The science behind the load, span and design of a safe bridge
Different kinds of bridges require different factors to be taken into consideration. HT explains:
New Delhi: When engineers design a bridge, how do they make sure it will not collapse under the load of those who use it?
Different kinds of bridges require different factors to be taken into consideration. Among these, a suspension bridge, the kind that collapsed in Morbi of Gujarat killing at least 130, stands out in terms of its load profile and, consequently, the way it is designed.
The dynamics at play also allow a suspension bridge to span longer distances than other kinds of bridges. The Morbi bridge is not particularly long — about 230 m — but there are longer examples: the Dobra-Chanti bridge over the Tehri lake in Uttarakhand is 725 m, while the newly constructed Çanakkale Bridge in Turkey runs over 2 km.
It is important to note that the Morbi bridge is not identical to the suspension bridge shown in the generic illustration. Typically, such bridges consist of three main parts: the main cable, the suspender cables holding up the main cable, and the supporting towers or piers. In the Morbi bridge, the supporting tower was not in the middle of the bridge but at the edge.
Either way, the distribution of forces is broadly the same.
“The deck of a bridge is subjected to live (imposed) load first. The load is then transferred to the main cable through cross-beam and suspender cables /bars. Finally, the load gets transferred to foundations and anchor blocks through the towers and cable anchorages respectively,” S K Deb, a civil engineering professor at IIT Guwahati, said in an email response.
To understand why such a structure allows for longer spans, it is necessary to first look at the forces that act on the bridge.
Forces at play
A bridge is designed in a way that it can safely carry the anticipated traffic. “According to the Indian Roads Congress, the load capacity of bridges is determined by the prevalent heaviest commercial vehicular load plying on the bridges and the extent of traffic congestion during peak hours,” said Manabendra Saharia, assistant professor of civil engineering at IIT Delhi.
The design of any bridge has to account for two kinds of forces. One is compression, which acts to compress the bridge, while the other is tension, which acts to expand it.
A spring provides an example of these two forces. When its two ends are pushed against each other, the spring is under compression. When the ends are stretched outward, the spring is under tension.
In a bridge, whether compressive or tensile forces are at play, and where, depends on what kind the bridge is. In most bridges, either or both kinds of forces are acting on the deck, or the road/surface. In a suspension bridge, on the other hand, the two kinds of forces are concentrated in the cables and the supporting tower (see illustrations).
How that helps
With the load shared almost entirely by the cables and the tower, the deck is neither in tension nor in compression, said Subhamoy Sen, assistant professor of civil engineering at IIT Mandi. All this reduces the dead weight of the structure, and a longer span becomes possible.
“The main cable and suspender cables are always in tension. They transfer a completely vertical load on the column, which is always in compression,” Sen said.
Other kinds of bridges do not have this constancy, with the stress profile changing according to the position of the vehicle. As an example, Sen cited cantilever bridges, in which a vehicle on one span causes “hogging” in the other span. The constancy also makes construction of suspension bridges less expensive, he said.
When something snaps
For a bridge that had survived over 140 years, what might have happened during maintenance that caused it to collapse?
When a structure has not failed for so long, Sen said, the chances that it will ever fail is very low. But during major maintenance, there are pulleys on the pier, and the structure gets oiled.
“Maybe, at some places, something was locked, and now it is freed, and the structural configuration is changed altogether,” said Sen, who heads IIT Mandi’s i4S Lab that works on the health of structural systems. It has been calling for a health check on Mandi’s Victoria Bridge, also a suspension bridge, and also over 140 years old.
The load in Morbi
Could overloading have been the cause of the Morbi tragedy? While Sen agrees that it likely contributed, he believes overloading was not the direct cause.
Normally, engineers provide up to 4-5 times more strengthening material than what is necessary, he said.
How much a bridge can withstand also depends on dynamic factors, such as the speed of traffic on it. Referring to videos of the collapse, Sen said a large crowd appeared to have queued up on the same section. “The bridge was actually rotating and suddenly one side of the cable snapped. The vertical force contributed to the twisting.”
If that amount of overloading had happened when the pedestrians were walking, Sen felt, “it was less likely to have happened”.