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Dr. Anna Maria Rakoczy
Transportation Technology Center, Inc. (TTCI)
Prof. Andrzej S. Nowak
Auburn University
Live Load Spectra for Railway Bridges in USA
Obciążenia zmienne dla mostów kolejowych w USA
Abstract
The objective of the paper is to review railroad live loads in the United States. Railroad
bridges are privately owned and the design codes are specified by American Railway
Engineering and Maintenance of Way Association (AREMA). Over the years, there has
been a considerable growth of railroad loads and, therefore, many older bridges were
designed for live load that is much lower than what is required in the current design
code. The paper provides the historical development of the design railroad loads, load
combinations, dynamic load and fatigue load. The knowledge of loading spectra to
which railway bridges are currently being subjected, rather than the design load, is
essential to perform a proper evaluation of an existing structure. Estimation of stress
cycles requires a statistical load model. Therefore, the design load is presented along
with the actual railroad loads based on the measurements using wayside load
detectors. The statistical parameters of railcar weights, truck and axle loads include
the mean and standard deviation or coefficient of variation. In addition to static loading,
load spectra are considered for dynamic loads and fatigue.
Keywords: Railroad bridges, live load, statistical parameters, axle load, fatigue load,
dynamic load
Streszczenie
Celem referatu jest przedstawienie obciazen zmiennych na mostach kolejowych w
USA. Koleje w Ameryce sa prywatna wlasnoscia a mosty kolejowe projektowane sa
na podstawie normy AREMA. Obciazenia normowe na jedna os byly zwiekszane
stopniowo od 89 kN sprzed ponad 100 laty do 356 kN obecnie. W przeszlosci,
glownym obciazeniem byla lokomotywa parowa, obecnie lokomotywa z silnikiem
Diesela lub elektryczna waza podopbnie jak wagony towarowe. W analizie
przydatnosci istniejacych mostow wazna jest znajomosc nie tylko obciazen
projektowych ale przede wszystkim aktualnych obciazen pomierzonych czujnikami.
Wyniki pomiarow byly podstawa do wyznaczenia parametrow statystycznych takich jak
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watrosci srednie, wspolczynniki zmiennosci i typ dystrybuanty dla calych wagonow
towarowych oraz poszczegolnych osi. W referacie rozpatrzono obciazenia statyczne,
dynamiczne oraz zmeczeniowe.
Słowa klucze: mosty kolejowe, obciazenie zmienne, statystyczne parametry,
obciazenie na os, obciazenie zmeczeniowe, obciazenie dynamiczne
1. Introduction
Railroad bridges are subjected to various train loads and the biggest loads/weights
are due to freight operations. Many countries are moving to increase speed and
volume of rail freight to relieve overburdened roads. In USA 40% of all transported
goods are moved by rail freight, while in EU only 20%, and in other countries (such
as Russia and China) about 10%.
The freight car weight varies by countries and by the freight car type. In general, axle
loadings and railcar weights in North America have historically been larger and
continue to be larger than in other countries. However, exceptions exist: in Australia,
Brazil, and South Africa, axle loads for movement of bulk commodities, mostly coal
and metallic ores, exceed those of North America but they are operated on specific
lines for moving those commodities.
A good comparison is China where the railroads mimic the North American freight
practice in equipment style and design but use a lighter axle loading. In North
American practice, the standard maximum axle loading for coal cars is 32.5 tonnes
(71,500 pounds). The Chinese maximum axle weight for coal cars ranges from
approximately 23 tonnes up to 25 tonnes (50,800 pounds up to 55,200 pounds).
Some cars up to 27 tonnes (59,600 pounds) have been built and used on certain
routes. Additional designs for larger axle loadings have been proposed but not
implemented. Many countries use axle loads that are lighter than these.
In European Union, the nominal capacity of a typical 4-axle railcar is 120 tonnes
(265,000 lb) and 30 tonnes (66,000 lb) per axle.
2. Design Live Load for Railroad Bridges
In USA, the current live load model is specified the design code of AREMA 2018 [1]
and it is referred to as the Cooper E80 load, which is composed of two steam
locomotives and a relatively smaller uniform trailing weight. Today’s freight trains are
quite different than this design loading. Over the last decades, trailing rail car weights
have increased, and the distributions of axle load have changed. Nowadays, the
diesel-electric locomotives have a similar axial load as freight cars.
2.1. Cooper's loading
Cooper's loading system is based on a standard of E10, shown on Figure 1, and this
means that a pair of 2-8-0 type steam locomotives is pulling an infinite number of rail
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cars.[2]. Each locomotive was given an axle loading of 44.5 kN (10,000 pounds) for
the driving axles; 22 kN (5,000 pounds) for the leading truck; and 29 kN (6,500
pounds) for the tender trucks. Each trailing rail car was given an axle loading of 4.45
kN (1,000 pounds) per foot of track.
Figure 1. Cooper's loading system - standard E10. (1,000 lb per lin ft = 14.6 kN/m)
During the 1880s, railway bridges were built using an equivalent rating of E20. By
1894, when Cooper presented his standard, he recommended a standard of E40, or
four times the E10 standard. By 1914, the standard had increased to E60. In the mid-
1990s, the American Railway Engineering Association, AREA, was recommending
E72 (7.2 times the E10 standard) for concrete structures, and E80 for steel
structures.[2] Since 2005, AREMA recommends E80 for concrete structures and E80
for steel structures. A set of forces with certain spacing characterize Cooper E80 and
is present in Figure 2.
Figure 2. Cooper's E80 load (8,000 lb per lin ft = 116.8 kN/m)
Moreover, AREMA allows use of Alternate Live Load on 4 axles, spaced as shown in
Figure 3 or in whichever order produces the greater stresses.
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Figure 3. Alternate live load on four axles (445 kN per each axle with spacing 1.5-1.8-
1.5 meter)
AREMA does not provide explicit load combinations, but it does incorporate
combinations in various design recommendations.[3] Table 1 outlines load
combinations that apply to the steel superstructure design found in various AREMA
recommendations.[4]
Table 1. Load combinations for steel railway superstructure design
Load
Case
Load Combinations Members FL
A1
DL + LL + I + CF
All members
1.00
A2
DL + LLT + I + CF
Truss web members
1.33
B1 DL + LL + I + W + LF + N + CWR
All members, except floor beam
hangers and high strength bolts
1.25
B1A DL + LL + I + W + LF + N + CWR
Floor beam hangers and high
strength bolts
1.00
B2
DL + LLT + I + W + LF + N +
CWR
Truss web members, except
floor beam hangers
1.66
C
(LL + I) range
All members
ffat
D1 SL + N + CF
Members resisting overall
instability
1.50
D2 Q
Members resisting overall
instability
1.50
E1
DL + EQ
All members
1.50
E2
DL + LL + I + CF + EQ
Members in long bridges only
1.50
F
W or LV
Members loaded by wind only
1.00
G DF
Cross frame, diaphragms,
anchor rods
1.50
H1 DL
Members stressed during lifting
or jacking
1.50
H2 DL
Members stressed during
erection
1.25
H3 DL + W
Members stressed during
erection
1.33
NOTE: FL = Allowable stress load factor (multiplier for basic allowable stresses), DL = Dead loads
(self-weight, superimposed dead loads, erection loads), LL = Live load, I = Impact (dynamic
amplification), CF = Centrifugal force on a curved railway bridge, W = Wind forces (on live load and
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bridge), LF = Longitudinal forces from equipment (braking and locomotive traction), N = Lateral
forces from equipment (nosing), CWR = Forces from bridge thermal interaction (lateral and
longitudinal), EQ = Forces from earthquake (combined transverse and longitudinal), DF = Lateral
forces from out-of-plane bending and from load distribution effects, LV = “Notional” lateral vibration
load, LLT = Live load that creates a total stress increase of 33% over the design stress (computed
from load combination A1) in the most highly stressed chord member of the truss, SL = Live load
on leeward track of 1200 lb/ft without impact, I, Q = Derailment load, ffat = Allowable stress based
on member loaded length and fatigue detail category.
2.2. Design Dynamic Load
In addition to static load, trains traversing a railway bridge create dynamic actions in
longitudinal, lateral, and vertical directions. The dynamic effect on the railway bridge is
a very complex issue because the dynamic effect on the bridge has various sources.
The parameters affecting the dynamic behavior of a steel railway bridges are:
• Dynamic characteristics of the live load (mass, vehicle suspension stiffness,
natural frequencies, and damping). For passenger vehicles, the train frequency
is generally in the range of 0.9 to 1.2 Hz (circular frequency 6-8 rad/sec). For
freight wagons this frequency can raise to 2.5 Hz in loaded and up to 4 Hz in
the tare condition (circular frequency 16-25 rad/sec).
• Train speed (a significant parameter).
• Train handling (causing pitching acceleration).
• Dynamic characteristics of bridge (mass, stiffness, natural frequencies, and
damping).
• Span length and continuity (increasing impact due to higher natural frequencies
of short-span bridges).
• Deck and track geometry irregularities on the bridge (surface roughness) are a
significant parameter).
• Track geometry irregularities approaching the bridge.
• Rail joints and flat or out-of-round wheel conditions (a significant parameter of
particular importance for short spans).
• Bridge supports (alignment and elevation).
• Bridge layout (member arrangement, skewed, and curved).
• Probability of attaining the maximum dynamic effect concurrently with maximum
load.
According to AREMA 2018, the impact load due to the sum of vertical effects and
rocking effect created by passage of locomotives and trainloads, is be determined by
taking a percentage of the live load and has to be applied vertically at top of each rail.
For all freight and passenger railcars and diesel locomotives (without hammer blow),
the vertical impact is calculated using the following equations:
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for L less than 100 ft
1600
3
40 2
L
I−
=
(1)
and
for L 100 ft and more
30
600
16 −
+= L
I
. (2)
For steam engines with hammer blow the impact factor is larger. For beam spans,
stringers, floor beams, posts of deck truss carrying a load from the floor beam only,
and floor beam hangers, the impact factor is calculated as follows:
for L less than 100 ft
500
60
2
L
I−=
(3)
and
for L 100 ft and more
40
1800
10 −
+= L
I
. (4)
For steam locomotives on truss spans the impact factor is calculated using the
following equation:
for truss spans:
25
400
15 +
+= L
I
(5)
where L is a length in feet, center to center of supports for main members.
As a summary of the equations above, the percentage of impact load for various span
lengths is presented in Table 2.
These equations and tabulated values are defined for open deck bridges. For ballasted
deck bridges, the impact load shall be reduced to 90% of that specified for open deck
bridges. Percentage of impact load for various span length is presented in Table 2.
Additional impact due to rocking effect, RE, is created by the transfer of the load from
the wheels on one side of a car or locomotive to the other side from periodic lateral
rocking of the equipment. RE is to be calculated from loads applied as a vertical force
couple, each being 20% of the wheel load without impact, acting downward on one rail
and upward on the other. The couple shall be applied on each track in the direction
that will produce the greatest force in the member under consideration. For traffic that
is classified as light rail or commuter rail, the dynamic factor is reduced to 35% of the
design value for fatigue analysis (AREMA 2007).
2.3. Fatigue Loading
The AREMA fatigue design criteria include Cooper E Loading and Alternate Live Load,
which were described in previous section. The Cooper E Loading has limited use since
the loading is governed by the uniform load pattern, unlike the actual railcar loading.
Alternate Live Load represents heavy axle loading on a shorter span and can be more
useful in fatigue analysis.
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Table 2. Load combinations for steel railway superstructure design
L, ft For equipment without hammer blow
(freight and passenger cars)
For steam locomotive with hammer blow
Beam spans
Trusses
10
40
60
129
20
39
59
104
30
38
58
88
40
37
57
77
50
35
55
68
60
33
53
62
70
31
50
57
80
28
47
53
90
26
44
50
100
25
40
47
120
23
33
43
140
21
28
39
160
21
25
37
180
20
23
35
200
20
21
33
250
19
19
30
300
18
17
27
350
18
16
26
400
18
15
24
The second source of design load is the Association of America Railroads (AAR) which
specifies minimum railcar dimensions for the design of new freight cars. The
dimensions for AAR design cars are listed in Table 3. All three cars have a similar total
length which is about 12.8 meter (42 ft) with some variation of axle spacing.
Table 3. Load combinations for steel railway superstructure design
Car Type SO, m
(ft) ST, m
(ft) SI, m
(ft) LO, m
(ft)
GW,
tonnes or t
(kips)
Empty car
weight, t
(kip)
AAR 1
1.02
(3.36)
1.78
(5.83)
7.19
(23.58)
12.79
(41.96)
130
(286.0)
22.7
(50.0)
AAR 2
1.18
(3.86)
1.78
(5.83)
6.87
(22.54)
12.78
(41.92)
130
(286.0)
22.7
(50.0)
AAR 3
1.33
(4.36)
1.78
(5.83)
6.55
(21.50)
12.77
(41.88)
130
(286.0)
22.7
(50.0)
*LO – overall length of railroad car measured over the pulling face of the coupler; SO –
Outboard Axle Spacing; ST – Truck Axle Spacing; SI – Inboard Axle Spacing
However, the actual loading is different than the design load, which is a crucial factor
for fatigue analysis. In predicting maximum fatigue damage it is important to consider
trainload with an axle configuration corresponding to current operating conditions.
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Maximum stresses on the bridge and the number of cycles have an influence on overall
performance of the bridge. The Cooper E80 Loading is, therefore, not suitable for
fatigue loading. Additionally, the current criteria focus on mid-span effect while fatigue
analysis needs to consider all critical location along plate girders as well as secondary
elements and connections.
In 2011, Dick et al. presented research on the development of a unique loading for
design and rating of a bridge for fatigue. The model was developed based on current
loading conditions. Figure 4 displays the general dimensions and descriptions of
equipment and Table 4 provides the specific lengths and weight values for the
locomotive and cars.
Figure 4. Dimensions used for analysis
NOTE:
P – Axle load
LO – overall length of railroad car measured over the pulling face of the coupler
SO – Outboard Axle Spacing
ST – Truck Axle Spacing
SI – Inboard Axle Spacing
Table 4. Dimensions for locomotives and railcars used in fatigue analysis
Car Type SO, m
(ft) ST, m
(ft) SI, m
(ft) LO, m
(ft) GW, t
(kip)
Empty
car
weight, t
(kip)
6-axles Locomotive
1.81
(5.95)
2.08
(6.83)
10.6
(34.79)
22.56
(74.0)
429 (195)
194.6
(429)
4-axles cars:
Sand/Cement
Hooper
1.02
(3.36)
1.78
(5.83)
7.19
(23.58)
12.79
(41.96)
129.7
(286)
22.7 (50)
Coal
1.03
(3.38)
1.78
(5.83)
10.57
(34.67)
16.18
(53.08)
129.7
(286)
29.5 (65)
Long Hopper
1.02
(3.36)
1.78
(5.83)
15.43
(50.63)
21.03
(69.00)
129.7
(286)
36.3 (80)
TOFC
3.48
(11.42)
1.78
(5.83)
18.34
(60.17)
28.86
(94.67)
129.7
(286)
34.0 (75)
In the research study conducted by Dick et al., they concluded that fatigue load should
have certain characteristics that would allow for a general use both for rating and
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design. Accordingly, it should possess a relatively high magnitude of repetitive
moment, should have a sufficient overall maximum moment, resemble the actual
equipment in its configuration, and should have simple dimensions.[5, 6] Table 5
presents the length and weight for the F80 loading along with F71.5. Using F80 cars
in a train allows the analysis for both maximum moment and repetitive moment that is
experienced during a train passage.[5, 6]
Table 5. Proposed fatigue car dimensions, four-axle cars [5, 6]
Car Type SO, ft ST, ft SI, ft LO, ft GW, t
(kips)
Empty car
weight, t
(kip)
Fatigue F80
0.9
(3.0)
1.5
(5.0)
18.3
(60.0)
23.2
(76.0)
145.2
(320)
40.8 (90)
Fatigue F71.5
0.9
(3.0)
1.5
(5.0)
18.3
(60.0)
23.2
(76.0)
129.7
(286)
40.8 (90)
3. Railcars and Locomotives used currently by railroads
The current loading spectra, to which railroad bridges are subjected, are significant for
bridge evaluation. Not only type of load and magnitude are important, but also statistical
parameters such as mean value, standard deviation, expected maximum load, and
probability of occurrence. The probabilistic characteristics of the maximum live load
depends on the temporal variation of the load, the duration of the sustained load, the
design lifetime, and statistics of the involved random variables.[7]
The general layout of railroad equipment has been in existence for almost the entire 200
years since the railroad was invented. During the passage of time many changes
occurred in the size, weight, and design of cars and locomotives. The breakthrough
happened when steam locomotives were replaced by diesel locomotives in 1940s. Until
that time, steam locomotives represented the heaviest load of the entire train.
Innovations were made in car design to increase the capacity of freight cars and safety
of passenger cars.
The main categories of locomotives are often subdivided in their usage in rail transport
operations by passenger locomotives and freight locomotives. The majority of
locomotives are built with two- or three-axle trucks. The overall dimension, spacing
between axles, and gross weight vary between different manufacturers. Typical diesel
electric locomotives are four-axles with total weight of 109-127 tonnes (120-140 tons)
and total length up to 18.3 m (60 ft)., or six-axles with total weight of 145-190 tonnes
(160-210 tons) and total length up to 24.4 m (80 ft). Passengers train equipment is
designed for moving people and for hauling express shipments and mail. The term
passenger car can also be associated with a sleeping, baggage, or dining car. The total
length of the car is usually 25.8 m (85 ft.) with a weight of 45.4 to 99.8 tonnes (50 to 110
tons). Most of the cars are four-axles.
Freight train equipment has been developed to transport every type of commodity
imaginable. There are, however, nine basic types of railcars used in international trade.
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They are: boxcar, refrigerated boxcar (reefer), flatcar, tanker, container carrier, gondola,
hopper, center partition railcar, auto transporter.
From their inception, boxcars have been the most common type of freight cars and are
used worldwide. Boxcars come in 15.2, 18.3, and 26.2-meter (50, 60, and 86-foot)
lengths with load capacities ranging from 64 to 95 tonnes (70 to 105 tons). Boxcars are
designed to carry many types of shipments such as paper products, canned goods, and
bulky freight. Different railcar manufacturers worldwide produce a variety of models
designed for specific applications, capacity and dimensions. Reefers (refrigerated)
boxcars are designed to carry perishable freight at specific temperatures. Common
commodities transported in reefer boxcars include vegetables, fruit, orange and other
juices, milk, meat, and poultry. Although the reefers are designed for different purposes,
the dimension and capacity is similar to the boxcars.
Flat cars are designed to transport any shipment that must be loaded from the side or
the top. Standard cargo for platform trailers include: heavy construction equipment, farm
tools, lumber, plywood, steel products, pipes and rebars. Length, capacity, and weight
depend on railcar manufacturer, railcar model, and rail system requirements. Tankers
are used to carry bulk liquids. Common commodities transported in tankers include
refined gasoline, heating oil, alcohol, industrial chemicals, acids, clay slurry, corn syrup
and other. Container carriers are designed to carry international standard 6.1, 12.2, 13.7,
14.6 and 16.2 – meter (20, 40, 45, 48, and 53-foot) ocean freight containers in various
stacking combinations.
Two types of gondolas are used for the shipments of the freight. Mill gondolas are
extremely sturdy railcars designed to transport iron and steel scrap, steel ingots, coiled
steel, sheet steel, pipes, and other steel products. Aggregate gondolas are designed to
transport industrial minerals, crushed rock and gravel. Both have standard lengths
ranging from 14.6 m to 20 m (48' to 66').
The purpose of hoppers is to transport free flowing dry bulk commodities like grains,
industrial minerals, plastic pellets, crushed rock, gravel, and sand. Hopper cars can be
covered or uncovered depending on the shipment material. Center partition railcars
(also called center beam flatcars) are designed to transport lumber, plywood, building
materials and other packaged products. Auto carriers are designed to transport
automobiles from and to automobile manufacturing plants, ocean import/export facilities,
and distribution centers. Rail auto carriers are the most efficient way to transport large
numbers of automobiles long distances by land.
Different railcar manufacturers worldwide produce a variety of models designed for
different container and stacking configurations. Tables 6, 7, and 8 present some types
of railcars with typical dimensions and capacities.
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Table 6. Examples of dimensions and capacity for various freight cars
Exterior
Length, m
Truck centers,
m
Freight Capacity,
tonnes
50' Standard Box
16.9 (55' 5")
12.4 (40’ 10”)
59.0 – 81.6
50' Hi-roof Box
17.8 (58' 4")
14.2 (46’ 8”)
81.6
60' Standard Box
20.7 (67' 11")
14.1 (46’ 3”)
81.6
60' Hi-roof Box
20.6 (67' 7")
-
81.6
86' Auto Box
28.5 (93' 6")
20.1 (66’ 0”)
86.2
Small Coal Hopper
15.1 (49’ 8”)
11.0 (36’ 2”)
81.6
Jumbo Coal Hopper
16.8-19.8
(55’ - 65’)
- 81.6 – 90.7
52’ Gondola
17.3 (56' 11")
13.2 (43’ 4”)
59.0 – 81.6
65’ Gondola
21.7 (71' 3")
17.4 (57’ 2”)
81.6 -90.7
Flat car
28.6 (93' 10")
20.7 (68’ 0”)
95.3
Tanker
27.6 (90' 6")
20.1 (66’ 0”)
93
Container Carrier 23.2 (76' 0") 18.7 (61’ 6”)
113,562 liters
(30,000 gal.)
Center Partition
24.5 (80' 6")
18.3 (60’ 0”)
95.3
Auto Transporter
44.3 (145' 4")
19.5 (64’ 0”)
45.4
Table 7. Examples of weight and axle load for various freight cars
Empty Car, t Gross Car Weights, t
Axle Loads, kN
(kips)
50' Standard Box 32.2 90.7 – 129.7
222 – 320
(50 – 72)
50' Hi-roof Box
33.6
129.7
320 (72)
60' Standard Box
36.0
129.7
320 (72)
60' Hi-roof Box
35.8
129.7
320 (72)
86' Auto Box
43.1
142.9
351 (79)
Small Coal
Hopper
28.0 119.3 294 (66)
Jumbo Coal
Hopper
- 119.3 – 129.7
294 – 320
(66 – 72)
52’ Gondola
29.7
286
320 (72)
65’ Gondola 34.0 119.3 – 129.7
294 – 320
(66 – 72)
Flat car
27.2
129.7
320 (72)
Tanker
27.2
129.7
320 (72)
Container Carrier
29.8
119.3
294 (66)
Center Partition
27.7
129.7
320 (72)
Auto Transporter
67.1
17.9
289 (65)
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Table 8. Examples of weight and axle load for different locomotives
Exterior
Length, m
Truck
centers, m
Gross
Weights, t
Axle Loads,
kN (kips)
4-axle GP 20D
17.1 (56' 2")
12.2 (40’ 0”)
108.9
267 (60.0)
4-axle GP 60
18.0 (59’ 2”)
13.3 (43’ 9”)
122.5
300 (67.5)
6-axle SD-70MAC
22.6 (74’ 0”)
18.3 (60’ 2”)
188.2
308 (69.2)
6-axle SD-90MAC
24.4 (80’ 2”)
20.7 (68’ 0”)
192.8
315 (70.8)
4. Loading spectra under current operation condition
4.1. Load spectra in late 90’s
The latest load spectra for railway bridges were developed based on the data collected
over 20 years ago by Tobias et al. (1996).[8, 9] Load data results from 508 trains were
recorded at five riveted steel bridges located in Illinois, Virginia, and Tennessee. The
data collected includes the speed of each train, the distance between each axle, and
dynamic wheel loads. The measured axle spacing was compared to known rail car
dimensions to determine general car types.
The basic statistics for car loading were developed based on the measured data for
the 1996 study. Approximately 60 percent of railroad equipment used at that time were
coal hoppers; mixed freight trains were approximately 20 percent, four-axle intermodal
cars were 7.5 percent, auto-racks were 3.5 percent, and 9 percent included
locomotives and other type of cars. The data collected was analyzed and five
probability distribution functions were chosen as the best fit to the measurements. The
determination of statistically-admissible distribution was performed using various
goodness-of-fit analyses.[8, 9]
The load spectra presented by Tobias et al. provides good information; however, the
dynamic effect included in the data can be affected by span type, length, and other
bridge parameters.[8] The data was collected from various bridge types including: open
deck double plate girder, ballasted deck double plate girder, Warren though truss, and
through-double plate girder. The span lengths varied from 12 to 47.5 meter (40 feet to
156 feet). Also, while loading was site-specific, the data reported was from only three
states: Illinois, Virginia, and Tennessee.
Updated, more comprehensive and representative data for a North American load
spectra for railway bridges was recently developed by TTCI using wayside data.
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Table 9. Basic Fit Probabilities and Basic Statistic for Car Loadings (1996)
Freight Type Best Fit
Distribution
Average
Car Load,
kN (kip)
Standard
Deviation, kN
(kip)
Maximum
Car Load,
kN (kip)
Coal hopper
Weibull
1181 (265.50)
89 (20.01)
1499 (336.99)
Coal hopper 91 t
Normal
1133 (254.71)
79 (17.76)
1508 (339.01)
Coal hopper 100 t
Normal
1253 (281.69)
43 (9.67)
1508 (339.01)
Ballast hopper
Log normal
1232 (276.96)
37 (8.32)
1357 (305.07)
Potash hopper
Log normal
1218 (273.82)
29 (6.52)
1339 (301.02)
Four-axle intermodal
Normal
634 (142.53)
151 (33.95)
1059 (238.07)
Auto-rack
Gamma
813 (182.77)
70 (15.74)
1170 (263.03)
Five-pack intermodal
(12 axles)
Beta
1828 (410.95)
595 (133.76)
3763 (845.96)
Two-axle intermodal
Beta
326 (73.29)
95 (21.36)
569 (127.92)
Four-axle mixed
freight
Bimodal
normal
356 (80.03);
1062 (238.75)
91 (20.46);
181 (40.69)
1463 (328.90)
Six-axle locomotive
Gamma
1838 (413.20)
98 (22.03)
2157 (484.91)
Four-axle locomotive
Gamma
1255 (282.14)
86 (19.33)
1610 (361.94)
Table 10. Basic Fit Probability and Basic Statistic for Axle Loadings (1996)
Freight Type Best Fit
Distribution
Average Axle
Load
(Kip)
Standard
Deviation
(Kip)
Maximum
Axle Load
(Kip)
Coal hopper
Log normal
295 (66.32)
27 (6.07)
485 (109.03)
Coal hopper 91 t
Log normal
283 (63.62)
24 (5.40)
485 (109.03)
Coal hopper 100 t
Gamma
313 (70.37)
22 (4.95)
471 (105.88)
Ballast hopper
Normal
308 (69.24)
19 (4.27)
474 (106.56)
Potash hopper
Log normal
304 (68.34)
23 (5.17)
423 (95.09)
Four-axle intermodal
Normal
160 (35.97)
44 (9.89)
302 (67.89)
Autorack
Normal
203 (45.64)
21 (4.72)
316 (71.04)
Five-pack intermodal
(12 axles)
Gamma
152 (34.17)
64 (14.39)
405 (91.05)
Two-axle intermodal
Normal
162 (36.42)
50 (11.24)
302 (67.89)
Four-axle mixed
freight
Bimodal
normal
90 (20.23);
268 (60.25)
26 (5.85);
45 (10.12)
423 (95.09)
Six-axle locomotive
Log normal
306 (68.79)
27 (6.07)
427 (95.99)
Four-axle locomotive
Log normal
313 (70.37)
30 (6.74)
458 (102.96)
14 | Strona
4.2. Most recent load spectra (2017)
Recently, TTCI developed a load spectra using wayside data from 28 locations in five
regions across North America under revenue service train traffic using wheel impact
load detectors (WILD). They used collected wayside data under revenue train traffic
from January 2017 to April 2017 from five regions across North America. Their study
concentrates on loads from conventional four-axle freight cars.[9] However, they also
performed investigation of loads from intermodal equipment, including articulated
double stack cars that is presented in previous report.[10]
The dataset was reduced to a selection of trains that can cause fatigue cycles on a
bridge. The initial dataset of WILD wheels between January 1, 2017 and April 30, 2017,
is 248 million wheel passes for all load conditions. However, the output train summaries
by car length and maximum weight was created using only 286-kip cars on the trains.
The analysis was carried out for 50 trains for each of the four train types for each of
the five regions.
Wayside data results from 130 tonnes (286,000-pound) gross weight cars were studied
in this project, including dynamic car weight, truck weight, axle load, and wheel load
for traffic in both directions. The traffic included in the data consisted of: (1) unit trains
of four-axle short cars, 13-meter (42-foot) long carrying cement or sand; (2) unit trains
of four-axle coal cars, 16-meter (53-foot) long; (3) unit trains of four-axle grain cars,
approximately 18-meter (60-foot) long; and (4) four-axle cars in mixed freight trains.
Over 72,000 cars were analyzed. Wayside data was sorted by region and car type.
Partially loaded cars (less than 104 tonnes, 230 kips) were excluded from the analysis.
Table 11 shows a summary of the sample size for each type of train at each region.
Table 11. Sample Size for Each Type of Train at Each Region [10]
Central
East
North
South
West
Total
13-m Unit
5,207
NA
4,987
5,130
NA
15,324
16-m Unit
6,582
5,148
5,712
6,154
405
24,001
18-m Unit
3,345
762
5,280
824
1,945
12,156
Mixed Freight
NA
8,476
5,403
1,442
5,543
20,864
Total
15,134
14,386
21,382
13,550
7,893
72,345
Load statistics describe the most probable range of loading for a specific train type and
are important for fatigue evaluations. The load comprises statistical parameters
derived from WILD data for each of the four train types listed above and for
measurements from each of the five regions. Figure 5 presents a comparison of car
weights for all car types at each region considered in this study.
15 | Strona
Figure 5. Dimensions used for analysis [10]
A summary of mean value, coefficient of variation (COV), and maximum value of car
load and axle load are presented in Tables 12 and 13, respectively.
Table 12. Basic Statistics for Current Car Loadings [10]
Car Type Mean, kN (kip) COV
(%)
Maximum
Load, kN
(kip)
Percent of Cars
Over Nominal
Values
13-m unit
1263 (283.9)
1.5
1459 (327.9)
30.2
16-m unit
1273 (286.1)
1.6
1447 (325.3)
57.6
18-m unit
1255 (282.1)
3.1
1391 (312.6)
29.2
Mixed Freight
1268 (285.1)
3.6
1449 (325.8)
62.1
Mean values of car weight were usually below the nominal maximum value of 286 kips.
COVs were very small for all car types: for 13-meter (42-foot) unit train cars and 16-
meter (53-foot) cars, the COV was less than 2 percent; for 18-meter (60-foot) cars and
mixed freight cars, the COV was between 3 and 4 percent. It should be noted that a
high percentage of cars exceeded the nominal maximum value of car weight (Table
12, last column), and 62 percent of mixed freight cars exceeded the nominal maximum
value. However, the small COVs suggest that although the number of overloaded cars
was high, the overloaded weight was not significant.
The mean values of axle loads were mostly below the nominal maximum value of 71.5
kips, except for the leading axles of 16-meter (53-foot) unit train cars and of mixed
freight cars (Table 13). For the 16-meter (53-foot) unit train cars and mixed freight cars,
the mean values of axles in a lead truck were heavier than the axles in a trailing truck,
indicating imbalanced load distributions.
16 | Strona
Table 13. Basic Statistics for Current Axle Loadings [10]
Car Type Axle Type
Mean, kN
(Kip)
COV
(%)
Maximum
Load, kN (Kip)
13-m unit
Leading
316 (71.0)
3.1
376 (84.6)
Trailing
315 (70.9
2.9
360 (80.9)
16-m unit
Leading
328 (73.7)
3.5
376 (84.5)
Trailing
309 (69.4)
4.0
385 (86.6)
18-m unit
Leading
314 (70.6)
4.4
372 (83.7)
Trailing
314 (70.5)
4.2
365 (82.0)
Mixed Freight
Leading
324 (72.8)
4.5
387 (87.1)
Trailing
315 (70.9)
4.3
370 (83.2)
The results show that distributions of car weight and axle load are close to normal
distributions. Mean values of car weights and axle loads are generally close to the
nominal maximum value. Also, imbalanced load distribution causes one truck to be
overloaded even if the total car weight is close to the nominal maximum value of 130
tonnes (286 kips). This was a common occurrence for coal cars. These events should
be considered when bridge stresses are calculated.
4.3. Comparison of design load to revenue service load
The equivalent Cooper loading is based on the design loading recommended by the
AREMA.[1] It is current practice to design railroad bridges for Cooper E-80 loads, which
have maximum axle loads of 80 kips. Many bridges currently in service were originally
designed for lesser loads, such as E-60.
As shown in Figure 6, short cars have greater equivalent Cooper loads compared to
standard length 16-meter (53-foot) cars (130 tonnes, 286 kips weight) for spans 18-
meter (60 feet) and longer. The standard 16-meter (53-foot) long car is identical to the
short car with the same weight of 130 tonnes (286 kips) (AAR 12.78-meter, 41 feet 11
inches) with the longest truck center spacing (9 meter, 29 feet 5 inches) for spans less
than 17 meter (55 feet). A typical six-axle locomotive governs for spans from 17 to 24
meter (55 to 80 feet) long.
The shorter spans are not affected by the shorter cars but they experience full cycles
due to each train; therefore they are prone to accumulate more cycles with higher
stress amplitude (Figure 7). The longer spans are more prone to be overloaded with
the shorter cars. However, longer spans do not experience full unloading and in that
case the cyclic stress ranges are often more important than the one maximum live load
stress cycle per train (Figure 8).
For a certain span to railcar length ratio, the stress range may be higher near quarter-
span locations than near mid-span locations. For example for 30-meter (100-foot) span
mid-span location has only one cycle due to train passage while the quarter location
has one big cycle due to train passage and multiple stress cycles due to individual car,
as shown in Figure 8. Figure 9 presents the ratio of moment range due to individual
car versus maximum moment due to train passage. For shorter spans each car
17 | Strona
produces full cycle but longer spans (see ratio span to car length) experience much
smaller cycles. Making assumption that each car produce maximum cycle provide
unrealistic and conservative fatigue life estimate.
Figure 6. Dimensions used for analysis [12]
Figure 7. Stress history for 9-meter (30-foot) span due to unit train of 16-meter (53-
foot) railcars
0.0 20.0 40.0 60.0 80.0 100.0 120.0
0
10
20
30
40
50
60
70
80
050 100 150 200 250 300 350 400
Span
length (m)
Equivalent Cooper Loading (E)
Span
length (ft)
Bending
Above current inventory
6-Axle Loco
AAR 41'11"
53'0" Coal Car
0
10
20
30
40
50
60
01000 2000 3000 4000 5000 6000
Bending stress, MPa
Time, s
Stress histories for 9-meter span
mid-span
quarter location
18 | Strona
Figure 8. Stress history for 30-meter (100-foot) span due to unit train of 16-meter (53-
foot) railcars
Figure 9. Ratio of moment range due to individual car versus maximum moment due
to train passage.
0
10
20
30
40
50
60
70
01000 2000 3000 4000 5000 6000
Bending stress, MPa
Time, s
Stress histories for 30-meter span
mid-span
quarter location
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
00.5 11.5 22.5 33.5 4
Ratio of moment range and max
moment
Span length to car length ratio
Ratio of Moment Range to Max Moment
Quarter location
Mid-span
19 | Strona
5. Summary
The paper provides a summary of the railroad design loads in the United States. The
considered loads include maximum expected, dynamic loads and fatigue load spectra.
The legal loads in the United States are higher than in most other countries. The actual
loads kept growing over the years and they are higher than the design loads of Cooper
E80.
However, to properly evaluate fatigue life the current load spectra are more important
than the design load. The design Cooper E loading does not correspond to the current
railroad load which is essential for calculating accumulated number of cycles. The
current loading spectra, to which railroad bridges are subjected, are required for bridge
fatigue evaluation. This is especially important for shorter spans that experience full
unloading as a train traverses and each railcar produces full stress cycles. On the other
hand, the longer spans are more prone to be overloaded with the shorter cars that
become more common nowadays.
The weights of conventional four-axle railcars are more predictable than loaded trucks
on highway. The current railcar weight and axle loads presented in this paper exhibited
approximately normal weight distributions. The mean value of car weight for loaded
cars is generally close to the nominal weight of 130 tonnes. The car weights were
distributed consistently around the mean value with small fluctuations, as indicated by
small coefficients of variation (COV).
References
[1] American Railway Engineering and Maintenance of Way Association (AREMA),
Manual for Railway Engineering, Chapter 15, Washington, D.C., 2018.
[2] Coopers Loading System, Wikipedia, the free encyclopedia, en.wikipedia.org,
2012.
[3] Sorgenfrei, D. F. and Marianos, W. N., “Railroad bridges”, Bridge Engineering
Handbook, Chen, W. F. and Duan, L. (Eds), CRC Press, Boca Raton, FL, 2000.
[4] Unsworth, J. F., “Design of Modern Steel Railway Bridges”, CRC Press, Boca
Raton, FL, 2010.
[5] Dick, S. M., “Bending Moment Approximation Analysis for Use in Fatigue Life
Evaluation of Steel Railway Girder Bridges”, Ph.D. Dissertation, University of
Kansas, Lawrence, Kansas, 2002.
[6] Dick, S. M., Otter, D. E., and Connor, R. J., “Comparison of Railcar and Bridge
Design Loadings for Development of a Railroad Bridge Fatigue Loading”, AREMA
2011 Annual Conference, Minneapolis, MN, September 20, 2011.
[7] Chalk, P. L., and Corotis R. B., “Probability models for Design Live Loads.” Journal
of the Structural Division (ASCE) 106, no.10, pp. 2017-2033, 1980.
[8] Tobias D. H., Foutch D. A., and Choros J., “Loading Spectra for Railway Bridges
under Current Operating Conditions”, Journal of Bridge Engineering (ASCE), pp.
127-134, 1996.
[9] Tobias, D. H., and Foutch, D.A., “Reliability-Based Method for Fatigue Evaluation
of Railway Bridges”, Journal of Bridge Engineering 2(2), pp.53-60, 1997.
20 | Strona
[10] Rakoczy, Anna M. and Duane Otter. “Current Loading Spectra for Fatigue
Evaluation of Railway Bridges.” Research Report R-xxx. AAR/TTCI, Pueblo, CO,
MONTH 2018.
[11] Rakoczy, Anna M., Duane Otter, and Stephen Dick. “Effects of Articulated Double-
Stack Cars on Bridges.” Technology Digest TD-17-020, AAR/TTCI, Pueblo, CO,
August 2017.
[12] Rakoczy, Anna, Duane Otter, and Stephen Dick. “Short Heavy Axle Load Cars:
Analysis.” Technology Digest TD-16-013, TTCI/AAR, Pueblo, Colorado. April
2016.
