French Bridges: 19. Passerelle Simone-de-Beauvoir, Paris

This is the last in my current series of Parisian bridges. I started with the oldest bridge over the Seine in central Paris, the Pont Neuf, and I'll finish with the newest, the Passerelle Simone-de-Beauvoir.

A design competition was organised in 1998 for a new crossing of the Seine, halfway between the existing Pont de Bercy and Pont de Tolbiac. The new bridge would link the Parc de Bercy with the National Library of France, as well as the riverbanks, which are here somewhat isolated from the rest of the cityscape by busy highways. Both park and library are like large plateaus situated well above river bank level.

Five teams were invited to submit designs: Tadao Ando / Setec TPI; SEEE / Patrick Berger; Marc Mimram; Arup / RFR / Chris Wilkinson; and Deitmar Feichtinger / RFR. In March 1999, the partnership of Feichtinger and RFR were declared the winner.

The winning proposal connects the riverbanks at lower and upper levels and avoids any supports in the river. The structure is therefore not also the latest bridge across the Seine, but also easily the longest span, with a 194m span between piers, and a total length of 304m. The deck is a generous 12m wide in total, although over most of its length this is split at different levels, so for practical purposes it's only 6m wide. The bridge was completed in 2006 at a total cost of 21 million euros.

By any standard, the bridge is enormous. I think it's particularly instructive to compare it to Patrick Berger's proposal, which was for a variant on a conventional suspension / stress ribbon bridge. This would have required substantially less material over the river, giving a lighter and less redundant appearance, but would have needed enormous anchorage structures well beyond the ends of the bridge itself.

Feichtinger's design (I'm going to call it his for the sake of shorthand, although clearly it was the result of a team effort) can be conceptualised structurally in several different ways. Think of a lenticular truss (like the Royal Albert Bridge, or the Maryhill House Footbridge). This can be thought of as a truss, with upper and lower chords carrying compression and tension, as well as shear forces by virtue of their inclination. It can also, however, be seen as an underspanned self-anchored suspension bridge, where a suspension cable below-deck is anchored not into the ground, but against the deck, which provides a balancing thrust.

The Passerelle Simone-de-Beauvoir is essentially the same type of bridge, except that the ends of the main span members, instead of meeting at a point where the forces balance, have been displaced vertically. The result of this is that although the horizontal forces from the suspension element and the compression arch element are broadly in balance, they are applied eccentrically, creating large overturning moments at both riverbank supports.

The overturning is restrained by a coupled foundation: the tension member passes vertically over a saddle, and into a deep anchor foundation. The saddle is balanced by an inclined leg, which connects directly to the ends of the main arch element. At this point, in a perfect world the horizontal forces would balance precisely. However, the suspension cable is significantly longer than the arch, and the forces do not balance, so there is a further inclined leg below the arch to carry the vertical loads from the bridge into the ground, via a massive deep caisson foundation. Taken together, the upper and lower inclined legs can be nicknamed the "boomerang".

For a pure lenticular truss of the same span, the foundation loads are vastly smaller, as the vertical load on the two foundations is equal to a half-share of the vertical weight of the bridge and whatever it carries. For the Passerelle Simone-de-Beauvoir, the main foundations must support the same vertical load, but must also react against the anchorage force, so the foundations are much more heavily loaded. However, the benefit is obvious: a much shallower structural form and one which better ties together the various ground levels. A lenticular truss of 194m span would sit ridiculously high in the air and look completely inappropriate.

The observant reader will, of course, have noted that the central part of the bridge is indeed a conventional lenticular truss, with upper and lower balancing elements coming together at a point. Indeed, this part of the bridge was fabricated precisely in this way: as an independent structure, fabricated elsewhere, assembled into its whole, and shipped up river ready for erection. In this respect, the structure can be seen as different structural form: the Gerber beam.

This concept was named after Gottfried Heinrich Gerber, whose idea was to take a continuous beam and insert hinges at the points of inflection in the diagram of bending moments (the points of theoretically zero moment). This transforms a structure which is complex to analyse into one which is simple to analyse, as well as eliminating troublesome side-effects of bending continuity such as vulnerability to foundation settlements. However, it retains the main advantage of continuity, which is reduced bending moments relative to simply-supported bridges. The exact position of the hinges is to some extent arbitrary, as the position of the theoretical points of inflection depends on the nature and position of loads applied to the span.

The central lenticular truss of the Passerelle is 106m long, and is structurally highly-efficient, just like the drop-in span of a Gerber beam. Here, the drop-in section is held aloft by cantilever structures either side, so another way to conceptualise this bridge structure is as an unbalanced cantilever bridge, like taking a single span of the Forth Railway Bridge and splitting it off from the rest by taking a giant machete down the centreline of the two towers. It's easy to image how much work would be required to haul back the severed towers and stop them from from simply toppling into the Forth Estuary, and that gives a good idea for how hard the Passerelle Simone-de-Beauvoir is working towards the same end.

One issue for the designers will have been how to combine the catenary and arch elements in a structurally and visually sensible manner. Catenary and suspension bridges typically employ circular cables as their main tension elements, but the Passerelle instead uses grade 355 steel plate as the tension elements, which although structurally inefficient makes visual sense.

These plates are 100mm thick at midspan, and 150mm over the anchor saddles, where they split into three bands before being anchored into the foundations. The plates are 1m wide, so each one can carry up to about 5000 tonnes without breaking. Each catenary can therefore carry the weight of roughly 15 fully-laden jumbo jets, which gives some idea quite how hard the bridge and its foundations are working. For comparison, this is a total tension load of roughly five times the total cable forces on London's Millennium Bridge, which is both shorter and narrower and lacks the arch element.

The tension plates are separated from the arches by bundles of four steel rods, which the architect nicknamed "obelisks". Compare the much smaller Maryhill House Footbridge, which has triangular struts in a similar arrangement, with the "pointy" end of the strut on the tension member and the thick end on the compression member. This creates a semi-Vierendeel arrangement, using the bending stiffness of the connection to the thicker compression element to prevent longitudinal movement and hence ensure the lenticular truss behaves as a fully integrated deep beam.

The bridge has two end spans across the adjacent highways which are more straightforward fishbelly trusses. These sit on the abutments at one end, and at the other are connected onto the main bridge saddle zones. If you compare the various photos, you'll see that the detailing of these areas is quite tricky, and the designers have generally done a very good job in keeping everything as simple as they can.

As with other long-span footbridges, the Passerelle Simone-de-Beauvoir could have been vulnerable to vibration. I didn't spot them on my visit, but there are tuned mass dampers below the decks to address flexural and torsional movements, and viscous dampers at the ends of the bridge to reduce longitudinal movement. Extensive crowd testing was undertaken to ensure these would perform correctly, and the bridge was also tested under static loads by filling 550 water tanks laid out along the length of the deck.

The layout of the bridge is not entirely as rational as it first appears. Although the upper deck surface follows precisely the contours of the structural form, the lower deck does not. At its ends, it sits at a higher level than the arch elements, a departure from the competition-winning scheme. Presumably, it just didn't prove possible to get the structural requirements properly matched against the topography of the site.

The bridge reminds me of the great wooden rollercoasters of the USA. As you walk onto the upper deck from the end, you at first see a wide expanse of timber and can't at first see the rest of the bridge. As you go further, great sweeping waves of bridge gradually rise into view. The change in perception of the structure is charming, and more so once you discover the ramps which lead both downwards and off the bridge and also down below the central crown.

Here, you find a sheltered and very different space, somewhere you can pause, rest, meet people, or contemplate the view. It's a shame that there's no seating at either level, as this is a bridge which is clearly as much about the creation of generous public space as it is about getting from A to B. It's a space which invites alternative uses, and has been used on several occasions for art events.

For me, the most interesting thing about the Passerelle Simone-de-Beauvoir is the relationship between its lightness and its massiveness. It's a structural design intended to maximise efficiency over a long span - the words "slender", "lightness" and "ribbon-like" are used in the architect's book describing the structure. I certainly admire the bridge's generosity of space, but it's this which for me also makes the bridge appear massive and heavy, something that I think is simply unavoidable for such a wide structure. However efficient the design, there's an accumulation of surface and metalwork which creates an enormous, unavoidably massive presence within the river surroundings.

Further information:

• Google maps
• Wikipedia
• Structurae
• Planete TP
• Deitmar Feichtinger Architectes
• Bridge Builders (Pearce and Jobson, 2002)
• The Bercy-Tolbiac Footbridge in Paris (Bardsley, Menard, and Consigny, Footbridge 2002, Paris, 2002)
• Passerelle Simone-de-Beauvoir, Paris (Feichtinger Architects, 2006)
• The Simone-de-Beauvoir Footbridge between Bercy Quay and Tolbiac Quay in Paris: Study and measurement of the dynamic behaviour of the structure under pedestrian loads and discussion of corrective measures (Hoorpah, Flamand and Cespedes, Footbridge 2008, Porto, 2008)
• Footbridges (Baus and Schlaich, 2008)
• Bridge Architecture + Design (van Uffelen, 2010)
• Footbridges: Small is Beautiful (ed. Humar, 2014)
• The Glow of Paris: The Bridges of Paris at Night (Zuercher, 2015)
• Bridges of Paris (Saint James, 2015)