CRITICAL ANALYSIS OF CALATRAVA’S CABALLEROS FOOTBRIDGE PROPOSAL

Michael I Gates

University of Bath

Abstract: This paper examines the concept Santiago Calatrava proposed for the crossing of the Segre river in Spain. It aims to provide a brief critical analysis of many aspects of the bridge, these will include: aesthetics; loading; strength; serviceability; construction; foundations and geotechnics; and durability. The Caballeros Footbridge was never built and consequently this paper has had to make a number of assumptions regarding many aspects of the bridge. Therefore sections of this paper will be logical suggestions of what Calatrava could have intended, and others will be direct analysis of what he did intend.

Keywords: Footbridge, Cable-stayed, deck, cantilever, steel

1 General Introduction

This footbridge was the entry made by the spanish architect and engineer Santiago Calatrava for a competition held in nineteen eighty five, organised by the city-fathers of Lérida (Lleida) in Catalonia, Spain. The bridge was to be an extension of the Calle del Caballeros (Street of the horseman), intended to bridge across the Segre River and connect the old urban area to the North-west, with the woods and fields of the rural region to the South-east. This can be seen from th arial photograph in Fig. 1.

Figure 1: River Segre and surrounding Lérida

Caballeros footbridge location

Rural side

Urban side

The reason why Calatrava’s design was rejected is not immediately obvious, but through the analysis a reason my become clear. Since the initial competition, a footbridge has been constructed across the Segre in Caballeros proposed position, however it is not clear whether this was a competing entry, or if it was developed after the original competition.

There are only a few known dimensions for this bridge, these are: length - 210 metres; pylon height - 28 metres; maximum span - 139.9 metres; and height above the river bank - 7 metres. Refs. [3,7,8]

2 Aesthetics

Fig. 3 is a photograph taken of the model submitted by Calatrava showing his final design proposal. It can be seen that his design calls for a large pylon cantilevering out over the river with an array of radially positioned cable stays that support a slender deck. The pylon was intended to be situated on the urban side of the Segre River and thus the design ensured small loads on the rural side where the ground conditions were known to be unstable. The differing geological conditions on either side of the river was the driving force for this innovative angled pylon design and as a result gave the structure a lot of character.

Bridge Engineering 2 Conference 200816 April 2008, University of Bath, Bath, UK

Figure 3: Caballeros footbridge model

Like many of Calatrava’s bridges, the Caballeros footbridge makes it clear what the structural intent is and the adopted projecting cantilever allows for the structural behavior of the bridge to be clearly expressed. Fig. 4 shows that the deck flies out over the water and is suspended by ties that run up into the cantilevering mast, what is observed is that the weight of the deck is trying to topple the pier over, but it is held in place by two ground supports, restraining any rotation. The back ties seem to be preventing the mast from splitting off its back support. Of course Calatrava is known for his deceptive structures, and only by examining the proposed foundations later, will we be clear on the actual behavior of the structure. Nonetheless, Calatrava designed the Caballeros footbridge with an obvious structural working, reassuring the bridge’s users to its reliability and structural security.

Figure 4: Cantilevering pier with cable ties

This structural security is echoed in the large, substantial pier element. This element is made in proportion with the rest of the bridge, and conveys an ability to support the load induced on it from the deck. Furthermore, Calatrava uses twisting and tapering of the members to portray elegance and refinement, and bends the members outwards to allow the deck to project through. At the point where the pier members meet, there is a thickening to give a reinforced tip for all the ties to run into, this point is significant and acts to emphasises the meeting of the town and the country. Care has been taken at this junction to make an attractive connection between the mast and the ties.

Figure 2: Caballeros plan

These ties, that are so important to the metaphor of connecting the two banks, are arranged radially with one layer of ties, this single layering avoids undesired crisscrossing of cables which would upset the order of the bridge. The back stays’ radial arrangement run down to make an impressive gateway and give the image of the bridge of a musical instrument.

Figure 5: Elevation of approach ramps

Figure 6: Backstay arrangement

The tension of the back stays is counteracted by a fan of suspension cables holding the deck up, these are released into the rural side. These two sets of ties are arrayed on different planes, and this brings a degree of complexity to the structure, this is juxtaposed next to the simplicity and elegance of the pylon and deck.

The deck element sails over the water as one elegant piece, there are no breaks or complicated geometries to deter from its purity. The suspension ties fork into two just before connecting to the deck which is an important refinement that helps to resist torsion, this again illustrates Calatrava’s understanding of how the structure works. The deck is covered to allow for a protected walk across the river, to allow for views out of this tunnel, Calatrava has placed a strip of glazing along the covering.

This use of glass along the walkway, as well as steel and aluminium for the deck gives an elegant, smooth appearance, the pylon too is one large steel component. With every element coloured white, the Caballeros bridge portrays grace, sophistication and sleekness.

Negatively, the bridge could be blamed for not fitting into the surrounding environment, this is a structure that has clearly been influenced by Calatrava’s trademark level of elegance, despite its perhaps more rural contextual setting. However this is a very aesthetically pleasing bridge, and even though it is impossible to say this objectively, it does satisfy nearly all of Fritz Leonhardt’s ten requirements for an attractive bridge. Refs. [1,3,7]

Figure 7: Bridge viewed from rural side

3 Construction

The specific construction process envisaged by Calatrava for this bridge is not publicly known owing to the fact that it never progressed from the design stage. However, the type of design is not unique and therefore we can assume that a similar construction method on equivalent cable-stayed bridges would have been implemented for this bridge. The common form of construction for these types of bridges is the balanced cantilever construction method.

The initial start to the construction would begin with an appropriate selection of contractor. There is no movement in the bridge and so no specialist team needs to be considered to handle a hydraulic system or any other mechanical system.

3.1 Foundations

As seen from Fig. 8, the foundations largely reflect the underlying ground conditions, with a large focus of pile foundations on the urban side where there was known to be the better quality soil, more suited for being loaded by the bridge. By also looking at Fig. 9,

we can see that this is a three by three pile group. Fig. 8 also shows shallow footings on the other bank. There is also a foundation related to the back-stays, and we can see the retaining wall that is acting to help stop any rotation of the pier.

The process of laying the foundations would be standard and would be completed before any on-site assembly took place. The piles would have been driven in using a pile driving machine, bored piles may be preferred because of the close proximity to the city, and steel pile caps would have been fitted. Because the piles are in the river, upon completion the pile cap would be submerged, and so temporary casing would have to be used to protect he top of the foundations. The back stay cables run into the ground and have a concrete tip, relying on skin friction with the surrounding soil to help reduce the rotation of the pier. These foundations would have to be placed with the cables already imbedded, and prior to the assembly of the pier for logistical reasons.

Figure 9: Section showing main pile group

3.2 Fabrication

There is an opportunity to utilise a large amount of prefabrication for this bridge’s construction, this is advantageous because it reduces potential dangers

associated with on-site construction and the disruption construction will cause to the surrounding area. The bridge lends itself to prefabrication because access can be made to the bridge from the river, and so transport difficulties can be avoided. Due to this being a relatively small bridge, a larger amount of the components can be prefabricated and easily transported to site.

3.2.1 PierThe pier will be prefabricated in a local factory off

site. The location of this site will have to be selected carefully to allow for transportation of the pier to the site. At this location the pier will be cut and welded together, the pier will be made in a number of section because of its irregular geometry. Full submerged-arc welding in the protected atmosphere of the factory will help to avoid impurities that would weaken the joints. These welded connections will have to be ground down to lay flush with the rest of the material to achieve the seamless architectural finish that Calatrava has specified. Any rough connections would severely detract from the aesthetic quality of sophistication and refinement that Calatrava was aiming for with the Caballeros bridge. Finally, before being transported to site, the pier would be painted with a protective and aesthetic coat, this would eliminate the costly and potentially dangerous attempt of painting the pier post assembly and in position. Any damages caused to the paintwork during erection would have to be reapplied after construction.

It may be possible to prefabricate the entire pier and simply lift it into position, however this is very dependent on the transportation viability and would have to be discussed with various seafaring crane suppliers to determine its feasibility. Alternatively, the pier could come in sections that are simply welded together on site.

3.2.2 DeckThe use of steel for the deck means that it can be

fabricated in a similar way to that of the pier. Attachment of the aluminium covering could also be attached off site. The sections of the deck will be divided in a way that means their weight balances the backstays that are attached simultaneously.

Figure 8: Side section showing foundations

Figure 10: Deck section

3.3 Assembly

As mentioned in section 3, the general construction method used for this type of bridge is the balanced cantilever construction method. The theory behind this method is that by balancing the forces about a pier, the deck can be incrementally extended.

Figure 11: Arial view of cantilever construction

Figure 12: Suspended cantilever construction

Firstly the pier would have to be installed prior to any other element. When the pier is permanently attached to its foundations, the main stays would be attached with wooden sleepers to prevent damage. The sections of the deck would then be lifted into position, across the water and attached to its cable stay and the rest of the bridge. Before release of the deck element, two backstays would be attached and pre-tensioned so as to balance the forces felt by the cantilevering pier. This simultaneous installation the back stays develops a balance; the more of the deck that is installed, the more back stays that are added. Also, the backstays would be pre-tensioned, and then as the construction continues, the cables would be post-tensions up to sustaining the design loads.

Figure 13: Balancing cantilever

The nine main stays that are attached along the deck’s roof would have a slight pre-tension introduced to stop them going slack in the wind. When the seven back stays had been post-tensioned, the bridge would be complete. Only finishing touches such as paving slabs and interior furnishing would follow, including deck surfacing, handrail installation, and attachment of the glazing units into the deck covering.

There may be a need for formwork and other additional supports during the construction due to the difficulty of practically providing a perfect balance of forces. Refs. [1,4,5]

4 Loading

Bridges are designed using a limit state philosophy. This means that the bridge must be checked at the Ultimate Limit State (ULS), because any form of failure of the structure is unacceptable, and Serviceability Limit State (SLS), to ensure that the bridge is serviceable. The main code that will be used is BS 5400 which covers the general design of steel, concrete, and composite bridges.

Consideration will need to be made regarding the dead loads, the superimposed dead loads, live pedestrian loads, wind loads, and temperature as these will produce the largest potential loads on the bridge. Other loading types will be discussed later, but are considered to not be as critical.

4.1 Load Factors

The nominal loads acting on the bridge will be multiplied by two partial safety factors, Ɣfl and Ɣf3. Where Ɣfl is a partial safety and Ɣf3 is an additional factor introduced to allow for possible inaccuracies in the analysis of particular types of bridge. From Table. 1, the various values of Ɣfl can be found.

For the ULS, Ɣf3 is taken as 1.00, and because an elastic analysis will be conducted instead of a plastic one, the SLS value of Ɣf3 is 1.10.

There are five combinations of load that need to be checked at both SLS and ULS, these will be outlined in section 4.7.

Table 1: Partial safety factors

Load Limit State

Ɣfl

Dead ULSSLS

1.051.00

Superimposed dead ULSSLS

1.751.00

Reduced load factor for dead and superimposed dead

ULSSLS

1.00NA

Load Limit State

Ɣfl

Wind During erection ULSSLS

1.101.00

with dead plus superimposed dead load only, and for

members primarily resisting wind

loads

ULSSLS

1.401.00

With dead plus superimposed dead

load plus other appropriate

combination 2 loads

ULSSLS

1.101.00

Relieving effect of wind

ULSSLS

1.001.00

Temperature

Restraint to movement except

friction

ULSSLS

1.301.00

Frictional restraint ULSSLS

1.301.00

Foot/cycle track bridges: live load and parapet load

ULSSLS

1.50 for

load combination

1, 1.25 for

others1.00

4.2 Dead Load

The dead load of the structure will be a combination of all the self weights of the materials used on the bridge. The significant self weights that are present on the Caballeros are listed in Table 1:

Table 2: Material densities

Material Density, ρ (kg/m3)

Steel 7850

Aluminium 2750

Glass 2500

Because this is a footbridge, it is assumed that any other material loads are sufficiently small so as to be neglected, for example the surface finish of the deck

will be so thin that it will not add a significant load to the bridge.

The factors and areas of application will be outlined when the loads are combined in section 4.7.

4.4 Live Load

Obviously, because this is a footbridge, the Caballeros will not be subjected to vehicular loading, however, it also has barriers at both ends of the bridge and therefore prevents any form of accidental vehicle loading, this means that HA and HB loading will not apply to the bridge.

For bridges under 30m, a nominal live load of 5kN/m2 is considered appropriate. However the bridge is longer than 30m, so this load must be reduced by a factor k:

Live load = 5k (1)

This value of k is found by applying Eq. (2):

k = HA loading/30 (2)

This nominal HA loading in Eq. (2) is found from Eq. (3):

HA loading = 151(1/L)0.475 (3)

HA loading = 151 x (1/210)0.475

HA loading = 11.9 kN/m

Substituting this value into Eq. (2) therefore gives k a value of 0.4m, and substituting this value into Eq. (1) gives the nominal live load of 2kN/m. However there may be worse situations due to a large amount of people crossing at once, however there is no evidence to suggest that this would be the case and so can be neglected for the purpose of this analysis.

The parapets should be designed to withstand a nominal 1.4kN loading per metre run.

4.4.1 Impact loadsThe pylon is a significant distance away from a

road to ensure that accidental impact from a vehicle is a very slim possibility, however there is the chance of a collision. Under such a circumstance the pier would be expected to not fail, though it may become unserviceable. Therefore the pylon should be designed to withstand 50kN nominal horizontal impact load.

There is a slim possibility that a truck may collide with the pier. For this case, 25 units of HB loading blah blah.

4.4.2 VibrationsVibrations due to pedestrians is an important issue.

Design to not vibrate excessively under SLS conditions. Initially we must calculate the fundamental natural frequency of the bridge using the Rayleigh-Ritz technique. Eq. (4) is the equation that should be used.

ɷn = (βnl)2√(EI/ml4) (4)

If this is greater than 5 hertz then the bridge is deemed as adequate.

4.5 Wind Load

BS 5400 derived wind loading according to 120 year return values.

4.5.1 Maximum wind gustLooking at Eq. (4) which gives the maximum wind

gust which would strike the bridge. The mean hourly wind speed is taken as 30 m/s because this is widely used generic conservative value. K1 is a wind coefficient and for this situation is taken as 1.37 because the length is 210 metres and is 7 metres above the river bank. S1 is a funneling factor and is taken as 1.00, unless the bridge is located in a valley or an a town location where the wind is likely to be funneled, however for this case, the Caballeros is not near any objects that would cause funneling. S2 is the gust factor and is taken as 1.00 because the bridge is 7 metres above the ground.

vc = v K1 S1 S2 (4)

vc = 30 x 1.37 x 1.00 x 1.00

vc = 41.1 m/s

However, because this is the bridge in question is a footbridge, an addition factor must be imposed so as to reduce this value. The reason for this factor is that a footbridge is allowed a lot more flexibility compared to a traffic bridge and so can absorb a lot more of this gust load. Because the bridge is 7 metres above the ground, this factor is 0.80.

vc = 41.1 x 0.8 (5)

vc = 33 m/s

4.5.2 Horizontal wind loadThis is acting at the centroid of the part of the

bridge that is under consideration. It is given by Eq. (7). Where q is known as the dynamic pressure head and is given by Eq. (6), taking the value of vc from Eq. (5). A1 is the solid horizontal projected area, the deck will be about 2.5 metres high, and given that its length is 210 metres, this gives a projected area of 525 metres squared. The depth of the deck is simplified because it has a permanent covering and so there is no change in area under live, or unloaded conditions. CD is the drag coefficient and is calculated as a function of the b/d ratio. By inspection of Fig. 10 the width of the deck seems to be the same as the height and so b/d will be 1, therefore CD is 2.2. It may be a good idea to check the drag properties of the deck in a wind tunnel due to the unusual cross-section.

q = 0.613 vc2 (6)

q = 0.613 x 332

q = 668

Pt = q A1 CD (7)

Pt = 668 x 525 x 2.2

Pt = 771.5 kN

4.5.3 Wind loading on parapets and piersThis must also be considered

4.5.4 Longitudinal wind loadingGiven in BS 5400

4.5.5 Wind uplift and downwards forceAn important action by wind is uplift or a vertical

downward force. This is calculated from Eq. (8) where q is the dynamic pressure head and is the same as from Eq. (6). A3 is the plan area which is 525 metres squared. CL is the lift coefficient and depends on the b/d ratio and is 0.4.

Pv = q A3 CL (8)

Pv = 668 x 525 x 0.4

Pv = 140.3 kN

4.5.6 Wind load combinationsThe following combinations are those that must be

applied to the bridge. They are: Pt alone; Pt in combination with ± Pv; PL alone; and 0.5Pt in combination with PL ± 0.5Pv.

4.6 Temperature Load

It is assumed that the entire cross section of the deck is increases by a uniform temperature of 25°C. This temperature increase will result in a swelling of the metal. If expansion joints were intended to be used (which they probably were) then this will result in a longitudinal expansion of the deck, however if expansion joints are not used, or if the ones in place

become clogged, then this will result in a large amount of longitudinal compressive stress in the deck.

4.7 Combination of Loads

Following is the combination of loads that need to be considered for the structure. The loads need to be applied so that we get the worst effect for each combination, they also need to be checked for both SLS and ULS. Only combination one has been carried out in this report. Additionally, stability needs to be checked so maximum overturning moments are resisted. Sliding of the foundations also needs to be prevented.

Figure 15: Section of moment diagram

4.7.1 Combination oneThis involves all permanent loads plus primary

live loads, which in this case will be pedestrians. This load needs to be applied with consideration made to the load factors so as to maximise hogging and sagging moments, Fig. 14 shows the application of loads to achieve this effect. Considering a simplified cross-section and using reasonable thicknesses for the materials, and using the densities provided in Table. (2) with an assumed value of 9.8 m/s2 for gravity, the dead weight is found to be 24 kN/m. , Using the value of 2 kN/m for live loading found in section 4.4 and applying the load factors from section 4.1 gives Eqs. (9,10,11) with their subsequent results:

ULS maximum = 24 x 1.05 + 2 x 1.50 (9)

ULS maximum = 103.2 kN/m

Figure 14: Loads applied to maximise sagging and hogging

ULS minimum = 24 x 1.00 (10)

ULS minimum = 24 kN/m

SLS = 24 x 1.00 + 2 x 1.00 (11)

SLS = 26 kN/m

By neglecting the continuous nature of the deck and only considering a single span between two cable-stays, the maximum sagging moment is 3302 kNm for ULS and the maximum hogging moment is 4390 kNm. This shows that the critical case is hogging and so by using Eq. (12), the size of the required members can be calculated, assuming a strength of steel of 205 kN/mm2.

σ = my/I (12)

The serviceability is similar but is more concerned with deflections rather than strengths. For a single span the maximum deflection is given in Eq. (13):

δ = 5wl4/384EI (13)

4.7.2 Combination twoThis involves all permanent loads, primary loads,

wind loads, and possible temporary erection loads.

4.7.3 Combination threeThis involves permanent loads, primary loads,

temperature effects, and possible temporary erection loads.

4.7.4 Combination fourThis involves permanent loads plus secondary live

loads (skidding, collision loads) and associated primary live loads.

4.7.5 Combination fiveThis involves all permanent loads plus loads due

to friction at supports.

4.8 Other Considerations

Steel does not suffer from the same shrinkage problems that are apparent when using concrete. This is also the case for creep phenomena. However, steel does allow stress relaxation.

Differential settlement of the supports will not be a serious problem with this particular bridge because there are only two ground supports. Erection loads may very well be a critical loading case, however the scope of the report is such that it will not be rigorously analysed here.

There will also be no snow loading because of the Spanish climate, and so this need not be taken into consideration. Similarly, ice pack collision from frozen debris in the river will also not be of any concern. Earthquakes are another consideration that will be unlikely given the location and its history of few seismic occurrences. However, because the pier

runs into the water, scouring may occur on the bed of the river Segre. A regular organised check to ensure that it is not upsetting the foundations would have to be arranged, and if the problem did occur, then more river bed material would have to be transported to site to replace the missing material.

6 Vandalism

Vandalism comes in many forms and in many degrees of severity. The Caballeros footbridge will be more likely to receive superficial damage rather than damage that will threaten its structural stability. There is easy access to many of the elements and, although a terrorist attack on this bridge seems unlikely due to its low profile status, less severe vandalism may take place due to the bridge being in the centre of an urban environment.

This means that there is a high likely hood that the bridge will have graffiti sprayed onto its surface. This would obviously ruin the aesthetic effect that Calatrava was aiming to achieve. Regular checks from the local authority would ensure quick rectification if any damage was induced, prevention is near to impossible.The easy access to elements and the fact that the bridge will be constantly being used by people on foot may mean that someone may damage of weaken smaller components such as bolts and things. A design that took this into account would ensure no obvious connectors or components that would allow an individual with simple home tools to weaken.

7 Suggested Improvements

Instead of using steel for the deck, which is prone to corrosion, a fibre-reinforced plastic deck could pose as a possible alternative. Even though the use of plastic would reduce the corrosion of the bridge, it does suffer from ultraviolet deterioration, and some of the elegant visual benefits of using steel would be lost.

8 References

[1] Ibell, T. 1997. Bridge Engineering.

[2] British Standards 5400.

[3] Frampton, K. Webster, A.C. Tischhauser, A. 1993. Calatrava Bridges.

[4] Yamin-Lopez, R.A. The Making of the Alamillo Bridge in Seville: Analysis of its construction operations using discrete event simulation. [Online] http: / /mail .s i . i tb.ac. id/~abduh/ sim/Examples/alamillo.htm

[5] Cobb, F. 2006. Structural Engineer’s Pocket Book.

[6] Powell-Baden, C. 2006. Architect’s Pocket Book.

[7] Jean, M. 1992. Cable-stayed bridge and c o n s t r u c t i o n p r o c e s s . [ O n l i n e ] www.freepatentsonline.com/5121518.html.

[8] Lecture 15B.2: Actions on Bridges. [Online] w w w . k u l e u v e n . b e / b w k / m a t e r i a l s / Teaching/master/wg15b/l0200.htm.

[9] C a b a l l e r o s F o o t b r i d g e . [ O n l i n e ] www.calatrava.info/bridges/Caballeros.asp.

[10] Arial Map Resource. [Online] maps.live.com.