axial
  wxi and moment load wzzi acting
• on each element i is given by

wxi ( Fi1 - Fi ) / li
wzzi ( Mi1 - Mi ) / li
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Equivalent Distributed Loading

• Resolving the prestressing forces into vertical
  and horizontal components, the equivalent
  uniformly distributed loads can be calculated
  from equilibrium equations

wxi ( Fi1 - Fi ) / li
wyi ( Vi1 - Vi ) / li wzzi ( Mi1 - Mi -
Vi1 li / 2 - Vi li / 2 ) / li
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Equivalent Distributed Loading

• These individual elements are then assembled back
  into the full structure.
• In doing so, the concentrated forces from
  adjacent elements acting on their
• common node cancel each other, leaving only the
  distributed loads and
• concentrated forces at the two end nodes.

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Equivalent Distributed Loading

• The structure is then analyzed using GTSTRUDL.
• The resulting moments are the total moments
  imparted on the structure due to prestress.
• The secondary moments can then be determined by
• Secondary Moments Total Moments - Primary
  Moments

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Method II Temperature Loading
Temperature Loading

• Topics
• Assumptions
• Sign Conventions
• Concept

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Temperature Loading

• Assumptions
• Concrete is assumed to remain elastic and
  uncracked.
• Post-tensioning tendons are assumed to be fully
  grouted and bonded to ducts so that the
  post-tensioning force is completely transferred
  to the concrete.
• As the post-tensioning tendons are explicitly
  modeled, there is a loss while transferring the
  applied prestressing forces to the center of
  gravity of the superstructure due to interaction
  within elements.

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Temperature Loading
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Temperature Loading

• Concept
• The superstructure is discretized into series of
  frame elements.

• The tendon profile is discretized into a series
  of truss elements.

• The truss elements are connected to the
  superstructure at the nodal points by rigid links.

• The rigid links can be modeled as
• Member eccentricities for frame elements
• Rigid elements with very high stiffness

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Temperature Loading

• The post-tensioning force Fi at each node is
• Fi Pjack x fci
• where

• ai thermal coefficient of truss element i
• Ei modulus of elasticity of truss element i
• Ai area of the truss element i

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Temperature Loading

• The thermal loads on the truss elements bring
  about a shortening effect in the tendon elements,
  similar to that caused by a post-tensioning
  force.

• The structure is then analyzed using GTSTRUDL.
• The resulting moments are the total moments
  imparted on the structure due to prestress.
• The secondary moments can then be determined by
• Secondary Moments Total Moments - Primary
  Moments

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Bridge Under Study

• Bridge under study

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Bridge Under Study
General Plan
Elevation
Plan
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Bridge Under Study
General Plan
Typical Section
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Bridge Under Study
General Plan
Tendon Profile
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Bridge Under Study
Salient Features
It is a curved, continuous three-span,
cast-in-place, post-tensioned box-girder
bridge. The bridge is one of the two bridges
under the long-term structural performance
monitoring program. Monitoring systems include
accelerometers, strain gauges, pressure sensors
and displacement sensors that have been installed
at strategic locations. The bridge is the first
and the only bridge in California with strain
gauges embedded which can provide exceptionally
valuable information regarding the structural
health condition.
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Bridge Under Study
Instrumentation
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Bridge Under Study
Instrumentation
Location of Accelerometers
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GT STRUDL Input File
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GT STRUDL Input File
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GT STRUDL Input File
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GT STRUDL Input File
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GT STRUDL Input File
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GT STRUDL Input File
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GT STRUDL Input File
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GT STRUDL Input File
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GT STRUDL Input File
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GT STRUDL Input File
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GT STRUDL Input File
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GT STRUDL Input File
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GT STRUDL Input File
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GT STRUDL Input File
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GT STRUDL Input File
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Results
Undeformed Shape
Deformed Shape
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Results
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Results
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Results
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Results
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Results
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Results
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Future Study

• Other models under study for the West Street
  Over-Crossing

Grillage Model
Plate Model
Compare the results from the various models to
the readings from the instrumentation and update
finite element models.
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Conclusions

• Given a proper analysis procedure, all necessary
  moments due to prestressing can be obtained using
  GTSTRUDL.
• The proposed methods yield comparable results to
  Caltrans BDS except for axial force distribution
  in middle spans.
• Methods can now be extended to more detailed
  models and verified with experimental results.

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Questions Comments Suggestions