1. Two-Span LRFD Design Example
Karl Barth and Jennifer Righman
West Virginia University

2. Objective The primary focus of this example
is to demonstrate the use of
Appendix A and Appendix B
for a two-span continuous structure

3. Appendix A Overview
Accounts for the ability of compact and non-compact sections to resist moments greater than My
Economy gained by Appendix A provisions increases with decreasing web slenderness
Effects of St. Venant torsion are incorporated

4. Appendix B Overview
Traditional AASHTO specifications have permitted up to 10% of the maximum pier section bending moment to be redistributed to positive bending regions
Appendix B provisions explicitly compute the level of redistribution based on an effective plastic moment concept for sections meeting prescribed geometric criteria

5. Design Information

6. Design Information
Framing Plan

7. Design Notes 2004 AASHTO LRFD Specifications, 3rd Edition
Structural steel: ASTM A709, Grade 50W
Normal weight concrete (145 pcf) with fc’=4 ksi
Fyr = 60 ksi for reinforcing steel
Operational importance, redundancy, and ductility factors = 1.0

8. Design Loads – DC1 DC1 loads are equally distributed to all girders
Slab =0.983 k/ft
Haunch (average wt/length) =0.017 k/ft
Overhang taper =0.019 k/ft
Girder (average wt/length, varies) =0.200 k/ft
Cross-frames and misc. steel =0.015 k/ft
Stay-in-place forms =0.101 k/ft
S =1.335 k/ft

9. Design Loads – DC2 and DW DC2 DW Barrier weight = 520 lb/ft
Weight/girder = (0.520)x(2)/(4) = k/ft DW
Future wearing surface = 25 psf
DW = (0.025 ksf)x(34 ft)/4 = k/ft

10. Design Loads – WS and WL WL WS
Wind forces are calculated assuming bridge is located 30’ above water in open country
Wind on upper half of girder, deck, and barrier assumed to be resisted by diaphragm action of the deck
WS = k/ft (on bottom flange) WL
Assumed to be transmitted by diaphragm action
WL is neglected

11. Design Loads – Live Load
Controlling case of:
Truck + Lane
Tandem + Lane
0.9 (Double Truck + Lane) (in negative bending)
Impact factors used for all vehicular live loads (excluding lane load)
I=1.15 for fatigue limit state
I=1.33 for all other limit states

12. Design Loads – Live Load
Live load effects are approximated using distribution factors
Interior girder
AASHTO empirical equations are used
Exterior girder
AASHTO empirical equation correction factor
Lever rule
Special analysis

13. Interior Girder Distribution Factors
Moment
Varies with girder dimensions due to Kg term
One design lane
Two or more design lanes

14. Interior Girder Distribution Factors
Shear
One design lane
Two or more design lanes (CONTROLS)

15. Exterior Girder Distribution Factors
AASHTO exterior girder correction factor
Moment
Shear
Empirical formulas for exterior girder will not control

16. Exterior Girder Distribution Factor
Lever Rule – One Design Lane

17. Exterior Girder Distribution Factor
Special Analysis
One design lane
Two or more design lanes
Controls for Moment

18. Distribution Factors for Fatigue
Based on one design lane
No multiple presence factor applied
Maximum one lane distribution factor results from the lever rule, i.e., EXTERIOR GIRDER CONTROLS
DF = 0.70

19. Unfactored Design Moments

20. Limit States
All applicable limits states for steel structures were considered
Strength
Strength I controls in this example
Strength I = 1.25DC + 1.5DW (LL+I)
Strength III = 1.25DC + 1.5DW + 1.4WS
Strength IV = 1.5(DC + DW)
Strength V = 1.25DC + 1.5DW (LL+I) + 0.4WS
Service
Service II = 1.0(DC + DW) + 1.3(LL+I)
Fatigue = 0.75(LL+I)

21. 6.10 Provisions Addressed Cross section proportion limits
Constructibility
Serviceability
Fatigue
Strength

22. Appendix A Design 63’ 54’ 12 x 3/4 16 x 1-1/4 16 x 1-1/2 16 x 2-1/2

23. Cross Section Proportion Limits

24. Constructibility For discretely braced compression flanges
Fnc may be computed using Appendix A which accounts for increased torsional resistance
For discretely braced tension flanges and continuously braced flanges

25. Constructibility - Loads
Vertical DC1 loads are determined considering deck casting sequence
Lateral flange bending stresses
are induced by the overhang form brackets
Construction dead and live loads considered

26. Constructibility Check
Stresses in compression flange of positive bending section control the allowable cross-frame spacing
Strength I
Strength IV

27. Service Limit State For top flange For bottom flange
Bottom flange in positive bending (controls)

28. Fatigue Limit State
Fatigue requirements significantly impact the design of the positive bending region
Bolted stiffener to flange connections employed at locations of maximum stress range, i.e., cross-frames at midspan
Bolted connections / Category B details
Welded connections / Category C’ details

29. Fatigue Limit State (cont.)
Use of bolted cross-frame connections requires that net section fracture requirements are satisfied
Assuming one 7/8” diameter bolt hole is used:

30. Positive Flexural Capacity
If , then
Otherwise
Unless certain geometric conditions are satisfied
Ductility check:

31. Negative Flexural Capacity Appendix A
Therefore, Appendix A is applicable.

32. Web Plastification Factors
Check if web is compact - NO
Noncompact web plastification factors are used

33. Web Plastification Factors (cont.)

34. Compression Flange Local Buckling Resistance
Check if flange is compact - YES

35. Lateral Torsional Buckling Resistance

36. Lateral Torsional Buckling Resistance

37. Negative Flexural Capacity Summary

38. Appendix A Performance Ratios Positive Bending Region
Constructibility
(Strength I)
Top Flange
0.94
Bottom Flange
0.30
(Strength IV)
0.93
0.36
Service Limit State
0.47
0.70
Fatigue and Fracture Limit State
Bolted Conn.
0.80
Welded Conn.
0.98
Strength Limit State
Flexure
0.69
Shear
0.83

39. Appendix A Performance Ratios Negative Bending Region
Constructibility
(Strength I)
Top Flange
0.46
Bottom Flange
0.34
(Strength IV)
0.55
0.39
Service Limit State
0.57
0.69
Fatigue and Fracture Limit State
Bolted Conn. NA
Welded Conn.
0.58
Strength Limit State
Flexure
0.96
Shear
0.78

40. Appendix B Design
Moment redistribution procedures are used to create a more economical design
63’
54’
12 x 3/4
16 x 1
16 x 1-1/2
16 x 2
36 x 7/16
36 x 1/2

41. Appendix B Requirements
Appendix B is valid for girders meeting certain geometric and material limits
Web Proportions

42. Appendix B Requirements (cont.)
Compression flange proportions
Lateral Bracing

43. Appendix B Requirements (cont.)
Shear
Section Transitions
No section transitions are permitted within the first cross-frame spacing on each side of the pier
Bearing Stiffeners
Bearing stiffeners are required to meet projecting width, bearing resistance, and axial resistance requirements

44. Redistribution Moment
Amount of moment redistributed to positive bending region is a function of the effective plastic moment, Mpe
Higher Mpe values are permitted for girders with either:
Transverse stiffeners placed at D/2 or less on each side of the pier
“Ultra-compact” webs such that
Alternative Mpe equations are given for strength and service limit states

45. Redistribution Moment (cont.)
Redistribution moment at pier:
Redistribution moment
varies linearly at other
locations along the span
Pier 1
Pier 2
Mrd1
Mrd2

46. Redistribution Moments (Strength I)

47. Appendix B Design Checks
Positive bending capacity
Evaluated for positive bending moment plus redistribution moment (at strength and service limit states)
Negative bending capacity within one lateral brace spacing on each side of the pier
Not evaluated
Negative bending capacity at other locations
Evaluated for negative bending moment minus redistribution moment
Otherwise, same as before

48. Appendix B Performance Ratios Positive Bending Region
Constructibility
(Strength I)
Top Flange
0.94
Bottom Flange
0.30
(Strength IV)
0.93
0.36
Service Limit State
0.47
0.70
Fatigue and Fracture Limit State
Bolted Conn.
0.80
Welded Conn.
0.99
Strength Limit State
Flexure
0.75
Shear
0.83

49. Appendix B Performance Ratios Negative Bending Region
Constructibility
(Strength I)
Top Flange
0.55
Bottom Flange
0.42
(Strength IV)
0.66
0.48
Service Limit State
0.62
0.79
Fatigue Limit State
Welded Conn.
Strength Limit State
Flexure*
Shear
0.78
* Design of negative bending region controlled by 20% limit

50. Appendix A / Appendix B Design Comparisons
Positive moment region same in both designs (controlled by fatigue)
Cross-frame spacing the same
(controlled by constructibility)
Appendix B negative moment region 18% lighter
Appendix B girder 6% lighter overall
63’
54’
12 x 3/4
16 x 1
16 x 1-1/2
16 x 2
36 x 7/16
36 x 1/2
16 x 1-1/4
16 x 2-1/2
APPENDIX A DESIGN
APPENDIX B DESIGN

51. Concluding Comments
Fatigue requirements significantly impact the design of the positive moment region due to the relatively high distribution factor for the exterior girder
Constructibility and Appendix B requirements led to the use of a 15 ft cross-frame spacing throughout
Use of Appendix A leads to increasing economy with decreasing web slenderness (that is a section with a noncompact web at the upper limit will gain very little from Appendix A)
Appendix B provides even greater economy

52. QUESTIONS?