Office of Research and 

Development 

Washington, DC 20590 

Bridge Approaches and Track Stiffness U.S. Department of 

Transportation 

Federal Railroad 

Administration

DOT/FRA/ORD-08-01 Final Report 

February 2008 

This document is available to the 

U.S. public through the National 

Technical Information Service, 

Springfield, VA 22161. 
NOTICE 

This document is disseminated under the sponsorship of the 

Department of Transportation in the interest of information 

exchange. The United States Government assumes no liability for 

its contents or use thereof. 

NOTICE 

The United States Government does not endorse products or 

manufacturers. Trade or manufacturers’ names appear herein 

solely because they are considered essential to the objective of this 

report. 

 
REPORT DOCUMENTATION PAGE Form Approved 

 OMB No. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503. 

1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE

February 2008 

3. REPORT TYPE AND DATES COVERED

4. TITLE AND SUBTITLE

Bridge Approaches and Track Stiffness 

6. AUTHOR(S)

Donald Plotkin and David Davis 

5. FUNDING NUMBERS 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

U.S. Department of Transportation 

Federal Railroad Administration 

Office of Research and Development 

Washington, DC 20590 

Transportation Technology Center, Inc. 

P. O. Box 11130 

Pueblo, CO 81001 

8. PERFORMING ORGANIZATION 

REPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

U.S. Department of Transportation 

Federal Railroad Administration 

Office of Research and Development 

Washington, DC 20590 

10. SPONSORING/MONITORING 

 AGENCY REPORT NUMBER 

DOT/FRA/ORD–08/01 

11. SUPPLEMENTARY NOTES 

 

12a. DISTRIBUTION/AVAILABILITY STATEMENT

This document is available to the public through the National Technical Information Service, 

Springfield, VA 22161. 

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

Over time, it is not uncommon for a dip in the track to develop off the end of a bridge—on the bridge approach. This dip, or 

bump at the end of the bridge, is often a rough-riding spot and one that requires resurfacing at more frequent intervals than does 

the rest of the track. A commonly held belief is that this dip in the track is caused by dynamic forces resulting from wheel loads 

crossing an abrupt change in stiffness between the track on the bridge and the track off the bridge. A literature search found no 

documented field measurements to support this belief, only two modeling studies which predicted that the effect would be 

negligible. Five different methods were then employed to evaluate the potential for a track stiffness change to produce dynamic 

loads of practical significance. These methods ranged from the most technically sophisticated to the most basic. The results from 

all five pointed to the same conclusion—that changes in track stiffness at a bridge end have no practical effect on either track 

settlement or ride quality at a bridge approach. 

15. NUMBER OF PAGES

41 

14. SUBJECT TERMS

Bridge approach, track stiffness, track deflection, track modulus 

16. PRICE CODE

17. SECURITY CLASSIFICATION 

 OF REPORT

 Unclassified

18. SECURITY CLASSIFICATION

 OF THIS PAGE

 Unclassified

19. SECURITY CLASSIFICATION 

 OF ABSTRACT

 Unclassified

20. LIMITATION OF ABSTRACT

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89) 

Prescribed by ANSI Std. 239-18 298-102

i
METRIC/ENGLISH CONVERSION FACTORS 

ENGLISH TO METRIC METRIC TO ENGLISH

LENGTH (APPROXIMATE) LENGTH (APPROXIMATE) 

1 inch (in) = 2.5 centimeters (cm) 1 millimeter (mm) = 0.04 inch (in) 

1 foot (ft) = 30 centimeters (cm) 1 centimeter (cm) = 0.4 inch (in) 

1 yard (yd) = 0.9 meter (m) 1 meter (m) = 3.3 feet (ft) 

1 mile (mi) = 1.6 kilometers (km) 1 meter (m) = 1.1 yards (yd) 

1 kilometer (km) = 0.6 mile (mi)

AREA (APPROXIMATE) AREA (APPROXIMATE) 

1 square inch (sq in, in2) = 6.5 square centimeters (cm2) 1 square centimeter (cm2) = 0.16 square inch (sq in, in2) 

1 square foot (sq ft, ft2) = 0.09 square meter (m2) 1 square meter (m2) = 1.2 square yards (sq yd, yd2) 

1 square yard (sq yd, yd2) = 0.8 square meter (m2) 1 square kilometer (km2) = 0.4 square mile (sq mi, mi2) 

1 square mile (sq mi, mi2) = 2.6 square kilometers (km2) 10,000 square meters (m2) = 1 hectare (ha) = 2.5 acres 

1 acre = 0.4 hectare (he) = 4,000 square meters (m2) 

MASS - WEIGHT (APPROXIMATE) MASS - WEIGHT (APPROXIMATE) 

1 ounce (oz) = 28 grams (gm) 1 gram (gm) = 0.036 ounce (oz) 

1 pound (lb) = 0.45 kilogram (kg) 1 kilogram (kg) = 2.2 pounds (lb) 

1 short ton = 2,000 pounds 

(lb) 

= 0.9 tonne (t) 1 tonne (t) =

=

1,000 kilograms (kg) 

1.1 short tons

VOLUME (APPROXIMATE) VOLUME (APPROXIMATE) 

1 teaspoon (tsp) = 5 milliliters (ml) 1 milliliter (ml) = 0.03 fluid ounce (fl oz) 

1 tablespoon (tbsp) = 15 milliliters (ml) 1 liter (l) = 2.1 pints (pt) 

1 fluid ounce (fl oz) = 30 milliliters (ml) 1 liter (l) = 1.06 quarts (qt) 

1 cup (c) = 0.24 liter (l) 1 liter (l) = 0.26 gallon (gal) 

1 pint (pt) = 0.47 liter (l) 

 1 quart (qt) = 0.96 liter (l) 

1 gallon (gal) = 3.8 liters (l) 

1 cubic foot (cu ft, ft3) = 0.03 cubic meter (m3) 1 cubic meter (m3) = 36 cubic feet (cu ft, ft3) 

1 cubic yard (cu yd, yd3) = 0.76 cubic meter (m3) 1 cubic meter (m3) = 1.3 cubic yards (cu yd, yd3)

TEMPERATURE (EXACT) TEMPERATURE (EXACT) 

[(x-32)(5/9)] °F = y °C [(9/5) y + 32] °C = x °F

QUICK INCH - CENTIMETER LENGTH CONVERSION

0 1 2 34

Inches

Centimeters 01 3 26 1 4 5 7 1 1098 1 12

5

3

QUICK FAHRENHEIT - CELSIUS TEMPERATURE CONVERSION

 -40° -22° -4° 14° 32° 50° 68° 86° 104° 122° 140° 158° 176° 194° 212°

 

°F

 °C -40° -30° -20° -10° 0° 10° 20° 30° 40° 50° 60° 70° 80° 90° 100°

For more exact and or other conversion factors, see NIST Miscellaneous Publication 286, Units of Weights and 

Measures. Price $2.50 SD Catalog No. C13 10286 Updated 6/17/98

ii 
Contents 

Figures ........................................................................................................................................... v 

Tables ......................................................................................................................................... vii 

Acknowledgements........................................................................................................................ ix 

Executive Summary........................................................................................................................ 1 

1. Introduction ....................................................................................................................... 3 

1.1 Background................................................................................................................... 3 

1.2 Objective....................................................................................................................... 4 

1.3 Approach....................................................................................................................... 5 

1.4 Scope............................................................................................................................. 5 

1.5 Track Stiffness and Track Modulus.............................................................................. 5 

1.6 The Track Stiffness Difference Theory ........................................................................ 6 

2. Analysis and Results ......................................................................................................... 7 

2.1 Literature Review.......................................................................................................... 7 

2.2 Dynamic Forces and Accelerated Track Settlement..................................................... 8 

2.3 Computer Modeling...................................................................................................... 9 

2.4 Wheel-Rail Force and Carbody Acceleration Measurements..................................... 11 

2.5 Bridge Approach Track Profiles ................................................................................. 19 

2.6 Simplified Analysis..................................................................................................... 20 

2.7 The Train Ride Test .................................................................................................... 25 

3. Summary and Conclusions.............................................................................................. 27 

4. Future Research .............................................................................................................. 29 

5. References ....................................................................................................................... 31 

Acronyms...................................................................................................................................... 33 

iii 
iv 
Figures 

Figure 1. Track settlement off a bridge end................................................................................... 3 

Figure 2. Measurements of track modulus at a ballast deck bridge............................................... 4 

Figure 3. Stiffness difference concept, illustrating an abrupt change in track modulus from 

10,000 to 2,000 lbs/in/in..................................................................................................6 

Figure 4. Estimated change in wheel load required to increase track settlement rate ................... 9 

Figure 5. Vertical forces on the ties from a 286,000-lb car crossing a stiffness change ............... 9 

Figure 6. FRA's research car T-16 ............................................................................................... 11 

Figure 7. Back of instrumented wheelset, in the shop with cover off (note strain gauges 

and connecting wires)....................................................................................................11 

Figure 8. Outside face of instrumented wheelset, in the shop with cover off (note 

strain gauges)................................................................................................................ 12 

Figure 9. Instrumented wheelset in place on T-16....................................................................... 12 

Figure 10. Instrumented wheelset configuration on T-16............................................................ 12 

Figure 11. Vertical carbody acceleration, top-of-rail profile, and vertical wheel-rail 

forces at 2 ballast deck bridges near MP 85.18, about 10.4 miles north of 

Baltimore, MD .............................................................................................................14 

Figure 12. Top-of-rail profile and vertical wheel-rail forces at a ballast deck bridge, MP 

51.95, near North East, MD.........................................................................................15 

Figure 13. Top-of-rail profile and vertical wheel-rail forces at a ballast deck bridge, MP 

51.89, near North East, MD.........................................................................................15 

Figure 14. Top-of-rail profile and vertical wheel-rail forces at a ballast deck bridge, MP 

42.51, near Elkton, MD................................................................................................16 

Figure 15. Top-of-rail profile and vertical wheel-rail forces at a ballast deck bridge, MP 

40.71, near Newark, DE...............................................................................................16 

Figure 16. Vertical carbody acceleration, top-of-rail profile, and vertical wheel-rail forces 

at an open deck bridge, MP 13.41, Chester, PA ..........................................................17 

Figure 17. Top-of-rail profile and vertical wheel-rail forces at an open deck bridge, MP 

13.25, Chester, PA .......................................................................................................18 

Figure 18. Top-of-rail profile and vertical wheel-rail forces at a ballast deck bridge, MP 

13.36, North Elizabeth, NJ...........................................................................................18 

Figure 19. Top-of-rail profile (with average gradient removed) for the bridge with stiffness 

data shown in Figure 2.................................................................................................20 

Figure 20. Change in track elevation under load, between track with a modulus of 10,000 

and track with a modulus of 2,000...............................................................................21 

Figure 21. Rail profile ramp when track modulus abruptly changes from 10,000 to 2,000 .........21 

v 
Figure 22. Rail deflection under load for beam-on-elastic-foundation theory .............................22 

Figure 23. Deflection of beam with fixed ends.............................................................................23 

Figure 24. A 10,000 to 2,000 modulus changein—a 1:400 ramp.................................................24 

vi 
Tables 

Table 1. Typical track modulus value ranges for track on main routes..........................................5 

Table 2. Static loads on T-16's instrumented wheelsets ...............................................................13 

Table 3. Distance from maximum to zero rail deflection for various track modulus values........23 

Table 4. Comparing the effect of a 10,000-2,000 track stiffness change with railroad runoff 

standards........................................................................................................................25 

Table 5. Summary of results .........................................................................................................27 

vii 
viii 
Acknowledgments 

Steve Chrismer of LTK Engineering Services conducted the general literature review. Stan 

Gurule of the Transportation Technology Center, Inc. produced the computer modeling data 

showing vertical forces below the rail. Brian Whitten and Brent Selby of ENSCO provided the 

instrumented wheelset data from the Northeast Corridor. Their work is gratefully acknowledged. 

The Federal Railroad Administration also acknowledges Amtrak for granting permission to use 

data from the Northeast Corridor. 

ix 
x 
Executive Summary 

Bridge approaches are a common source of poor ride quality and often require more frequent 

resurfacing due to track settlement within about 50 feet from the bridge end. The source of the 

problem is often said to be the difference in stiffness between the stiffer track on the bridge and 

the less stiff track off the bridge. As the less stiff track will experience greater vertical deflection 

under load, this has the effect of creating a track surface deviation (a bump in the track) at the 

point where track stiffness changes. 

As is well known and documented, track surface deviations cause dynamic loads or impacts 

when trains pass over them. In addition, track subjected to higher loads will settle more than 

track not subjected to these loads. 

Numerous attempts have been made to eliminate the bridge approach track dip by reducing the 

track stiffness difference or by creating a more gradual stiffness transition; yet none of these 

have worked to any great degree. This inability to eliminate the bridge approach problem 

prompted a study to examine the track stiffness difference concept to determine why its past 

application had been repeatedly unsuccessful. 

For a stiffness difference to cause track settlement or have an adverse effect on ride quality, it 

must produce dynamic forces large enough to have these effects. While the stiffness difference 

theory itself appears unquestionably correct, a literature search found no evidence documenting 

the magnitude of its actual effect in track. The literature search did find results of two modeling 

studies, which predicted that the stiffness change effect would be negligible. 

The following five methods were then employed to evaluate the potential effect of track stiffness 

difference, ranging from the most technically sophisticated to the most basic: 

1. Analysis with the NUCARS® track/train dynamics computer program 

2. Examination of vertical force and carbody acceleration data collected with instrumented 

wheelsets 

3. Examination of settlement and top-of-rail profile data at bridge approaches 

4. Calculations using simple beam deflection equations and beam-on-elastic-foundation 

track deflection theory, with the results compared to common railroad track maintenance 

criteria 

5. The train ride test—a simple but revealing observation that can be made aboard a 

moving train 

The results from the literature search and the five analysis methods all pointed to the same 

conclusion—that changes in track stiffness have no practical effect on ride quality or track 

settlement at bridge approaches. 

 

1 

1. Introduction 

1.1 Background 

Over time, it is not uncommon for a dip in the track to develop off the end of a bridge—on the 

bridge approach, as shown in Figure 1. This dip, or bump at the end of the bridge, is often a 

rough-riding spot and one that requires resurfacing at more frequent intervals than does the rest 

of the track. 

Figure 1. Track settlement off a bridge end 

To estimate the extent of the occurrence of bridge approach roughness, the Transportation 

Technology Center, Inc. (TTCI) commissioned a survey to sample railroads from North 

America, Australia, and Europe on this subject (Briaud, et al., 2006). Responses from 11 

railroads, including 4 major North American carriers, indicated that approximately 50 percent of 

bridge approaches were said to develop a low approach which adversely affected ride quality, 

frequently required a speed restriction, and generally required above average surfacing 

maintenance. Responses indicated the formation of low spots on bridge approaches ranging 

from 1/4 to 4 in. in depth and from 4 to 50 ft in length. 

In an Association of American Railroads (AAR) project to measure freight car load environment, 

dynamic loads from a loaded coal gondola were recorded while traveling from the mine to a 

power plant—a trip of more than 1,000 miles. A description of the locations causing high 

vertical and lateral forces was provided. During the trip, four locations registered vertical loads 

above twice the static wheel load level. Of these four, three were described as bridges or 

culverts (Koch, 2007). The fourth was a turnout. All had in common a significant track surface 

deviation (at or near Federal Railroad Administration (FRA) track safety limits for the track 

speed operated). 

3
A commonly held belief is that low spots in the track at bridge approaches are caused by 

dynamic forces resulting from wheel loads crossing an abrupt change in stiffness between the 

track on the bridge and the track off the bridge. Figure 2 shows one case of the measured 

difference in track stiffness (or track modulus) between the track on a ballast deck bridge and the 

track off the bridge. In this figure, data is averaged over a 30-ft moving window. 

 Figure 2. 

 

Distance (ft)

Dynamic Track Modulus

1200 1300 1400 1500 1600 1700

(lb/i .) n./in

Figure 2. Measurements of track modulus at a ballast deck bridge 

Many attempts have been made to remedy the bridge approach problem by trying to reduce the 

abrupt stiffness change. These attempts have included increasing the track stiffness on the 

approach by using gradually longer ties or by installing a concrete or asphalt pad below the 

ballast, or reducing the track stiffness on the bridge by installing rail seat pads. None of these 

methods have produced much success. 

This inability to eliminate the bridge approach problem prompted a study to examine the track 

stiffness difference concept to determine why its past application had been repeatedly 

unsuccessful and, further, to find effective and affordable methods for remedying ride quality 

and track settlement problems at bridge approaches and other track transitions—locations where 

track construction changes, as at bridges, turnouts, road crossings, and track crossings. This 

report presents the first product from the study. 

1.2 Objective 

The objective of this first part of the bridge approach and track transition study was to quantify 

the effect that changes in track stiffness at bridge ends might have in causing track settlement 

and adversely affecting ride quality at bridge approaches. 

0

2000

4000

6000

8000

10000

12000

14000

BRIDGE

Dynamic Track Modulus (lb/i .) n./in

Distance (ft)

1200 1300 1400 1500 1600 1700

0

2000

4000

6000

8000

10000

12000

14000

BRIDGE

4
1.3 Approach 

No field tests were conducted specifically for this work. The approach was to first see if existing 

data and analysis methods could provide a satisfactory answer to the question being investigated. 

To compensate for the absence of targeted field tests, the plan was to look at the possible effect 

of track stiffness difference using several different methods. If the results from each were in 

sufficient agreement and collectively, sufficiently conclusive, then field tests would not be 

necessary. 

1.4 Scope 

This phase of the study examined only the possible effect that abrupt changes in track stiffness 

might have in producing dynamic loads of sufficient magnitude to cause additional track 

settlement or adversely affect ride quality. The study did not cover other applications of track 

stiffness theory or measurements. 

1.5 Track Stiffness and Track Modulus 

Track stiffness, its resistance to deflection when subjected to a vertical load, is typically 

indicated by a measure called track modulus. Track modulus is most commonly expressed in 

units of pounds required to cause a 1-in length of track to deflect 1 in. 

Track modulus is not a fixed value. For any location, it will typically vary over the course of 1 

year, often by a factor of 2 or more. In areas of the United States that have cold winters and 

snow, track modulus is highest when the ground is frozen and during long dry periods. In these 

areas, track modulus is usually lowest during the spring thaw and after long periods of heavy or 

steady rain when the subgrade is at or near saturation from surface water infiltration and/or a 

temporary rise in the water table. Table 1 shows common ranges of modulus values for wellmaintained track on a primary main route and during periods when ballast and subgrade are not 

frozen and the subgrade is near its average moisture content. 

Table 1. Typical track modulus value ranges for track on main routes 

Track Type Typical Modulus Range 

Wood Tie Track 2,000 to 3,500 

Concrete Tie Track 3,500 to 6,000 

Track on a Concrete Ballast Deck Bridge 8,000 to 12,000 

The values in Table 1 can serve as references when stiffness differences are examined in 

following sections. 

5
1.6 The Track Stiffness Difference Theory 

As normally built, track on a bridge is relatively stiff, being supported by a rigid bridge structure. 

Track off a bridge is supported by an earth subgrade, which is not so rigid as a bridge and thus 

permits more deflection when subjected to the same load. In level track, with no load present, 

the top of rail off the bridge is even with that on the bridge. As a loaded wheel rolls over the end 

of a bridge and passes from the stiffer track on the bridge to the less stiff track off the bridge, 

however, its weight causes the less stiff track to deflect further, causing a difference in vertical 

deflection, which creates a bump in the track—a track surface deviation. Figure 3 illustrates this 

concept, showing a difference in deflection as wheels of a fully loaded freight car cross a change 

in track modulus from 10,000 to 2,000 lbs/in/in. 

10,000

2,000

Change in Rail Deflection

Figure 3. Stiffness difference concept, illustrating an abrupt change 

in track modulus from 10,000 to 2,000 lbs/in/in 

Track surface deviations cause dynamic loads or impacts when trains pass over them. In 

addition, track subjected to higher loads will settle more than track not subjected to these loads. 

This is how an abrupt change in track stiffness is said to cause settlement at bridge approaches. 

To show that this theory has a practical effect, it must be shown: 

• How large dynamic forces must be to cause additional bridge approach settlement or 

affect ride quality 

• That crossing a stiffness change does produce dynamic loads of this magnitude 

• That the dynamic forces produced are actually responsible for the increased settlement or 

adverse effect on ride quality 

6
2. Analysis and Results 

To search for evidence that a stiffness difference could cause dynamic forces sufficient to affect 

track settlement or adversely affect ride quality at bridge approaches, a literature review was 

conducted, followed by analyses using five different methods. 

2.1 Literature Review 

A search was conducted to find sources that offered credible information quantifying the 

stiffness difference effect at bridge ends. Many sources either stated or referred to the theory, 

but none provided field measurements or other evidence to demonstrate that crossing a stiffness 

change produced dynamic loads sufficient to cause accelerated track settlement or to adversely 

affect ride quality. Two sources documented modeling studies conducted to predict the 

magnitude of dynamic loads that a stiffness change might produce. 

In one modeling study, Lundquist and Dahlberg (2005) constructed a finite element model to 

analyze wheel-rail forces from a 24,000-lb wheel load crossing an abrupt change in track 

stiffness from approximately 2,775 to 7,000 lbs/in/in at 200 mph. When moving in the direction 

from the softer to the stiffer track, the model calculated a dynamic increase in wheel load of 

approximately 2,000 lbs, an 8.3 percent increase over the static load. When moving in the 

opposite direction, a dynamic wheel load increase of 1,600 lbs resulted, a 7 percent increase over 

the static load. 

In an unpublished study (see Singh, 2003), the NUCARS® track-train dynamics model was used 

to simulate a loaded 100-ton hopper running at 60 mph on theoretically perfect and uniform 

track, which included a stiffness change from 2,000 to 30,000 lbs/in/in. In crossing the stiffness 

change, the model calculated that the wheel-rail force would increase from 32,964 lbs to 35,181 

lbs, a 6.7 percent increase. 

While these two studies did show that, under certain conditions, a stiffness change could cause 

some increase in dynamic load, neither indicated how this load increase might affect track 

settlement. As will be covered in Section 2.3, dynamic forces produced at the rail surface are not 

always or completely transmitted to the ballast and subgrade and thus do not necessarily have the 

same effect on track settlement as they do at the rail surface. Section 2.2 will further show that 

vertical forces on the ballast and subgrade must increase by a certain percentage to produce 

noticeably accelerated track settlement. 

In addition to the general literature review, portions of the Talbot Reports (AREA, 1980) were 

re-read to determine if any of their content may have suggested the stiffness difference theory or 

a practical effect from it, as it was these reports that established the concept and application of 

track stiffness in the United States. In particular, Report 1; Report 2–Part 3; Report 5–Section 

57; and Report 6–Parts 5, 6, and 8 deal with the general theory and application of track 

7
deflection and track stiffness.1

 Nothing was found in this material to suggest either the stiffness 

difference theory or its potential to have a practical effect in producing dynamic wheel-rail 

forces. 

2.2 Dynamic Forces and Accelerated Track Settlement 

The literature search found 2 model studies which predicted that crossing a stiffness change 

could cause dynamic wheel-rail forces in the range of 7 percent to 8 percent under certain 

circumstances, requiring either considerably higher speed or substantially greater stiffness 

change than would likely occur in current U.S. railroad operations. 

What needs to be determined or estimated is how much dynamic force would be required to 

cause accelerated track settlement, that is, track settlement at a rate noticeably higher than 

normal or average. 

If observation of the track surfacing interval is used as an indicator of track settlement rate, a 

judgment could be made of the relative surfacing interval that would be considered noticeably 

shorter than normal or average. It would appear necessary to have an interval at least 25 percent 

shorter than usual to be clearly noticeable. Thus, for example, in territory typically having a 4-

year surfacing cycle, the surfacing requirement at a location would need to be 3 years or less to 

be considered abnormally frequent. 

For track at a ballast deck bridge, how much additional vertical force would be needed to cause a 

location off the bridge to settle at least 25 percent faster than track on the bridge? Figure 4 

shows data from a track settlement model being developed by TTCI (Davis et al., 2007), which 

is used to provide this estimate. As this graph indicates, about a 50 percent increase in load 

below the rail would be required to produce what is considered to be a noticeably greater 

differential track settlement rate. 

From this determination, the first observation is that even if all the increased force predicted by 

the Singh (2003) and Lundquist and Dahlberg (2005) studies, with their extreme conditions, was 

transmitted through the rail to the ties, it would not be enough to produce accelerated track 

settlement. By the minimum criteria defined above, to have a noticeable effect, forces would 

have to be at least six times higher than these studies indicate could be produced. 

 

1

 Reports of the Special Committee on Stresses in Railroad Track. This work by a joint American Railway 

Engineering Association (AREA)-American Society of Civil Engineers (ASCE) committee was the first effort in 

the United States to systemically investigate the nature of various stresses in track. The results appeared in seven 

reports published from 1918 to 1940, subsequently reprinted as a compilation by AREA in 1980. Included in this 

work is the introduction of the concepts and significance of track stiffness, track deflection, and track modulus. 

The work related to vertical track deflection and track stiffness was published beginning with the First Progress 

Report in 1918 and ending with the Sixth Progress Report in 1933. 

8
0

5

10

15

20

25

30

0 10 20 30 40 50 60

LOAD INCREASE (%)

SETTLEMENT INCREASE (%)

Figure 4. Estimated change in wheel load required to increase differential 

track settlement rate 

2.3 Computer Modeling 

The NUCARS® track-train dynamics computer program is designed to compute various forces 

and accelerations produced by a freight or passenger car moving over the track. It was used to 

model the effect of an abrupt track stiffness change. Figure 5 shows results of modeling the 

vertical forces produced below the rail (on the ties) when 286,000-lb freight cars cross a 10,000 

to 2,000 stiffness change at 50 mph. In the graph, the vertical scale is a normalized load, with 

1.0 equal to the typical force on 1 tie on the bridge as a loaded wheel passes directly over it 

(roughly equal to about 45 percent to 50 percent of the wheel load). The left half of the graph 

shows forces on the bridge, with the end of the bridge at tie 192. The wheel is traveling from left 

to right. 

0.0

0.5

1.0

1.5

2.0

2.5

185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200

Tie Number (Spaced @ 20")

Normalized Vertical Force Under Ties

Bridge Approach

Direction of Travel

50 mph Operation

Bridge: 10,000 lbs/in/in

Approach: 2,000 lbs/in/in

Figure 5. Vertical forces on the ties from a 286,000-lb car crossing a stiffness change 

9
The graph shows that the load increases on the last 2 ties on the bridge, up to about 70 percent 

above the nominal level, and then drops to about half its nominal value on the first tie off the 

bridge (tie 193), returning to a steady state by about the third tie past the bridge (tie 195). The 

main observation from the graph is that in the approximately 13 ft off the bridge, no forces on 

the ties are either above the nominal level (1.0) or the lower steady-state level off the bridge. 

At first, the modeling results in Figure 5 may seem to differ from those reported in Section 2.1 

by Singh (2003) and Lundquist and Dahlberg (2005). The differences relate to the location 

within the track structure where the forces are being measured. 

Singh (2003) and Lundquist and Dahlberg (2005) reported forces at the wheel-rail interface. As 

these will travel both upward into the car and downward into the track, they have the potential to 

affect ride quality and track settlement. They may, however, have only some or even no effect 

on either due to the filtering actions of the car's suspension and the rail. To affect ride quality, 

forces must create an impact large enough in magnitude and long enough in duration to get 

through the car's suspension. Wheel-rail forces of duration less than about 1/150 of a second (or 

dynamic forces with frequency above 150 Hz) are not well transmitted to the ballast and 

subgrade and therefore do not significantly affect track settlement. At shorter durations, forces 

are dissipated in the rail as vibrations or minute elastic rail deformations (see Eisenmann, 1992, 

and Jenkins, 1974, p. 5). 

What can be concluded from the Singh (2003) and Lundquist and Dahlberg (2005) studies is that 

if wheel-rail forces increase by the reported 7 percent to 8 percent, forces transmitted to the 

roadbed cannot increase by more than this, but the amount transmitted to the roadbed may be 

less. 

To assess the potential effect on track settlement, the NUCARS® model was run to estimate the 

forces transmitted below the rail, on the ties. At this level, even with no change in applied force 

from above, forces on one tie may differ from that at adjacent ties if support conditions are not 

the same, which would mean that not all ties are sharing the load equally. The data in Figure 5 

should reflect the combined effect of applied loads from the passing train, as well as any unequal 

load sharing due to the stiffness change. 

As the Singh (2003) and Lundquist and Dahlberg (2005) studies resulted in wheel-rail force 

increases of about 7 percent to 8 percent (but at more extreme conditions, higher speed or greater 

stiffness change than in this example), this indicates that at least 90 percent of the load increase 

seen in Figure 5 at tie 192 (edge of the bridge) results from the change in support at that location. 

The most important figure, though, is the total magnitude of the load on a tie—regardless of the 

source, as this is what could affect track settlement. As Figure 5 shows, the high load peak 

occurs at the last tie on the bridge, not on the approach track. 

Figure 5 also shows a lower steady-state tie force off the bridge, about 85 percent of nominal 

(1.0) at ties 195 to 200. This is due to the softer support (2,000 modulus), which has the effect of 

spreading out the wheel load over a somewhat longer length of track and results in any single tie 

receiving and supporting a somewhat smaller percentage of the wheel load. This effect is 

10
expected and was demonstrated by the Talbot Committee through their numerous field and lab 

experiments related to vertical track stiffness conducted from 1914 to 1933 (see AREA, 1980). 

2.4 Wheel-Rail Force and Carbody Acceleration Measurements 

Data were examined from vertical wheel force measurements taken by FRA's research car T-16. 

This car (Figure 6) is sometimes equipped with instrumented wheelsets, which are the nearest 

two wheelsets in this picture. Figures 7, 8, and 9 show these wheels in more detail. 

Figure 6. FRA's research car T-16 

Figure 7. Back of instrumented wheelset, in the shop with cover off 

(note strain gauges and connecting wires) 

11
 Figure 8. Outside face of instrumented wheelset, in the shop with cover off 

(note strain gauges) 

Figure 9. Instrumented wheelset in place on T-16 

Through their numerous strain gauges, as shown in Figures 7 and 8, these wheels are capable of 

measuring a variety of forces and accelerations, in different directions, at speeds up to 160 mph, 

with measurements recorded up to 300 times a second (300 Hz). Figure 10 shows the location 

designation of the four instrumented wheels. The data examined for this report was taken on 

Track 2 of the Northeast Corridor between Washington and New York on December 2, 2003, 

with the static wheel loads as given in Table 2. 

12
Figure 10. Instrumented wheelset configuration on T-16 

Table 2. Static loads on T-16's instrumented wheelsets 

Wheel Static Load Wheel Static Load 

2A 17,661 lbs 1A 17,298 lbs 

2B 16,564 lbs 1B 16,714 lbs 

Figures 11 through 18 show data for 400-foot sections of track, selected to show vertical wheelrail forces when approaching a bridge, while on the bridge, and just past the bridge. This series 

includes seven ballast deck bridges and two open deck bridges.2 Vertical carbody acceleration is 

also shown at two ballast deck bridges (Milepost (MP) 85.18) and one open deck bridge (MP 

13.41). The force and acceleration data are filtered at 50 Hz, so any force or acceleration of 1/50 

second duration or longer will appear. The system should register any force greater than about 

300 lbs. The location error for the bridge ends with respect to the data traces is a maximum of 

30 ft. In all graphs, the train is running left to right—northbound, with the bridge location 

marked below the data, as indicated in each caption. The operating speed at the time data was 

taken ranges from 84 to 123 mph, as marked on the graphs. 

Examination of the vertical force data shows that even in the best track, a dynamic component is 

always added to the static load. This nominal dynamic addition would be considered the noise 

level. When running at these speeds, most of the track is typically subjected to this load level. 

Therefore, this is the reference (or zero) point for examining the significance of vertical forces. 

In this case, the noise level is at the 20,000-lb level. All of the vertical force graphs have a 

horizontal line drawn at this level for reference. 

As the train is traveling from left to right in all the figures, the most important focus is the 50 feet 

adjacent to the right (north) end of the bridges. If crossing the bridge-to-track stiffness change 

does produce dynamic forces of significance on a bridge approach, they should be visible in this 

area. 

In all cases, the forces on the north bridge approach are either at or barely above the noise level. 

If the bridge locations were not marked, no indication would be apparent from the force 

measurements that a deviation or change of any kind was present in the track. According to the 

railroad, no alterations were made to the track to change stiffness on the approaches or on the 

bridges; all is standard construction. 

The 300-ft point in Figure 14 and the 40- to 60-ft range in Figure 17 are examples of an 

instantaneous force spike and force increases that occasionally occur even in good track and 

 

2

 Bridges are often categorized by the manner in which track is constructed across them. The two main types are 

open and ballast deck. With an open deck bridge (as seen in the cover photo), the rail is supported by bridge ties 

(a larger version of track ties) fastened directly to the bridge structure. No ballast is used, and open spaces exist 

between the ties. With a ballast deck bridge (as seen in Figure 1), a solid floor or deck is used on which a 

conventional ballasted track section is constructed. Track on a ballast deck bridge is surfaced and lined in the 

same manner as track off the bridge. 

13
would be considered inconsequential. None of the forces in the north bridge approaches in any 

of the figures are nearly at these levels. 

Figures 11 and 16 include data for vertical carbody accelerations, to provide an indication of ride 

quality at two ballast deck bridges and one open bridge. While defining ride quality can become 

complex, as a general indication, an acceleration would need to be higher than approximately 

minus to plus 0.2g and sustained for at least 1 second before a noticeable sensation would be 

typically felt. This would require acceleration at or above the top of the vertical scale in the 

acceleration graphs in these 2 figures, remaining at this level for at least 160 ft in Figure 11 and 

130 ft for Figure 16. As shown, the accelerations are far below this level. The acceleration data 

at the other five bridges was similar. 

Figure 11. Vertical carbody acceleration, top-of-rail profile, and vertical wheel-rail forces 

at 2 ballast deck bridges near MP 85.18, about 10.4 miles north of Baltimore, MD 

14
Figure 12. Top-of-rail profile and vertical wheel-rail forces at a ballast deck bridge, MP 

51.95, near North East, MD 

Figure 13. Top-of-rail profile and vertical wheel-rail forces at a ballast deck bridge, MP 

51.89, near North East, MD

15
Figure 14. Top-of-rail profile and vertical wheel-rail forces at a ballast deck bridge, 

MP 42.51, near Elkton, MD

Figure 15. Top-of-rail profile and vertical wheel-rail forces at a ballast deck bridge, 

MP 40.71, near Newark, DE 

16
Figure 16. Vertical carbody acceleration, top-of-rail profile, and vertical wheel-rail forces 

at an open deck bridge, MP 13.41, Chester, PA 

17
Figure 17. Top-of-rail profile and vertical wheel-rail forces at an open deck bridge, MP 

13.25, Chester, PA

Figure 18. Top-of-rail profile and vertical wheel-rail forces at a ballast deck bridge, 

MP 13.36, North Elizabeth, NJ

18
2.5 Bridge Approach Profiles 

Track settlement at a location would be greater than it is elsewhere for either or a combination of 

two main reasons: 

• The track support is weaker (for any of numerous reasons). 

• Vertical forces are higher. 

Of these two, an abrupt change in track stiffness could only affect the second. Thus, if bridge 

approaches do not typically have stronger support than does the rest of the track, it would be 

expected that if abrupt changes in track stiffness did cause bridge approaches to be subjected to 

higher vertical forces, track at approaches would typically settle more than track farther away 

from the bridge. 

From what is known about bridge approaches, these locations have mostly about equal or lower 

support strength than does track in general, with weaker support often the case where the 

approach is on a narrow embankment with steep side slopes or is weakened by poor drainage. If 

the stiffness difference theory is true, it would be expected that the majority of bridge approaches 

would develop low spots. 

A limited examination of bridge approach settlement, as indicated by unloaded top-of-rail 

profile, showed variation in the approach profile patterns. Observed and measured profiles 

similar to that shown in Figure 19 were common, in which top-of-rail elevation within about 50 

ft or so adjacent to the bridge was sometimes lower than in track farther away but often not. 

Even on the same route, where traffic was the same and bridge construction similar, track 

profiles at bridge approaches varied. 

The view as seen in Figure 1 was also common. In that picture, a pronounced drop in track 

elevation off the bridge end is evident, but the top-of-rail elevation near the bridge is not lower 

than in track farther away, suggesting that track settlement on the approach was not greater than 

it was elsewhere. To be more definitive, information would be needed about traffic level, 

predominate direction of loaded cars (if any), and track surfacing history. 

Even within the limitations of these observations, however, if the stiffness difference theory was 

correct, a more consistent appearance of low spots at bridge approaches would have been 

expected. These observations indicate that bridge approaches often settle at about the same rate 

as does the rest of the track, which suggests that vertical forces on bridge approaches are often 

not significantly greater than elsewhere along the track. 

19
Figure 19. Top-of-rail profile (with average gradient removed) for the bridge with stiffness 

data shown in Figure 2 

2.6 Simplified Analysis 

Without access to such technology as instrumented wheelsets or track/train dynamics computer 

programs, is there a simpler way to get a general idea of how large the stiffness difference effect 

might be? The following method relies on readily available information to accomplish this. 

This example will use a stiffness difference represented as the difference between a track 

modulus of 10,000 lbs/in/in on a bridge and 2,000 lbs/in/in on the adjacent approach track, 

estimated to be about as large a difference as would usually be found. The initial (unloaded) topof-rail profile is level; the only changes that occur are due to the loads as the wheels roll over the 

example section. 

Under a passing train, the sudden change in stiffness is said to produce a deflection difference, 

which, in concept, appears somewhat as shown in Figure 20. For this example, the load on the 

track will be that from fully loaded 286,000-lb freight cars traveling at 50 mph. The 

representative wheel load is 41,500 lbs.3

 The track has 136-lb rail. 

The most important observation is that, while the support below the rail can have an abrupt step 

as shown in Figure 20, the rail cannot bend in that fashion. For the case illustrated in Figure 20, 

the rail surface will appear much closer to that shown in Figure 21; it will form a ramp between 

 

3

 Recent data from instrumented wheelsets and wheel load impact detectors suggest that good wheels (not out-ofround or with flat spots) on good track with welded rail and traveling near the highest speed allowable for that 

FRA track class, commonly produce a dynamic load about 15 percent greater than their static load. For a 

286,000-lb car, the static wheel load is 36,000 lbs, and the total dynamic load would be 1.15 x 36,000, or about 

41,500 lbs. Li (2006) is one example reference showing wheel load data. 

20

99.5

99.6

99.7

99.8

99.9

100

100.1

100.2

100.3

100.4

100.5

0 100 200 300 400 500

DISTANCE (FEET)

RAIL ELEV. (FT)

GRADE CORRECTED BRIDGE ENDS
the elevation difference. Still oversimplified in this figure, near the ends of the ramp, the rail 

will of course bend in vertical curves, but the general idea is that the actual wheel path over the 

stiffness change will be along a ramp and not down a step. 

10,000

2,000

Change in Rail Deflection

Figure 20. Change in track elevation under load, between track with a modulus of 10,000 

and track with a modulus of 2,000

10,000

2,000 Y

L

Figure 21. Rail profile ramp when track modulus abruptly changes from 10,000 to 2,000 

The next steps are to determine the height of the ramp (Y) and its length (L), which will 

give an indication of this bump's severity in the track. The ramp height would be the 

difference between the deflection of the 2,000 modulus track and the 10,000 modulus 

track. This can be calculated by using the track deflection equation, as found in Hay 

(1982, p. 249):4

Y = P

(64EIu3

)

0.25

Y = vertical rail deflection (in) 

P = wheel load (lbs) 

 41,500 in this example 

E = Young's modulus for steel 

 29,600,000 psi 

I = rail moment of inertia 

 94.2 in4

 for 136-lb rail 

u = track modulus 

 

4

 This is the well-known track deflection equation from the theory of representing the track as a beam (the rail) on 

an elastic foundation. 

21
 For the 2,000 modulus track, Y = 0.213 in 

 For the 10,000 modulus track, Y = 0.064 in 

 The difference = 0.149 in 

Rounding off, the ramp height is then 0.15 in. Some initial thought might be given to how big an 

effect a bump of this size could possibly have and its potential capability to generate dynamic 

forces that would affect track settlement along a bridge approach of approximately 50 feet or so 

in length. One observation is that this vertical difference, even if relatively abrupt, would 

represent a relatively small track surface deviation. 

The analysis now continues toward estimating the ramp length. This will be more difficult, as no 

simple equation exists for calculating the rail bending length when the strength of the support 

under the wheel load varies. To produce an estimate, two simplified methods are used to 

determine what could be called a theoretical worst case—the shortest length over which the rail 

would probably bend to accommodate a 0.15-in change in support elevation. 

The beam-on-elastic-foundation theory once again provides something usable. Figure 22 

illustrates the general arrangement for this approach, with the arrow at W representing the wheel 

load applied to the line representing the flexible rail and the upward arrows under the rail 

representing the support reaction. X2 is the distance between the point of maximum rail 

deflection and the point of zero rail deflection, or about the same as the ramp length L.5

 

 

W

X2

Figure 22. Rail deflection under load for beam-on-elastic-foundation theory

The following equation for X2 can be found in Hay (1982, p. 250), but this theory does assume 

that the support under the rail (the track modulus) is uniform along the track segment being 

loaded. Generally, it should be clear that given the same vertical deflection, the stiffer the track 

support, the sharper the rail bending will be to return to the zero deflection point. Table 3 shows 

results from several trial stiffness values. As the track stiffens, X2 approaches a value in the 

range of 58 to 61 in, although it takes a stiffness above 25,000 to produce that short a bending 

length. 

 

5

 As Figure 22 shows, the rail rises slightly above the unloaded elevation on the far right and left, but no load on the 

rail occurs at these points. The length of the stiffness change ramp being analyzed is assumed to be as short as the 

distance X2. 

22
 

X2 = 3/4π (4EI/u)0.25

X2 = distance from point of maximum rail 

deflection to point of zero rail deflection 

(in) 

E = Young's modulus for steel 

 29,600,000 psi 

I = rail moment of inertia 

 94.2 in4 for 136-lb rail 

u = track modulus 

Table 3. Distance from maximum to zero rail deflection for various track modulus values 

Another way to estimate how short the rail bending length could possibly be is to use a simple 

beam bending formula, with an arrangement as shown in Figure 23. This figure shows the rail as 

a beam with fixed ends (allowing no rotation) and no support between endpoints. Compared to 

the actual case in track, the fixed ends would provide more upward support than actually occurs, 

but the absence of support under the beam is severe in the opposite effect. 

Track Modulus X2 (In) 

10,000 77 

15,000 69 

20,000 64 

25,000 61 

30,000 58 

W

L

2 L

Y

Figure 23. Deflection of beam with fixed ends 

23
The equation for the distance L is: 

L = (24 EI Y/W)1/3 

L = distance from beam endpoint to 

center, the point of maximum 

deflection (in) 

E = Young's modulus for steel 

 29,600,000 psi 

I = rail (beam) moment of inertia 

 94.2 in4

 for 136-lb rail 

Y = vertical rail deflection (in) 

 0.15 in this example 

W = wheel load (lbs) 

 41,500 in this example 

For a center deflection of 0.15 in, L is 60 in. From the 2 methods it appears that a ramp length of 

about 60 in is a reasonable estimate of the likely shortest length. This results in a ramp in track 

as shown at the top of Figure 24, with the height and length normalized in the lower 

illustration—a ramp of 1 in 400. 

 

10,000

2,000 0.15

60

10,000

2,000 1

400

10,000

2,000 0.15

60

10,000

2,000 1

400

Figure 24. A 10,000 to 2,000 modulus change—a 1:400 ramp 

What effect might a 1:400 ramp have on a passing train? One way to estimate this is through a 

comparison with track surfacing runoff requirements, the minimum length for transitioning from 

the end of a section of track that has been surfaced and raised to the adjacent track that was not 

surfaced. Table 4 shows a comparison with runoff standards from one large U. S. railroad. 

According to the railroad, these runoffs are said to provide a smooth ride at the given speeds. 

By the criteria in Table 4, the 10,000-2,000 stiffness change ramp is about equivalent to a runoff 

that provides a smooth ride at approximately 70 mph—as a probable worst case. If so, what is 

the likelihood that this track profile would produce vertical dynamic loads sufficient to cause 

noticeably accelerated track settlement on a bridge approach? 

24
Table 4. Comparing the effect of a 10,000-2,000 track stiffness change with railroad 

runoff standards 

Runoff 

(or Equivalent) 

Maximum Speed for 

Smooth Ride 

1:331 60 mph 

Example 10,000-2,000 

Stiffness Change 1:400 

1:496 80 mph 

2.7 The Train Ride Test 

Another simple but revealing observation is the train ride test, what can be sensed aboard a 

moving train while traveling over a bridge and bridge approaches. When the track at a bridge 

(either open deck or ballast deck) is well surfaced, no vertical roughness or movement can be 

felt, and only a change in sound will be apparent while traveling over the bridge. This indicates 

that the change in stiffness clearly has no effect on ride quality. Regarding vertical force level, 

the car suspension can filter out forces at frequencies that could transmit to and through the 

track, so no clear conclusion can be made about this aspect. It would, however, raise the 

question of whether forces large enough to cause abnormally greater track settlement could be 

generated when not even a slight vertical sensation is apparent from inside a passing train. 

25
26
3. Summary and Conclusions 

Table 5 summarizes the results of the literature review and analyses. The results refer to the 

possibility that crossing a stiffness difference at bridge ends might: 

• Produce dynamic loads large enough to cause accelerated track settlement at bridge 

approaches 

• Adversely affect ride quality 

Table 5. Summary of Results 

Analysis or Source Result6

General Literature 

Search 

No data showing magnitude of dynamic loads produced by crossing a 

track stiffness difference. 

Review of Talbot 

Reports 

No indication that crossing a track stiffness difference might produce 

dynamic loads. 

Model Studies: 

• Lundquist and 

Dahlberg (2005) 

• Singh (2003) 

• Gurule and Davis 

• A 7 percent increase in wheel-rail load when crossing a 7,000 to 

2,775 stiffness change at 200 mph. 

• A 6.7 percent increase in wheel-rail load when crossing a 2,000 to 

30,000 stiffness change at 60 mph. 

• Crossing a 10,000 to 2,000 stiffness change at 50 mph caused a 

higher reaction force below the rail on the stiff edge of the 

transition (the bridge end), but no reaction forces above static load 

for 13 feet after the transition (on the bridge approach). 

Wheel-Rail Force and 

Carbody Acceleration 

Measurements 

• No wheel-rail forces above the dynamic noise level at bridge 

ends—data from 9 bridges, at speeds from 84 to 123 mph. 

• Vertical carbody accelerations appear well below the sensation 

level. 

Bridge Approach 

Track Profiles 

Bridge approach settlement often appeared no greater than in track 

away from the bridge, suggesting that vertical forces on approaches are 

often not significantly greater than elsewhere along the track. 

Simplified Analysis The effect of a 10,000 to 2,000 stiffness change is, at worst, roughly 

equivalent to a 1 in 400 track runoff, said to be good for a smooth ride 

at 70 mph. 

Train Ride Test Crossing a well-surfaced bridge approach has no effect on ride quality. 

The literature search found no sources to support the claim that crossing a change in track 

stiffness at bridge ends produced dynamic loads of any significance, much less of sufficient 

 

6

 All stiffness values are given in units of lbs/in/in. 

27
magnitude to cause accelerated track settlement at bridge approaches. This finding alone would 

be sufficient to dismiss the idea, as any such claim would require satisfactory supporting 

evidence to warrant acceptance. 

Following the literature search, five different methods, ranging from the most technically 

sophisticated to the most basic, were employed to evaluate the possibility that a stiffness 

difference between the track on a bridge and off the bridge might cause accelerated track 

settlement or adversely affect ride quality at bridge approaches. To provide a benchmark for 

comparison, it was estimated that vertical forces on a bridge approach would have to be 50 

percent higher than elsewhere on the track to cause noticeably accelerated track settlement 

(judged to be at least 25 percent greater than average). 

 

These analyses found that any vertical dynamic forces generated by crossing an abrupt track 

stiffness change are not large enough to be sensed aboard a passing train or to be measured by 

instrumented wheelsets. Both simple analysis and computer modeling indicate that the ballast 

and subgrade on a bridge approach are not subjected to increased vertical dynamic forces. 

Observations of the track profile at bridges indicate that approach settlement is often not greater 

than in track farther away, which suggests that these approaches are not subjected to higher 

forces. The results from all five methods pointed to the same conclusion—that even the largest 

changes in track stiffness do not generate dynamic loads of practical significance and, otherwise, 

have no practical effect on track settlement or ride quality at bridge approaches. 

To clarify, the conclusion is not that changes in vertical stiffness along the track cannot or do not 

have an effect on track settlement. The computer modeling results shown in Figure 5 clearly 

indicate such an effect is not only possible, but likely, through highly uneven loading. Even the 

initial work of the Talbot committee, first published in 1918, indicates this possible effect (see 

AREA, 1980). The conclusion is that a change in stiffness at one location (the bridge end) 

cannot and does not result in the generation of dynamic loads that cause or affect track settlement 

across a bridge approach. As Figure 5 indicates, a change in track stiffness affects track loading 

only in the vicinity (within about 4-5 ft) of the stiffness change, not on the adjacent 50 ft of track. 

Further, the localized variation in track loading at a bridge end actually causes a reduced loading 

on the track immediately adjacent to the bridge, with the offsetting increase in load occurring on 

the bridge structure. 

28
4. Future Research 

This report presented the first product from a study initiated by FRA to find effective and 

affordable methods for improving ride quality and reducing differential track settlement at bridge 

approaches and other track transitions. 

As this initial study concluded that track stiffness differences had no practical effect on track 

settlement at bridge approaches, the main source of the settlement difference appears to result 

from changes in construction. Bridge structures are designed to keep settlement to negligible 

levels, with support provided by deeply driven piling or piers constructed on bedrock, while 

track constructed on a crushed rock ballast section over an earth subgrade will experience 

moderate levels of settlement. As a bridge approach represents a junction between these two 

construction types, over time, a distinct settlement difference can often occur. 

Subsequent work will include further examination of the factors that affect track settlement at 

bridge approaches, which may accelerate the development of a low spot. These efforts will 

address both the strength of the track support and the vertical forces acting on the track. The 

results from this work will serve as a basis to search for effective and affordable methods for 

providing and maintaining smooth transitions between the track on and off a bridge. 

29
30
5. References 

AREA (American Railway Engineering Association). (1980). Stresses in Railroad Track—The 

Talbot Reports. 

Briaud, J.L., Nicks, J. E., and Smith, B.J. (December 2006). The Bump at the End of the 

Railway Bridge; Texas A&M University. 

Davis, D., Anaya, R., Chrismer, S., and Smith, L. (2007). Development of a Differential 

Settlement Model for Design and Maintenance of Track Transitions. Technology Digest. 

Transportation Technology Center, Inc. TD-07-002. 

Eisenmann, J. (1992). Railway Track Foundation Dynamics. Rail Engineering International, 

No. 2, pp. 17-20. 

Hay, W.W. (1982). Railroad Engineering. John Wiley & Sons, New York. 

Jenkins, H.H., Stephenson, J.E., Clayton, G.A., Morland, G.W., and Lyon, D. (1974). The Effect 

of Track and Vehicle Parameters on Wheel/Rail Vertical Dynamic Forces. Railway 

Engineering Journal. January, 1974. 

Koch, K. (June 2007). Measurement of Coal Hopper Dynamic Load Environment 286,000-

Pound Gross Rail Load Unit Train Service—August 2004 to May 2006. Transportation 

Technology Center, Inc. Association of American Railroads Research Report R-984. 

 

Li, D., Meddah, A., Davis, D., and Kohake, E. (2006). Measurement of Load Environment and 

Performance of Insulated Joints at Western Mega Site. Technology Digest. Transportation 

Technology Center, Inc. TD-06-028. 

Lundquist, A., and Dahlberg, T. (2005). Load Impact on Railway Track Due to Unsupported 

Sleepers. Journal of Rail and Rapid Transit, Vol. 219, No. F2. 

Singh, S.P. (2003). Effect of Track Stiffness Transition Between Approach and Bridge, and 

Perturbation-Generated Impact Loads in This Region. Transportation Technology Center, 

Inc. Unpublished. 

31
32
Abbreviations and Acronyms 

AAR Association of American Railroads 

AREA American Railway Engineering Association 

ASCE American Society of Civil Engineers 

FRA Federal Railroad Administration 

ft foot/feet 

in inch/inches 

lb pound/pounds 

MP Milepost 

mph miles per hour 

TTCI Transportation Technology Center, Inc. 

33