Building Bridges

D. Indumathi, The Institute of Mathematical Sciences, Chennai

All of you must have seen several bridges, some spanning a river, some going over a valley, or even passing over a rail track! 
In the old days, bridges were functional and simply used materials easily available locally. For instance, locally available stones were used to build one of the world's oldest bridges, the Arkadiko bridge in Greece.
Log bridges are convenient to build in wooded areas (see the animals in the picture crossing a striking log bridge in Tibet). The Incas of South America built several rope bridges over deep canyons in their mountainous terrain, which were sufficient since they did not have motorised vehicles!
Slowly, bridges began to get more sophisticated and aesthetically pleasing to look at. Numerous bridges over rivers in Europe were designed to look beautiful as well as house shops in buildings that were part of the bridge, as in the Pulteney bridge in Bath. 
In the twentieth century, bridges became more sleek and longer, as engineers discovered how to safely build longer and longer bridges. Today we have marvellous bridges over the world that appear to be the latest in fashion, design and engineering.

Types of bridges
There are mainly three types of bridges: cantilever bridges, suspension bridges and cable-stayed bridges.

Cantilever bridges
A cantilever is a beam supported on only one end. This is in contrast to a simply supported beam supported at both ends. The load in the simply supported beam is applied between the supports (for instance in a children's swing).
Sometimes, it is not possible to support the beam at both ends. For example, balconies of many houses project outwards without being supported at the outer end. All these are built using the cantilever design.
A cantilever bridge is a bridge built using cantilevers. So the structures project horizontally into space and are supported on only one end. For small footbridges, the cantilevers may be simple beams. Once the span is larger, just one beam is insufficient and an entire steel structure may be used instead.

Suspension bridges
Suspension bridges were first built in the 19th century. The bridge has two parts: the deck which is the actual bridge on which people walk or vehicles ply. The other part is a set of suspension cables which literally hold up the deck (hence the name). The cables themselves are suspended between towers.
The deck is hung from vertical suspenders (called hangers) that are designed to carry the entire weight of the deck, as well as all the traffic on it. The length of the suspension cables is such that the deck is either flat or may even curve upwards.
The suspension cables must be firmly fixed or anchored at each end of the bridge, otherwise they will collapse. They are usually connected to towers or pillars at each end. However, the cables do not stop there: they are continued beyond the pillars to supports at the deck-level, and from there are firmly fixed to the ground on either side (see picture).
For smaller bridges, there may be just a pair of pillars at each end and the suspended bridge in the middle. The length of the bridge from pillar to pillar (the actual suspended part) is called the span. In longer bridges there may be more than one set of pillars and so more than one span. Usually there is a main span that will be the longest part in the middle. This span is reached by smaller spans on either side. 

How it works
In a suspended deck bridge, cables suspended via towers hold up the deck. The weight is transferred by the cables to the towers, which in turn transfer the weight to the ground.
First a large cable is made up by looping wires between two towers, and fastening them firmly at each end to the ground or to a massive structure. These cables form the primary load-bearing structure for the bridge deck.
Before the deck is installed, the cables are under tension from only their own weight. Smaller cables or rods are then suspended vertically down from the main cable, and used to support the load of the bridge deck, which is lifted in sections and attached to the suspender cables. As this is done the tension in the cables increases. The tension on the cables are transferred to the earth by the anchorages at each end.
Since the deck (and all traffic on it) is supported by the suspension cables, the cables are always under tension. These cables are connected to the pillars, and transfer this load to them as a compression. However, since the cables are vertical, almost all the force on the pillars is vertically downwards. So the pillars can be made quite slender. This is what gives the elegant and delicate look to suspension bridges.
Since the cables are very light compared to the deck that they support, the main cables of a suspension bridge will hang in a curved shape called a parabola.
This makes the suspension bridge much simpler to design and analyse than a cable-stayed bridge, where the deck itself is under compression.
A suspension bridge can be made out of simple materials such as wood and common wire rope. Minimum use of material for the corresponding span makes it cheaper as well. One of the main advantages in this kind of bridge is when it is not possible to work at the water-level, under the bridge, during construction.
The Bosphorus Bridge in Istanbul, Turkey, connects the continents of Europe (left) and Asia (right).

Cable-stayed bridges
In the cable-stayed bridge, the towers themselves form the primary load-bearing structure unlike the suspension bridge where the cables bear the load along with the towers.
Near the towers, a cantilever approach is often used for support of the bridge deck. Parts of the deck farther away from the towers are supported by cables running directly from the deck to the towers.
This has the disadvantage, compared to the suspension bridge, of the cables pulling to the sides as opposed to directly up. This results in both horizontal and vertical compression loads, unlike suspension bridges. So the bridge deck must be stronger to resist the resulting horizontal compression loads.
On the other hand, since the cables are slanting, they can provide horizontal force balancing by themselves. So the towers need not be so strong as in suspension bridges. So in such a bridge less cable is needed than in a suspension bridge, and also the towers are smaller. See the picture of the Abdoun bridge in Amman, Jordan.
A further advantage of the cable-stayed bridge is that any number of towers may be used. This bridge form can be as easily built with a single tower, as with a pair of towers. However, a suspension bridge is usually built only with a pair of towers.

Choice of bridge
If a bridge is short, a cantilever is sufficient. As the span increases, the cantilever spans will get heavier and it is better to use cable-stayed bridges where the portion near the tower is suspended like a cantilever, and the portion far away is supported by cables. Also, if the span is not long enough, full suspension cabling is more expensive and so a cable-stayed bridge is preferred.
When the span gets longer than about 500 m, the suspension bridge type is preferred. For instance, the Akashi-Kaikyo Bridge in Japan has the world's longest mainspan of nearly 2 km and is a suspension bridge.

Some bridges in India

The Howrah Bridge (Rabindra Setu)
The Howrah Bridge (Rabindra Setu) is a bridge that spans the Hooghly River in West Bengal, India. It links the city of Howrah to its twin city, Kolkata. It is the world's 6th longest cantilever, with 457 m long span.
The bridge is one of the four on the Hooghly River and is a famous symbol of Kolkata and West Bengal. The other bridges are the Vidyasagar Setu (popularly called the Second Hooghly Bridge), the Vivekananda Setu and the newly built cable-stayed Nivedita Setu. Apart from bearing the stormy weather of the Bay of Bengal region, it successfully bears the weight of a daily traffic of approximately 80,000 vehicles and, possibly, more than 1,000,000 pedestrians.

The Bandra-Worli Sea Link
One of the new cable-stayed bridges, the Rajiv Gandhi Sea Link, has recently been completed in Mumbai. It has a total length of 5.6 kilometers and eight lanes of traffic. It's longest span is 250 m (two such).
The Bandra-Worli Sea Link spans the Mahim Bay and links Bandra and other western suburbs of Mumbai in the north with Worli and central Mumbai in the south.
Mahim Causeway was the only link connecting the western suburbs to the island city of Mumbai. This north-southwestern corridor was highly congested resulting in a bottleneck at rush hours. The sea link was thus proposed to act as an alternate route between the western suburbs of Mumbai and central Mumbai, in addition to the existing Mahim Causeway, thus easing congestion.
It is for the first time that cable stay bridges have been attempted on open seas in India. Images of the bridge and a close-up of the central cable supports are shown.

Sea Link Trivia
. Length of the steel wires used is equal to the circumference of the Earth.
. Weight of the Sealink Bridge is equivalent to the weight of 50,000 elephants.
. Height of the cable-stay towers equals that of a 43 storied building
. Length of the Sealink Bridge is 63 times the height of the Qutub Minar.

--With images from Wikimedia Commons and several other sources