AREMA- Design for Longitudinal Loads

AREMA Annual Technical ConferenceStructures Session

Tuesday, September 19, 2006KICC, Louisville, KY

Designing for Longitudinal Force

Design of Steel Bridges for Longitudinal Force

John F. Unsworth, P.Eng.Manager, Structures Planning & DesignCANADIAN PACIFIC RAILWAYCalgary, Canada

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


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

t

Traction

Braking

Time History of Longitudinal Force

LF

in s

pan

= N

i


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)


Rail boundary conditions:N1(0)=N4(L4)=0

N1(L1)-LFL1=N2(0)

N2(L2)-LFL2=N3(0)

N3(L3)-LFL3=N4(0)

u1(L1)=u2(0)

u2(L2)=u3(0)

u3(L3)=u4(0)

Span boundary conditions:

N5(L5)=N6(L6)=0

u5(0)=u6(0)=0

Particular boundary conditions:

Expansion joints at end of bridge, L1=L4=0

CWR across bridge, L1=L4

No longitudinal rail restraint (free rails), k2=0

Rails fixed (direct fixation to deck), k2

dx

xduAExN i

iii

)()( =

∞

∞

Determine ui(x) and


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


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 axlesBraking Force of 15% of Cooper train load

AREA 1968: 15% of Cooper train load x (L/1200)L=length of bridge in feet


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 axlesBraking Force of 15% of Cooper train load

1997-2001: AAR research and testing of FAST and revenue service bridges

2001 AREMA: New design equations for Tractive and Braking Forces


Longitudinal Forces

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350 400

Length, L (ft)

Longitudin

al F

orc

e (

kip

s)

Max LF 1996 AREAMax LF 1997 AREAMax LF 2001 AREMAAAR Traction Tests (E80)1997 AAR Test (E80)Traction LF 2001 AREMA Braking LF 2001 AREMA


TTCI Traction Force Testing 1997-2000:

from Technology Digest 00-018, “Development of Design Guidelines for Longitudinal Forces in Bridges”, Otter, Sweeney & Dick, August 2000, TTCI, AAR


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

•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



•Distribution between point of LF application and bridge supportsdepends on arrangement, orientation and relative stiffness of;

�Bridge members in the load path

�Bearings (type, fixed, expansion)

�Substructures

Longitudinal Braking Force (kips) = (acting 8 ft above top of rail)(approximately 15% of Cooper E80 train loan)

LLFB

2.145 +=

LLFT

25=


Longitudinal Traction Force (kips) = (acting 3 ft above top of rail)

L= Length (feet) of portion of bridge under consideration(AREMA 15.1.3.12 & 15.9.1.3.12)

Magnitude of Longitudinal Force: (AREMA 15.1.3.12)

AREMA Longitudinal Force

0

100

200

300

400

500

600

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400

Length, L (ft)

Long

itudi

nal F

orce

, LF

(kip

s)

LF Traction LF Braking


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 15.1.3.12)•Orientation & geometry•Relative stiffness of members

Design of Steel Bridges for Current AREMA Chapter 15 Longitudinal Forces


•Bearings and Substructure•Type•Orientation & geometry•Relative stiffness of members

•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:

Steel Bridge Superstructure


•Longitudinal Force distributed through main girders or trusses

•Girders and trusses adequate to transfer LF to bearings and substructure

�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


Traction Frames to Direct Single Track Longitudinal Loads in Stringers to Open-deck Main Trusses or

Girders

Main girder/truss

Floorbeam

Stringer

Traction Frames to Direct Double Track Longitudinal Loads in Stringers to Open-deck Main

Trusses or Girders

StringerFloorbeam

Mai

n gi

rder

/tru

ss

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

�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


Traction Frames to Direct Single Track Longitudinal Loads in Stringers to Ballasted-deck Main Trusses

or Girders

LF

Mai

n gi

rder

Floorbeam

Diaphragm

~ Deck plate ~

•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

Steel Bridge Substructure



•Steel towers of trestle bridgesLongitudinal Force affects:

•Longitudinal bracing (affects optimum span lengths)•Post dimensions

8 0 ’ 4 0 ’

4 4 0 ’

T o w e r 1

T o w e r 2

T o w e r 3

4 0 ’

1 0 0 ’

6 0 ’

1 0 ’

= f i x e d b e a r in g = e x p a n s i o n b e a r in g

S p a n 1

S p a n 7

6 0 ’

1 0 ’

C r o s s S e c t io n T o w e r 3

E le v a t io n o f B r id g e

Example from AREMA Longitudinal Force Seminar

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


Longitudinal Force Resisted By Towers•entire viaduct deflects uniformly •stiffer elements of the structure "attract" a greater proportionof the applied longitudinal force•relative horizontal stiffness of towers

1002480Total

15370Tower 3

8196Tower 2

29714Tower 1

481200Resisting Abutment

Relative Stiffness (%)

Stiffness, k, (kip/in per rail)

Substructure


from AREMA Longitudinal Force Seminar Example

Distribution of Longitudinal Force

Braking Force, LFB = 45 + 1.2(440) = 573 kips (287 kips per rail)

Traction Force = LFT = 25 = 524 kips (262 kips per rail)440

2914433

158232

5528831

LF to Tower Leg with 80’ DPG fixed bearing

LF to Tower Leg with 40’ DPG fixed bearing

LF (kips)Tower

∆LF = 0.117”



E EF F

LFB

H40=28 k H80=55k

V40 V80

40’

yB+ 10’

TOWER 1

yB=8’ (braking force)

V40=28(18)/40= +/-13 k

V80= V40 -55(18)/80= 0



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.


Darn, Shouldn’t have

used L/1200L/1200

Thank You

““Designing For Longitudinal ForceDesigning For Longitudinal Force””

by by Richard D. PayneRichard D. Payne

PresidentPresident

ESCA Consultants, Inc.ESCA Consultants, Inc.

Tuesday September 19, 2006Louisville, KY

Designing for Longitudinal ForceDesigning for Longitudinal Force

Tuesday September 19, 2006 Louisville, KY

WHAT DOES AREMA CHAPTER 8 SAY?WHAT DOES AREMA CHAPTER 8 SAY?• Longitudinal Braking Force (kips) = 45 + 1.2L, 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.



•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?



•The resistance of the backfill behind the abutments shall be used where applicable



•How much movement of the wall into the soil is required to mobilize the passive state?

Dense Cohesionless Soil .005HLoose Cohesionless Soil .01HStiff Cohesive Soil .02HSoft 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.



•The mechanisms (rail, bearings, load transfer devices, etc.) available to transfer the force to the various components shall also be considered.



•For most ballasted deck steel pile trestles, friction is the primary factor in transferring load.

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).



•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.

OTHER CONSIDERATIONSOTHER CONSIDERATIONS



•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.

OTHER CONSIDERATIONS (Cont.)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 PaperBroms ASCE Journal, Vol. 91, No. SM3Davisson Highway Research Record No. 333Reese and Matlock Special Publication No. 29, Bureau of

Engineering Research, University of Texas – AustinDavisson and Robinson 6th 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 HandbookStructural Engineers Handbook, Gaylord & GaylordPile Foundation Know How, American Wood PreserversDrilled Pier Foundations, Woodward, Gardner, & GreerPile Design & Construction Practice, M.J. TomlinsonUS Navy Facilities, DM-7 (7-13-15)

OTHER CONSIDERATIONS (Cont.)OTHER CONSIDERATIONS (Cont.)







• 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.



•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 (4.4.3.6).

•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= 329.4k (Emergency Braking); 384.9k (Traction).

DESIGN CRITERIADESIGN CRITERIA



•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”.

DESIGN CRITERIA (Cont.)DESIGN CRITERIA (Cont.)



Load - Deflection Chart

0

20

40

60

80

100

120

140

160

180

200

0 1 2 3 4 5 6 7 8 9 10 11 12

Longitudinal Deflection (inches)

Long

itudi

nal L

oad

(kip

s)10' Bent

20' Bent

35' Bent

'Downhill'Abutment



•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 210k << 385k design

•The bridge is not stiff enough. What do we do?


0

20

40

60

80

100

120

140

160

180

200

0 1 2 3 4 5 6 7 8 9 10 11 12


Long

itudi

nal L

oad

(kip

s)

10' Bent

20' Bent

35' Bent

'Downhill'Abutment








0

50

100

150

200

250

300

350

400

0 1 2 3 4 5 6 7 8 9 10 11


Lo

ng

itu

din

al L

oad

(ki

ps)

20' Pier 1/2:12

20' Pier 1:12

20' Pier 2:12



•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 kipsTwo – 10’ Bents 40Two – 20’ Bents 10Two – 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.



WHAT IS COMMITTEE 8 DOING NEXT?WHAT IS COMMITTEE 8 DOING NEXT?

••We are thinking about the issue of probability as it relates to We are thinking about the issue of probability as it relates to emergency emergency braking. We believe that many bridges may be more likely to expbraking. We believe that many bridges may be more likely to experience EQ erience EQ loading than “Emergency” Braking. Yet, we currently allow a muchloading than “Emergency” Braking. Yet, we currently allow a much greater greater overstress in the bridge foundations for EQ than we do for LF.overstress in the bridge foundations for EQ than we do for LF.

•We may remove the longitudinal deflection limitation for Emergency Braking.



Any Questions?



Thank You.

AREMA- Design for Longitudinal Loads

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