This document discusses modeling and analysis techniques for bridge superstructures and substructures. It covers modeling bridge decks using various element types including beam, grid, plate-shell, and solid models. It also discusses modeling bridge piers and foundations using solid elements, beam elements, or springs to represent soil-structure interaction. The document emphasizes the importance of modeling both superstructure and substructure together to accurately capture their interaction, and discusses challenges like modeling bearings and soil.

1. Dr. Naveed Anwar
Modeling and Design of Bridge
Super Structure and Sub Structure
Topic 3
Day 2
Naveed Anwar

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1. Over view of Bridge Design Process and Bridge Types
2. Advances and recent trends in Modeling and Analysis of Bridges
3. Design of Bridge Super Structure and Sub Structure
4. International Bridge Design Standards and Approaches

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Why do we want to treat
Sub Structure Separately ?
(for analysis purposes)

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20 m
1.6 m
6 m
10 m
A Very Simple Bridge

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Using Simple Model : Pin-Roller

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Using Simple Model : Pin-Pin

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Using Modified Model : Pin-Roller

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Using Modified Model : Pin-Pin

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20 m
1.6 m
6 m
10 m
Remember the Simple Bridge

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Add Piers

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Add Piers with Moment Release

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Full Model

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For Gravity Loads - same as Pin Roller Beam

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What about Lateral Loads?

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Full Model – Without Bearing

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What can we note
• It is possible, and preferable to model and analyze the super and sub-
structure together
• We need to take care of:
• Connection between deck and sub-structure parts
• Connection between piers and footings
• Interaction between footing, piles and soil
• Specially, complex behavior of Abutments.
• Key issues
• Bearing modeling
• Soil modeling
• Boundary conditions

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Link Elements to model Bearings
Link Elements to model
Bearings

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Full Modeling

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Shell Model of Bridge Pier
Modeling of solid & hollow
piers with shell elements

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Practical Modeling Considerations
• Using the right software that supports the modeling option being
selected
• The skill in using the software properly
• Obtaining, determining or computing the properties and parameters
required for the model being considered
• For sophisticated models, such as D-G, the ability to carry out
parametric and sensitivity analysis to ensure proper use of properties
and program options

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Some Sample Models
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Some Sample Models
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Some Sample Models
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Full Model with Deck,
Bearings, Footings, Piles

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Modeling of Deck

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Modeling of the Bridge Deck
• Beam Model
• Grid Model
• Grid-Plate Model
• Thin Wall model
• Plate-Shell Model
• Solid Model

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Deck Modeling Options

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Beam Model
• Simple Beam Model
• Only the CL of the Deck is modeled by Equivalent beam elements
• Full Beam Model
• Every bridge component is modeled by beam elements

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Beam Model

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Grid Model
• In the model the deck is represented as
a grillage made from beam elements.
• Girders, Slab, Diaphragm etc are all
converted to equivalent beams
• This is generally for out-of plane analysis
for gravity and traffic loads

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Grid Model
• Most suitable for I beam or T beam deck with diaphragms
• Suitable for transverse distribution of traffic load
• Generally made for one or two spans for local analysis
• Slab can be represented by equivalent beam strips
• Can be in 2D or in 3D
• Can be combined with the full Beam Model

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A Typical Grid Model

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Beam-Plate Model
• Beam Plate model is the combination of beam
and plate elements in which girders and
diaphragms are modeled with the beam
element and the slab is modeled with the plate
element.
• The use of the plate element improves the
modeling of slab behavior in comparison with
Grid Model

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Beam-Plate Model
• Special consideration are needed to account for difference in the
center line of the girders and the plate (slab).
• The stiffness matrix of the girders and diaphragms are modified with
the sub-structure method.
• An offset connection needs to be specified between beam and plates

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Beam-Plate Model
h +

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Beam-Plate Model
h
The problem of the offset Connection needs special handling
• Use of Rigid Offsets
• Special Elements in the program
• Connection between Girder CL and Support

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Shell Model
• In plate-shell model, all girders,
diaphragms, slabs etc. are modeled
with the plate elements
• This model suitable for detailed analysis
in transverse as well as in longitudinal
direction

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Plate - Shell Model
• Can handle bridges of arbitrary cross-
section and geometry
• Specially suitable for deck slab
analysis, highly skew & curved bridges
• Needs a very large number of
elements
• Applying moving loads may be difficult
• Difficult to apply Prestress load
• Difficult to interpret results for design
Full shell model for
girder bridge

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Shell Model
• Can handle bridges of arbitrary cross-section and geometry
• Specially suitable for deck slab analysis, highly skew and curved
bridges
• Needs a very large number of elements
• Applying moving loads may be difficult
• Difficult to apply Prestress load
• Difficult to interpret results for design

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Spine Model

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Spine Model With Modified Support

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Frame Model

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Grid Model

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Frame Shell Model

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Full Shell Model

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Beam Model VS Shell Model

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Shell Model

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Shell Model of Box Girder Bridge
Horizontal curvature & variable
box girder depth

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Connecting “Spine” Models to Cable/Supports
Rigid Link modeled as Link Element at Connection
between Deck and Cable
Cable
Rigid Link
Deck

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Steps for Beam and Girder Design
Develop
General
Sections
Develop
Typical
Section
Design of RC
Concrete
Deck
Select
Resistance
Factors
Select Load
modifiers
Select Load
Combinations
Calculate Live
Load Effects
Investigate
Service Limit
State
Investigate
Strength
Limit State

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Steps for Slab Bridges
Check Minimum
Recommended
Depth
Determine Live
load Strip Width
Applicability of
Live Loads for
Decks
Design Edge
Beam
Investigate
Shear
Investigate
Reinforcement
Distributions
Check Min &
Max Dimensions
Design
Diaphragm (if
Not Solid Slab)
Check Design
Requirements

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Handling Prestress Cables

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Conventional Approach
• Bridge modeled and analyzed for DL, LL and other loads  Actions
• Section stresses checked for combined effect of actions and pre-stress
• Will not work well for continuous structures or where secondary effects due to
prestressing are significant
Stresses due
to Actions
Stresses due
to Prestressing Final Stresses+
- =

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Single Element Approach
Mx (+)
PP
ey
y
Mp = P ey (-)
+ =
xx
x
xx
p
a
I
yM
I
yM
A
P
f 

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Integrated Approach
• Prestressing is considered as just another load and the final stresses
are obtained directly from the final actions
• Stresses due to actions  Final Stresses
• Will work in every case.
• Drawback:
• Prestress has to be estimated right from the start, requires iteration
• A combination of these two approaches is often suitable

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Load Due to Prestress
• The Cable Profile produces balancing loads
• Balancing loads produce additional reactions on supports in continuous beams
• Additional reactions generate secondary moments in the beam, in addition to the moment due to eccentricity of prestressing
force

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Why to use Integrated Approach?
• The prestress forces are applied to the full structural model the
secondary effects are automatically included
• Load Balancing analysis is not required
• Effect of prestressing on the entire structure is evaluated including
the continuity, stiffness, shortening, shear lag, eccentricities, etc.
• Most software have the ability to compute stresses and stress profiles
for computed actions so no separate stress calculations are needed

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Why to use Integrated Approach?
• Effects of sequential construction, staged prestressing, etc. can be
carried out more comprehensively
• Prestressed structures are more suitable and relevant for linear-
elastic analysis mostly used by general FEM Software
• The interaction of axial load, moment and prestress load can be
considered more consistently

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Anchor Block Analysis

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Design of RC Deck
• Design of decks is carried out on the basis of approximate method of
analysis in which the deck is subdivided into strips perpendicular to the
supporting components.
• Extreme positive moment in any deck panel between girders shall be taken
to apply to all positive moment regions. Similarly, the extreme negative
moment over any beam or girder shall be taken to apply to all negative
moment regions.
• Strip method is applicable for slab bridges and concrete slabs spanning less
than 15.0 ft

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Width of Equivalent Interior Strip
Type Direction of Primary Strip
Relative to Traffic
Width of Primary Strip
(in.)
Cast-in-place Overhang 45.0 + 10.0X
Either Parallel or
Perpendicular
+M: 26.0 + 6.6S
−M: 48.0 + 3.0S
Cast-in-place with
stay-in-place
concrete formwork
Either Parallel or
Perpendicular
+M: 26.0 + 6.6S
−M: 48.0 + 3.0S
Precast, post-
tensioned
Either Parallel or
Perpendicular
+M: 26.0 + 6.6S
−M: 48.0 + 3.0S
For Concrete deck

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Type Direction of Primary Strip
Relative to Traffic
Width of Primary Strip
(in.)
Open grid Main Bars 1.25P + 4.0Sb
Filled or partially filled
gridk
Main Bars Article 4.6.2.1.8 applies
(LRFD Bridge Design
Specification)
Unfilled, composite
grids
Main Bars Article 4.6.2.1.8 applies
(LRFD Bridge Design
Specification)
For Steel Deck
Width of Equivalent Interior Strip

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Steps of Bridge Substructure
Design

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Sub Structure, Support Structure
Connections
Ancillary Components
Deck
Slab Girders Diaphragms
Transoms
Piers
Cables
Arches
Foundations, Supports
Footings Pile Caps
Piles
Caissons
Pylons
Bearings Joints Restrainers
Isolators
Approach
Abutment
Typical Bridge
Barriers Drainage Lighting

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Sub Components of Typical Bents
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Bottom of Girder
Bottom of Bearing
Bottom of Pier/Column
Bottom of Footing
Pile Tip
Soil Layers
Bearings
Columns, Frame, wall
Footing, PileCap
Piles, Caisons

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Modeling of Pier Bents

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Solid element Model for bridge Pier

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Solid Model for Pier and Pier Head

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Pier with Spread Pier Head
Extraction of Strut and Tie Model from 3D Solid Mesh Analysis
Solid element
model

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Extraction of Strut and Tie Model from 3D Solid Mesh Analysis
Principal Compressive
Stress Contours
Principal Tensile
Stress Contours
Results Output from Program

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Pier with Curved Pier Head
Extraction of Strut and Tie Model from 3D Solid Mesh Analysis
Solid element
model

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Extraction of Strut and Tie Model from 3D Solid Mesh Analysis
Principal Compressive Stress
Contours
Principal Tensile Stress
Contours
Results Output from Program

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Beam Model of Bridge Pier Solid element Model for bridge Pier

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Modeling of Bridge Pier
Beam Model Shell Model
Solid Model

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Problem of Centerline Alignment for a Variable Section Column
Actual Improved Model
(Load eccentricity included)
Simple Model
(Load eccentricity not included)
Non-Prismatic Member

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Modeling of Foundations

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Sub-Structure
• The Structural Members and Systems below the Bearings or the Main
Deck or the Main Framing
• Actual division depends on bridge type
• May include:
• Lateral Framing System
• Piers
• Foundations

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Modeling of Supports
• Actual Supports
• Isolated Footings
• Combined Footings
• Rafts
• Pile Cap
• Special Supports
• Pile Piers
• Caissons

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Modeling of Supports

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Using Springs to Model Footings
Also can use Area Springs

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• A = Spacing of Springs in X
• B = Spacing of Springs in Y
• Ks = Modulus of sub-grade reaction
(t/cu m etc.)
• K = Spring constant (t/m etc)
A
K= ks*A*B
B
A
B
Computing Spring Stiffness

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Modeling Laterally Loaded Pile
Soil strata in layers
D
M
H
P
Pile cap
Fixed soil level
hf
Actual Pile
Embedded in S oil
S oil Represented by
Lateral S prings
H
Beam or truss
element (Si)
Beam
elements (Pi)
M
H 1
2
4
6
3
5
7
Frame Model
N+1
Water level hf
hs
Ls
hs
1
N
2 Also can use Line Springs

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Ks = P/(L*W*H)
Units = T/m3
How to Obtain
• Plate Load Test
• Theory of Soil Mechanics
• Bearing Capacity
• Related g, N, qc etc
1m
1m
1m
P
Load required to produce unit settlement in a unit area
What is Modulus of Sub-grade Reaction


q
k

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Using Solid
elements to model
soil around a Pile

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Pile Cap Models – Should Improve
The Pipe and Pier
should be
connected a “Stiff”
pedestal or
Contraint to avoid
stress
concentrations

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Strut and Tie Approach
L=2.5
a=1.6
d=1.4 h=1.6
T
P=10,000 kN

a) Simple "Strut & Tie" Model c) Modified Truss Model B
L=2.5
a=1.6
d=1.4
d=1.4 h=1.6
T
1


 = tan-1 d/0.5L
 = 48 deg
T = 0.5P/tan
T = 4502 kN
 = tan-1
d/0.5(L-d1)
 = 68.5 deg
T = 0.5P/tan
T = 1970 kN

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Space Truss Models

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Use Space Truss Models

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Bridge Bearings and Joints

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F
V1 ? V2 ?
Elastomeric Bearing
Shear Modulus G
Modeling Elastomeric Bearings

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Nonlinear Links For Bearings

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Location of Bearings - All Shell Model

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Location of Bearings : Beam-Shell

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Modeling of Diaphragm
2m
3~2.5m
0.5m
Use Plate
Elements
Special
Modeling
Needed
May be modeled as Beam
or as Plate elements
Sectional Elevation at Pier

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Modeling of Cross-Beam
1.5m
2.5m
2.0m
Use Brick
Elements
Sectional Elevation at Pier
Thick Cross-beam

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Bearing Example - 1
X
Z
How to Model this?

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Modeling of Joints and Bearings
• In finite element models, by default all element connected to a node
share the Nodal Degree of Freedom (DOF)
• This is suitable for fully connected structural members
• At Joints, full connection may not be available or desired
• We can either “release” or “constrain” the DOF to change this default
behavior and to model joints

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Bearing and Expansion Joints
• Effectively Modeling of Support conditions at bearing and expansion
joints requires careful consideration of the continuity of each
translation and rotational components of displacement.
• Joints may behave linearly or non linearly
• Linear Joints
• Roller, Pin
• Elastomeric Pads
• Nonlinear Joints
• Expansion Joint, Gap
• Restraining Block, Gap or Hook

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Bearing and Expansion Joints
• Degrees-of-freedom representing discontinuous components must be
disconnected
• Stiffness/ flexibility of bearing pads and other connections should be
modeled

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Bearing and Expansion Joints
• Effectively Modeling of Support conditions at bearing and expansion
joints requires careful consideration of the continuity of each
translation and rotational components of displacement.
• Joints may behave linearly or non linearly
• Linear Joints
• Roller, Pin
• Elastomeric Pads
• Nonlinear Joints
• Expansion Joint, Gap
• Restraining Block, Gap or Hook

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Bearing and Expansion Joints
• Method –1: Using Constraints
• Use more than one node at the same
location to connects individual
elements which automatically
disconnects all degrees-of-freedom
between the elements
• Constraining together the connected
degrees-of-freedom using equal or
local constraints

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Bearing and Expansion Joints
• Method-2: Using Releases
• Attaching several elements to a
common joint which automatically
connects all degrees-of-freedom
between the elements
• Using Frame element end release to
free the unconnected degrees-of-
freedom

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Bearings and Expansion Joints
• Method-3: Using Springs
• Specially useful for modeling of
Elastomeric bearings, semi-rigid
connections, elastic connections and
passive resistance of soil within the
elastic range
• The elements are connected to each
other by spring elements or equivalent
spring elements in appropriate DOF

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Bearings and Expansion Joints
• Method-4: Using Nonlinear
Links
• Specially useful for modeling of
complex connections that have
nonlinear properties such as
gaps, nonlinear sprints,
restraining blocks etc.
• The elements are connected to
each other by NL Link elements
in appropriate DOF

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Bearing and Expansion Joints
62 5
4
1
3
Method (1)- Use of Separate Joints at Common Location
Joints 4,5,6:
Same Coordinates
Equal Y-Translation
Equal Z-Translation
Equal X-Rotation
Joints 4,6:
Equal X-displacement

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Bearing and Expansion Joints
Method (2)- Use of Common Joints and Elements End
Releases
Moment & Axial Force
release
2 4
1
3
Moment release
Moment release

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Using Springs/Links
• Use one spring for each DOF
• Stiffness value is specified to
link Force and Displacement
• Use one Link for each DOF
• May have a linear part
(similar to spring) and a
nonlinear part
represented by a
relationship between
Force and Displacement

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In-Span Expansion Joint
X
Z
Pier
Pier Head or GirderGirder
Joint

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In-Span Expansion Joint
32 5 6 4
1
Method(1)- Use of Separate Joints
at Common Location
Joints 5,6:
Same Coordinates
Equal Y-Translation
Equal Z-Translation
Equal X-Rotation
32 5 4
1
Method(2)-Use of Common Joints
and Elements End Releases
Moment &
Axial Force
release
Moment release

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Modeling of Abutments

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Role of Abutments
• For Gravity Loads
• Retain the soil on road way side
• Support the vertical component of girder reaction
• Accommodate bearing movement due to temperature change and elastic
shortenings
• Provide restrain for lateral reaction due to longitudinal loads
• Additional Role for Seismic Loads
• Impart and resist longitudinal loads due to mass-acceleration

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Abutment Behavior
• Behavior depends on the type of abutment and intended purpose
• In general, the overall behavior
• Subjected to active soil pressure causing over-turning towards the span
• Imparts passive pressure to the soil due to longitudinal forces and
movements
• Vertical load transferred to the soil either through retaining wall or through
the transom and pile system

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Modeling Issues
• How can the active and passive soil pressure be modeled
simultaneously
• How can the soil “stiffness” be included when subjected to passive
loading
• How can the soil separation be included when deck moves away from
the abutment
• How can the behavior of restraining blocks for seismic movement be
included
• How can the elastomeric bearings be included
• How can the damping effect be considered
• What about soil dynamic, non-linear and liquefaction effects

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Modeling Options
• A – Consider as support node
• B - Consider and as a linear spring
• C - Consider as a node and a linear link
• D – Consider as a node and a non-linear link
• E – Consider as a node, non-linear link and a damper
• F – Model as a combination of plate elements, links, dampers and
springs
• G – Model as a combination of plate elements, links, dampers and
solid elements

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Independent Design of Abutment

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Integrated Software

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CSI Bridge

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Wonder if Software can handle this ?

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Modeling Options
• A- As Frame Nodal Support
• Consider either as pin or a roller
• If both are considered as roller, then all longitudinal loads should be resisted
by the piers
• If roller-pin combination is considered then amount of longitudinal load
transferred to pin-end will depend on the stiffness of piers, length of deck,
joint between the pier and the deck
• May be appropriate for preliminary analysis, especially when using frame
model
• None of the stiffness, movement effects can be considered

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Modeling Options
• B – As Frame Spring Support
• The sprint support can be use to represent the combined stiffness of the
bearing, the abutment and the passive resistance of the soil
• The spring stiffness can be computed based on the shear modulus of the
bearings, lateral modulus of sub-grade reaction of soil and the contact area
• C – As Frame Support Node and Linear Link
• The linear link can be used instead of spring support to represent the
combined (lumped) stiffness of all elements involved

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Modeling Options
• D – As Frame Support Node and a Non-linear link
• The non-linear link can model the linear stiffness as spring, as well as capture
non-linear behavior, such as soil separation, expansion joint, restraining block,
soil liquefaction etc.
• E – As Frame Support Node, Non-linear Link and Damper
• Can model all of the behavior in D, in addition the combined effect of modal
and material damping
• This option is most comprehensive and can be used efficiently in frame
models
• Option C, D, E require manual determination of stiffness, nonlinear
and damping properties for springs, links and dampers

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Modeling Options
• F – As Plate Elements, Links, Dampers and Springs
• The abutment wall is modeled with plate elements
• The soil is represented as springs
• The connection with the deck is modeled by links and dampers
• G As Plate Elements, Links, Dampers and Solids
• The abutment wall is modeled with plate elements
• The soil is modeled by solid elements
• The connection with the deck is modeled by links and dampers
• The connection between soil and wall may be further modeled by non-linear
links

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Consider as a Support
Spring/ Link Model

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Shell/Spring/Link Model

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Shell Model

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Often Used Concept: Equitant Springs

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Abutment Models
Backwall
Foundation
Springs
Superstructure
Bearing
Wingwall
Wing wall
Back wall
Bearing
Piles
Soil Backfill
Foundation
Embankment
Expansion Join

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Shell Elements Model
Solid Elements Model
Frame Elements Model

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Sample Models of Bridge Structures
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Solid Model of Substructure Full Abutment Model
Full Arch Bridge Model

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Structural Analysis and Design of
Flyover Bridge at Lagos , Nigeria
A Case Study

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Objective and Scope of Work
• Overall review of flyover bridges from design criteria and drawing
provided by client.
• Detailed review and design of structure system for 30m and 50m
spans at middle of two bridges including pier and foundation.
• Estimation of structure system only for 30m and 50m spans at middle
of two bridges including pier and foundation
• Provide final design drawing and calculation report for structure
system for 30m and 50m spans at middle of two bridges including
pier and foundation

135. Dr. Naveed Anwar
135
Overall Layout
Overall Layout

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136

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137
Deck, Girders, Cross Beam, Foundations and Piles (Segment 1)

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138
Deck
Girders
Cross Beam
Finite Element Modeling (Segment 1)

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Footing and Piles

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Bearings and Links
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