Designing for Longitudinal Force - AREMA · PDF fileDesign of Steel Bridges for Longitudinal Force Analytical Finite Element model for a single span bridge: Analytical model (SAP90)

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 iiii
)()( =
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 & geometryRelative stiffness of members
Design of Steel Bridges for Current AREMA Chapter 15 Longitudinal Forces

Bearings and SubstructureTypeOrientation & geometryRelative 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 trussesLocalized traction at transverse floorbeam decks (direct fixation)Deck plate well fastened to closely spaced floorbeams may transmit LF through diaphragm or deep beam actionGirders 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 membersSubstructure type, geometry and spacing
Bearings TypeFixedExpansionElastomeric
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

Documents

Designing for Longitudinal Force - AREMA · PDF fileDesign of Steel Bridges for Longitudinal Force Analytical Finite Element model for a single span bridge: Analytical model (SAP90)