Simplified Live Load Distribution Formula NCHRP 12-62

Transcription

1 Simplified Live Load Distribution Formula NCHRP Research Team Jay A. Puckett, Ph.D., P.E. Dennis Mertz, Ph.D., P.E. X. Sharon Huo, Ph.D., P.E. Mark Jablin, P.E. Michael Patrick, Graduate Student Matthew Peavy, P.E. NCHRP Manager: David Beal, P.E.

2 Objective The objective of this project is to develop new recommended LRFD live-load distribution-factor design equations for shear and moment that are simpler to apply and have a wider range of applicability than those in the current LRFD. The need for refined methods of analysis should be minimized.

3 The Problem

4 Basics Behavior Stiff Deck relative to Girders better distribution, more uniform All analysis and numerical approaches attempt to quantify this behavior Somewhere between Equal (Rigid body) and Lever Rule

5 Accuracy Simplicity

6 Simplicity Accuracy

7 Literature Review Current Specifications & Simplified Approach Modeling Techniques Field Testing Parametric Effects Bridge Type Nonlinear effects

8 PI Bias for a Simple Method Analytically based approach Canadian Specification Orthotropic Plate Theory space

9 Supporting Components Steel Beam Closed Steel or Precast Concrete Boxes Type of Deck Cast in place concrete slab, precast concrete Cast in place concrete slab AASHTO Letter (see Table ) a b Analytical Group Type slab on girders slab on girders Q Number of Bridges NBI most NBI Total Number Skewed recent Inventory % 43.8% % 63.4% Open Steel or Precast Concrete Boxes Cast-in-place concrete slab, precast concrete slab c slab on girders Cast-in-Place Concrete Multicell Boxes Cast-in-Place Concrete Tee Beam Precast Solid, Voided, or Cellular Concrete Boxes with Shear Keys Precast Solid, Voided, or Cellular Concrete Boxes with Shear Keys and with or without Transverse Posttensioning Precast Concrete Channel Sections with Shear Keys Precast Concrete Double Tee Section with Shear Keys and with or without Transverse Posttensioning Precast Concrete Tee Section with Shear Keys and with or without Transverse Reinforcement Precast Concrete I or Bulb- Tee Sections Monolithic Concrete Monolithic Concrete Cast-in-place concrete overlay Integral Concrete Cast-in-place concrete overlay Integral Concrete Integral Concrete Cast-in-place concrete, precast concrete d e f g h i j k slab on girders slab on girders monolithic slab and girders monolithic slab and girders slab on girders slab on girders slab on girders slab on girders 3.8% 62.0% % 65.3% % 40.3% % 53.6% % 49.0% % % % 35.3% % 35.3% % % NBI Database Wood Beams Cast-in-place concrete or plank, glued/spiked panels or stressed wood l slab on girders % % Slabs Not Applicable Not Applicable Slabs Total: 14.3% 37.1% % 42.6%

10 Summary Table (NBI Data) Type Steel Beam Bridge Percentages by Type 1990-present Total Inventory 30.0% 42.8% Concrete I 29.8% 15.1% Precast Concrete Boxes with Shear Keys 11.2% 5.0% Slabs 14.3% 15.8% 85.3% 78.7%

11 Data Source NCHRP TN Tech Set 1 Reference Total No. Bridges LRFR Number Parameter Ranges Bridge Types of Number of Span Length (ft) Girder Spacing (ft) Slab Thickness (in) Skew Angle (deg) Aspect Ratio (L/W) Bridges Spans min. max min max min max min max min max Conc. T-Beam 71 n/a Steel I-Beam 163 n/a Prestressed I-Beam 94 n/a Prestressed Conc. Box 112 n/a n/a n/a n/a n/a R/C Box 121 n/a n/a n/a n/a n/a Slab 127 n/a n/a n/a Multi-Box 66 n/a n/a n/a Conc. Spread Box 35 n/a Steel Spread Box 20 n/a Precast Conc. Spread Box Precast Conc. Bulb-Tee Precast Conc. I-Beam CIP Conc. T-Beam CIP Conc. Multicell Steel I-Beam Steel Open Box Slab on RC, Prest., and Steel Girders N/A N/A Parametric Bridges N/A 74 Spread Box Beams N/A N/A Adjacent Box Beams N/A N/A Slab on Steel I-Beam N/A N/A Summary:

12 Data Sources 1. NCHRP Bridge Database Bridges can be used in an automated process to generate simplified and rigorous analyses. 2. Tenn. Tech. Database Detailed descriptions and rigorous analysis are available from a recent TT study for TN DOT. Results, structural models, etc., are readily available. 3. Virtis/Opis Database Bridges 650+ bridges may be exported from Virtis/Opis to supply real bridges to both simplified and rigorous methods. 4. Parametrically Generated Bridges 74 Bridges were developed to test the limits of applicability of the proposed method. Condense to a Common Database Common Database A Format NCHRP 12-50

13 A Common Database Format NCHRP BRASS-Girder (LRFD) TM Simplified Analysis Methods: Standard Specifications (S over D) LRFD Specifications Rigid Method Lever Rule Adjusted Equal Distribution Method Canadian Highway Bridge Design Code Sanders Rigorous Analysis (Basis) SAP AASHTO FE Engine Ansys B Common Database Format NCHRP 12-50

14 B Common Database Format NCHRP Studies Directed Toward: Skew Lane Position Diaphragms Simplified Moment and Shear Distribution Factor Equations Specification and Commentary Language Design Examples Final Report Iterative Process Involving Tasks 7,8, and 9 through 12. Comparisons and Regression Testing (NCHRP Process) Tasks 6 & 9 Regression testing on real bridges (Virtis/Opis database, NCHRP database) (compare proposed method to current LRFD method) Comparisons from parametric bridges and rigorous analysis

15 Grillage Method (structural model)

16 Influence Surfaces (structural model)

17 Automated Live Load Positioning Critical live load placement Actions (shear, moment, reaction, translation) Single and multiple lanes loaded Critical longitudinal position Accounts for barrier, etc. 4-ft truck transverse truck spacing POI at least tenth points

18 Computation of Distribution Factor Distribution Factor M g M rigorous beam Rigorous Action / Number Lanes g Action from Beamline for same Longitudinal Position

19 Using Distribution Factors M M g design( rigorous estimate) beam

20 Example of Standard Specification Results 1.4 Moment at 1.4 One-lane Loaded Exterior I-Girder Std. S/D vs. Rigorous Unit slope = good Std. Spec. (S/D) Distribution Factor y = x R 2 = Poor R 2 = little hope 1 R 2 = poor Rigorous Distribution Factor

21 Lever Rule Results 1.4 Moment at 1.4 One-lane Loaded Exterior I-Girder Lever Rule vs. Rigorous slope = poor Lever Rule Distribution Factor y = 1.63x R 2 = R 2 = good Apply affine transformation Rigorous Distribution Factor

22 Calibrated Lever Rule Results 1.4 Moment at 1.4 One-lane Loaded Exterior I-Girder Calibrated Lever Rule vs. Rigorous slope = good Calibrated Lever Rule Distribution Factor y = 0.978x R 2 = R 2 = good and is the same Rigorous Distribution Factor

23 Affine Transformation Concept Simple Method Rotation to Unity by multiplication Original Simple Method Raise or lower by addition/substratio n Rigorous Method

24 Affine Transformation (example) y1 1.63x y 2 y 1.63x x y1 y y x x g a g b ( Calibrated lever rule) m Lever rule m where 1 a 0.61 and b m m 1.63 and g g ( Calibrated lever rule) ( Lever rule) Unit slope is the calibrated distribution factor, and Unit slope is the lever rule distribution factor computed with the typical manual approach.

25 Affine Transformation Concept Simple Method Rigorous Method

26 Moment Distribution Factor Computation Number of Loaded Lanes Girder Distribution Factor Multiple Presence Factor One Interior and Exterior N L mgm m am g lever rule b m m N g m = 1.2 Use integer part of Two or more Loaded Lanes Interior and Exterior WcFst N L mg m m a m 10N g N g W c 12 to determine number of loaded lanes for multiple presence. m shall be greater than or equal to 0.85.

27 Multiple Presences Number of Loaded Multiple Presence Factor Lanes "m" or more 0.65

28 Lever Rule Equations (aids) Girder Location Number of Loaded Lanes Distribution Factor Range of Application Loading Diagram Number of Wheels to Beam 1 d e 2 2S d S 6 ft d e e S d e 6' S d e S 3 6 S d S ft e de 6' S 2 Exterior d 3 1 e S S d S 10 ft e de 6' 4' S S 6' 2 2 or more d e 2S S 10 d S 16 ft e de 6' 4' 6' S 3 2d 16 S S 2 e 16 d S 20 ft e de 6' 4' S 6' 4

29 Calibration Coefficients (Moment) Moment AASHTO One Loaded Lane LRFD Cross Exterior Interior Structure Type Section Type a m b m a m b m Steel I-Beam a Precast Concrete I-Beam k Precast Concrete Bulb-Tee Beam k Precast Concrete Double Tee with Shear Keys with or without Post- i Tensioning Precast Concrete Tee Section with Shear Keys and with or without j Transverse Post-Tensioning Precast Concrete Channel with Shear Keys h Cast-in-Place Concrete Tee Beam e Cast-in-Place Concrete Multicell Box Beam d Adjacent Box Beam with Cast-in- Place Concrete Overlay f Adjacent Box Beam with Integral Concrete g Precast Concrete Spread Box Beam b, c Open Steel Box Beam c Use Article

30 Calibration Coefficients (Moment) Moment AASHTO One Loaded Lane LRFD Cross Exterior Interior Structure Type Section Type a m b m a m b m Steel I-Beam a Precast Concrete I-Beam k Precast Concrete Bulb-Tee Beam k Precast Concrete Double Tee with Shear Keys with or without Post- i Tensioning Precast Concrete Tee Section with Shear Keys and with or without j Transverse Post-Tensioning Precast Concrete Channel with Shear Keys h Cast-in-Place Concrete Tee Beam e Cast-in-Place Concrete Multicell Box Beam d Adjacent Box Beam with Cast-in- Place Concrete Overlay f Adjacent Box Beam with Integral Concrete g Precast Concrete Spread Box Beam b, c Open Steel Box Beam c Use Article

31 Calibration Coefficients (Shear) Structure Type Steel I-Beam Precast Concrete I-Beam Precast Concrete Bulb-Tee Beam Precast Concrete Double Tee with Shear Keys with or without Post- Tensioning Precast Concrete Tee Section with Shear Keys and with or without Transverse Post-Tensioning Precast Concrete Channel with Shear Keys AASHTO LRFD Cross Section Type a k k i j h One Loaded Lane Exterior Shear Two or More Lanes Loaded Interior a v b v a v b v a v b v a v b v One Loaded Lane Two or More Lanes Loaded 0.05 Cast-in-Place Concrete Tee Beam e Cast-in-Place Concrete Multicell Box Beam d Adjacent Box Beam with Cast-in- Place Concrete Overlay f Adjacent Box Beam with Integral Concrete g Precast Concrete Spread Box Beam b, c Open Steel Box Beam c Use Article

32 Structural Factor (Moment) Multiple Lanes Loaded Two or more loaded lanes AASHTO LRFD Cross F st Structure Type Section Type Steel I-Beam a Precast Concrete I-Beam k Precast Concrete Bulb-Tee Beam k Precast Concrete Double Tee with Shear Keys with or without Post- i Tensioning 1.15 Precast Concrete Tee Section with Shear Keys and with or without j Transverse Post-Tensioning Precast Concrete Channel with Shear Keys h Cast-in-Place Concrete Tee Beam e 1.10 Cast-in-Place Concrete Multicell Box Beam d Adjacent Box Beam with Cast-in- Place Concrete Overlay f 1.10 Adjacent Box Beam with Integral Concrete g Precast Concrete Spread Box Beam b, c 1.00 Open Steel Box Beam c Use Existing Specification Uniform Distribution N lane / N girder

33 Example 2 6 P/2 P/2 R g exterior Lever Rule P 6 P P g a g b g Calibrated m Lever Rule m Calibrated

34 Calibration Results Slab-on-Girder Bridges Type of Bridge Calibration Constants Action Girder Location Basic Method Lanes Loaded Initial Trend Line - Lever Rule and Henry's Method (Henry's Method already calibrated) Computed Calibration Factors (for Lever Rule Calibration) Recommended Calibration Factors Slope Intercept R 2 Figures a b a or F st b Regression Plot R 2 I-Girders (a, h, i, j, k) Shear Moment Exterior Interior Exterior Interior Calibrated Lever 1 Lane a, N b, K or More Lanes a, N b, K Lane a, N b, K or More Lanes a, N b, K Calibrated Lever 1 Lane a, N b, K Henry's Method 2 or More Lanes a, N-51 n/a n/a 1.15 n/a 18b, K Calibrated Lever 1 Lane a, N b, K Henry's Method 2 or More Lanes a, N-19 n/a n/a 1.15 n/a 20b, K Quite Good (typical)

35 Statistical Comparison Conceptual Mean Number of Samples Standard deviation 1.00 g g simplified rigorous

36 Shift Simple Upward by a factor Increase by a factor that is related to the COV a 1.00 Simple / Rigorous

37 Analysis Factors Type of Bridge I-Girders (a, h, i, j, k) Action Shear Moment Basic Method Calibrated Lever Calibrated Lever Henry's Method Calibrated Lever Henry's Method Analysis Factor Computations No. of Std. Dev. Offset b = 1 No. of Std. Dev. Offset b = 0.5 No. of Std. Dev. Offset b = 0.0 Ratio of No. of Computed Rounded Rounded Computed Rounded Girder Location Lanes Loaded Figures Inverse COV Means Std. Dev. Analysis Analysis Factor No. of Std. Computed Analysis Factor No. of Std. Dev. Dev. Offset Analysis Factor Offset Analysis Analysis Offset Factor ( b = 1) (b = 0.5) Factor Factor (b = S/R (S/R) -1 V S/R β g a g a (rounded) β g a g a (rounded) β g a g a (rounded) Exterior Interior 1 Lane 1 Lane 13c 15c or More Lanes 2 or More Lanes 14c 16c Exterior Interior 1 Lane 17c or More Lanes 18c Lane 19c or More Lanes 20c High due to high COV

38 Example Continued R g exterior Lever Rule P 6 P P g a g b g Calibrated m Lever Rule m Calibrated 0.71 Previous Example g Calibrated g 0.71 mg a mg a

39 All effects are now separated an understandable Analysis mg a mg a Variability in analysis Effect of Multiple Presence

40 Skew Adjustments for shear No iteration Commentary M&M Study Neglect decrease for moment

41 Curvature No change

42 Type of Superstructure Concrete Deck, Filled Grid, Partially Filled Grid, or Unfilled Grid Deck Composite with Reinforced Concrete Slab on Steel or Concrete Beams; Concrete T- Beams, T- and Double T-Section Applicable Cross-Section from Table a, e and also h, i, j if sufficiently connected to act as a unit Range of Correction Factor Applicability tan S L 240 N b 4 Precast concrete I and bulb tee beams K tan S L 240 N b 4 Cast-in-Place Concrete Multicell Box Concrete Deck on Spread Concrete Box Beams Concrete Box Beams Used in Multibeam Decks D 12.0L tan 70d B, c Ld tan 6S f, g 12.0L 1.0 tan 90d S L d 110 N c S L d 65 N b L d b 60 5 N 20 b

43 W 1'-9" 1'-9" t s Push-the-limits bridges Overhang S S S Overhang Bridge No. Girder Spacing, S (ft) Recommended minimum slab thickness (AASHTO STD Table 8.9.2) Slab Thickness, t s (in) Span Length, L (ft) Total Bridge Width, W (ft) No.of girders Overhang (ft)

44 Many Parameter Studies Skew Diaphragm Cross-frame Stiffness End Cross-frames Intermediate Cross-frames Typical Example

45 Span 1 Span 5 R = kips DF = R = kips DF = R = kips DF = R = kips DF = With Support Diaphragms R = kips DF = R = kips DF = R = kips DF = R = kips DF = R = kips DF = R = kips DF = R = kips DF = R = kips DF = With Support Diaphragms 30 R = kips DF = R = kips DF = R = kips DF = R = kips DF = R = kips DF = R = kips DF = R = kips DF = R = kips DF = With Support Diaphragms R = kips DF = R = kips DF = R = kips DF = R = kips DF = 0.330

46 Regression Testing Complete database used to compare: LRFD S/D Rigorous Again, used 12-50

47 Is this simpler? Consistent approach for most bridge types Based upon lever rule (shear and onelane moment) and adjusted Based uniform distribution (multiplelanes loaded and adjusted Independently accounts for multiple presence

48 Is this simpler? Independently accounts for variability of simple analysis wrt rigorous Lever rule aids are provided in appendix No iterative approach, i.e., independent of cross section and span lengths Same for positive and negative moment areas Skew corrections are based upon S/L (readily known)

49 Is it simpler? Many pages shorter Many variables eliminated from notation and section Once affine transformations are understood the adjustments from lever are readily seen

50 Go to report

51 Additional work Recalibrate uniform method parallel the calibrated lever Improve one-lane loaded for moment Review/revise tub girder systems Develop presentation materials to help explain this in a more understandable manner Suggestions welcome!

52 Questions, Discussion

53 End of AASHTO Talk

54 Extra slides

55 Modeling Appendix Exterior Longitudinal Girder l e1 l i /2 l i t 1 h h 1 h 2 t w t w h s Centroid Axis of Box-Girder l e2 l i /2 Interior Longitudinal Girder l i t 2 l e1 l i h l e * l e2 Exterior Longitudinal Girder Interior Longitudinal Girder Closed Section For Torsional Rigidity

56 Shear Distribution Factors for CIP Concrete Multicell Box Beam Bridges -- Validation Bridge Type Multicell Box Beam TTU BridgeID No. Lanes Beam SAP2000 BTLiveLoader Difference Span Bridge No. Ext Int Loaded End Exterior Interior Exterior Interior Exterior Interior 1 L % 1.84% 1 2 L % 1.45% 3 L % 1.69% L % 3.03% 2 2 L % 0.68% 3 L % 0.93% 1 L % 2.08% 1 2 L % 5.36% 3 L % 0.95% L % 9.10% 2 2 L % 11.18% 3 L % 7.50% 1 L % 2.52% 1 2 L % 0.65% 3 L % 1.02% L % 2.26% 2 2 L % 1.18% 3 L % 0.63% 1 L % 0.95% 1 2 L % 2.40% L % 5.12% 2 2 L % 8.30%

57 Method Rating Based on the Value of the Correlation Coefficient (R 2 ) between Each Simplified Method and Rigorous Analysis Bridge Set excellent > good > acceptable > poor 0.50 bad < 0.5 Action Shear Moment Shear Moment Shear Moment Shear Moment Method Girder Lanes Locations Loaded Lever Rule Henry's LRFD CHBDC STD Sanders Best Method Method Exterior Exterior Exterior Exterior Exterior Exterior Exterior Exterior 1 excellent acceptable excellent poor acceptable bad Lever 2 or more excellent excellent excellent acceptable acceptable poor Lever 1 excellent poor excellent acceptable acceptable poor Lever 2 or more excellent excellent excellent good good acceptable Lever 1 poor bad bad poor bad bad CHBDC 2 or more acceptable good poor poor poor bad Henry's excellent good excellent excellent poor good good good excellent poor good good good good poor bad bad poor poor poor bad bad poor poor poor bad bad poor poor poor Lever Lever Lever Henry's CHBDC 2 or more 2 or more 2 or more 2 or more 2 or more excellent good excellent excellent good acceptable good excellent excellent excellent good good excellent excellent good bad poor poor poor poor bad acceptable poor poor acceptable bad bad poor poor poor Lever Lever Lever Henry's Henry's Interior Interior Interior Interior Interior Interior Interior Interior 1 bad bad bad bad bad bad CHBDC 2 or more acceptable excellent acceptable acceptable acceptable poor Henry's excellent excellent poor excellent acceptable excellent bad poor poor bad acceptable bad poor excellent good excellent excellent excellent poor acceptable bad good excellent acceptable acceptable bad good poor good good poor good poor excellent bad good good poor poor bad acceptable bad Lever Lever LRFD Lever Lever STD Henry's 2 or more 2 or more 2 or more 2 or more 2 or more 2 or more 2 or more excellent good poor good poor excellent poor excellent excellent excellent excellent excellent excellent good excellent good excellent excellent poor excellent poor good excellent good good bad good poor good good good excellent poor excellent poor good excellent good poor bad acceptable bad Lever Henry's Henry's Henry's Henry's Henry's Henry's Slab On I CIP Tees vvcc Spread Boxes vvcccvc Adjacent Boxes vvcc

58 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) EI EI 2 d w dx 3 2 d w dx 3 M ( x) V ( x)

59 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

60 Task 1 -- Literature Review Michael Patritch Graduate Student TN Tech

61 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

62 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

63 AASHTO LRFD NCHRP 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

64 Sanders and Elleby (cont) g ( wheel) S / D D N L 5 10 N L N 3 7 L D C Double for LFRD Design Lane g For For S C C / D 3 3

65 Equal Distribution Method (TN DOT) All beams carry equal live load (interior/exterior) g = N L /N g Interpolate number of lanes Adjust g by empirical factors from research Research is on interior beams Simple but purely empirical Limited sample for rigorous comparison

66 TN DOT Equal Distribution Method

67 Sanders and Elleby (cont) C W L E 2 G J 1 I1 J t 1 2 Bridge Type C = K(W/L) Beam Type and Deck Material K but Beam and slab (includes concrete slab bridge) 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

68 Canadian Specification Analytically based upon orthotropic plate theory Very similar to Sanders and Elleby Use either stiffness parameter approach or good estimation tables (easy) Few limitations More rational limits for skew and curvature

69 Canadian Specification (cont) Slab Voided slab, 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 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.

70 Canadian Specification (cont) Ng m M n M Lane avg g avg g m g M F M e f m C C F N S F

71 Canadian Specification (cont) F m S N C f F C e 100 Lane position effect Lane width effect F C K Span Length

72 Canadian Specification (cont) Similar procedures for shear different values

73 Canadian Specification (cont) Skew limit Plan View BridgeWidth tan( skew angle) Span Length Slabs Slab on Beams

74 Canadian Specification (cont) b Span Radius Length 2 of Curvature 1.0

75 Kennedy and Sennah Steel Boxes Possibly concrete with modifications Similar to LRFD approach (authors claim better accuracy) Empirical Ugly equations

76 European Practice

77 Examples AASHTO LRFD Henry (old method) CSA Sanders and Elleby

78 Summary Method AISI Example 2 PCI Example 4 Interior Exterior Interior Exterior Moment Shear Moment Shear Moment Shear Moment Shear AASHTO LRFD Canadian Bridge Design Code Sanders and Elleby Equal Distribution Factor Method

79 Task 2 Range of structural forms, materials and range of application Range of application There is no reason at this point to limit range of application (we can include range outside of conventional practice and geometries) All parameters will be included in the database A large amount of data is available from several sources (see Task 6 tables) Additional data can be added

80 Task 3 -- Analytical method Mathematical model Equilibrium, compatibility, and constitutive relationships Beam theory Kirchhoff plate theory Results in governing ODE or PDF 4 d w dx 4 p x EI x p x, y 4 w D

81 Task 3 -- Analytical method Numerical methods Finite difference Finite element method (plate or shell elements) Grillage Finite Strip Method Harmonic analysis (Sanders and Elleby)

82 Theorem Requirements Independent of the modeling assumptions! Calculated internal actions and applied forces are in equilibrium No instability or fracture Materials and section/member behavior must be ductile

83 The lower bound theorem is one of the most important theorems/concepts in structural engineering.

84 The lower bound theorem is one of the most important theorems/concepts in structural engineering. Offers wonderful assurance as the models are often simple approximations to the real world.

85 Task 4 -- Process Detail and Chaining Database NCHRP TN Tech, Set NCHRP CSA Sanders LRFR Process Effort Do it? Sample > BRASS -> Computation -> Small yes > BRASS -> Input File -> FEA -> Large yes > BRASS -> Input File -> FSM -> Medium yes 4 TT Set 1 -> Process 1 Small-> Small yes All 5 TT Set 1 -> Process 2 Small -> Large yes All 6 TT Set 1 -> Process 3 Small -> Medium yes All 7 TT Set 2 -> Process 1 Small-> Small yes Typical 8 TT Set 2 -> Process 2 Small -> Large yes Typical 9 TT Set 2 -> Process 3 Small -> Medium yes Typical 10 CSA -> Process 1 Depends maybe 11 CSA -> Process 2 Depends maybe 12 CSA -> Process 3 Depends maybe 13 Sanders -> Process 1 Small-> Small maybe 14 Sanders -> Process 2 Small -> Large maybe 15 Sanders -> Process 3 Small -> Medium maybe 16 LRFR -> Process 1 Small-> Small yes Typical 17 LRFR -> Process 2 Small -> Large yes Typical 18 LRFR -> Process 3 Small -> Medium yes Typical

86 Task 4 -- Process Matrix Comparison of Methods and Available Database Databases of Bridges Notes NCHRP TN Tech Set 1 NCHRP CSA Sanders LRFR AASHTO Std S/D equation, program into an automated approach process 1 process 4 process 7 process 10 process 13 process 16 AASHTO LRFD AASHTOLRFD Eqs, LRFD program into an automated approach process 1 process 4 process 7 process 10 process 13 process 16 AASHTO LRFD Rule Program into an automated approach process 1 process 4 process 7 process 10 process 13 process 16 AASHTO LRFD Rigid Method Program into an automated approach process 1 process 4 process 7 process 10 process 13 process 16 Sanders Lever Rule Program into an automated approach process 1 process 4 process 7 process 10 process 13 process 16 Canadian Specification (CSA) Program into an automated approach process 1 process 4 process 7 process 10 process 13 process 16 Henry (Modified) Program into an automated approach process 1 process 4 process 7 process 10 process 13 process 16 Rigorous FEA FEA engine and/or a commercial FEA engine process 2 process 5 process 8 process 11 process 14 process 17 Rigorous FSM Available FSM program process 3 process 6 process 9 process 12 process 15 process 18 Method AASHTO Std Spec. Rigid method CSA Modified Henry JOSE Rigorous FEA Rigorous FSM

87 Task 6 Parametric Study Slab on Steel Girders 321 Total Data Sets AASHTO Type A

88 Task 6 Parametric Study Slab on Precast I and Bulb Tee Girders 176 Total Data Sets AASHTO Type K

89 Task 6 Parametric Study Slab on Concrete Tees 74 Total Data Sets AASHTO Types E and J

90 Task 6 Parametric Study Slab Bridges 127 Slab Data Sets

91 Task 6 Parametric Study Spread Concrete Boxes 94 Total Data Sets AASHTO Types B and C

92 Task 6 Parametric Study Adjacent Concrete Boxes 307 Total Data Sets AASHTO Types D, F, and G

93 Task 6 -- Wood Bridges Wood bridges will not be addressed

94 Additional Load Distribution Issues Additional Parameters Parameters Skew Barriers Diaphragms Location Skew Yes Maybe Yes Maybe Barriers Maybe Yes Maybe Yes Diaphragms Yes Maybe Yes Maybe Location (e.g. Fatigue) Maybe Yes Maybe Yes Perform separate parametric studies to focus exclusively on these effects

95 Three primary questions for the panel Lane width to determine the number of lanes Live load position Multiple presence factors

96 Number of Lanes Loaded Issue for our study not total design load for girder systems Integer number or decimal value Should not be overly sensitive to the distribution factor

97 Live Load Position Interior Girder (critical) (critical) (critical)

98 Live Load Position (exterior girder)

99 Multiple Presence separate from live load distribution Task 6 distribution factors will be computed for one-, two-, three-, etc-lanes loaded. This could be combined, if necessary, later. Research simplified methods will not include m. Rearch simplified methods will permit one-, two-, three-, etc-lanes loaded to be computed and independently applied. The specification can clearly indicate (apriori) how the number of controlling lanes, i.e., it can be explicit and simple.

100 Example Number of lanes loaded or more Multiple Presence Factor Factor Required by Method x.x y.y z.z w.w Controls for Strength I