Transcript gt strudl - 株式会社 日本科学技術研修所

Evaluation of the Sandwich Plate System
in Bridge Decks Using a Plate Approach
A Comparison Between
ANSYS and GT STRUDL Models
Devin Harris – Michigan Tech
Chris Carroll – Virginia Tech
Project Overview
SPS Introduction
STEEL FACEPLATES
Design Approach
POLYURETHANE CORE
Element Validation
ANSYS Models
Comparison
GT STRUDL Models
SPS for Civil Structures
Introduction to SPS
• Developed by Intelligent Engineering
– Maritime industry
– Bridge Application (deck)
Pre-fab Panels
Advantages
Disadvantages
– Lightweight
– Rapid installation
– New/rehab
– Cost
– Limited application
– No design provisions
Prefabricated Decks/Bridges
Structured Panel Deck
•
•
•
•
Fabricated panel – limited girder configuration
Wide girder spacing
Larger cantilevers
Fast erection
Steel Face Plates
Polymer Core
(Unexposed)
Welded
Connection
Cold-Formed
Angle
Slip-Critical Bolt
Panel Edge Plate
(Cold-Formed Angle)
Built-up or
Wide Flange
Section
Half-Scale Bridge (VT Laboratory)
• Span ≈ 40 ft; width ≈ 14.75 ft
• Deck ≈ 1 in. (3.2-19.1-3.2)
• 8 SPS panels
– Transversely welded/bolted
– Bolted to girders (composite)
• 2 girder construction
Diaphragm Angles
2 x 2 x 0.31
Top and Bottom
Sandwich Plate
PL 0.125 x 60 x 177.2
Bent Angle
PL 0.19 x 7.9 x 177.2
Girder Web
PL 0.25 x 21.4 x 480
Top Flange Plate
PL 0.625 x 6 x 480
Bottom Flange Plate
PL 1 x 6.4 x 480
4'-10"
5'-1"
4'-10"
Elastomer Core
0.75 x 60 x 177.2
Shenley Bridge (St. Martin, QC)
• Completed - November 2003
– 7 days of total construction
• Span ≈ 74 ft; width ≈ 23 ft
• Deck ≈ 2 in. (6.4-38-6.4)
• 10 SPS panels
– Transversely welded/bolted
– Bolted to girders (composite)
• 3 girder construction
Sequence of SPS Construction
ERECT GIRDERS
& BRACING
BOLT
PANELS TO
BEAMS &
TOGETHER
LAY PANELS
WELD
DECK
SEAM
Sequence of SPS Construction
ERECT BARRIERS
COAT DECK
LAY ASPHALT
Prefabricated Decks/Bridges
Simple Plate Deck
•
•
•
•
•
Simple plate – many girder configuration
Small girder spacing
Short cantilevers
Girders attached to deck in factory
Very fast erection
Steel Face Plates
Polymer Core
(Unexposed)
Welded
Connection
Wide Flange
Section
Cedar Creek Bridge (Wise County, TX)
•
•
•
•
•
2-Lane rural road
SPS Deck (integral girders)
Span = 3@50 ft
Width = 30 ft
Deck ≈ 1-5/8 in.
• 5/16”-1”-5/16”
Fabrication Process
Current Bridge Projects
New Bridge IBRC – Cedar Creek – Texas – June ‘08
Research Objective
• To develop a simple design procedure for
SPS decks for bridge applications
SPS Deck Design Approach
–
–
–
–
Linear Elastic (Equivalent Strip)
Inelastic (Yield-Line)
Empirical (R/C only)
Orthotropic Plate
• Limit States
St
rip
W
id
th
(S
)
AASHTO Deck Design
• Design Methods
Equivalent Strip
Equivalent Strip on Rigid Girders
– Serviceability
– Strength
– Fatigue
SPS Approach (Layered Plate)
– Variable loads and B.C.s
– Assume deflection controls
Plastic hinges
SPS Plate Representation
Simple Support
Fixed Support
Arbitrary Loading
Cut-out
Arbitrary Loading
Cut-out
Traffic Direction
Slab Section Cut-out
Deck Continuity
Slab-Girder Bridge
Slab Section Cut-out
Slab-Girder Bridge
Arbitrary Loading
Arbitrary Loading
Edge BCs
Simplified
Edge BCs
Simplified
Plate Representation of Bridge Deck
Plate Representation of Bridge Deck
Deck Continuity
Edge BCs
Simplified
Edge BCs
Simplified
Analysis Options
• Classical Plate Approach
– Navier
– Levy
– Energy (Ritz)
Approach primarily
dependent on B.C.s
• Finite Element Approach
– Shell
– Solid
– Grid (line elements)
FE Model Approach
• Shell Model
– Advantages
•
•
•
•
Ideal for thin elements
Computationally efficient
Membrane/bending effects
Single thru thickness
element
– Disadvantages
• Element compatibility
• Element connectivity
• Stacking limitations*
• Solid Model
– Advantages
• Realistic geometry
representation
• Element connectivity
– Disadvantages
• Can be overly stiff
• User error (more likely)
• Complicated mesh
refinement
Material Properties
Face Plates
(Steel)
Young’s
Modulus
(E -ksi)
Poisson’s
Ratio (n)
Flexural
Rigidity
(D)
Core
(Polyurethane)
29,878
Composite Section
Eequiv 
109
0.287
0.36
N/A
12 Dt 1 n eq2 
3
ttotal
3
3

3 

tc   tc  
 E pn p  t p       E n  tc  
 
c c
2   2  
2 



2

n eq 

2
3Dt 
1

n


1 n c2  
p



2
Dt 
Ep
3

*Dt = flexural rigidity for layered plate (equivalent to EI for a beam)
*Ventsel, E., and Krauthammer, T. (2001). Thin plates and shells:theory,
analysis, and applications, Marcel Dekker, New York, NY.
3
3
3
 tc
  tc  
tc  


t


p
  
 
 2 
 2

 Ec 2 2 
2
1 n c  
1 n p 
Element Validation (Generic)
Givens:
–
–
–
–
Boundary Conditions: Fully Restrained
Material Properties: E=29,000 ksi; n=0.25
Dimensions: thickness=6” (constant); a=b=L [L/t … 1-200]
Load: q = 0.01 ksi (uniform)
q
ANSYS
• Shell 63 (4-node)
• Shell 91/93 (8-node)
• Solid 45 (8-node)
• Solid 95, Solid 191 (20-node)
b
Fixed Edge
a
GT STRUDL
• BPR (4-node plate)
• SBHQ6 (4-node shell)
• IPLS (8-node solid)
• IPQS (20-node solid)
Midpanel Deflection (wmax)
wclassical
0.00126  q  L4

D
Convergence Comparison of ANSYS and STRUDL Elements
(Square Fixed Plate with Uniform Load )
1.50
wmidspan(FE) /wmidspan (classical)
1.45
1.40
Shell 91 / 93
1.35
1.30
IPLS
1.25
1.20
Solid 45
1.15
Shell 63
1.10
BPR
IPQS
Solid 95 / 191
1.05
1.00
SBHQ6
0.95
1
10
SHELL 63
IPLS
Span/thickness ratio (L/t)
SHELL 91 / 93
SOLID 45
IPQS
BPR
100
SOLID 95 / 191
SBHQ6
GT STRUDL Models
Element Types
BPR
SBHQ6
IPLS
IPQS
GT STRUDL Models
Mesh Verification
IPLS Element Validation
1.5
IPLS 6x6x6
1.4
IPLS 3x3x3
IPLS 2x2x2
1.3
IPLS 1x1x1
d FEA/d CLASSICAL
1.2
IPLS 2x2x1
1.1
1
0.9
0.8
0.7
0.6
0.5
1
10
100
L/t Ratio
1000
GT STRUDL Models
Two Dimensional Example
IPLQ
(2D equivalent of IPLS)
Linear Shape Function
60 in.
A shape function is
the relationship of
displacements within
an element.
IPQQ
(2D equivalent of IPQS)
Quadratic Shape Function
60 in.
GT STRUDL Models
Two Dimensional Example
60 in.
One Layer
60 in.
GT STRUDL Models
Two Dimensional Example
60 in.
Two Layers
60 in.
GT STRUDL Models
Two Dimensional Example
60 in.
Three Layers
60 in.
GT STRUDL Models
Two Dimensional Example
60 in.
Four Layers
60 in.
GT STRUDL Models
Two Dimensional Example
120 in.
120 in.
GT STRUDL Models
Two Dimensional Example
2D Element Comparison Example
1.00
0.95
0.90
d FEA/d Classical
0.85
IPLQ 1 Layer
IPLQ 1 Layer
0.80
IPLQ22Layers
Layers
IPLQ
IPLQ
IPLQ33Layers
Layers
0.75
IPLQ
IPLQ44Layers
Layers
0.70
IPQQ 1 Layer
0.65
IPQQ 2 Layers
0.60
0
5
10
15
15
Divisions
Num ber of Longitudinal Divisions
20
20
25
25
GT STRUDL Models
Aspect Ratios (IPLS vs. IPQS)
Small Aspect Ratios
Large Aspect Ratios
SPS Models
• Case I
– Simple Support on all edges
• Cold-formed angles – assume minimal rotational
restraint
Simple Support
Fixed Support
Girder Line
Girder
Spacing
Girder Line
Panel Length
SPS Models
• Case II
– Simple supports perpendicular to girders
– Fixed supports along girders
• Rotation restrained by girders & cold-formed angles
Simple Support
Fixed Support
Girder Line
Girder
Spacing
Girder Line
Panel Length
SPS Models
• Case III
– Full restraint on all edges
• Rotation restrained by girders & cold-formed angles
Simple Support
Fixed Support
Girder Line
Girder
Spacing
Girder Line
Panel Length
GT STRUDL Models
Boundary Conditions/Symmetry
Full Model:
Reduced Model:
345,600 Elements
406,567 Joints
1,229,844 DOF
86,400 Elements
102,487 Joints
307,461 DOF
GT STRUDL Models
Model Construction
•
•
•
•
•
•
Simple – Simple
Simple – Fixed
Fixed – Fixed
2” Thick Plate
1” Thick Plate
Symmetry
GT STRUDL Models
Model Construction
GT STRUDL Models
Model Construction
½”
½”
GT STRUDL Models
Model Construction
• Stiffness Analysis
• GTSES
• GTHCS
The GTHCS solver partitions the global
stiffness matrix into hyper-column blocks of
size VBS, and stores these blocks on the
computer hard drive, with only two of these
blocks residing in the virtual memory at a time
reducing the required amount of virtual
memory space.
DPM-w-selfbrn, The module 'SPWNDX' may not be branched to recursively
Convergence Comparison of ANSYS and STRUDL Elements
(Square Fixed Plate with Uniform Load )
1.50
wmidspan(FE) /wmidspan (classical)
1.45
1.40
Shell 91 / 93
1.35
1.30
IPLS
1.25
1.20
Solid 45
1.15
Shell 63
1.10
BPR
IPQS
Solid 95 / 191
1.05
1.00
SBHQ6
0.95
1
10
SHELL 63
IPLS
Span/thickness ratio (L/t)
SHELL 91 / 93
SOLID 45
IPQS
BPR
100
SOLID 95 / 191
SBHQ6
Summary of Element Validity
• ANSYS Solids
– Converged with single thru thickness element
• ANSYS Shells
– Minimal mesh refinement required for convergence
• STRUDL Plate/Shells
– Converged but no multiple layer capabilities
• STRUDL Solids
– Converged with sufficient thru thickness refinement
All Elements are capable of Modeling thin plates, but consideration must be
given to mesh density. Especially, thru thickness density for solid elements
Suggested Improvements
•
•
•
•
Layered element for composite materials
Redraw Issues in GT Menu
Contour plots without mesh
Undo Button in GT Menu
Model Validation – SPS Panel
Full Scale SPS Panel
Model Validation – SPS Panel
2'-1"
2'-1"
5'-11"
10'-0"
9'-9"
10'-0"
9'-9"
• SPS Plate (0.25” plates; 1.5” core)
• Support by W27 x 84 beams
• Loaded to 77.8 k with concrete filled tires (assumed 10” x 20”)
CASE III (Fixed)
CASE II (Fixed @ Beams)
CASE I (SS)
Experimental vs. Shell Model Predictions
ANSYS
Experimental vs. Shell Model Predictions
ANSYS
Load vs. Mid-panel Deflection - Full-Scale Panel (ANSYS)
90
Applied Load (kip)
80
Case I
Case II
Case III
70
60
50
40
30
20
10
0
0.0
Measured
-0.1
-0.2
SS Plate (Case I)
-0.3
Deflection (in.)
-0.4
Fixed @ Beams (Case II)
-0.5
-0.6
Fully Fixed (Case III)
Experimental vs. Solid Model Predictions
ANSYS
Load vs. Mid-panel Deflection - Full-Scale Panel (ANSYS)
90
Applied Load (kip)
80
Case III
Case I
Case II
70
60
50
40
30
20
10
0
0.0
Measured
-0.1
-0.2
SS Plate (Case I)
-0.3
Deflection (in.)
-0.4
Fixed @ Beams (Case II)
-0.5
-0.6
Fully Fixed (Case III)
Experimental vs. Solid Model Predictions
GT STRUDL
Experimental vs. Solid Model Predictions
GT STRUDL
Load vs. Mid-panel Deflection - Full-Scale Panel (GT STRUDL)
90
Case III
Applied Load (kip)
80
Case II
Case I
70
60
50
40
30
20
10
0
0.0
Measured
-0.1
-0.2
-0.3
SS Plate (Case I)
-0.4
-0.5
Deflection (in.)
Fixed @ Beams (Case II)
-0.6
-0.7
-0.8
Fully Fixed (Case III)
Model Validation – SPS Bridge
Half-Scale SPS Bridge
Model Validation – SPS Bridge
Panel 2
Panel 3
Panel 4
Panel 5
Panel 6
Panel 7
Panel 8
4.84 ft
Panel 1
4
7
1
GIRDER "A"
6
5.09 ft
3
9
"G"
5
6
2
1
3 8
7
4
5
"G"
4.84 ft
GIRDER "B"
2
5 ft
= STRAIN GAGES
XX = STRAIN GAGES LOCATED ON OPPOSITE FACE
X = DISPLACEMENT TRANSDUCERS (WIRE POT OR DIAL GAGE)
9
3,6,8
7
• SPS Plate (0.125” plates; 0.75” core)
6
• Support5 by Built-up 3Girders2 1,2(depth
~ 23”)
4,5
• Loaded ~ 24 k with bearing4 7pad
(9” x 14”)
40 ft
ELEVATION "G-G"
1
CASE III (Fixed)
CASE II (Fixed @ Beams)
CASE I (SS)
Experimental vs. Shell Model Predictions
ANSYS
Experimental vs. Shell Model Predictions
ANSYS
Load vs. Mid-panel Deflection - Half-Scale Bridge (ANSYS)
30
25
Case III
Case II
Case I
Load (kip)
20
15
10
5
0
0
Measured
-0.1
-0.2
SS Plate (Case I)
-0.3
-0.4
-0.5
Midspan Deflection (in.)
Fixed @ Beams (Case II)
-0.6
-0.7
Fully Fixed (Case III)
Experimental vs. Solid Model Predictions
ANSYS
Load vs. Mid-panel Deflection - Half-Scale Bridge (ANSYS)
30
25
Case III
Case II
Case I
Load (kip)
20
15
10
5
0
0
Measured
-0.1
-0.2
SS Plate (Case I)
-0.3
-0.4
-0.5
Midspan Deflection (in.)
Fixed @ Beams (Case II)
-0.6
-0.7
Fully Fixed (Case III)
Experimental vs. Solid Model Predictions
GT STRUDL
Experimental vs. Solid Model Predictions
GT STRUDL
Load vs. Mid-panel Deflection - Half-Scale Bridge (GT STRUDL)
30
25
Case III
Case II
Case I
Load (kip)
20
15
10
5
0
0
Measured
-0.1
-0.2
-0.3
-0.4
-0.5
Midspan Deflection (in.)
SS Plate (Case I)
Fixed @ Beams (Case II)
-0.6
-0.7
-0.8
Fully Fixed (Case III)
Comparison of ANSYS and GT STRUDL
Models
0.75
Maximum SPS Panel Deflections @ Peak Load
Measured vs. FEA
0.5
0.25
0
SPS Panel
Measured
GT STRUDL Solid
SPS Bridge
ANSYS Shell
ANSYS Solid
Conclusions
• SPS deck behavior can be modeled as plate
with variable boundary conditions
• Solid and shell elements are applicable
• Attention to mesh refinement critical to solid
elements
• Higher order elements significantly increase # DOFs
• Layered elements ideal for efficiency
• GT STRUDL and ANSYS yield similar results,
but not identical
– Future investigation of differences in solid/shell
boundary conditions
Acknowledgements
•
•
•
•
Virginia Department of Transportation
Intelligent Engineering (www.ie-sps.com)
GT STRUDL Users’ Group
Virginia Tech