BridgeTech, Inc. Modeling Appendix h h 1 h 2 l e1 l e2 l i /2 l i /2 l i i l t w t 1 2 t h s t w Centroid Axis of Box-Girder Exterior Longitudinal Girder Interior Longitudinal Girder h l e1 e2 l i l l e * 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 BridgeTech, Inc. AASHTO LRFD  NCHRP 12-26  Empirically based  Includes stiffness parameters in equations  “Ugly” equations  Embedded multiple presence factors  No rational analytical basis  Resort to lever rule when empiricism fails  Works reasonably well for interior girders  Limitations are of concern BridgeTech, Inc. Sanders and Elleby (cont) 3For 10 5 3For 3 1 7 2 3 10 5 / 2                  C N D C CNN D DSg L LL DSwheelg /)(  Double for LFRD Design Lane [...]... including multi-cell box girders with sufficient diaphragms, Slab-on-girders Steel grid deck-on-girders Shear-connected beam bridges in which the interconnection of adjacent beams is such as to provide continuity of transverse flexural rigidity across the cross-section Box girder bridges in which the boxes are connected by only the deck slab and transverse diaphragms, if present Shear-connected beam... t  but C = K(W/L) Bridge Type Beam and slab (includes concrete slab bridge) Beam Type and Deck Material K Concrete deck: Noncomposite steel I-beams 3 0 Composite steel I-beams 4 8 Nonvoided concrete beams (prestressed or reinforced) 3 5 Separated concrete box-beams 1 8 Concrete slab bridge 0 6 BridgeTech, Inc Canadian Specification  Analytically based upon orthotropic plate theory  Very similar... slab and transverse diaphragms, if present Shear-connected beam bridges in which the interconnection of adjacent beams is such as not to provide continuity of transverse flexural rigidity across the cross-section Numerous wood systems … BridgeTech, Inc Canadian Specification (cont) M g avg n  Lane  M m  Ng M g Fm  g avg M S N Fm     Cf Ce  F  1  100   100    BridgeTech, Inc Canadian . Voided slab, including multi-cell box girders with sufficient diaphragms,  Slab-on-girders  Steel grid deck-on-girders  Shear-connected beam bridges in. application), than empirically-based methods.  Analytically-based approaches can be as simple as empirical approaches BridgeTech, Inc. Task 1 -- Literature Review