Live Load Distribution in Multi-Cell Box-Girder Bridges and its Comparison with Current AASHTO LRFD Bridge Design Specifications

Transcription

1 Live Load Distribution in Multi-Cell Box-Girder Bridges and its Comparison with Current AASHTO LRFD Bridge Design Specifications by Rob Y.H. Chai, Eddy Shin-Tai Song & Karl M. Romstad Department of Civil & Environmental Engineering University of California, Davis & Susan E. Hida California Department of Transportation

2 AASHTO LRFD Live Load Distribution Factors

3 Range of Applicability of Live Load Distribution Factors Bridges of constant deck width Number of girders greater than or equal to 4 Parallel girders with approximately equal spacing Span length must exceed 2.5 times the deck width Plan curvature of less than 12 degrees in any one span These requirements are very restrictive for the inventory of box-girder bridges in California. Structures outside of these limits require refined 3D models, which are not a part of the routine design

4 Objectives of Study Conduct a detailed study of the limits imposed by the 1998 AASHTO LRFD Specifications Investigate whether these limits can be broadened to include typical box-girder bridges in California Emphasis is placed on these three parameters: Non-prismatic cross-sections Plan aspect ratio (length/width) less than 2.5 Plan curvature > 12 degrees in any one span

5 Selection of Bridge Parameters Reference NCHRP 12-26/1 Parameter Mean Std. Deviation Span length 89.5 ft 2 ft Depth 4.94 ft 5 ft Number of cells Width (curb-to-curb) 46.6 ft 24.6 ft Caltrans Memo-To-Designers 15-2 (May 1989) Box-girder Type Girder spacing-to-depth ratio Reinforced concrete 1.5 Prestressed concrete 2.0

6 Load Cases For Comparison Between Grillage and Finite Element Models Grillage model per Hambly (1991) Analysis tool SAP2000 Load Case 1 Load Case 2 Load Case 3 L L L L L kn L kn L kn kn CL CL CL L kn L L L Girder Girder Girder Load Case 4 Load Case 5 L L kn kn L CL L L L kn kn L CL L Girder Girder

7 Results from Grillage and Finite Element Models Moment (kip-ft) Moment (kip-ft) Shear Force (kip) (m) Girder Grillage F.E.M (ft) (m) Girder Grillage 2000 F.E.M (ft) (m) Girder 3 Case 2, Girder #2 Case 4, Girder #4 Grillage F.E.M (ft) Case 5, Girder #3 (kn-m) (kn-m) (kn)

8 AASHTO HL-93 Design Vehicular Loads Design truck with lane load Design tandem with lane load 33% dynamic load allowance applied to design truck and design tandem

9 Dual Truck and Dual Tandem Load Dual Truck Load Dual Tandem Load 33% dynamic load allowance applied to dual truck and dual tandem

10 Live Load Distribution Factor Definition QConBridge SAP2000 Beam-line model Mmax = M1 Vmax = V1 Grillage Model Distribution to girder: Mmax = M2 Vmax = V2 Live Load Distribution Factor g = M2 M1 or V2 V1 Definition applies to both interior and exterior girders

11 Definition of Acceptance Ratio Longitudinal mg(m) = m x Mgrillage Mbeamline mg(v) = m x Vgrillage Vbeamline Acceptance Ratio = mg(from analyses) mg(lrfd formula)

12 Non-Constant Deck Width Bridge Two Spans C C Section C-C & Section D-D B B @ Section B-B A A 9.09 Two-Span Continuous 6.25% flare (1:16) All dimensions are in meters Section A-A 96 52

13 Distribution Factor and Acceptance Ratio for Non-Constant Deck Width Bridges

14 Plan Aspect Ratio & Cell Width-to-Depth Ratio Cell width-to-depth ratio (S/D): 1.25, 1.83 and 2.25 Plan aspect ratio (L/W): ~ 3.3

15 Distribution Factor for Interior Girder Moment (2 Lanes Loaded) L/W LRFD formula S/D:1.25 S/D:1.83 S/D: S/D mg L/W Analyses S/D:1.25 S/D:1.83 S/D: S/D mg

16 Distribution Factor for Exterior Girder Moment (3 Lanes Loaded) L/W LRFD formula S/D 0 mg L/W Analyses S/D 0 mg

17 Distribution Factor for Exterior Girder Shear Force (More Than 3 Lanes Loaded) L/W LRFD formula S/D 0 mg L/W Analyses S/D 0 mg

18 Acceptance Ratio for Interior Girder Moment (2 Lanes Loaded) 1 Acceptance Ratio L/W S/D 1.25

19 Acceptance Ratio for Exterior Girder Moment (3 Lanes Loaded) 1 Acceptance Ratio L/W S/D 1.25

20 Acceptance Ratio for Exterior Girder Shear Force (More Than 3 Lanes Loaded) Acceptance Ratio for Exterior Girder 1 Shear Force (More Than 3 Lanes Loaded) Acceptance Ratio S/d L/W

21 Span 1 L = m Span 2 L = 3 m Span 3 L = m Span 4 L = m R = m 122 m 183 m m Curved Bridges Symmetric Cross Section Curvature in Plan (degrees) Span 1 L=22.875m Span 2 L=3m Span 3 L=45.75m Span 4 L=34.313m Bridge 1, R=76.25 m o o o o Bridge 2, R=122 m 14 o o o o Bridge 3, R=183 m 7.16 o 9.55 o o 14 o Bridge 4, R= m 5.73 o 7.64 o o 8.59 o

22 Distribution Factor for Interior Girder Positive Moment 2 Lanes Loaded mg Span Length (m) LRFD formula R = m R = 122 m R = 183 m R = m

23 Distribution Factor for Exterior Girder Negative Moment 2 Lanes Loaded mg Span Length (m) LRFD formula R = m R = 122 m R = 183 m R = m

24 Distribution Factor for Interior Girder Shear Force - 2 Lanes Loaded mg Shear of Interior Girders, 2 Lanes Span Length (m) LRFD Formula R = m R = 122 m R = 183 m R = m

25 Acceptance Ratio for Interior Girder Positive Moment 2 Lanes Loaded Acceptance Ratio Outside of LRFD Limits Curvature in Plan (degrees) Bridge 1, R=76.25 m Bridge 3, R=183 m Bridge 2, R=122 m Bridge 4, R= m

26 Acceptance Ratio for Exterior Girder Negative Moment 2 Lanes Loaded Acceptance Ratio Outside of LRFD Limits Curvature in Plan (degrees) Bridge 1, R=76.25 m Bridge 3, R=183 m Bridge 2, R=122 m Bridge 4, R= m

27 Acceptance Ratio for Interior Girder Shear Force 2 Lanes Loaded Acceptance Ratio Outside of LRFD Limits Curvature in Plan (degrees) Bridge 1, R=76.25 m Bridge 3, R=183 m Bridge 2, R=122 m Bridge 4, R= m

28 Conclusions The current AASHTO LRFD distribution factor for boxgirder bridges is conservative, even for bridges outside their range of applicability The limit for plan aspect ratio may be expanded to 1 instead of the current limit of 2.5 The LRFD distribution factor may also be used for nonconstant deck width bridges with flare up to the limit of 6.25% or 1-in-16 The plan curvature limit of 12 degrees appears unnecessary, and may be increased to about 35 degrees