What if a bridge weighed nothing?

A bridge holds up the trucks that drive over it.

But a bridge is heavy too. It must hold up its own body. What if it weighed nothing?

When we think about a bridge being strong, we usually picture heavy trucks rolling across it. But the bridge itself is heavy too. Steel and concrete beams can weigh far more than any truck, and the bridge has to hold all of that up, every second of every day.

So here is a strange question: what if a bridge weighed nothing at all? How much stronger would it seem? In this lab you can switch a beam's weight off in a model and find out.

Bridge engineers split the loads on a structure into types. The dead load is the weight of the bridge itself; the live load is the weight of the vehicles using it. Wind, earthquakes and temperature changes add more.

This lab asks what fraction of a beam's strength is spent on its own dead load. It uses a simple beam model to compare the same 60 m steel span with and without its self-weight, then looks at what real designers do because self-weight matters so much on long spans.

Real bridges are made of steel and concrete. These are very heavy.

A long bridge works hard just to hold itself up.

A beam bridge is a long beam resting on supports at each end. When it carries weight, it bends a little: its top is squeezed and its bottom is stretched.

In our model, a solid steel beam 60 meters long, 1 meter deep and half a meter wide weighs about 236 tonnes. That is nearly 12 times as heavy as the 20-tonne truck parked in the middle. With both the truck and its own weight to carry, the model's beam has a safety factor of only about 1.0: it is barely strong enough, and engineers would call it far too risky.

The model treats the bridge as a solid rectangular steel beam supported at both ends, with a yield strength of 250 MPa. At a 60 m span, 1 m deep and 0.5 m wide, it has a mass of about 236 t. A 20 t truck at midspan plus the beam's own weight produce a peak bending stress of about 243 MPa, a safety factor of 1.0 and a sag of about 886 mm.

Even the empty beam, with no truck, has a safety factor of only 1.2. Engineers usually want at least 2, the threshold the model uses for 'safe'. So this beam, as drawn, spends almost all its strength holding itself up.

In Olly's model, the bridge suddenly weighs nothing.

Now it only holds up the truck. It bends much less, and it is much safer!

Now switch the beam's own weight off in the model, and keep the same truck. The beam's biggest sag drops from about 886 millimeters to about 106. Its safety factor jumps from about 1.0 to 7.1, so now it is more than seven times as strong as it needs to be.

Nothing about the steel changed. All that strength was there before; it was just busy holding up the beam. A bridge that weighed nothing could carry much heavier traffic. In the model, even a 60-tonne truck leaves it with a safety factor of 2.4.

With the self-weight switched off, the same 60 m beam with a 20 t truck at midspan has a peak stress of about 35.3 MPa, a safety factor of 7.1 and a sag of about 106 mm. Using the model's equations, the beam's own weight was producing about 85 percent of the bending moment: w·L²/8 from the even load against P·L/4 from the truck.

The weightless beam can also carry the heaviest truck the model allows, 60 t, at a safety factor of 2.4. With its weight included, that truck would break it (safety factor 0.8). Remember this is a thought experiment: a real structure always has weight.

A short bridge is light, so it mostly holds up trucks.

A long bridge is very heavy. It mostly holds up itself!

A truck is one heavy spot on the bridge. The bridge's own weight is spread along its whole length, and a longer bridge has more of it. In the model, the bending caused by the beam's own weight grows with the square of the span: twice as long means four times as much. The bending caused by one truck only doubles.

So the longer the bridge, the more of its strength goes into holding itself up. Working it out from the model's equations, a 20-meter beam uses about two thirds of its effort on its own weight; a 60-meter beam uses about 85 percent.

For a simply supported beam, a point load P at midspan gives M = P·L/4, while an even self-weight w per meter gives M = w·L²/8. Self-weight bending therefore grows with L², and its sag with L⁴. Worked out by hand from the model's equations (it is not a readout), the share of the peak moment due to self-weight rises from about 66 percent at 20 m to about 85 percent at 60 m.

The model's limits matter here. It is a single solid rectangle of steel, while real long-span girders are I-shaped, boxes or trusses that put material where it works hardest. It checks only bending stress and sag, not buckling, twisting, shear, wind, vibration or fatigue, and its truck is a single point load. Its numbers show the trend, not a real design.

Engineers try to make long bridges as light as they can.

Lighter parts leave more strength for cars and trucks.

Real engineers see the same pattern. A 1995 working paper written for the U.S. Federal Highway Administration says that on a short bridge, about 40 feet (12 meters) long, roughly 70 percent of the main beams' strength may go to carrying traffic. On a long bridge, about 1,000 feet (305 meters), only about 25 percent goes to traffic and about 75 percent holds up the bridge itself.

That is why designers of long bridges hunt for lighter structures. One example is a deck made of thin steel plates stiffened with ribs, which the FHWA says has been used in the United States for long spans where keeping the weight down is paramount.

A 1995 working paper written for the Federal Highway Administration's Comprehensive Truck Size and Weight Study gives rough figures: for a 40 ft span, about 70 percent of the main members' load-bearing capacity may be needed for live load and 30 percent for the bridge's own weight; for a 1,000 ft span, about 25 percent for live load and 75 percent for dead load.

Designers respond by cutting dead load. A 2012 FHWA article describes orthotropic steel decks, thin steel plates stiffened by closely spaced ribs and floor beams, and notes that in the United States they have mostly been used on long-span structures where minimizing dead load is paramount, such as the new Tacoma Narrows Bridge in Washington State. PBS's Building Big gives a rough teaching rule that beam bridges rarely span more than about 250 ft (76 m); far longer crossings use other forms.