Proceedings of Bridge Engineering 2, Conference 2007

23 April 2008, University of Bath, Bath, UK

Y.C. Tsui

yct20@bath.ac.uk

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

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

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

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.

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.

�� � � ������. 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:

* � 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.

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

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

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.