Page 1
Proceedings of Bridge Engineering 2, Conference 2007
23 April 2008, University of Bath, Bath, UK
Y.C. Tsui
[email protected]
A STRUCTURAL REVIEW OF THE NEW RIVER GORGE BRIDGE
Y C TSUI1
1University of Bath
Abstract: This paper is written to give a detailed review of the New River Gorge Bridge. The aim of this
paper is to give the reader an insight into the issues surrounding a major bridge and includes sections on
the design, aesthetics, construction, future changes, durability and structural analysis.
Keywords: New River Gorge Bridge, arch, cantilever, truss, steel
1. Introduction
The New River Gorge Bridge was opened on the
22nd
October, 1977 and had been the world’s longest
single span arch bridge since the opening until 2003.
The deck of the bridge is 267m above the New Rivers
with a width of 21.1m. It has a total length of 924m
with the main arch spanning over 518m.
The bridge was built in order to link both sides of
New River Gorge reducing the travelling time from 45
minutes to just over 1 minute.
2. Design
A private engineering firm, Michael Baker, Jr., Inc,
was contracted by the West Virginia Department of
Highways to design the bridge. During the design
process, factors such as construction cost, maintenance
cost and aesthetics had to be taken into account in
order to produce the most effective bridge design.
Three designs were considered before the final
solution was found.
2.1.1. Continuous Truss Design
Figure 1: Continuous truss design
The design shown in Fig. 1; Ref. [1]; was
discarded as the piers would be enormous and almost
the height of a modern tall building. This would lead to
a few problems such as large foundation area and deep
piles foundation in order to resist plane failure,
increasing the amount of material required.
The water pressure is another consideration as it is
constantly fluctuating throughout the design life of the
bridge due to the close proximity of the river, this
would affect the condition of the soil near the
foundation of the piers. This means that the foundation
would need to be over designed lowering the cost
effectiveness of the design.
2.1.2. Suspension Bridge Design
Figure 2: Suspension bridge design
The design shown in Fig. 2; Ref. [1]; was also
rejected. This is considered to be once again due to the
foundation. The high vertical force from the piers could
cause plane failure in the valley sides unless a stable
foundation is built to withstand this problem but such a
foundation would be very costly and would exceed the
budget of the project.
2.1.3. "Jack Knife" Arch Truss Design
Figure 3: "Jack knife" arch truss design
This design in Fig.3; Ref. [1]; was again dismissed
as extra concrete would be required to stabilise the
Page 2
restricted number of supports for the arch. Once again,
increasing the material costs. Also importantly is that
the aesthetics of the design are poor with little order in
the truss members.
2.1.4. Single Span Arch Design
Figure 4: Single span arch design
The final design of the bridge is a steel trussed
arch as shown in Fig. 4; Ref. [1]. Details of this design
will be discussed in later sections.
This design is the most suitable solution compared
to the other three proposals as the load follows a clear
path which is not apparent in the design shown in Fig.
3. An important aspect of the final design is the
foundations. Use of a system such as that shown in Fig.
1 and Fig. 2 would require extensive and costly
foundations, making both designs uneconomic.
3. Aesthetic of the Bridge
The aesthetic of the bridge can be defined
according to the 10 “rules” that Fritz Leonhardt; Ref
[2]; stated. This section compares the aesthetic of the
New River Gorge Bridge against these 10 “rules”.
Figure 5: View of New River Gorge Bridge
The first and most important aesthetical aspect is
the fulfilment of function. The simply structured New
River Gorge Bridge has achieved this with great
success. The structure shows a clear load path from the
deck to the arch, it is apparent to the viewer the way in
which the structure works. The only objection to this
rule is that the structure looks almost too frail when
viewed from far distance.
Almost equally important are the proportion of the
structure. The New River Gorge Bridge appears to be
exceptionally slender; this is most noticeable in the
taller piers. The depth of the deck is approximately half
that of the arch which emphasises the structural
integrity of the arch aiding the fulfilment in function of
the structure.
The order of the bridge is of great importance for
aesthetical considerations. It is sometimes difficult to
achieve good order when designing truss bridges. This
problem is overcome in the New River Gorge Bridge
by the repeating pattern and symmetry of the truss
which results in a clear structure. A common problem
with truss bridges is crossing of members when viewed
from an oblique angle such as in Fig. 5; Ref. [2].
However, it is obvious in the picture that this problem
does not exist. The clear lines in the structure are
aesthetically strong as they are continuous without
breaks. The other key feature that is shown in Fig. 5;
Ref. [2]; is the elements of the truss are all in plane
which emphasises the excellent order of the bridge.
The plane of the truss is also evidence of good
refinement of the design. Another key attribute of the
design is the tapering of the piers. Leonhardt made the
observation that aesthetically straight piers have
incorrect proportion as they appear wider at the top
which makes little sense structurally. The correct
elements sizing, placement and pattern are all evidence
of good refinement in the design. However, the
constant size of the piers has given a negative effect on
refinement as the taller piers appear to be more slender
and weaker.
The bridge shows its strong character through the
integration into the environment and the impressive
way the bridge naturally blends into its surroundings.
The slender piers and the complex truss members
resemble the branches of the trees below. This is aided
by the low solidity ratio of the bridge. The hidden
substructure helps to integrate the bridge into the
environment by given it a more organic feel.
By the use of unpainted cor-ten steel, it gives a
natural weathered matt finish to the bridge which looks
most appropriate to the environment. The natural
colour of the steel is good for many reasons. One of the
most obvious reasons is that no maintenance is
required to keep the appearance of the bridge and the
similar colour tone works harmoniously with the
surroundings. Conversely, the natural colour allows the
bridge to stand out against the sky when viewed from
below, making the slender bridge seem stronger.
Although the bridge is constructed from a simple
shape, the constituent elements give good complexity
to the structure. The New River Gorge Bridge expertly
achieves the balance between simplicity and
complexity. The simplicity comes from the single span
arch allowing the viewer to appreciate the simple
structure, whereas the more complex truss elements
give visual stimulation.
Leonhardt’s final guideline regarded the
incorporation of nature into the design. This is
Page 3
achieved by the use of “K” – bracing in the arch which
resembles a spine. The slender piers and truss
members echo the forest below.
Overall, the New River Gorge Bridge has achieved
aesthetic success both in the public and engineers’ eyes.
4. Geology
Over thousands of years the New River has eroded
the “V” shape valley which can be seen today. This
pattern of erosion has left the strong resistant rock on
the valley walls. This strong rock has resisted
weathering throughout the years but is likely to be
heavily faulted, therefore the process of bank
stabilisation would be required as part of the
construction. The major drawback of the steep valley
side is the high possibility of rock falls and slope
failure.
The vegetation growing on the valley walls gives
further cause for concern. This has the effect of
speeding up the erosion of the valley walls and
enhancing the faulting.
4.1. Earthquakes
West Virginia is located in the centre of the North
America tectonic Plate; Ref. [3]. This would suggest
that the area is unlikely to experience earthquakes.
However, it is not impossible for intra-plate earthquake
to take place. This was shown by the massive New
Madrid earthquake in 1812 which was estimated to
have been approximately 8 on the Richter scale.
Therefore the structure has to be designed to withstand
the effects due to earthquakes.
4.2. Mining Activity
During a site survey an abandoned mine was
discovered near the location of the foundations for the
main supporting piers. If undiscovered, this could
potentially have caused major failure to the bridge.
5. Geotechnics
As previously mentioned, slope failure would be a
major concern for the design. For this reason, the single
span arch design shown in Fig. 4 seems to be the most
appropriate structural solution in this location. The
main reason for the use of an arch is that its direction
of thrust acts almost normal to the valley walls as
shown in Fig.6. This compresses the rock layers and
reduces the chance of slope failure.
Figure 6: Sketch of perpendicular load on valley walls
However, stabilisation of the valley sides was still
required to ensure that the valley walls were capable of
withstanding the high compressive force generated by
the arch and to reduce settlement as well as providing
stability. This is done in two stages. Firstly, loose
weathered material must be removed from the valley
walls. Followed by actual stabilisation of the valley
walls, this can be done by a number of methods; Ref.
[4]. The most common methods are rock anchors and
injecting cement grout into pre-drilled holes in the rock
face.
Generally, settlement of foundations would be a
major concern for bridge designers but due to the
loading system and geological location, settlements of
the structure would be minimal.
Referring to the problem outlined in section 4.2, a
process of mine stabilisation was carried out. This was
done by filling the mines with gravel and grout.
6. Construction
To speed up the construction process, different
parts of the construction were carried out
simultaneously. When filling the mines, the concrete
footings for the arch and the piers were constructed at
the same time. Whilst, the vegetation was being cleared
from the slope of the gorge and the Foster Creighton
Company were making the steel.
6.1. Preliminary Construction
All of the steel members for the trusses were
prefabricated in American Bridge Division’s Ambridge
plant and transported close to site by river where they
were loaded onto trucks and transported to site by road.
On arrival at the site there were bolted together into
segments. However, it was difficult to construct the
structure over a deep valley. This problem was
resolved by the contractor who decided to build a
temporary cableway which was to act as a crane across
the valley as shown in Fig. 7; Ref. [1].
Figure 7: Early construction
Two 91.4m tall towers were built on each side of
the valley to allow the set up of the 1524m long
cableway. An initial light weight cable was lifted into
place by helicopter; a stronger cable was attached to
this and pulled back across the valley. The final cable
was 76.2mm thick, due to its stiffness and weight; it
Page 4
was able to withstand the strong wind and the heavy
load which it was later subjected to during the
construction of the arch.
With the aid of the cableway, it was possible to
build the deck out to the foundations of the arch. This
was done by making use of the cableway to position all
the elements in place. Due to the high compression
force induced to the end piers of the deck during the
construction of the arch, they are made double the size
of the other piers in order to take higher compression
force and to obtain additional stiffness. The high
compression force in the piers is due to the downward
component of force from the suspension cables. Fig. 8
indicates the odd bigger pier.
Figure 8: Picture showing the wider end piers of the
preliminary construction phase
The high compression force from the piers from
this stage of construction would increase the chance of
slope failure. This would be a strong design
consideration for the foundations.
6.2. Construction of the Arch
The enormous depth of the gorge also made
construction of the arch challenging. To resolve this
problem, the suspended cantilever construction method
was employed.
This technique makes use of the temporary cable
stays to support the arch cantilever during construction
stage.
Figure 9: Construction of the arch
However, it was considered that the high moment
and deflection due to the wind loading during this stage
would be a major concern. This will be discussed in a
later section.
6.3. Final Construction
After the completion of the arch, thirteen piers,
which range in height from 7.92m to 93.0m, were built
from the centre of the arch to the abutments.
The deck of the bridge was constructed by using
the cableway to lift the steel segments in place. Once
they are positioned, the segments were connected
through bolt groups. After the deck was constructed,
the surface of the deck was completed by in-situ
reinforced concrete.
6.4. Summary of Construction
A total construction period of 40 months (from
June, 1974 to Oct 1977) was achieved. It was
considered that the construction method was effective
due to the relatively short construction time. This was
greatly helped by the cableway and the good
construction management which allowed for
simultaneous construction of various elements. The
construction period is also very good considering the
harsh winters in West Virginia.
7. Loading
Determining different loading conditions that
would be experienced by the bridge allows structural
analysis to be carried out. This will be discussed in a
later section. The major loading conditions of the New
River Gorge Bridge are dead load, super-imposed dead
load, traffic live loading, wind loading and the effect of
temperature.
For analysis purposes in this report, loads are
calculated in accordance with BS 5400-2:2006; Ref.
[5]; with relevant partial factors, γfl and γf3 applied for
both Ultimate Limit State (ULS) and Serviceability
Limit State (SLS).
The value for γfl is dependent on the load
combination considered. BS 5400-2:2006; Ref. [5];
considers 5 crucial load cases, although others would
need to be considered in full design. The load
combinations considered in BS 5400-2:2006; Ref. [5];
are as follows:
1. All permanent loads plus primary live loads.
2. Combination 1, plus wind loading, and
temporary erection loads if erection
considered.
3. Combination 1, plus effects of temperature,
and temporary erection loads id erection
considered.
4. All permanent loads plus secondary live loads
and associated primary live loads.
5. All permanent loads plus loads due to friction
at supports.
γfl can then be obtained from Table 1 in BS 5400-
2:2006; Ref. [5].
γf3 is used to allow possible imprecision in the
analysis. For a steel bridge, this is taken to be 1.00 for
SLS and 1.10 for ULS for the New River Gorge Bridge.
Page 5
7.1. Dead Load
In general, the largest loading that a bridge is
subjected to is the weight of its structural elements.
The New River Gorge Bridge is composed of steel
elements and a concrete slab.
As the dead weight of the structure is so significant,
the contractor decided that high yield steel was to be
used since it has a high strength to weight ratio.
Table 1 shows the sizing of main members, these
have been assumed in the absence of official
dimensions.
Table 1: Sizing of members
Components Size
Reinforced concrete slab 400mm thick
Deck steel members 300×150×16mm RHS
Piers steel members 400×400×20mm SHS
Arch steel members 400×400×20mm SHS
Table 2 shows the dead weights of the bridge
components.
Table 2: Dead load of the bridge
Elements Load (kN/m)
Reinforced concrete slab 199
Deck 22.0
Piers 9.14
Arch 15.7
Total 246
7.2. Super-Imposed Dead Load
When a bridge is constructed, pedestrians and
vehicles are not the only user of the bridge. Many
services companies (gas, electric and water etc.) see the
construction of a new bridge as a great opportunity to
lay new services. Besides this, road furniture should
also be taken into account.
Due to the unpredictable nature of the loading, a
high load faction (γfl) has to be applied. The typical
values used are 1.75 for ULS and 1.20 for SLS.
Table 3: Super-imposed dead load of the bridge
Components Load (kN/m)
Services 21.1
Fill and Black top 63.3
Total 84.4
7.3. Live Traffic Loading
The bridge carries vehicular traffic travelling along
U.S. Highway 19. For the purpose of this paper traffic
loads have been calculated in accordance with UK
Highways Agency guidelines from BS 5400-2:2006;
Ref. [5].
For analysis worst case loading needs to be
assessed. An important feature of BS 5400-2:2006; Ref.
[5]; is that live loading is applied to ‘notional’ lanes
which differ from ‘marked’ lanes. As the bridge carries
only vehicular traffic the carriageway width for the
purpose of this paper will be taken as the overall width
of the deck (21.1m) which corresponds to 6 notional
lanes. Therefore each notional lane is 3.52m wide.
According to the guidelines of Highways Agency,
there are two types of live traffic loadings, HA and HB
loading.
HA loading simulates the effect of heavy and fast
moving traffic. It includes a uniformly-distributed load
(UDL) acting along a notional lane and a knife-edge
load (KEL) applied at the most severe position. For
deck lengths over 380m, the nominal HA UDL is
9kN/m and the KEL is always taken as 120kN.
HB loading is designed to simulate abnormally
heavy trucks. Full HB loading is taken as 45 units
where each unit equals 10kN per axle therefore full HB
loading is 1800kN for the whole truck. The dimension
of the truck can be varied to obtain the most adverse
case. To attain the most unfavourable effect to the
bridge, two cases would generally be considered. For
the worst sagging effect on the deck the truck should
have minimum dimensions and be applied mid-way
between supports. The maximum dimensions of the
truck should be considered for hogging and the load is
applied over the supports.
In general, full HA loading is applied over two
notional lanes and the remaining lanes loaded with 1/3
of the full HA loading. The loaded lengths and position
of the KEL are varied to produce the adverse load
condition. HB loading should also be applied
simultaneously with HA loading and different positions
of the load combinations exist. This is shown in Fig. 13
of BS 5400-2:2006; Ref. [5].
For the purpose of this paper, all the calculations
in later sections involving HA and HB loading will be
considered under the load case shown in Fig. 10.
Figure 10: Application of HA and HB loading
7.4. Wind Loading
The location of the bridge means that wind loading
is a critical issue, especially during the construction of
the arch. This loading is considered with a 120-year
return period according to BS 5400-2:2006; Ref. [5].
The following section details the design wind loading
for this location.
A problem was encountered with finding the mean
hourly wind speed (v) of the site, it was found from Ref.
[6] that the maximum wind speed in West Virginia is
25.9m/s and this was taken as v for the calculation for
the maximum wind gust.
Page 6
�� � � ������. 1� Where, K1 = 1.85, S1 = 1.10 and S2 = 1.66. This
gives a value for vc of 87.5m/s.
The dynamic pressure head (q) can then be
obtained from the following equation:
� 0.613 ���. 2� This gives a value for q of 4.69kN/m
2.
The horizontal and vertical wind loadings can then
be obtained.
It is considered for this bridge type the
longitudinal wind loading is not significant and
therefore would not be considered in this paper.
7.4.1. Horizontal Wind Loading
The horizontal wind load (Pt) acting on the bridge
can be found by Eq. (3) shown below:
�� � ���� . 3� Where, A1 is the solid horizontal projected area
and CD is the drag coefficient. For single open truss
bridges, this is dependent on the solidity ratio. The
solidity ratio is the ratio of the net area to the overall
area, from this CD was found to be 1.9.
Two scenarios should be considered for obtaining
A1. However, for this paper, the resultant effect of wind
acting on the vehicles and deck will not be considered.
Three horizontal wind loadings were obtained as a
shown in Table 4. These loadings are applied along the
length of the bridge as a UDL.
Table 4: Horizontal winding loadings on the bridge
Components Load (kN/m)
Arch 11.3
Deck 9.34
Piers 4.42
Complete Structure 25.1
7.4.2. Vertical Wind Loading
The vertical wind loading (Pv) acting on the bridge
can be calculated by Eq. (4) showing below:
�� � ���� . 4� Where, A3 is the plan area and CL is the lift
coefficient obtained from a chart dependent on the
breadth to depth ratio which is 0.355 in this case,
resulting in a value of 0.4 for CL.
Two values of vertical wind loading are obtained
as shown in Table 5. These loadings are calculated as
UDL acting along the length of the bridge.
Table 5: Vertical winding loading of the bridge
Components Load (kN/m)
Arch 2.82
Deck 39.6
Overall, it is shown that the arch is subjected to a
horizontal wind loading which is roughly 5 times that
of the vertical wind loading. This horizontal wind load
will have a significant effect during the construction of
the arch.
7.5. Effects of Temperature
Under temperature fluctuation, steel and concrete
components of the bridge would expand and contract.
Without the existence of the expansion joints, residual
stresses would be a major problem. This section
provides example calculations for the movement of the
expansion joint and the change in residual stress in the
absence of an expansion joint.
The movements and stresses due to temperature
are both related to the strain. The strain in the material
can be calculated by Eq. (5)
� � � ∆�. 5� Where, α is the coefficient of thermal expansion
and ∆T is the change in temperature. For the purpose of
this paper, ∆T is taken as 25°C. For both concrete and
steel, the value of α can be taken as 12×10-6
/ °C. This
gives a value for ε of 300µε.
Once the strain of the material is obtained,
calculation of the material’s extension and stresses can
be found according to Eq. (6) and Eq. (7) respectively.
� � !. 6� Where, l is the length of the bridge and δ is
expansion or contraction due to the change in
temperature. ! � 924m $ � 300 % 10&' %924 � 0.277m
The movement for both materials is the same as
the length of the bridge is constant for the truss deck
and the concrete slab. If the bearings restrict the
longitudinal movement of the deck, a moment will be
induced in the piers. Therefore careful design of the
bearings should be made.
σ � � *. 7� Where, E is the Young’s modulus of the material
and σ is the stress in the material.
As Young’s modulus for concrete and steel are
different, the truss deck would experience different
stress from the concrete slab. This is shown in the
following calculations.
For concrete: * � 30 000 N/mm� - � 300 % 10&' % 30 % 10� σ � 9 N/mm�
For steel:
Page 7
* � 200 000 N/mm� - � 300 % 10&' % 200 % 10� σ � 60 N/mm�
These calculations show that both materials are
experiencing very high stresses in the absence of an
expansion joint.
The axial load on the elements due to the stresses
can be calculated using Eq. (8).
� � -� 8� Pconcrete is found to be 76.0kN and Psteel on the deck
would be 3210kN. This value is excessively high but is
a result of the assumption made that the entire deck
cross section experiences a change of 25°C.
8. Structural Performance of the Bridge
The bridge has been standing in its current location
for over 30 years. This section gives sample
calculations to prove the structural integrity of the
bridge. A number if assumptions have been made for
the purpose of this paper, these are discussed in earlier
sections.
8.1. The Strength of the Bridge
The bridge is exposed to a number of different
load conditions from construction to everyday traffic
loading. It is considered that the most severe loading
acting on the arch is during the construction stage
whereas the deck would experience this during its life.
This section checks the bending capacity of the
structure at ULS. In order to carry out strength checks,
it is necessary to obtain the plastic modulus for both
the arch and the deck. This is found by taken the first
moment of area about the equal area axis. Table 6 and
Table 7 show the plastic modulus of the components of
the bridge.
Table 6: Plastic modulus of the arch components
Sxx 827×103 cm
3
Syy 1259×103 cm
3
Table 7: Plastic modulus of the deck components
Sxx 388×103 cm
3
Syy 723×103 cm
3
All the calculations shown in this section are
carried out under load combination 1 as mentioned in
section 7.
8.1.1. Construction stage
During the construction stage, the arch effectively
acts as two cantilevers. It is obvious that at this stage
the bending moment, due to the horizontal wind
loading, would be the highest that the arch is subjected
to throughout its life. The following calculations check
the bending capacity of the arch.
For the ULS, γfl and γf3 are taken as 1.1. This gives
a factored wind load of 13.7kN/m acting on the arch.
/ � 01�12 . 9� Where, M is the bending moment, W is the wind
load and L is the length of the arch.
The maximum bending moment would occur just
before the insertion of the last segment of arch and
therefore the cantilever would be of a length of
251.45m.
/234 � 13.7 % 251.45512
/234 � 433 /67
The moment capacity of the section can be
calculated according to Eq. (10).
/� � 89�99 . 10� Where, py is the design strength of the steel
(440N/mm2) and Syy is the plastic modulus of the
section. /� � 440 % 1259 /� � 554 /67
This shows that the arch section is capable of
taking the bending moment induced by the horizontal
wind load.
8.1.2. Effect of Horizontal Wind Loading on the
Structure
The horizontal wind load would also have a
significant effect on the deck. It is important to check
that the deck can withstand the bending moment
caused by such high wind loading.
As mentioned in the construction section, parts of
the deck were built before the construction of the arch.
Therefore it is considered that the central span of the
deck is connected to the side spans with a fixed
connection. This is shown in Fig. 11.
Figure 11: Sketch showing fixed connections on the
bridge
For the ULS, γfl and γf3 are taken as 1.4 and 1.1
respectively. This gives a load of 14.4kN/m acting
horizontally to the deck.
Page 8
Maximum moment of the bridge is calculated as
shown in Eq. (9) where L equals to 518m. This gives a
maximum bending moment of 322MNm in the deck.
The moment resistance of the bridge is calculated with
Eq. (10) where py equals 460N/mm2 and Syy is 723×10
3
cm3. This gives a bending moment resistance of
333MNm and demonstrates that the deck would just
work under this condition.
The effect of the horizontal wind loading on the
whole structure was also considered. Calculations show
that the factored load on the bridge would be
38.7kM/m and this would give a maximum bending
moment of 865MNm. The bridge has a moment
capacity of 872MNm. This shows that the bridge
would be able to withstand the high horizontal wind
loading with the aid of the arch.
8.2. Effects of Vertical Loading on the Structure
The permanent dead load, super-imposed dead
load and the high traffic load will create significant
moments and forces in the structure. Therefore some
design checks for these loadings are required to prove
the capability of the structure to withstand these
loadings. Some sample calculations are shown below.
After applying γfl and γf3 to all the loadings, the
final factored load is obtained as shown in Fig. 12.
Figure 12: Loading applied to the deck
It can be shown that the maximum hogging
moment at the supports is 81.8MNm and the maximum
moment at mid-span is 60.8MNm.
The moment capacity of the section can be
calculated from Eq. (11)
/� � 89�44 . 11� Where, py is taken as 460N/mm
2 and Sxx is the
plastic modulus, along the y-axis, of the section. /� � 158/67
This shows that the deck should be able to
withstand almost twice the load that is currently
applied. This seems to be a very conservative moment
capacity but other more adverse load cases might exist
which might cause a higher bending moment. However,
it can also be due to the fact that a number of
assumptions have been made in the absence of exact
information.
When a UDL is applied to a parabolic arch, such
as the arch of the New River Gorge Bridge, the
members of the arch would only be subjected to axial
forces. However, bending moments would be induced
when uneven load is applied. Such loading would also
cause deflection and deformation in the arch which is
discussed in a later section.
In order to obtain the uneven loading on the arch,
it is considered that half of it is loaded by factored dead,
super-imposed dead and live traffic (w1) and
unfactored dead and super-imposed dead loads are
applied on the other side (w2). This is shown in Fig. 13
with assumed dimension of the arch.
Figure 13: Uneven loading on the arch
The resultant uneven load on one half is calculated
by the difference between w1 and w2. This load is
obtained as 163kN/m.
It was calculated that the maximum moment would
occur at position D, this can be shown to be 1100MNm.
This shows that the moment induced in this scenario
has exceeded the calculated moment capacity of the
section (364MNm). This is most likely due to the
wrong assumption of member sizes or strength class of
the steel. This indicates that in reality, special cross
sections of steel members might be used instead of the
standard ones and the dimensions of the cross section
would be different. Calculations of the compressive
capacity of the axial members further shows that the
assumptions made are incorrect. The compressive
capacity of the assumed section can be shown to be
30.4MN which is lower than the applied axial load in
this scenario (41.8MN).
The huge bending moment can also be due to the
assumption on the heights of the arch, position D and
position E. Even a small change on that dimension
would cause a dramatic change on the bending
moments at both position D and position E. It is
suggested that the assumed values might be smaller
than estimated to give such a high value of bending
moment.
8.3. Effects of Change in Temperature
As shown in section 7.5, movement due to change
in temperature would cause moment in the piers.
However, reducing the size of the piers means less
moment would be experienced in the piers and
therefore using a more slender pier would actually help
the pier to withstand this moment.
8.4. Fundamental Natural Frequency
The check for fundamental natural frequency is a
serviceability check. If the value falls outside of the
acceptable range (5Hz – 75Hz), discomfort would be
caused to the users of the bridge. The natural frequency
Page 9
of the bridge can be calculated according to the
Rayleigh-Ritz method. This method is an initial
calculation and does not represent the true natural
frequency of the bridge. Calculations using this method
are shown below and are carried out using Eq. (12).
: � ;<!��= *>7!5 . 12� Where m is the mass density per unit (2243kg/m), l
is the length of the span (42.5m), E is the Young’s
modulus of steel (200 000N/mm2) and I is the second
moment of area of the section (0.897m4).
For a clamped-pinned beam shown in Fig. 14,
(βnl)2 is 15.42.
Figure 14: Clamped-pinned beam
: � 15.42 % =200 % 10� % 0.8972243 % 42.55
: � 76.3Hz For a Clamped-clamped beam as shown in Figure
15, (βnl)2 is 22.37.
Figure 15: Clamped-Clamped beam
: � 22.34 % =200 % 10� % 0.8972243 % 42.55
: � 111Hz Extrapolation from these values is required to
determine a fundamental frequency for a pinned-pinned
situation which resembles the actual state of the deck.
Extrapolating the values would give a fundamental
frequency of approximately 41.6Hz. This falls into the
acceptable range therefore the New River Gorge
Bridge should experience no problem with vibrations.
8.5. Deflection
To satisfy SLS, deflection of the bridge should be
limited. Deflections will occur both during and after
construction.
8.5.1. Construction Stage
During construction of the arch, the deflection due
to the horizontal wind loading on the cantilevered
sections could create significant construction difficulty.
The largest deflection would occur just before the last
segment of steel was inserted to link the two halves of
the arch. The following calculations show the
maximum deflection expected.
For SLS, both γfl and γf3 are taken as 1.00, giving a
wind load of 11.3kN/m acting along the length of the
arch. The length of the arch just before the last segment
was inserted is taken as 251m. The deflection of the
cantilever can be calculated by Eq. (13).
� 0!�8*> . 13� � 11.3 % 251 % 105�8 % 200 % 10� % 1304 % 10�A
� 2.17m
This defection is considerably higher than the
permissible deflection which was calculated as 1.40m
according to BS 5950-1:2000; Ref. [5]. This problem
was overcome by the use of cable stays which would
make the section behave as a propped cantilever,
greatly reducing the deflection. However, the extension
in the cable needs to be considered if the arch segment
is to be treated as a propped cantilever.
∆1 � B1*�. 14� Where, F is the force acting through the cable, L is
the length of the cable (290m), E is the Young’s
modulus of the cable (assumed to be 200N/mm2) and A
is the cross sectional area of the cable (assuming a
single cable of 76.2mm thick, A is 4560mm2).
It can be shown that by assuming the cable meets
the end of the arch at angle of 30° and that there is only
a single cable (very unlikely) the force in the cable can
be obtained by assuming that the cable acts as the prop
for the cantilever. The force in the cable can be shown
to be 2130kN.
Therefore from Eq. (11) the extension in the cable
can be shown to be 677mm. The horizontal component
of the extension would be 338mm and this would be
the deflection of the end of the arch section.
This simple calculation shows the solution to the
problem of excessive deflection due to horizontal
loading. It is likely that more than one cable would be
used as the stress in a single cable would be greater
than the yield stress and deflections would occur in the
plastic range.
8.5.2. Post Completion
After completion of the bridge, vertical deflections
would be experienced in the arch and the deck. Load
applied over half of the arch would cause the most
severe deflection. This deflection can be calculated by
virtual work but it will not be attempted in this paper.
As the arch is the main load carrying structure, the
Page 10
vertical deflection of the deck would be less severe
than that of the arch. For this reason calculations will
not be shown here.
9. Durability
A common problem to steel is corrosion which can
cause failure in the material over a period of time. This
is obviously a major concern in the New River Gorge
Bridge. This problem is overcome by the use of Cor-
ten steel. During the steel’s early life, it will undergo
rusting. In the later year, this rust layer will protect the
steel from further corrosion. The use of this material
has an added advantage of not requiring painting
during its working life.
As mentioned in section 8.1, fatigue is another
concern to the bridge. In order to protect the bridge
against this type of failure, the amplitude of the cyclic
loading should not exceed design limits. This is
controlled by using a high yield steel which can
withstand much greater loads.
The continuous flows of traffic would erode the
surface of the road. This therefore requires regular
maintenance and replacement.
Overall, it is considered that the bridge is durable
enough to withstand the above concerns for a number
of years.
9.1. Fatigue
Fatigue is the single largest cause of failure in
metals; Ref. [7], almost 90% of metallic failures occur
under this condition. This type of failure can affect
bridges as a constantly varying traffic load would
induce fluctuating stresses in the steel. Fatigue in
metals causes failure to occur at stress levels
significantly lower than the yield stress and happens in
a brittle fashion without warning.
9.2. Creep
Although the top of the deck is constructed from a
concrete slab, the creep in this element would be
negligible and therefore would not be included in this
paper. However, fatigue in the steel should be
considered and will be discussed in the next section.
9.3. Vandalism
After the events of September, 11th
, the threat of
terrorism is of a greater concern to all structures.
Accidental blast loading should be taken into account
when designing the structure. The slenderness of the
piers would make them appear a weak target. When
steel is deforming plastically, a large amount of energy
is absorbed and this would help the structure withstand
a terrorist attack.
It is worth mentioning that a traffic accident would
have no impact on the structure as the bridge is under
the road surface.
10. Future Changes
The properties of the materials decrease with time
due to fatigue, corrosion and increased live traffic load
on the bridge. It might therefore become necessary to
reinforce the bridge in the future. One possible solution
is to apply Fibre Reinforce Plastic (FRP) to the bridge
or weld on additional stiffening plates.
Due to the increased population and possible
business and housing developments near the area,
expansion of the bridge might be required. One
possibility would be to add a second level for traffic
under the current surface. However, this possibility is
very limited as the arch or the foundation might not be
able to withstand the addition dead and live traffic load.
11. Suggested Improvements on the Bridge
Overall, it was felt that it would be challenging to
expand the bridge for future increased in traffic. It
could have been designed for initially by increasing the
width of the arch. However, expansion is possible but
would be considerably costly. The initial construction
cost could have been reduced by choosing a location
where the used mines would have no effect on the
bridge. Moreover, the appearance of the bridge could
be improved by decreasing the slenderness of the
bridge.
Acknowledgement
The author of the paper would like to acknowledge the
author of Examples of Structural Analysis (McKenzie,
W.M.C.) and Knudsen, C.V. who have written the
article, ‘River Gorge Bridge: World’s Longest Steel
Arch’, published in the Civil Engineering journal in the
USA.
References
[1] Koors, R.
http://filebox.vt.edu/users/rkoors/Index.htm
[2] http://cs101.wvu.edu/media/1/10/11/New%20Riv
er%20Gorge%20-%20US%2019%20Bridge.jpg
[3] Press, F., Siever, R., Grotzinger, J. and
Jordan,T.H. 2004. Understanding Earth, 4th
Edition, W.H. Freeman and Company, New
York, USA.
[4] http://en.wikipedia.org/wiki/Landslide_mitigatio
n
[5] British Standards. 2002. Structural Design,
BS5950-1:2000, BS5400-2:2006.
[6] http://www.met.utah.edu/jhorel/html/wx/climate/
windmax.html.
[7] Callister, W.D. 2007. Materials Science and
Engineering an Introduction, 7th
Edition, John
Wiley & Sons, Inc., New York, USA.