EVALUATION OF THE LOAD CAPACITY OF A REHABILITATED STEEL ARCH RAILWAY
BRIDGE J.F. Unsworth, P.Eng.
Manager, Structures Planning and Design, Canadian Pacific Railway, Suite 700 401 – 9th Ave. SW, Calgary, Alberta, Canada Tel. 403-319-6614 Fax. 403-205-9033
EVALUATION OF THE LOAD CAPACITY OF A REHABILITATED STEEL ARCH RAILWAY BRIDGE
J.F. Unsworth1
1Manager, Structures Planning and Design, Canadian Pacific Railway, Calgary, Canada
ABSTRACT
The load carrying capacity of a 336 foot span steel arch bridge carrying heavy freight railway
traffic, originally constructed in 1893 and extensively strengthened in 1929, was recently
evaluated through detailed visual inspection, non-destructive testing and three-dimensional finite
element structural analysis. This paper reviews the load capacity evaluation of the bridge and the
results of the evaluation in light of present railway traffic loads on the structure. The evaluation
shows that the bridge is adequate to safely carry modern railway traffic. Also, based on the load
rating, a simple procedure for the evaluation of infrequent very heavy loads can be established.
INTRODUCTION
Canadian Pacific Railway’s Stoney Creek bridge is a single track steel deck arch railway bridge
spanning a 300 foot deep canyon about 200 miles west of Calgary, Alberta, near the summit of
Canada’s Selkirk Mountain Range (Fig. 1). The bridge consists of two parallel three-hinged steel
pin-connected truss arches spanning 336 feet with a rise of 100 feet on each side of the railway
track. The parallel truss arches are at a batter of 1:10 (H:V), are 48 feet apart at the base and
taper to 28 feet at the crown. This arrangement of the arches creates an elegance of form as well
as providing considerable lateral stiffness. The track is supported by deck plate girder spans on
spandrel bents. The single railway track is tangent across the bridge, with the exception of a
horizontal spiral curve commencing at the west quarter of the arch. The spiral curve provides a
transition to an 11 degree simple curve starting about 50 feet off the west end of the bridge. The
bridge is on a grade of 2% ascending westward.
The Original Stoney Creek Bridge (1885)
The original railway bridge at this location was a four span wooden Howe truss supported on
timber tower piers constructed in 1885 and designed by prominent American civil engineer C. C.
Schneider. With its 230-foot high central tower, the bridge was reputed to be the highest railway
bridge in the world (Lavallée 1974). However, Gustave Eiffel's Garabit Viaduct, constructed in
1884 of wrought iron, rises 400 feet above the Truyère River in France, disputing this claim.
Nevertheless, it may have been the highest timber bridge constructed. The introduction of heavier
locomotives, considerable maintenance requirements associated with large timber bridges and
risk of destruction by fire precipitated its replacement with a steel arch bridge after only eight
years of service.
The Steel Arch Bridge (1893)
The steel arch bridge was constructed in 1893 on falsework within the deep canyon. The bridge
consisted of single three-hinged steel pin-connected truss arches spanning 336 feet with a rise of
100 feet on each side of the railway track. The track over the arch was supported by seven deck
lattice girder spans on spandrel bent columns. The spandrel bent columns connected to every
third panel point from each end of the truss arch and deliver reactions to the arch at six points
(Fig. 2).
In order to create a statically determinate three-hinged structure, the main hinge pins are
located at the crown and ends of the arch at the lower chord only with a sliding pin arrangement
at the crown of the top chord. This arrangement precludes axial stress in the top chord members
in the center panels but makes it necessary that the bottom chord of the truss arch carry most of
the live load. However, the three-hinged design allows for a better distribution of forces between
top and bottom chords of the truss arch than a two-hinged arch arrangement. The forces in the
top chord of the Stoney Creek arch are about 20% of that in the bottom chord at the end supports.
In contrast, the forces in the top chord of the Hell Gate arch bridge in New York City (a two-hinged
steel truss arch of similar design to Stoney Creek) are about 6% of that of the lower chord at the
end supports (Ammann 1918).
The bridge was designed for a live load consisting of two consolidation locomotives with axle
loads of 30 kips, 48 kips and 42.5 kips (196 ton nine axle locomotives) and a uniform train load of
3000 lb/ft without a dynamic load allowance (Fig. 2). Lateral wind forces of 360 lb/ft applied 7 feet
above the rail on the moving train and 30 lb/ft2 on the bridge were used for lateral bracing design.
Lateral wind forces for the unloaded bridge condition were taken as 50 lb/ft2. The wind pressures
were applied to twice the elevation surface area of the bridge. Arch truss member forces due to
wind were superimposed on member forces due to dead and live load only when the member
forces due to wind were in excess of 25% those due to dead and live load. Longitudinal forces
due to tractive effort and braking were calculated as 20% of the vertical live load.
The steel was specified to have an elastic limit of 33 ksi (Motley 1930). Allowable tension and
compression design stresses for the truss arch member were specified sufficiently low to account
for dynamic load amplification and preclude elastic instability. Typical specification for truss chord
allowable tension was 12 ksi and for allowable compression
2
2
200001
10000
R
L+ ksi ; where L= length
of the compression member (in.) and R= least radius of gyration (in.).
After construction, vertical arch deflections of less than ¾ in. at the crown were reported under
usual train loads of 1893 (Engineering News 1894).
The Reinforced Steel Arch Bridge (1929)
Further increases in locomotive weights required that the railway either replace or rehabilitate the
Stoney Creek bridge. Initially, it was decided to replace the 1893 steel arch with a new 311 ft
cantilever deck truss with 111 ft flanking anchor spans adjacent to the existing steel arch.
However, foundation conditions in the canyon curtailed the economical construction of a new
bridge and rehabilitation of the existing 1893 construction was undertaken in 1929. The
rehabilitation consisted of the erection of two additional truss arches 5 feet to the outside of the
existing truss arches. The wider overall bridge geometry provides a greater lateral stiffness to
resist lateral loads due to wind, centrifugal force and live load. Longitudinal forces due to traction
and braking are transmitted to the arches through new latticed struts between spandrel bents.
The new trussed arches were designed to be identical in geometry with member sections and
materials of close similarity to the existing 1983 arches (Motley 1930). Furthermore, the arches
were tied together with pinned diaphragms to provide for a uniform stiffness and distribution of
live load to each pair of arches. Equalizing diaphragms were designed to connect between the
top chords of the parallel arches at each panel point in the end quarter spans and at every
second panel point in the central portion of the arches. This arrangement transfers spandrel bent
column loads to each arch at thirteen locations (Fig. 3). However, due to construction constraints
and the shortening of the track spans supported by the spandrel bents, the original end spandrel
bent columns were not replaced and remain supported by the original 1893 arches only. The
spandrel bent columns are pinned at the top and have disc-type bearings at the base where they
connect to the panel point equalizing diaphragms.
Equalization of loading also required burdening the new arches with dead load at each panel
point corresponding to the dead load existing on the 1893 arches before connecting the trusses.
This necessitated construction of the new arches at higher elevations than the existing arches in
accordance with the calculated dead load deflection of 5/8 in. at the centre of the arches (Motley
1930). Equalized dead load deflections were confirmed by field measurements at the time of
construction. After construction, deflections under a static test live load consisting of four
locomotives (ranging in weight from 230 to 376 tons) with a total weight of 1100 tons showed a
uniform deflection of 1-5/8 in. at the arch centres. It is interesting to note that under the usual in-
service train loading conditions of 1929, the original 1893 arch deflected 2-3/4 in. at the centre pin
(Motley 1930).
An analysis for Cooper’s E-60 design live load (Fig. 3) illustrated that some members of the
original arches required reinforcement. It is generally considered that the rehabilitation improved
the bridge aesthetics as well as structural behaviour.
EVALUATION OF THE REHABILITATED BRIDGE UNDER MODERN TRAIN LOADS
Bulk commodity unit train traffic introduced in the early 1970’s created train axle loads of almost
70 kips (200 ton six axle locomotives and 110 ton four axle cars). An evaluation was made in
1970 based on parameters of the original design and in accordance with American Railway
Engineering Association recommended methods of the time. These methods are similar to the
"maximum" load rating methodology outlined in the American Railway Engineering and
Maintenance-of-Way Association Manual of Recommended Practice (AREMA 1998) current at
the time of the investigation (Conway 2001). The 1970 load rating, using a yield stress of 30 ksi,
exhibited that all elements of the structure were adequate for train loads less than Cooper’s E-104
live load at 60 mph. The governing demand to capacity (D/C) of arch members was 0.77 for
member TC2.
Regular unit freight train traffic with car axle loads of 72 kips and business pressures to
increase car commodity volumes that create 80 kip axle loads, precipitated a further investigation
of the structure using modern methods of analysis and strength rating in 1998 and 1999.
Furthermore, recent inspections revealing vertical elongation of the bottom pin holes at the 1893,
and to a lesser extent in the 1929, truss arch vertical end members, indicated a need to
determine the behaviour of the bridge in greater detail.
The 1999 strength evaluation consisted of three-dimensional modelling the structure (Fig. 4)
with linearly elastic frame elements (Buckland and Taylor 2000). Connections between the 1893
and 1929 trusses were modelled with appropriate pinned end connections. It was recognized that
the deformations associated with the elongated pin holes at the end verticals of the arch generate
geometrically non-linear structural behaviour. However, it was considered appropriate to proceed
with a linear elastic analysis based on deformations producing only slight non-linearity that would
not invalidate the linear elastic analysis for purposes of a practical strength rating (Cook 1981).
The evaluation investigates the load distribution, strength and behaviour of the bridge under a
Cooper’s E-80 loading. Cooper’s E-80 loading is identical to that shown in Figure 3 with axle
loads increased proportionally by 33%.
The load rating was carried out in accordance with AREMA methods for "normal" and
"maximum" ratings. "Normal" ratings are based on design allowable stresses and "maximum"
ratings on allowable stresses of up to 80% of specified material yield stress. At Canadian Pacific
Railway "normal" ratings are generally used to assess existing structures for safe passage of
traffic over the expected service life of the bridge and "maximum" ratings are used to assess the
effects of infrequent loads. "Maximum" ratings may also be used to assess structures for usual
railway traffic where traffic volumes are such that the remaining useful life of the structure is not
substantially affected (AREMA 1998).
The yield stress of the steel used in the determination of member capacity was 30 ksi, but
reduced by 15% for the 1893 truss due to some uncertainty regarding the actual material
properties of the 1893 steel (Motley 1930). The demand on a member or pin, from a Cooper’s E-
80 loading at a train speed of 60 mph, was calculated by the three-dimensional elastic frame
analysis. Deficient members were reviewed for demand with reduced centrifugal and dynamic
(impact) loads at reduced speeds to determine the permissible maximum train speeds for the
Cooper’s E-80 loading. If train speeds cannot be reduced to attain a D/C≤1.0 then the maximum
equivalent Cooper’s loading for the D/C=1.0 condition is developed for a 60 mph train speed.
SUMMARY OF RESULTS OF THE EVALUATION
The three-dimensional analysis revealed that an unequal distribution of load is being transferred
to each arch. Furthermore, at the west end of the bridge the demand requirements on the arches
is considerably greater due to the centrifugal effects from track curvature. The centrifugal force,
F c (kips), is;
100R
6.7PV F
2
C
= (1)
where P =axle load (kips); V = train speed (mph); and R = radius of track curvature (ft), which
varies from R = ∞ at the beginning of the curve at the west quarter point of the truss (P4) to R=
695 ft at the west end of the bridge. In accordance with AREMA specifications this horizontal
force is applied at each axle location at a point 6 feet above the rail.
All elements of the bridge are of sufficient strength for Cooper’s E-80 loading at 60 mph at
"maximum" rating member capacity, with exception of the west 26 ft deck plate girder span and
the main pin for the north 1929 truss arch at the west end. The results of the analysis showed D/C
values of 0.85 and 0.74 for "maximum" rating of the 1893 and 1929 arch members TC2,
respectively. Member TC3, with a D/C=0.89, governed the "maximum" strength rating for truss
arch members. The moderate differences between the 1970 and 1999 strength evaluations are
primarily due to the assumption of equal distribution of live load to each arch and the omission of
centrifugal effects in the 1970 assessment.
However, the "normal" load rating indicated that, for a Cooper’s E-80 loading, many members
of the bridge are of deficient capacity, as shown in Table 1. "Normal" rating results show that all
truss arch diagonals, truss member end pins and arch main pins (all pins were rated for the
governing effects due to coexisting member forces) are of sufficient capacity for Cooper’s E-80
loading at 60 mph. However, many other members of the truss arches are of deficient capacity
under Cooper’s E-80 loading at 60 mph. The two spandrel bent transverse beams that support a
21 ft. and 42 ft. deck plate girder span are also deficient at "normal" rating stresses. In addition,
the four deck plate girders at the west end of the bridge are deficient at "normal" rating stresses.
All other spandrel frame members, transverse beams and deck plate girders are sufficient at
"normal" rating stresses.
DISCUSSION OF RESULTS
"Maximum" Rating Results
The 26 ft. deck plate girder span at the west end of the bridge has a D/C=1.37 at "maximum"
rating stresses. The governing criteria is flexural stress at mid-span. For loads equivalent to
Cooper’s E-80, the demand can be reduced, so that D/C≤1.0, through a reduction in centrifugal
force and impact by limiting train speeds to 30 mph. This information may be used to establish
speed restrictions or impasses to special or infrequent heavy loads by establishing the equivalent
Cooper’s E load, based on mid-span flexure, for the load being considered.
The main pin of the north 1929 truss arch at the west end has a D/C=1.03 for "maximum"
rating based on bearing stresses between the main pin and pin plates. The AREMA Manual
allows that bearing stresses on pins may be disregarded for bridge rating unless there is visible
deformation of contact parts. Visible deformations have been reported at these pins. As proper
functioning of these pins at the hinged skewbacks is of primary importance to the behaviour of the
arch, and because AREMA does not provide for explicit "maximum" pin bearing rating stresses,
allowable stresses corresponding to a "normal" rating were used to assess the capacity.
Therefore, the D/C values reported for the main arch pins at the base can be considered
conservative and disregarded with respect to the evaluation of infrequent heavy loads of the
bridge.
"Normal" Rating Results
The situation is a more complex with respect to "normal" rating. “Normal” rating results indicate
that either strengthening of deficient members or load reductions are required. A combination of
selective member strengthening in conjunction with application of a maximum train speed that
does not compromise the efficiency of train operations is a cost effective means of ensuring safe
load carrying capacity of the bridge. Effective reductions in live load can be reached through
speed restriction developed in accordance with the formula given by AREMA for centrifugal force
(Eq. 1) and reduction of dynamic effects, I R , (Eq. 2). Eq. 2 is applied to only the vertical effects
components of the AREMA impact equation.
( )
−−= 2
R 602500
80.01I V (2)
Table 2 shows deficient members for the "normal" rating and speed reductions required to
safely pass Cooper's E-80 loads. In some cases, even a static application of the Cooper's E-80
load creates a demand that exceeds member capacity. Due to track grade and curvature at the
bridge, current train speeds are limited to 25 mph. Table 3 shows the maximum Cooper's E axle
loading for members that remain deficient for Cooper's E-80 loading below 25 mph.
The pins at the base of the truss were shown to have D/C values approaching 1. Observations
of pin hole elongation at the base of the truss end verticals would appear to indicate that, prior to
the 1929 rehabilitation, elongations were likely occurring; and may have continued after the
strengthening due to the end spandrel bent being supported directly over the 1893 arches.
Based on the "normal" rating results, train loads should be limited to E-59 as governed by
member TC3 at the west end of the 1893 trusses.
Fatigue Consideration
In 1988 a new track was constructed lower down the canyon and the Stoney Creek bridge loading
regime became primarily that of empty eastbound traffic. A life cycle fatigue analysis (CPR 1992)
using modern methods of stress range prediction and damage accumulation rules (Dick &
McCabe 1991) was conducted. The analyses indicated that, until regular unit freight train
operations commenced in 1974, very few stress range cycles with magnitude greater than the
tension member constant amplitude fatigue stress thresholds were likely developed. However,
even though fatigue damage accumulation between 1974 and 1988 was considerable for the
short span girders, it did not approach the theoretical fatigue life. Since 1988, traffic volume and
loading reductions (primarily empty unit trains) on the bridge have reduced the frequency of
equivalent constant amplitude stress range magnitudes (computed as the root mean cube stress
range using Rainflow cycle counting technique) above the fatigue stress limit for these riveted
members; and a further a study of remaining fatigue life was not deemed necessary.
CONCLUSIONS AND RECOMMENDATIONS
General
Non-uniform distribution of live load to the trusses, in conjunction with lateral forces due to
centrifugal effects at the west end of the structure, establish the governing strength rating of the
bridge.
The existence of relatively high bearing stresses at the main pins at the end of the arch and the
observation of pin hole elongation and material bearing failure, indicates that periodic non-
destructive testing and further investigation (geometric non-linear analysis) of local conditions and
effect on the overall structural bevavior should be considered.
"Maximum" Rating Results
The passage of infrequent heavy loads across the bridge is governed by mid-span flexure of the
26 ft. deck plate girder span at the west end of the bridge. Therefore, a simple determination of
the safety of infrequent heavy loads across the bridge is available.
"Normal" Rating Results
Several bridge components (Fig. 5) were found to be deficient at "normal" rating stresses with
respect to the demand created by Cooper’s E 80 load at a track speed of 25 mph. However, with
the present lower traffic volumes and train weights, the remaining useful life of the structure is not
substantially affected and the immediate consideration of load carrying capacity for usual traffic
may be based on "maximum" ratings. This indicates that the bridge is currently safe to carry train
loads equivalent to Cooper's E-80 at 25 mph.
However, in order to ensure the capacity of the structure to safely sustain present and future
train loads, the deficient members in Table 3 may require strengthening. In order to effectively
plan an appropriate maintenance program, an analysis of the equivalent Cooper's E rating for
present train configurations for the deficient members was performed. The results of that analysis
indicated that the members shown in Table 3 are sufficient under present train loadings and track
speeds. The information developed from this study on the structural behavior of the Stoney Creek
bridge under modern train loadings will enable the strategic planning of a rehabilitation program
that will ensure the safety of train operations for future railway traffic over Stoney Creek Bridge.
ACKNOWLEDGEMENT
The writer wishes to acknowledge Mr. D.P. Gagnon, P.Eng. of Buckland and Taylor Ltd. and
Mr. D.E.J. Adamson, P.Eng. of Canadian Pacific Railway for their assistance in the preparation of
this paper.
REFERENCES
American Railway Engineering and Maintenance-of-way Association (AREMA 1998). Manual
of Recommended Practice: Steel Structures: Existing Bridges, Chapter 15, Part 7. Washington,
D.C.
Ammann O.H. (1918). The Hell Gate Arch Bridge and Approaches of the New York
Connecting Railroad over the East River in New York City. Transactions of the American Society
of Civil Engineers 82, New York.
Buckland and Taylor Ltd. (1999 & 2000). Stoney Creek Arch Bridge Load Rating. North
Vancouver, B.C.
Canadian Pacific Railway (CPR 1992). Coal Route Fatigue Study. Montréal, QC.
Conway W.B. (2001). Practical Application of the Rating Rules. 2001 AREMA Annual
Conference, Chicago, IL.
Cook R.D. (1981). Concepts and Applications of Finite Element Analysis. J. Wiley, New York
Dick, S.M. & McCabe, S.L. (1991). Improved Techniques for Evaluation of Railway Bridge
Fatigue, 8th Annual International Bridge Conference, Pittsburgh, PA.
Engineering News (1894). Stony Creek Arch, Canadian Pacific Railway. Engineering News
August 2. New York.
Lavallée O. (1974). Van Horne’s Road. Railfare Enterprises, Montréal, QC.
Motley P.B. (1930). Reinforcement in Place of the Stoney Creek Arch Bridge. Engineering
Journal Vol. XIII, No. 5. Montréal, QC.
LIST OF TABLES TABLE 1. Number of Deficient Bridge Members at “Normal” Rating TABLE 2. Governing Deficient Members of Each Member Type TABLE 3. Maximum Cooper’s Axle Load for D/C = 1.0 LIST OF FIGURES FIGURE 1. Stoney Creek Bridge FIGURE 2. General Elevation, Plan and Design Wheel Load for 1893 Steel Arch FIGURE 3. General Elevation, Cross Section and Design Wheel Load for 1929 Steel Arch FIGURE 4. Three Dimensional Model of Arch FIGURE 5. Deficient Members of Truss Arch
TABLE 1. Number of Deficient Bridge Members at "Normal" Rating
number in parenthesis denotes total number of members of that type in the bridge TC=Top Chord; BC=Bot. Chord; V=Verticals
1893 Truss Arches
1929 Truss Arches
TC (32)
BC (32)
V (34)
TC (32)
BC (32)
V (34) 16
25
2
6
3
2
TABLE 2. Governing Deficient Members of Each Member Type
Combined Forces from 3D Analysis (Demand)
D/C at 60 mph
Max. Speed for E-80 & D/C=1.0 (mph)
Member
Axial (kip)
MLONG (kip-ft)
MLAT (kip-ft)
Truss Arch Top Chord Members TC2 1893 (4)*
-353
10
35
1.21
4
TC2 1929 (4)*
-405
13
36
1.08
29 TC3 1893 (4)*
-358
17
28
1.32
not possible
TC3 1929 (2)*
-474
20
38
1.02
42 TC4 1893 (4)*
-342
22
2
1.10
16
TC5 1893 (2)
-301
26
2
1.04
28 TC6 1893 (2)
-267
56
-31
1.14
not possible
Truss Arch Bottom Chord Members BC1 1893 (3)*
1172
0
-59
1.09
43
BC2 1893 (4)*
1198
85
-57
1.22
not possible BC2 1929 (1)*
1185
97
-57
1.04
44
BC3 1893 (4)*
1196
101
-20
1.18
not possible BC4 1893 (4)*
1152
92
-19
1.23
not possible
BC5 1893 (4)
1069
94
-5
1.14
not possible BC6 1893 (2)
988
100
-17
1.14
not possible
BC7 1893 (4)
848
56
-41
1.14
not possible BC7 1929 (2)
829
81
-69
1.03
35
Truss Arch Verticals P0 1893 (1)*
364
1
-65
1.08
59
P4 1893 (1)
175
3
9
1.01
55 P8 1929 (2)
-80 8
-4
1.21
not possible
Spandrel Bent Members Transverse Beam P4
20
3071
147
1.11
24
Deck Plate Girders 26 ft span at west
85
1146
48
1.82
26
38 ft span at west
85
2133
16
1.14
41 21 ft span (P0 - P1)*
85
741
10
1.22
38
21 ft span (P1 - P2)*
85
720
6
1.10
45
number in parenthesis denotes total number of deficient members of that type in the bridge, values shown in the table are those of governing member * members with governing D/C at west end of the bridge subject to track curvature
Table 3. Maximum Cooper’s Axle Load for D/C = 1.0
Member D/C
Cooper’s Axle Load (@ 60 mph)
TC2 1893 (4)
1.21
E-64
TC3 1893 (4)
1.32
E-59 TC4 1893 (4)
1.10
E-73
TC6 1893 (2)
1.14
E-70 BC2 1893 (4)
1.22
E-60
BC3 1893 (4)
1.18
E-64 BC4 1893 (4)
1.23
E-61
BC5 1893 (4)
1.14
E-67 BC6 1893 (2)
1.14
E-67
BC7 1893 (4)
1.14
E-67 P8 1929 (2)
1.21
E-64
FIGURE 1. Stoney Creek Bridge
FIGURE 2. General Elevation, Plan and Design Wheel Load for 1893 Steel Arch
FIGURE 3. General Elevation, Cross Section and Design Wheel Load for 1929 Steel Arch
FIGURE 4. Three Dimensional Model of Arch
FIGURE 5. Deficient Members of Truss Arch (E80 @ 25 mph)
