MIDASCivil Analysis Algorithms

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MIDAS/Civil Analysis Algorithms
2005 MIDAS Technical Support Civil 2005.11.21

• 2005. 11. 21
• MIDAS IT

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MIDAS/Civil Analysis Algorithms

• Calculation of member forces and losses due to
  tendon prestress
• Concept of Construction Stage Analysis
• Geometric Stiffness of Beam Element
• Unknown Load Factors
• Initial Tangent Displacement
• Forward Stage Analysis
• Cable Elements and Pretension Loads
• Lack of Fit Force
• Geometric Nonlinear analysis in forward analysis
  method
• Composite section for construction Stage
• Mass handling in MIDAS Eigenvalue analysis
• Section Offset

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1. Member Forces and Losses due to Tendon
Pre-stress

• Tension Losses
• Instantaneous Tension Loss at Stressing
• Anchorage Slip
• Frictions between PS tendons and sheaths
  (Friction Wobble)
• Time Dependent Tension Losses after Stressing
• Concrete Creep
• Concrete Shrinkage
• PS Steel Relaxation
• Elastic Shortening

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1. Member Forces and Losses due to Tendon
Pre-stress

• Loss due to Frictions between PS tendons and
  sheaths (Instantaneous Loss)
• Friction Loss
• Curvature Friction Loss Loss due to the
  curvature effect of tendons (Curvature Effect)
• Wobble Friction Loss Loss due to frictions
  between tendons and sheaths (Length Effect)

k frictional coefficient per unit length m
frictional coefficient per unit angle (radian)
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1. Member Forces and Losses due to Tendon
Pre-stress
Loss due to Anchorage Slip (Instantaneous
Loss) Loss due to anchorage slip when PS tendons
are tensioned and released. Overstressing
tendons to compensate for loss. Tendon length in
the anchorage zone, which is affected by
anchorage device, is a function of friction loss.
The length becomes shorter with large frictional
losses and vice versa.
Area of Triangle ( )
Dl anchorage slip Ap tendon cross-section
area Ep modulus of elasticity P frictional
loss per unit length DP loss due to anchorage
slip lset length of the tendon being
subjected to pre-stress loss due to anchorage slip
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1. Member Forces and Losses due to Tendon
Pre-stress

• Loss due to Elastic Shortening of Concrete
• Elastic Strain

Elastic strain of concrete at a tendon
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1. Member Forces and Losses due to Tendon
Pre-stress

• Loss due to Relaxation
• Relaxation When tension in a PS tendon is
  activated and its strain is maintained, the
  tension stress in the tendon gradually decreases
  with time.
• Relaxation using Maguras formulation

• fsi initial stress
• fs stress at time t after applying tension
• fy yield stress (0.1 Offset yield Stress)
• C constant unique to product (normal tendon
  10, low relaxation tendon 45)

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1. Member Forces and Losses due to Tendon
Pre-stress

• Loss due to Relaxation
• Relaxation using CEB-FIP formulation
• Calculation based on reduction of initial
  stress at a constant rate with time

1000 (days)
500000 (days)
1000 (days)
500000 (days)
fsi initial stress RP rate of
Relaxation () tn , tn-1 times at
construction stages n n-1 (days) ts
duration of tension being applied (days)
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1. Member Forces and Losses due to Tendon
Pre-stress

• Member forces due to tension force and profile of
  tendons
• Method of converting PS loads to equivalent loads

 

Calculation by converting to end loads
equiv. distributed loads
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1. Member Forces and Losses due to Tendon
Pre-stress

• When tendon is placed in curvature

• Material properties and geometry

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1. Member Forces and Losses due to Tendon
Pre-stress

• Theoretical calculation

Shift in NA due to transformed areas of tendon
duct
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1. Member Forces and Losses due to Tendon
Pre-stress
Theoretical Result
Equivalent tendon force at Each Part
MOMENT
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1. Member Forces and Losses due to Tendon
Pre-stress

• Comparison between theoretical result and result
  from MIDAS/Civil

Unit N, N-m
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1. Member Forces and Losses due to Tendon
Pre-stress

• When tendon is placed in curvature

• Material properties and geometry

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1. Member Forces and Losses due to Tendon
Pre-stress

• Theoretical Result
• Friction loss

Tension forces at L/4 points
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1. Member Forces and Losses due to Tendon
Pre-stress

• Tension loss due to anchorage slip

Tension loss graph due to anchorage slip
When lset in zone ii
?P1/2
?P2/2
?Pk
When lset in zone i
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1. Member Forces and Losses due to Tendon
Pre-stress

• Tension loss due to anchorage slip

Equation for calculating relaxation loss
Tension forces at each point reflecting loss due
to relaxation ( t 100 days )
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1. Member Forces and Losses due to Tendon
Pre-stress

• Tension Result from MIDAS/CIVIL

Tension with Friction Loss
Tension with Friction Anchorage Slip Losses
Tension with Friction, Anchorage Slip
Relaxation Losses
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1. Member Forces and Losses due to Tendon
Pre-stress

• Comparison between theoretical result and result
  from MIDAS/Civil

Unit N
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1. Member Forces and Losses due to Tendon
Pre-stress

• Calculation of tension loss due to elastic
  shortening

• Material properties and geometry

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1. Member Forces and Losses due to Tendon
Pre-stress

• Theoretical Result

Elastic shortening due to 2nd tendon
Reduction in member shortening due to tension loss
Increase in tension force
Equiv. area reflecting tendon area
Equiv. area after 2nd tendon is anchored
Process of repeated calculations
Elastic shortening of member
Final tension force in 1st tendon
Tension loss in 1st tendon due to tensioning 2nd
tendon
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1. Member Forces and Losses due to Tendon
Pre-stress

• Result from MIDAS/CIVIL

Comparison between theoretical result and result
from MIDAS/Civil
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1. Member Forces and Losses due to Tendon
Pre-stress

• Tension Loss
• Table of tension losses by tendon groups and
  construction stages
• Classification of losses for elastic shortening,
  creep/shrinkage relaxation at the induction of
  tension

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2. Concept of Construction Stage Analysis

• Concept of Construction
• Each structure is composed for each Step, and
  analysis results are accumulated.

Structure Active / Inactive
Active Structural members are created at a
corresponding construction stage.
Inactive Structural members are removed at a
corresponding construction stage. Forces in
members being removed are transferred to the
remaining structure.
Load Active / Inactive
Active Loads are created at a corresponding
construction stage.
Inactive Loads are applied in reverse directions
at a corresponding construction stage.
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2. Concept of Construction Stage Analysis
Boundary Active (Deform / Origin)
Inactive
Active Boundary conditions are created at a
corresponding construction stage.
Deform boundary conditions imposed on the
deformed shape
Origin boundary conditions imposed on the
structure, which has been forced to the
undeformed shape
Inactive Boundary conditions are removed at a
corresponding construction stage. Forces
resisted by boundary conditions being removed are
transferred to the remaining structure.
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2. Concept of Construction Stage Analysis
CS1 Active Structure
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2. Concept of Construction Stage Analysis
CS2 Inactive Structure
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2. Concept of Construction Stage Analysis
CS3 Inactive Load
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2. Concept of Construction Stage Analysis
CS4 Active (Deform) / Inactive Boundary
Active Load
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2. Concept of Construction Stage Analysis
CS5 Active (Origin) Boundary
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3. Geometric Stiffness of Beam Element
Beam Element Geometric Stiffness
F Axial Force L Length
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4. Unknown Load Factors
Unknown Load Factors
Object Function
Constraint Condition Equality Inequality
Influence Matrix
Constraint Values
Parameter
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4. Unknown Load Factor
Cable Stayed Bridge Example
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4. Unknown Load Factor
Unknown Load Factor Input Result Data
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4. Unknown Load Factor
Influence Matrix Result
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5. Initial Tangent Displacement

• Initial Tangential Displacement
• Tangential displacements of elements, which are
  newly created in
• each construction stage

Cs1 Displ.
Cs2 Node 5,6,7 Tangential Displ.
Cs2 Current Displ.
Cs2 Cs1 Displ. Cs2 Current Displ.
Cs2 Cs1 Displ. Cs2 Tangential Displ. Cs2
Current Displ.
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5. Initial Tangent Displacement
Construction Stage Final Displ. w/o Tangential
Displ.
???? ?? ??(????? ???)
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5. Initial Tangent Displacement
Construction Stage Final Displ. w/ Tangential
Displ.
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6. Forward Stage Analysis
Forward Stage Analysis Analysis method by
which a final structure is sequentially created
and analyzed corresponding to the natural process
of construction stages
Stage 1
Stage 6
Stage 14
Stage 19
Stage 24
Stage 29
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7. Cable Elements and Pretension Load
Elastic Catenary The stiffness of an
elastic catenary cable element is calculated from
the equilibriums of current location, undeformed
length, load per unit length and nodal forces.
,
Flexibility Matrix
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7. Cable Elements and Pretension Load
Equivalent Truss Element Stiffness
resulting from Tension Force, Length and Weight
Density Stiffness resulting from Sag
Elastic Modulus
Area
Cord Length
Horizontal Length
Tension Force
Weight Density / Unit Length
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7. Cable Elements and Pretension Load
Pretension Load Pretension Load is used
for truss element and causes deformation
corresponding to the Pretension. External
Type Load Case Pretension causes member forces
for Truss.
Pretension Load
Elastic Modulus
Area
Pretension Load P10
Pretension Load P10
External Type Load Case
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8. Lack of Fit Force

• Lack of Fit Force in Truss Element

Lack of Fit Force
Pretension In Construction
Cable in Equilibrium Stage
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8. Lack of Fit Force

• Lack of Fit Force in Beam Element

• Calculate specified displacements for closing
  the Key Segment.
• ? Convert the specified displacements into
  member forces and
• apply these forces to the Key Segment.

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8. Lack of Fit Force

• Truss Example

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8. Lack of Fit Force

• Equilibrium Analysis
• Calculate cable pretension to minimize girder
  displacements through optimization

Max. Displacement 0.057588 mm
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8. Lack of Fit Force

• Forward Construction Stage Analysis
• Apply self-weight of girder, place cable
  pretension loads by construction stages and apply
  Lack of Fit Force function.

Stage 1
Stage 6
Stage 14
Stage 19
Stage 24
Stage 29
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8. Lack of Fit Force

• Lack of Fit Force Table

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8. Lack of Fit Force
Result Moment of Girder Case1 Initial
Equilibrium State Analysis Case2 Forward
Analysis using Lack of Fit Force and Cable
Pretension Loads at the Final
Stage
Moment of Girder
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8. Lack of Fit Force

• Beam Element Example

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8. Lack of Fit Force
Forward Construction Stage Analysis Stage 1
Install main girders, temporary bents and
fixed supports Stage 3 Install girders in
the side spans Stage 5 Remove temporary
bents Stage 13 Close Key Segment
Stage 1
Stage 3
Stage 5
Stage 7
Stage 11
Stage 13
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8. Lack of Fit Force
Result Final Stage Displacement of
Girder Case 1 Equilibrium Analysis Case 2
Forward Analysis using Cable Pretension Loads at
the Final Stage and Lack of Fit
Force
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8. Lack of Fit Force
Result Final Stage Cable Tension Case 1
Equilibrium Analysis Case 2 Forward Analysis
using Cable Pretension Loads at the Final Stage
and Lack of Fit Force
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9. Geometric Non-linear analysis in forward
analysis

• Geometric Non-linear analysis in forward
  analysisIndependent Stage
• - Independent non-linear analysis for
  each step of a construction stage (not affected
  by a
• previous stage)
• Accumulative Stage
• - Geometric Non-linear
• - Time Dependent Effect (Creep, Shrinkage
  Tendon Loss)
• - External Type Pretension
• - Use Previous Results Tangential
  Displacements as Initial Conditions

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9. Geometric Non-linear analysis in forward
analysis
Geometric Non-linear analysis in forward analysis
(Accumulative Stage)
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9. Geometric Non-linear analysis in forward
analysis
Geometric Non-linear analysis in forward analysis
(Accumulative Stage)
Cs38-1
Cs37
Cs38-2
Cs36
Cs35-1
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10. Composite section for construction stage

• Composite section for construction stage
• - Self-weight and Section Properties vary with
  construction sequence of a composite section.
• - Different Material Properties can be used for
  each Section Part.
• - Creep/Shrinkage effects reflecting different
  age of each Section Part
• - Independent member force results at the
  centroids of each Section Part

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10. Composite section for construction stage
Composite section for construction stage
Cs11st Girder Before Composite
Cs21st Girder After Composite 2nd Girder
Before Composite
Result of Each Section Part
Cs21st Girder After Composite 2nd Girder
After Composite
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11. Section Offset

• Section Offset Specify section offset by an
  arbitrary offset position

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11. Section Offset
Section Offset Equivalent to Rigid Link
between a node and the centroid of a section.
Affects Local Axis,
Stiffness, Mass and Beam Load.
Beam Offset Global Type
Rigid Link Constraint
Center Line of Beam
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12. Mass handling in MIDAS Eigenvalue analysis
Mass Type Lumped Mass (with Offset)
Consistent Mass
Offset can be considered only in case
of converting self-weight into masses.
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12. Mass handling in MIDAS Eigenvalue analysis
Mass Offset Centroidal Axis gt Reference Axis
z'
x'
Reference Axes - Nodal Coordinate
System Centroidal Axes - Element Centroid
Coordinate System Centroidal Mass gt
Equivalent Mass
Centroidal Mass
Centroidal Axes
z
j
y'
x
zg
Translation
Reference Axes (Offset Axes)
xg
y
p
Statically Equivalent Mass
yg
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12. Mass handling in MIDAS Eigenvalue analysis
Mass Offset of Beam - Mass Transformation
M Mass Matrix of Centroidal Axes M Mass
Matrix of Reference Axes (Offset Axes) T Mass
Transformation Matrix (Centroidal Axis gt
Reference Axis)
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12. Mass handling in MIDAS Eigenvalue analysis
Consistent Mass of Beam
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12. Mass handling in MIDAS Eigenvalue analysis
Eigenvalue Analysis
Geometric Stiffness by Initial Force