Giải thích hệ số PBN - Modeling Appendix

BridgeTech, Inc.
Modeling Appendix
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Centroid Axis
of Box-Girder
Exterior
Longitudinal
Girder
Interior
Longitudinal
Girder
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Interior
Longitudinal
Girder
Exterior
Longitudinal
Girder
Closed Section For
Torsional Rigidity
BridgeTech, Inc.
Shear Distribution Factors for CIP Concrete Multicell
Box Beam Bridges -- Validation
Ext Int Exterior Interior Exterior Interior Exterior Interior

1 L 0.620 0.344 0.618 0.338 0.29% 1.84%
2 L 0.644 0.876 0.644 0.889 0.06% 1.45%
3 L 0.654 0.900 0.653 0.915 0.25% 1.69%
1 L 0.618 0.346 0.620 0.336 0.34% 3.03%
2 L 0.637 0.885 0.640 0.891 0.51% 0.68%
3 L 0.645 0.904 0.649 0.913 0.57% 0.93%
1 L 0.643 0.317 0.639 0.310 0.63% 2.08%
2 L 0.669 0.861 0.664 0.815 0.80% 5.36%
3 L 0.679 0.885 0.672 0.877 1.00% 0.95%
1 L 0.635 0.318 0.547 0.289 13.84% 9.10%
2 L 0.667 0.854 0.606 0.759 9.06% 11.18%
3 L 0.679 0.883 0.629 0.817 7.37% 7.50%
1 L 0.722 0.264 0.718 0.257 0.43% 2.52%
2 L 0.774 0.955 0.780 0.948 0.70% 0.65%
3 L 0.779 1.022 0.784 1.033 0.67% 1.02%
1 L 0.706 0.267 0.698 0.261 1.17% 2.26%
2 L 0.767 0.941 0.769 0.930 0.15% 1.18%
3 L 0.776 1.016 0.778 1.022 0.24% 0.63%
1 L 0.652 0.317 0.658 0.314 0.88% 0.95%
2 L 0.675 0.914 0.681 0.936 0.83% 2.40%
1 L 0.642 0.319 0.645 0.335 0.43% 5.12%
2 L 0.671 0.908 0.675 0.983 0.62% 8.30%
SAP2000 BTLiveLoader DifferenceBridge
Type
TTU
Bridge No.
BridgeID No.
Span
Lanes
Loaded

Beam
End
1
2
10141013
2
1
14 1011 1012
2
13
15
Multicell Box Beam
1
2
12 1007 1008
10101009
1
BridgeTech, Inc.
excellent ≥0.9 bad < 0.5
Lever Rule Henry's
Method
LRFD CHBDC STD Sanders Best
Method
1 excellent good good bad bad bad Lever
2 or more excellent acceptable good bad bad bad Lever
1 excellent poor good good good good Lever
2 or more excellent excellent excellent good good good Lever
1 good good good bad bad bad Lever
2 or more good good good poor acceptable bad Lever
1 bad bad bad bad bad bad CHBDC

2 or more acceptable excellent acceptable acceptable acceptable poor Henry's
1 excellent good good poor poor poor Lever
2 or more excellent excellent excellent poor poor poor Lever
1 excellent poor excellent excellent good good Lever
2 or more good excellent good excellent good excellent Henry's
1 excellent excellent good poor poor poor Henry's
2 or more excellent excellent excellent poor poor poor Henry's
1 poor bad excellent acceptable poor poor LRFD
2 or more poor excellent excellent good good good Henry's
1 excellent acceptable excellent poor acceptable bad Lever
2 or more excellent excellent excellent acceptable acceptable poor Lever
1 excellent acceptable excellent acceptable good poor Lever
2 or more good excellent excellent good excellent poor Henry's
1 poor poor poor poor poor poor CHBDC
2 or more good excellent good poor acceptable poor Henry's
1 acceptable bad poor bad poor bad Lever
2 or more poor excellent poor bad poor bad Henry's
1 excellent poor excellent acceptable acceptable poor Lever
2 or more excellent excellent excellent good good acceptable Lever
1 excellent poor acceptable good excellent acceptable STD
2 or more excellent excellent excellent good excellent acceptable Henry's
1 poor bad bad poor bad bad CHBDC
2 or more acceptable good poor poor poor bad Henry's
1 bad excellent bad poor bad bad Henry's
2 or more poor good poor poor poor bad Henry's
Method Rating Based on the Value of the Correlation Coefficient (R
2
) between Each Simplified
Method and Rigorous Analysis
Lanes

Loaded
Girder
Locations
Action
Bridge
Set
Method
0.90 > good ≥0.80 0.80 > acceptable ≥0.70 0.70 > poor ≥0.50
4
3
2
1
Moment
Moment
Shear
Moment
Shear
Moment
Shear
Shear
Exterior
Interior
Exterior
Interior
Exterior
Interior
Exterior
Interior
Exterior
Interior

Exterior
Interior
Exterior
Interior
Exterior
Interior
Slab On I
CIP Tees
Spread
Boxes
Adjacent
Boxes
vvcc
vvcccvc
vvcc
BridgeTech, Inc.
Basics Continued
 Deflection is the easiest state
variable to predict
analytically/numerically
 Interior girder load effects are
easier to predict than exterior
 Loads near midspan distribute
more uniformly than load
applied near supports.
 Relative stiffness is primary
and flexure is more important
than is torsion
 Most important parameter is
the girder spacing (or

cantilever span)
2
2
3
3
( )
( )
d w
EI M x
dx
d w
EI V x
dx


BridgeTech, Inc.
Prerequisites
 We are not proposing to take any one simplified
method “as is”. (unless it really works well).
 Analytically-based approaches can be
implemented at different levels (i.e., compute
stiffness parameters) – empirical methods cannot.
 Analytically-based approaches can be more easily
extended (in case of limits of application), than
empirically-based methods.
 Analytically-based approaches can be as simple as
empirical approaches
BridgeTech, Inc.
Task 1 -- Literature Review
Michael Patritch

Graduate Student
TN Tech
BridgeTech, Inc.
Task 1 -- Literature Critical Findings
Simplified methods
 Sanders and Elleby
 “Equal Distribution Method” – name is a
misnomer
 Canadian Standards
 Juxtaposition of stiffness extremes
Stiffness effects
Testing
Analysis and modeling
BridgeTech, Inc.
Sanders and Elleby
 NCHRP study
 Limitations
 Span to 120-ft
 Slab on Beam (Orthotropic Plate Theory)
 Multi beam (Articulated Orthotropic Plate)
 CIP Boxes (Folded Plate)
 Considered
 Aspect ratio
 Relative long/trans flexural stiffness
 Relative torsonal stiffness
 Field tests for some validation