Designing for Longitudinal Force

Transcription

1 AREMA Annual Technical Conference Structures Session Tuesday, September 19, 2006 KICC, Louisville, KY Designing for Longitudinal Force Design of Steel Bridges for Longitudinal Force John F. Unsworth, P.Eng. Manager, Structures Planning & Design CANADIAN PACIFIC RAILWAY Calgary, Canada

2 Design of Steel Bridges for Longitudinal Force Contents of Presentation Longitudinal Forces in Steel Bridges Development of Current AREMA Chapter 15 Longitudinal Force Provisions Design of Steel Bridges for Current AREMA Chapter 15 Longitudinal Forces Summary

3 Design of Steel Bridges for Longitudinal Force Longitudinal Forces in Steel Bridges Longitudinal force due to rolling friction: Small at constant train speeds Large at variable train speeds due to adhesion between wheels and rails required for acceleration and braking New locomotives with adhesion of up to 50% of weight (175% increase over older locomotives with wheel slip) Dynamic braking forces large in new locomotives (up to 100% increase over older locomotives) Braking forces applied simultaneously throughout train and varied in accordance with car weight

4 Design of Steel Bridges for Longitudinal Force LF in span = N i t Traction Braking Time History of Longitudinal Force

5 Design of Steel Bridges for Longitudinal Force Analytical model and equations of equilibrium for two span bridge: Static state at maximum longitudinal force Independent of flexural deformations Bar elements (rails horizontally free at ends) Horizontal springs, k, for rail/deck/bridge connection (elastic fasteners)

6 Design of Steel Bridges for Longitudinal Force Rail boundary conditions: Span boundary conditions: N 1 (0)=N 4 (L 4 )=0 N 1 (L 1 )-LF =N L 1 2 (0) N 2 (L 2 )-LF =N L 2 3 (0) N 3 (L 3 )-LF =N L 3 4 (0) u 1 (L 1 )=u 2 (0) u 2 (L 2 )=u 3 (0) u 3 (L 3 )=u 4 (0) N 5 (L 5 )=N 6 (L 6 )=0 u 5 (0)=u 6 (0)=0 Particular boundary conditions: Expansion joints at end of bridge, L 1 =L 4 =0 CWR across bridge, L 1 =L 4 No longitudinal rail restraint (free rails), k 2 =0 Rails fixed (direct fixation to deck), k 2 Determine u i (x) and N i ( x) = E i A i du i dx ( x)

7 Design of Steel Bridges for Longitudinal Force Analytical Finite Element model for a single span bridge: Analytical model (SAP90) developed at the University of Illinois in conjunction with AAR/TTCI testing in 1996/97: Girders modeled with bar & plate elements Track (rail/tie/ballast) with frame, plate, spring elements Reliable predictions of LF for single span open deck plate girder bridges after Report R-905, November 1987, TTCI, AAR

8 Design of Steel Bridges for Longitudinal Force Development of Current AREMA Chapter 15 Longitudinal Force Provisions AREA 1905: 20% of specified live load AREA 1920: Reduced longitudinal forces for ballasted deck and short spans AREA 1932: Tractive force of 25% Cooper driving axles Braking Force of 15% of Cooper train load AREA 1968: 15% of Cooper train load x (L/1200) L=length of bridge in feet

9 Design of Steel Bridges for Longitudinal Force mid-1990s: Introduction of high adhesion locomotives 1996: AAR test on 50 DPG shows longitudinal forces 25 times that in AREA 1997 AREA: Tractive force of 25% Cooper axles Braking Force of 15% of Cooper train load : AAR research and testing of FAST and revenue service bridges 2001 AREMA: New design equations for Tractive and Braking Forces

10 Design of Steel Bridges for Longitudinal Force Longitudinal Force (kips) Max LF 1996 AREA Max LF 1997 AREA Max LF 2001 AREMA AAR Traction Tests (E80) 1997 AAR Test (E80) Traction LF 2001 AREMA Braking LF 2001 AREMA Longitudinal Forces Length, L (ft)

11 Design of Steel Bridges for Longitudinal Force TTCI Traction Force Testing : from Technology Digest , Development of Design Guidelines for Longitudinal Forces in Bridges, Otter, Sweeney & Dick, August 2000, TTCI, AAR

12 Design of Steel Bridges for Longitudinal Force Observations from Testing of Steel Bridges for Longitudinal Forces due to Traction: Large for modern railway freight equipment Tractive effort greatest at low locomotive speeds Traction forces due to locomotives may affect a smaller length of bridge

13 Design of Steel Bridges for Longitudinal Force Participation of rails is relatively small (due to relatively stiff elastic fastenings used in modern bridge deck construction) Grade related traction relatively insignificant for modern high adhesion locomotives Negligible difference in open deck and ballast deck behavior Ability of approach embankments to resist longitudinal forces reduced when bridge and approaches are loaded

14 Design of Steel Bridges for Longitudinal Force Distribution between point of LF application and bridge supports depends on arrangement, orientation and relative stiffness of; Bridge members in the load path Bearings (type, fixed, expansion) Substructures

15 Design of Steel Bridges for Longitudinal Force Magnitude of Longitudinal Force: (AREMA ) Longitudinal Braking Force (kips) = (acting 8 ft above top of rail) (approximately 15% of Cooper E80 train loan) LF B = L Longitudinal Traction Force (kips) = (acting 3 ft above top of rail) LF T = 25 L AREMA Longitudinal Force 600 Longitudinal Force, LF (kips) LF Traction LF Braking Length, L (ft) L= Length (feet) of portion of bridge under consideration (AREMA & )

16 Design of Steel Bridges for Longitudinal Force Design of Steel Bridges for Current AREMA Chapter 15 Longitudinal Forces Magnitude of Longitudinal Force: L= Length (feet) of portion of bridge under consideration (loaded length) Distribution of Longitudinal Forces: (applied longitudinal force to supporting substructure) Superstructure Load Path (AREMA ) Orientation & geometry Relative stiffness of members

17 Design of Steel Bridges for Longitudinal Force Bearings and Substructure Type Orientation & geometry Relative stiffness of members

18 Design of Steel Bridges for Longitudinal Force Steel Bridge Superstructure Span length loaded for braking and traction Orientation and relative stiffness of members Open and ballasted deck plate girder and truss spans without floor systems: Longitudinal Force distributed through main girders or trusses Girders and trusses adequate to transfer LF to bearings and substructure

19 Design of Steel Bridges for Longitudinal Force Open deck and through plate girder and truss spans with floor systems: Load path: stringers > lateral system > main girders or trusses to preclude transverse bending of floorbeams Girders and trusses adequate to transfer to bearings and substructure

20 Floorbeam Main girder/truss Stringer Traction Frames to Direct Single Track Longitudinal Loads in Stringers to Open-deck Main Trusses or Girders

21 Floorbeam Stringer Main girder/truss Traction Frames to Direct Double Track Longitudinal Loads in Stringers to Open-deck Main Trusses or Girders

22 Frame analysis shows very small web member loads and negligible transverse bending of floorbeams

23 Design of Steel Bridges for Longitudinal Force Ballasted deck and through plate girder and truss spans with floor systems: Load path: deck > main girders or trusses Localized traction at transverse floorbeam decks (direct fixation) Deck plate well fastened to closely spaced floorbeams may transmit LF through diaphragm or deep beam action Girders and trusses adequate to transfer to bearings and substructure

24 Main girder ~ Deck plate ~ Floorbeam LF Diaphragm Traction Frames to Direct Single Track Longitudinal Loads in Stringers to Ballasted-deck Main Trusses or Girders

25 Steel Bridge Substructure Entire length loaded for braking and traction Traction and dynamic braking forces distributed to many supports Braking (air-braking) occurs along entire train Continuous track structure across the bridge Orientation and relative stiffness of members Substructure type, geometry and spacing Bearings Type Fixed Expansion Elastomeric Design of Steel Bridges for Longitudinal Force

26 Design of Steel Bridges for Longitudinal Force Steel towers of trestle bridges Longitudinal Force affects: Longitudinal bracing (affects optimum span lengths) Post dimensions Span 7 = fixed bearing Span = expansion bearing Tower Elevation of Bridge Tower 3 Tower Example from AREMA Longitudinal Force Seminar Cross Section T o w e r 3

27 Design of Steel Bridges for Longitudinal Force In steel railway viaduct bridges: relative distribution of longitudinal force at span bearings relative stiffness of supporting substructures (towers, abutments) type of bearing (fixed, expansion) longitudinal forces transferred through the superstructure to the towers as horizontal and vertical forces at the span bearings

28 Longitudinal Force Resisted By Towers entire viaduct deflects uniformly stiffer elements of the structure "attract" a greater proportion of the applied longitudinal force relative horizontal stiffness of towers Total Design of Steel Bridges for Longitudinal Force Substructure Resisting Abutment Tower 1 Tower 2 Tower 3 Stiffness, k, (kip/in per rail) Relative Stiffness (%) from AREMA Longitudinal Force Seminar Example

29 Design of Steel Bridges for Longitudinal Force Distribution of Longitudinal Force Braking Force, LF B = (440) = 573 kips (287 kips per rail) Traction Force = LF T = = 524 kips (262 kips per rail) Tower LF (kips) LF to Tower Leg with 40 DPG fixed bearing LF to Tower Leg with 80 DPG fixed bearing LF = from AREMA Longitudinal Force Seminar Example

30 Design of Steel Bridges for Longitudinal Force LF B y B + 10 V 40 V 80 E F H 40 =28 k H 80 =55k E F y B =8 (braking force) 40 V 40 =28(18)/40= +/-13 k V 80 = V 40-55(18)/80= 0 TOWER 1 from AREMA Longitudinal Force Seminar Example

31 Design of Steel Bridges for Longitudinal Force Summary Determine appropriate portions of the structure to consider; on which to apply braking and traction longitudinal forces. Determine relative stiffness of supporting members for portions of structure considered; to determine distribution of longitudinal forces.

32 Darn, Shouldn t have used L/1200

33 Thank You

34 Designing For Longitudinal Force by Richard D. Payne President ESCA Consultants, Inc. Tuesday September 19, 2006 Louisville, KY

35 Designing for Longitudinal Force WHAT DOES AREMA CHAPTER 8 SAY? Longitudinal Braking Force (kips) = L, where L is the length in feet of the portion of the bridge under consideration (Note this is Emergency Braking. The force associated with normal braking operations is much less). Longitudinal Traction Force (kips) = 25 L These are the E80 Loads. For design loads other than E80, these forces shall be scaled proportionally. The effective longitudinal force shall be distributed to the various components of the supporting structure, taking into account their relative stiffness. The passive resistance of the backfill behind the abutments shall be used where applicable. The mechanisms (rail, bearings, load transfer devices, etc.) available to transfer the force to the various components shall also be considered. Tuesday September 19, 2006 Louisville, KY

36 Designing for Longitudinal Force The effective longitudinal force shall be distributed to the various components of the supporting structure, taking into account their relative stiffness. All other parameters being equal (soil conditions, pile type, superstructure stiffness, etc ) which substructure unit is stiffer? Tuesday September 19, 2006 Louisville, KY

37 Designing for Longitudinal Force The resistance of the backfill behind the abutments shall be used where applicable Tuesday September 19, 2006 Louisville, KY

38 Designing for Longitudinal Force How much movement of the wall into the soil is required to mobilize the passive state? Dense Cohesionless Soil.005H Loose Cohesionless Soil.01H Stiff Cohesive Soil.02H Soft Cohesive.04H For most pile bent railroad bridges, cohesionless soil will be present behind the abutments. It may not be dense immediately after installation of a new abutment and wings, since this is often done in a hurry in between trains. How fast does the first train cross the bridge, just after completion of a construction task? At what speeds are the maximum longitudinal traction forces likely to be developed? If the required movement into the soil is greater than the anticipated longitudinal deflection of the bridge, then the at-rest pressure should be used, since the passive state will not be mobilized. Do not rely upon railroad surcharge behind abutment to resist LF. The abutment can be called upon to resist LF when there is no railroad load behind the abutment. Before assuming wings are effective with either at-rest or passive pressure, be sure to check the load path, and be assured that the wings are stiff enough and that the connection between the wings and the cap/piling is sufficient to transfer the load. Tuesday September 19, 2006 Louisville, KY

39 Designing for Longitudinal Force The mechanisms (rail, bearings, load transfer devices, etc.) available to transfer the force to the various components shall also be considered. Tuesday September 19, 2006 Louisville, KY

40 Designing for Longitudinal Force For most ballasted deck steel pile trestles, friction transferring load. is the primary factor in NEW AREMA 2006 Provisions The longitudinal deflection of the superstructure due to longitudinal force shall not exceed 1 inch (25mm) for E-80 (EM360) loading. For design loads other than E-80 (EM 360), the maximum allowable longitudinal deflection shall be scaled proportionally. In no case, however, shall the longitudinal deflection exceed 1-1/2 inches (38 mm). Since the force is distributed based upon relative stiffness, deflections must be computed anyway. Committee 8 cleared the 1 inch limitation with Committee 1 (Roadway and Ballast) and 5 (Track). Tuesday September 19, 2006 Louisville, KY

41 Designing for Longitudinal Force OTHER CONSIDERATIONS When is the bridge first called upon to resist longitudinal force? Figure shows distribution of LF on embankment, where embankment is uniform. Bridge can be called upon to resist longitudinal force before the train arrives on the bridge. Tuesday September 19, 2006 Louisville, KY

42 Designing for Longitudinal Force OTHER CONSIDERATIONS (Cont.) What else resists longitudinal force, besides at-rest (or passive) pressure at the downhill abutment? Flexure in piles. Batter in piles. What about the uphill abutment? The uphill abutment can be used to resist LF. However it is often reserved solely to resist the railroad surcharge force, which is acting in the same direction as the LF. Tuesday September 19, 2006 Louisville, KY

43 Designing for Longitudinal Force OTHER CONSIDERATIONS (Cont.) Methods for Analysis of Piles in Flexure There are many methods available. The Illinois Department of Transportation, in their Bridge Manual, recommends any one of the methods described in the following publications: Author Paper Broms ASCE Journal, Vol. 91, No. SM3 Davisson Highway Research Record No. 333 Reese and Matlock Special Publication No. 29, Bureau of Engineering Research, University of Texas Austin Davisson and Robinson 6 th International Conference on Soil Mechanics Vol. 2 One or more of these methods are also recommended and described in the following publications: US Steel Highway Structures Design Handbook Structural Engineers Handbook, Gaylord & Gaylord Pile Foundation Know How, American Wood Preservers Drilled Pier Foundations, Woodward, Gardner, & Greer Pile Design & Construction Practice, M.J. Tomlinson US Navy Facilities, DM-7 ( ) Tuesday September 19, 2006 Louisville, KY

44 Designing for Longitudinal Force Tuesday September 19, 2006 Louisville, KY

45 Designing for Longitudinal Force Tuesday September 19, 2006 Louisville, KY

46 Designing for Longitudinal Force Replacing an existing ballast deck timber trestle. Existing bents are on 13 centers. New structure depth limited due to hydraulics (High Water near bottom of structure). Track raise is not desirable. Offset alignment undesirable due to ROW, Environmental, and/or Geometric concerns (i.e. park land adjacent to the job, or extensive trackwork required to offset alignment due to adjacent yard facility, etc.) New structure will be built with track mounted equipment on existing alignment. 26 PPC spans chosen, to fit in between existing 13 timber spans. 39 spans would have excessive structure depth. Tuesday September 19, 2006 Louisville, KY

47 Designing for Longitudinal Force DESIGN CRITERIA Group III Loading D+L+I+CF+E+B+SF+0.5W+WL+LF+F For this example, CF, B, SF, and F are assumed to be negligible The effect of E (without surcharge) is taken into account by the software when computing the resistance at the downhill abutment. The uphill abutment is not counted on for resistance to LF. The design of the abutment for E is outside of the scope of this presentation. Therefore we are looking at D+L+I+0.5W+WL+LF at 125% of allowable stress. Piles are HP 14x89. Fy = 36.0 ksi. Maximum stress due to axial load not to exceed 12,600 psi ( ). Piles will be analyzed as beam-columns. The maximum stress in the piles due to combined bending and axial load will be per Chapter 15 for a steel beam-column. Impact to be included only in evaluating the pile as a structural member (4.2.2). LF= k (Emergency Braking); k (Traction). Tuesday September 19, 2006 Louisville, KY

48 Designing for Longitudinal Force DESIGN CRITERIA (Cont.) Piles are assumed to be laterally supported below the ground line by the earth. The top 5 feet of earth is ignored, to account for the possibility of scour. Maximum allowable longitudinal deflection of the bridge due to E80 loading is assumed to be 1. Tuesday September 19, 2006 Louisville, KY

49 Designing for Longitudinal Force Load - Deflection Chart Longitudinal Load (kips) ' Bent 20' Bent 35' Bent 'Downhill' Abutment Longitudinal Deflection (inches) Tuesday September 19, 2006 Louisville, KY

50 Designing for Longitudinal Force Load - Deflection Chart Longitudinal Load (kips) ' Bent 20' Bent 35' Bent 'Downhill' Abutment Longitudinal Deflection (inches) Determine load required to move the trial bridge 1 It takes 150 kips to move the downhill abutment 1 The two 10 high bents take 20 kips each before they move 1 The four 20 high bents take about 5 kips each to move 1 The two 35 bents provide negligible resistance The bridge as a unit moves 1 with an applied load of 210 k << 385 k design The bridge is not stiff enough. What do we do? Tuesday September 19, 2006 Louisville, KY

51 Designing for Longitudinal Force Tuesday September 19, 2006 Louisville, KY

52 Designing for Longitudinal Force Tuesday September 19, 2006 Louisville, KY

53 Designing for Longitudinal Force Longitudinal Load (kips) Load - Deflection Chart 20' Pier 1/2:12 20' Pier 1:12 20' Pier 2: Longitudinal Deflection (inches) Tuesday September 19, 2006 Louisville, KY

54 Designing for Longitudinal Force Adding piers with battered piles helps. We added two 8-pile piers (20 tall). Now our resistance for 1 bridge deflection is: Downhill Abutment 150 kips Two 10 Bents 40 Two 20 Bents 10 Two 20 Piers 150 Total 350 kips Deflection for this configuration is 1.1 If 1 is an absolute limit, then an additional pier can be added, or the two piers can be braced longitudinally to the ground line. Tuesday September 19, 2006 Louisville, KY

55 Designing for Longitudinal Force WHAT IS COMMITTEE 8 DOING NEXT? We are thinking about the issue of probability as it relates to emergency braking. We believe that many bridges may be more likely to experience erience EQ loading than Emergency Braking. Yet, we currently allow a much greater overstress in the bridge foundations for EQ than we do for LF. We may remove the longitudinal deflection limitation for Emergency Braking. Tuesday September 19, 2006 Louisville, KY

56 Designing for Longitudinal Force Any Questions? Tuesday September 19, 2006 Louisville, KY

57 Designing for Longitudinal Force Thank You. Tuesday September 19, 2006 Louisville, KY