A STRUCTURAL REVIEW OF THE NEW RIVER GORGE BRIDGE

Transcription

1 Proceedings of Bridge Engineering 2, Conference April 2008, University of Bath, Bath, UK A STRUCTURAL REVIEW OF THE NEW RIVER GORGE BRIDGE Y C TSUI 1 1 University 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 22 nd October, 1977 and had been the world s longest single span arch bridge since the opening until 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. 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 Suspension Bridge Design 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 Continuous Truss 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 "Jack Knife" Arch 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. 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 Y.C. Tsui yct20@bath.ac.uk

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 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

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 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 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. 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 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]. 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 7: Early construction Figure 6: Sketch of perpendicular load on valley walls 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

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 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 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 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 :2006; Ref. [5]; with relevant partial factors, γ fl and γ f3 applied for both Ultimate Limit State (ULS) and Serviceability Limit State (SLS). The value for γ fl is dependent on the load combination considered. BS :2006; Ref. [5]; considers 5 crucial load cases, although others would need to be considered in full design. The load combinations considered in BS :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. γ fl can then be obtained from Table 1 in BS :2006; Ref. [5]. γ f3 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.

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 mm RHS Piers steel members mm SHS Arch steel members mm 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 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 (γ fl ) 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 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 :2006; Ref. [5]. For analysis worst case loading needs to be assessed. An important feature of BS :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 :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 :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.

6 . 1 Where, K 1 = 1.85, S 1 = 1.10 and S 2 = This gives a value for v c of 87.5m/s. The dynamic pressure head (q) can then be obtained from the following equation: 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 Horizontal Wind Loading The horizontal wind load (P t ) acting on the bridge can be found by Eq. (3) shown below:. 3 Where, A 1 is the solid horizontal projected area and C D 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 C D was found to be 1.9. Two scenarios should be considered for obtaining A 1. 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 Vertical Wind Loading The vertical wind loading (P v ) acting on the bridge can be calculated by Eq. (4) showing below:. 4 Where, A 3 is the plan area and C L is the lift coefficient obtained from a chart dependent on the breadth to depth ratio which is in this case, resulting in a value of 0.4 for C L. 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 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 / 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 m 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: N/mm σ 9 N/mm For steel:

7 N/mm 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 P concrete is found to be 76.0kN and P steel 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 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 S xx cm 3 S yy cm 3 Table 7: Plastic modulus of the deck components S xx cm 3 S yy cm 3 For the ULS, γ fl and γ f3 are taken as 1.1. This gives a factored wind load of 13.7kN/m acting on the arch 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 m The moment capacity of the section can be calculated according to Eq. (10).. 10 Where, p y is the design strength of the steel (440N/mm 2 ) and S yy is the plastic modulus of the section This shows that the arch section is capable of taking the bending moment induced by the horizontal wind load 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. All the calculations shown in this section are carried out under load combination 1 as mentioned in section 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. Figure 11: Sketch showing fixed connections on the bridge For the ULS, γ fl and γ f3 are taken as 1.4 and 1.1 respectively. This gives a load of 14.4kN/m acting horizontally to the deck.

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 p y equals 460N/mm 2 and S yy is cm 3. 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 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 γ fl and γ f3 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). 11 Where, p y is taken as 460N/mm 2 and S xx is the plastic modulus, along the y-axis, of the section. 158 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 (w 1 ) and unfactored dead and super-imposed dead loads are applied on the other side (w 2 ). 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 w 1 and w 2. 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 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 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

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).. 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 ( N/mm 2 ) and I is the second moment of area of the section (0.897m 4 ). For a clamped-pinned beam shown in Fig. 14, (β n l) 2 is 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 γ fl and γ f3 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) m Figure 14: Clamped-pinned beam Hz For a Clamped-clamped beam as shown in Figure 15, (β n l) 2 is Figure 15: Clamped-Clamped beam Hz 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 Deflection To satisfy SLS, deflection of the bridge should be limited. Deflections will occur both during and after construction Construction Stage During construction of the arch, the deflection due to the horizontal wind loading on the cantilevered This defection is considerably higher than the permissible deflection which was calculated as 1.40m according to BS :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.. 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/mm 2 ) and A is the cross sectional area of the cable (assuming a single cable of 76.2mm thick, A is 4560mm 2 ). 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 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

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 Corten 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 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 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 Vandalism After the events of September, 11 th, 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. [2] er%20gorge%20-%20us%2019%20bridge.jpg [3] Press, F., Siever, R., Grotzinger, J. and Jordan,T.H Understanding Earth, 4 th Edition, W.H. Freeman and Company, New York, USA. [4] n [5] British Standards Structural Design, BS5950-1:2000, BS5400-2:2006. [6] windmax.html. [7] Callister, W.D Materials Science and Engineering an Introduction, 7 th Edition, John Wiley & Sons, Inc., New York, USA.