A CRITICAL ANALYSIS OF THE ELECTRIC WHARF BRIDGE, COVENTRY

Transcription

1 Proceedings of Bridge Engineering 2 Conference 2011 April 2011, University of Bath, Bath, UK A CRITICAL ANALYSIS OF THE ELECTRIC WHARF BRIDGE, COVENTRY Joe Darcy year Undergraduate of the University of Bath Abstract: This article provides an in depth analysis of the Electric Wharf bridge designed by Price and Myers. Background information and comments on the aesthetics are made before applying the 3 loading cases to the structure. Any assumptions are clearly stated before the calculations, which were done predominantly in MS Excel. Keywords: arch, footbridge, inclined suspension rods, steel The design solution provided by Price & Myers in response to the constraints was a bridge which on plan resembled a horse shoe, with self-supporting access ramps at either side of the suspended deck. The arch is parabolic in shape, crosses the deck diagonally and is connected to it by 6 angled rods. The arch is made more efficient by the cross section changing in response to the local induced stresses. The side ramps help provide lateral stability to the deck. 2 Aesthetics Figure 1: View of the bridge from the ramp 1 Background The Electric Wharf bridge is a steel deck suspended from an arch spanning 30 metres over the Coventry canal [1]. It was commissioned by Complex Development Projects as part of their 3.7m regeneration of the redundant power plant and surrounding area at Electric Wharf. On completion of the overall scheme 68 loft units, 21 eco-homes and 3,500 sq.m of high-tech office accommodation will be constructed, coupled with a revitalised public realm and spaces provided for public art [2]. Due to the scheme s close proximity to the city centre, a bridge was essential in order to remove the obstruction caused by the canal, and providing the necessary connection to the city centre to allow the project to thrive. Whilst a route to the centre was important the bridge couldn t inhibit the canal or canal path in any way. This influenced the design; first by raising the bridge deck to allow adequate clearance for water users, second by the requirement for access ramps allowing a seamless junction to the canal path. The bridge works by the arch providing support at regular intervals, allowing a slim deck to be used. The slender deck and arch combine with the sweeping access ramps creating an elegant design, matching the fluid motion of the canal, and the apparent scale of the arch is reduced by the raised position of the deck. The addition of stairs on one side of the bridge is to allow users travelling in either direction to access the bridge. The Electric Wharf side doesn t require bi-directional access due to the back of the wharf being fenced off. A minimal approach has been taken when detailing the structure. For visual effect the suspension rods are arranged in parallel lines on each side of the bridge, the limited number of rods providing sufficient structural support with minimal clutter. This arrangement however, may cause additional stresses in the deck, magnifying bending stress in the y-y axis. These stresses are further exaggerated by the diagonal span of the arch, with opposite sides of the deck attached to opposite parts of the arch. Sections have been optimised for both structural and aesthetic reasons. The arch has been optimised to a triangular cross section in response to the loading it experiences from the deck. It varies along its length due to the incident forces from the rods, allowing the forces to be 1 Joe Darcy jd311@bath.ac.uk

2 efficiently distributed into the arch. This logical amendment to the section variation is structurally honest, and contributes to the success of the design. The viewer s eye follows the rod up from the deck to the intersection with the arch in line with the centroid of the arch. The opposite end of the rod connects to a circular member that projects either side of the deck. The length of each member is unique to the rod in order to achieve the required position relative to the arch. The deck surface is steel plate with a raised a pierced pattern, which allows drainage but has a slight unpleasant feel underfoot. The handrail is very tactile with a smooth ergonomically stainless steel design giving a comfortable guide across the bridge. Lights are integrated into structure on alternate parapet supports, this detail continues along the access ramps. The surface finish of the bridge is grey paint with noncorrosive layers to protect the steel beneath. The quality of the finish leaves a lot to be desired in particular coupled with small locations of exposed steel which have begun to rust and a repaint is required. The bridge has an attractive understated feel about it. Every component has been specifically designed to fulfil its requirements whilst using minimum material. The parapet structure is repeated to a good effect on the ramps to the bridge. The photographs provided by Price & Myers show the bridge in an architectural, way expressing its beauty and elegance. In reality, up close the bridge doesn t have the immaculate surface finishes expected from the photos and this, combined with vibration issues under light loads mean that the bridge is a disappointment falling short of the standards I would expect of Price & Myers. 3 Loading All loading is based on the British Standard BS5400-2:2006 [3]. Loading case 1 and 3 are covered in this section. Due to the complexity of wind loading, case 2 is applied separately in its own section. The loading calculations have only been applied to the main bridge span, excluding the support ramps. It has been assumed to be modelled as a beam supported by inclined rods from the arch. 3.1 Dead load The dead load is taken as all the structural components, excluding the parapet. It is broken down into two different sections; arch and deck, allowing each to be analysed separately. Component weights are taken from standard sizes in Tata steel Deck Table 1: Deck components and weights Total weight per metre length of bridge Component ULS SLS Edge beams 0.582KN/m kn/m T-Beams: Longitudinal Transverse KN/m KN/m kn/m kn/m Diagonal plate KN/m kn/m (Component weights are multiplied by f3 1.1 for steel and fl ULS=1.05 SLS=1.0) Factored Dead load: ULS: 1.39 kn/m SLS: 1.32 kn/m 3.12 Arch The arch is assumed to have a constant cross section for ease of later analysis. The section comprises three hot rolled circular sections (CHS) with a diameter of 42.4mm and thickness of 5mm. The steel plates forming the surfaces of the arch are 10mm thick. Table 2: Arch components and weights Total weight per metre length of bridge Component ULS SLS Top CHS kn/m kn/m Bottom CHS kn/m kn/m Surface plates kn/m kn/m (Component weights are multiplied by f3 1.1 for steel and fl ULS=1.05 SLS=1.0) Factored Dead load: ULS: 1.51 kn/m SLS: 1.44 kn/m 3.2 Superimposed Dead Load (SiDL) The SiDL comprises of the steel plate decking and the parapet. Due to their steel construction the weight is less likely to vary, therefore the minimum value of fl is taken. Table 3: SiDL components and weights Total weight per metre length of bridge Component ULS SLS Steel decking kn/m kn/m Parapet kn/m kn/m Handrail kn/m kn/m

3 (Component weights are multiplied by f3 1.1 for steel and fl ULS=1.20 SLS=1.0) Factored SiDL: 3.3 Live Loading ULS: 1.49 KN/m SLS: 1.24 KN/m The access to the bridge prevents any vehicles using it therefore the only live load is nominal pedestrian live load, set at 5kN/m 2 due to the span being below 36m. Table 4: UDL Live loading cases Live Load per metre length of bridge ULS SLS Loading case 15.0 kn/m 10.0 kn/m 1 Loading case kn/m 10.0 kn/m (Nominal load is multiplied by fl: ULS=1.50 SLS=1.0 for loading case 1 and fl: ULS=1.25 SLS=1.0 for loading case 3) 3.4 Loading distribution The rod pairs act at the same point. The cross section of the arch remains constant. The arch dead load is uniform along its plan length. The arch has pin connection to the foundations Full Loading The full loading applies the uniformly distributed load (UDL) across the entire span of the deck. It is likely to cause the largest individual reactions thus inducing the highest shear stresses. Live load: SiD load: Dead load: Figure 3: Loading on three times redundant beam The central rod supports will transmit their reaction through the rods to the arch, allowing stress analysis to be carried out on the arch. The flexibility method was used in conjunction with excel allowing a variety of input values to be used and yielding the different forces under ULS and SLS. It also allowed the structure to be modified by inserting a factor assuming settlement of the central supports, from inadequate tension in the rods. This assumption is taken from my visit to the bridge when it was clear that the rods weren t fully tensioned, as I was able to force the rods to vibrate. Table 5: Full loading reactions Figure 2: Loading on model of the bridge The loads are applied to the deck. The following assumptions have been made in order to analyse the structure: Live load: SiD load: Dead load: The deck is a three times redundant beam. There is no vertical and horizontal curvature of the deck. The supports only provide vertical reactions. The rods only induce in plane forces to the arch. Reactions (kn) R 1 R 2 R 3 R 4 R 5 Loading Full ULS Full SLS Plotting the reactions along the length of the deck gives the moments it will experience under full loading. ULS: 43.5kNm SLS: 30.9kNm ULS: 42.0kNm SLS: 28.8kNm Figure 4: Full loading bending moment diagram

4 The inadequate tension in the rods will cause the deck to settle. Applying a settlement of 1mm to the centre supports redistributes the applied loads. This will reduce the tension in the rods acting at supports two and four and increase the tension in rods at support three. Table 6: Full loading reactions with settlement Loading & Reactions (kn) settlement R 1 R 2 R 3 R 4 R 5 Full ULS Full SLS ULS: 78.9kNm SLS: 42.8kNm Figure 5: Full loading with settlement bending moment diagram The reduction in the forces in the rods will induce lower stresses to the arch. Therefore the arch experiences the worse case loading with no settlement, while the deck experiences it with settlement Part Loading ULS: 60.7kNm SLS: 40.1kNm Part loading is required as arches tend to experience their largest stress under this. Arches experience maximum bending stress when only half of the deck is loaded with live load. Due to the arrangement of the rods transferring the load from the deck it is possible that part loading will be less significant. This is due to the UDLs applied to the deck being transferred more evenly to the whole arch. Live load: SiD load: Dead load: Table 7: Part loading reactions Reactions (kn) Loading R 1 R 2 R 3 R 4 R 5 Part ULS Part SLS As footbridges are heavily influenced by live loads the most affected sections of the beam are those with complete loading applied. In these sections a maximum reaction occurs, hence producing a maximum hogging moment. The maximum sagging moment occurs between this large reaction and the end reaction, as expected as they are the highest values. ULS: 48.7kNm SLS: 34.2kNm ULS: 40.8kNm SLS: 28.6kNm Figure 7: Part loading bending moment diagram The second half of the deck experiences minimal forces and bending moments, as it only has to resolve moments from the dead loads. Table 8: Part loading reactions with settlement Loading & Reactions (kn) settlement R 1 R 2 R 3 R 4 R 5 Part ULS Part SLS Applying a settlement to the centre supports redistributes the loads. This increases the magnitude of the odd number reactions as they experience no relative settlement. Despite the introduction of settlement the location of the maximum bending moments will not alter, they will however change magnitude. Figure 6: Loading on three times redundant beam The locations of the supports relative to the applied load means that some reactions will be considerably reduced while others will experience maximum forces. The distribution of the forces along the arch will differ from the deck, as the forces are transferred via the inclined rods. ULS: 40.6kNm SLS: 38.2kNm ULS: 44.1kNm SLS: 32.0kNm Figure 8: Part loading with settlement bending moment diagram Due the drop in the reaction at the second support a lower hogging moment occurs, as the load has been

5 distributed to the supports either side. This does however yield a larger sagging moment from the increased reaction at support one. Under the loading case the deck experiences different locations of maximum moments. While these locations may yield maximum stress the consideration of shear stress must be taken into account, due to its effect on the allowable stress of the section. Therefore shear force will be calculated in order to check the capacity; this is covered in the strength section. length of the arch; F is the force applied, h and L are the vertical and horizontal dimensions of the arch. A similar equation is used to calculate the horizontal force due to the self weight. Then the horizontal forces are summed, allowing moments to be taken along the arch. The process is repeated for the different loading cases to find the worst case scenario. ULS full: 31.5kNm ULS part: 69.2kNm ULS full: 385kNm ULS part: 232kNm 3.43 Arch The loading on the arch is comprised of its own self weight and the forces transferred by the rods. The forces from the rods will have greater influence on the bending within the arch, however it is difficult to guess which loading case will yield the highest bending moments. An arch tends to have purely vertical forces acting on it, when five approximately equal evenly spaced loads are applied their total can be assumed to act as a UDL. The arch loading can t be modelled as a UDL due to the angle on the rods, instead each force has to be modelled individually, superimposed. The inclined nature of the rods induces horizontal forces into the arch; these forces aren t present in the deck as they cancel out at rod intersections. Live load: SiD load: Dead load: Figure 10: ULS bending moment diagram SLS full: 53.4kNm SLS full: 215kNm Figure 11: SLS bending moment diagram The shape of the bending moment diagrams is dominated by the horizontal forces. Instead of the vertical forces causing the arch to sag, the horizontal forces pull the sides together with a greater magnitude giving hogging. The maximum values can then be used to calculate the induced stresses along the arch using UDL loading and the SLS loading for the serviceability deflections. 3.5 Temperature Figure 9: Loading on the Arch The arch has been modelled as a two pin arch, this is the worse case as a rigid connection would reduce the maximum bending. This makes the structure singularly redundant. Each force is separated out into vertical and horizontal components. The vertical forces are then individually analysed to find the horizontal forces at the base of the arch, using the equation below from [4]. (1) Where k denotes the ratio between the force s horizontal distance from the support and the horizontal The bridge has been designed to cope with a 1 in 120 year environment and is categorized as group 2. Applying the relevant factors the bridge will experience a minimum shade air temperature of -19 C and a maximum shade air temperature of 45 C. Therefore assuming the bridge was installed at the average of these temperatures it will have to cope will 13 C±32 C. Using the Coefficient of thermal expansion of steel (12 x 10-6 / C) it is possible to calculate the additional stress on the deck and arch. (2) (3)

6 3.51 Deck (2) (3) (4) (5) 4.12 Maximum sagging 3.52 Arch (4) (2) (3) Upon inspection of the bridge I was unable to find any evidence of expansion joints. Therefore, any expansion in the deck will cause thermal stresses. Arch has rigid connections but it will be able to expand by changing shape, limiting the thermal stresses within it. 4 Strength The bridges, strength is determined by the grade of steel chosen for each particular section. The member has to cope with several different stresses; bending, shear, axial and temperature. The section has to have sufficient capacity in order to allocate a proportion to each stress induced. Loading case 1 negates temperature stress which will be covered in loading case 3. The initial assumption for both the deck and arch is that they are made from S Deck The deck experiences the worse bending and shear under full loading with a settlement. Therefore the deck will be checked for stresses at maximum hogging and sagging with their associated shear values. (4) (5) (6) The calculated second moment of area (I) is mm 4, y h is 110mm, y s is 120mm and A is 9660mm Maximum Hogging The deck is only checked for bending stresses as this maximum moment occurs at zero shear, section passes in sagging. The critical location of the deck is at mid span under a hogging moment and shear force Loading case 1 Combining the stress blocks allows the maximum stress of the section to be calculated Loading case 3 (6) In addition to loading case 1 a temperature change is assumed inducing thermal stresses. It is only necessary to apply to the highest stress in loading case 1, in order to check the sections capacity. 4.2 Arch (7) The arch experiences higher moments than the deck, this is magnified by the inclined rods inducing horizontal forces. The worst case hogging occurred under full load whereas the part load was worst for sagging. The calculated second moment of area (I) is mm 4, y h is 160mm, y s is 320mm and A is mm Maximum Hogging The deck has sufficient capacity to resist the hogging moment, no shear force present. (4)

7 4.22 Maximum sagging 5.1 Deck (4) (5) The worse case for the deck under SLS loading is full loading with settlement in the first span. The serviceability limit is therefore: (9) 4.23 Axial compression The arch is forced into compression by the loading applied to it. It can be approximated to be the resultant of the forces acting at the pins. UDS full: (8) (8) 5.2 Arch (10) The worse case for the arch under SLS loading is full loading. As the arch affects the deflection of the deck the serviceability limit is the same as the deck, 17.67mm. UDS part: 5.21 Deflection at sagging (10) (8) 5.22 Deflection at hogging 4.24 Loading case 1 The worst loading case when the arch is in hogging and axial compression Loading case 3 (6) The thermal stress from temperature change is added to the maximum stress in loading casing 1. 5 Serviceability (7) The serviceability is checked by using the loading of SLS to calculate deflections. It is limited to span/300 whereby if the deflection is larger than that value it is said to have exceeded its SLS. This has no structural implications only comfort and damage to brittle materials. The deflections are found using excel and the flexibility method. 6 Wind Loading (10) The wind loading on the bridge may cause instability and induce further stresses to both the deck and the arch. The wind pressure is calculated in accordance with British Standards BS :2006 allowing the stresses due to the wind to be analysed. The wind loading will be applied to the deck and the arch individually. Allowing the horizontal deflection to be calculated, for the arch and additional stresses calculated for the deck. In order to calculate the pressure exerted by the wind the maximum wind gust speed (V d ) is required. Where by S g is a gust factor and V s is the site hourly mean wind speed. (11) (11) (9)

8 V b represents the base hourly mean wind speed found using the national wind chart, the other factors are taken the tables from section (12) All factors have been taken from section (13) The load is applied to the projected area of the arch. To find the deflection of the arch it is modelled as a cantilever in the y-z plane and a beam with rigid connections in the x-z plane. Assuming both have the same second moment of area, it possible to calculate the deflection at the peak of the arch. Using the value of P T a UDL can be found for each plane Arch cantilever: y-z plane (19) (14) (15) 6.22 Arch fixed beam: x-z plane (20) The dynamic pressure head (q) is dependent on the maximum gust speed. Pa 6.1 Loading case 2 (16) Using the dynamic pressure head it is possible to calculate the nominal vertical wind load (P v ). This can be converted into a UDL to allow stress profiles to be found for the deck. The value of C L is taken from BS :2006, and A 3 is the plan area of the deck. (17) The net displacement is 2.63mm at the peak, this will have a minimal effect on the stresses in the arch and the rods. 7 Natural frequency The natural frequency of the bridge influences how it will behave when loaded. This is particularly critical with footbridges, if pedestrians pass across the bridge at the natural frequency the magnitude of the oscillation will suddenly increase. The natural frequency is calculated using the equation below from section Annex B in British standards. (21) Assuming the load is evenly distributed across the deck it will apply a UDL of 0.536kN/m. This will yield a maximum additional stress of 0.003N/mm Arch The dynamic pressure head can also be used to calculate the nominal transverse wind loading on the arch thus allowing a deflection to be calculated. (18) A 1 is the solid area and the C d drag coefficient is set at 2 for footbridges. N (18) The factors are taken from tables and the equation is applied to the largest span as it is the most critical. (21) This frequency is acceptable as it is not low enough to be susceptible to the frequency of a person walking, and isn t high enough to cause discomfort to its users. When calculating the strength of the deck a settlement was applied, this effectively means the deck acts as a beam. Therefore the deck has to be checked as a beam with no central supports.

9 (21) As this frequency is less than 5Hz it must be check for maximum acceleration to pass serviceability, limited by the equation below. (22) The acceleration is found using the following equation; all values are taken from BS :2006. (23) This explains the discomfort felt when moving across the bridge, as bridge is just behaving as a simply supported beam. 8 Bending in y-y axis In order to analyse the structure it was necessary to assume that the rod pairs met at the same point. The reality is actually that they are separated by deck. This will cause a couple about the middle on the deck, forcing the beams into bending about the y-y axis. Further analysis would then be required to check that the sections have the capacity to resist these moments. 9 Fabrication The fabrication of the bridge and supporting ramps was contracted out to a local steel contractor, Remnant. The arch was constructed in two sections from steel panels and steel rods. The rods were bent in sections, each rod unique due to the complexity of a varying cross section. They were then welded together, forming three part arches. Plates were used to affix the arches to one another, additional plates were added into the section located at the joints of support rods, simplifying their connection and improving force distribution through the cross-section. Steel plates were welded between each rod to form the surfaces, shaped in order to cope with the changing cross section and curvature along the arch. For the ground connection a steel plate was attached to provide an adequate junction with the pile cap. One side of the arch is connected to the deck by a T-beam arm providing extra stability. attach. A centre spine of two angle beams provides longitudinal strength, offset from another to allow the passage of a power cable for lighting. The same angles are also used transversely connecting the edge beams to the central beams; additional diagonal plates have been added to increase the stiffness and stability. The deck and ramps have the same fabrication allowing them to be made in sections, making the bending of beams and transportation easier. This sectional approach is maintained in the parapet. Whose supports for the hand rail incline inwards and are joined by bars to gain the required safety whilst minimising the visual obstruction, and inhibiting users climbing on the parapet. Every other support doubles up to allow a cable to pass along transverse angles through the edge beam and up into the integrated light fitting. The support plates are welded to the edge beam and bolted to one another. The ramps are supported by columns situated where the transverse and diagonal members converge. 9 Construction The bridge was assembled next to site on an unused plot of land. First the two arch halves were welded together, and then held upright with the help of a crane. The deck span was positioned beneath the arch on a supporting structure while the rods were attached and tensioned. The arch and deck were then lifted in place by a crane, with the arch supported at quarter span. This will have induced stress in the arch, causing it to deflect inwards, where by the base points of the arch would move together. The deflection is found in two different ways, first the horizontal and then the rotation of the unsupported arch. This is calculated below assuming only dead loads act on the arch as shown in figure Horizontal deflection 9.2 Rotation (10) (10) The deck comprises a channel edge beam that has been curved in places giving a fluid shape where the ramps

10 pointless other than reaching the opposite side of the canal, which most canal users achieve further along the canal. It therefore doesn t fulfil its intended use; if development on the opposite bank to place it would have increased use and maintenance, which would reduce the likelihood of vandalism. 13 Future Changes and Improvements SiD load: Figure 12: Construction loading on the arch Once in situ the arch was bolted to the pile cap allowing the transfer of moments when the deck was loaded. The columns for the support ramps were now put in place along each of the ramps, which were added as two complete sections and connected to the bridge. With the bridge s structure complete the wiring for the lights was laid. The steel deck was then lain on top of the structure and fastened back to the edge and central beams. The stainless steel handrail was installed last, welded to a threaded rod allowing height adjustment relative to the support. 10 Foundations The bridge requires a variety of different foundations to support it. The support ramps will be satisfied by simple shadow foundations; however the arch requires something more substantial. A pile will be used for the arch providing the necessary resistance to moments and forces. 11 Durability The durability of the bridge is dependent on two main issues. The first is the existence of chipped paint allowing the steel work beneath to corrode. The second is more critical as it has the potential to limit the life span of the bridge. The incorrect tension in the rods allows the bridge deck to experience unnecessary excitation, which causes the rods to oscillate. Over time this will cause extensive fatigue damage, reducing the strength capacity of the bridge. 12 Vandalism Dead load: From my visit to the bridge it was evident that vandalism has been and will continue to be a problem. There were several lights graffitied and smashed, despite the toughened glass evident by the small shatters scattered about. Currently the bridge has limited use as the site opposite the electric wharf is an unused plot owned by the council, rendering the bridge The aim of the entire Electric Wharf project is to revitalise the surrounding area encouraging much needed redevelopment. Once this has occurred the bridge will perform as intended, becoming a vital crossing point over the canal, however it will require increased maintenance to prevent the bridge. In addition the rods must be retensioned to remove the small excitation under low loads, allowing it to behaviour as designed. Amendments could also be made to the ramp to incorporation the design of the new development. 14 Conclusion The bridge design is unique and elegant, however it has been let down by the attention to detail in construction. In particular the lack of tension in the rods prevents it from behaving as intended. The rod design improves the distribution of the load to the arch, as a consequence this induce high moments in the y-y axis, causing additional stress to the deck sections. The overall design is tailored to the future expectations of the site. Once redevelopment occurs in the surrounding area it will preform as intended.. 15 References [1] Price & Myers, Electric Wharf Bridge. Available from: [2] BPN Architects Electric Wharf case study. Available from: rf_made.pdf [3] British Standards Institution Steel, concrete and composite bridges part 2: Specification for loads. [4] Megson, T. H. G Structural and stress analysis. Oxford: Butterworth-Heinemann.