What if a bridge had no supports?

Lay a ruler across two books. Put a toy on it. The ruler holds it up.

Now take the books away. What happens to the ruler?

A beam bridge is a very simple kind of bridge: a long, strong beam resting on supports. When a heavy truck drives across, the beam bends a little, but it holds.

But what is actually holding the bridge up? Is it the beam's strength, or the supports underneath? In this lab, a truck sits on a steel beam bridge. You can change the supports, from both ends, to one end only, to none at all, and see what happens.

Every structure must carry its loads to the ground. In a beam bridge, the beam carries the weight of traffic and of itself sideways to its supports by bending, and the supports carry it down to the foundations.

This lab uses Euler–Bernoulli beam theory for a solid steel beam 20 m long, 1 m deep and 0.5 m wide, with a 20 t truck at midspan. It compares three cases: supported at both ends, fixed at one end only (a cantilever), and no supports at all.

Our bridge rests on supports at both ends. A big truck drives on.

The bridge bends just a tiny bit. It is safe and strong.

In the model, the steel beam rests on a support at each end. A 20-tonne truck stops in the middle.

The beam sags by only about 14 millimeters over its whole 20-meter length. The steel inside works at only about one seventh of its strength, so the model says the bridge is safe. Each support pushes up on the beam, sharing the weight between them.

Simply supported, with the 196 kN truck load at midspan plus the beam's own weight (78.5 t of steel), the model gives a maximum sag of 13.6 mm and a peak bending stress of 34.9 MPa against a yield strength of 250 MPa: a safety factor of 7.2.

Bending puts the top of the beam in compression and the bottom in tension. The two supports supply the upward reactions that balance the total weight, each carrying half for a central load.

Now the bridge is held at one end only. It bends much more!

Then Olly takes away every support. Nothing holds the bridge up. It falls.

First, hold the beam at one end only, so it sticks out like a diving board. With the truck in the middle, it now sags about 112 millimeters, about eight times as much, and the steel works about three times harder. Drive the truck to the far tip and the model calls it risky.

Now choose no supports. The model doesn't even calculate a bend: with nothing pushing up, there is nothing to balance the weight, and the beam simply falls. A beam can only hold weight if something holds the beam.

Fixed at one end with the truck at midspan, the model gives 112 mm of sag and 116 MPa of stress (safety factor 2.2). With the truck at the free tip the moment reaches P·L plus self-weight, the stress 139 MPa and the safety factor 1.8, below the model's threshold of 2, so it is rated risky.

With no supports the model does not compute stresses: with no reactions, the net force is the full weight and the beam accelerates downward. The model labels this case an idea, not a calculation.

The supports push up on the bridge. That push holds it up.

No supports means no push. So the bridge falls down.

Gravity pulls down on the bridge and the truck all the time. The bridge stays still only because the supports push up just as hard. Supports at both ends share the job, so the beam only has to bend a little to carry the weight to them.

Held at one end, the beam has to carry all the weight back to that one support, so it bends much more. With no supports, nothing pushes up, and the beam falls. Our model treats the beam as one solid block of steel; real bridges are shaped more cleverly.

Equilibrium needs the forces and moments to balance. Two end supports give reactions with short lever arms, so the peak moment is P·L/4 for a central load. A cantilever must resist the whole moment at its fixed end, P·a for a load at distance a, so moment and stress rise. With no supports, ΣF ≠ 0 and the beam accelerates.

Model limits: small elastic bends, one solid rectangular section, a point load and an even self-weight; no buckling, twisting, shear failure, fatigue, wind or vibration, and the supports themselves are not checked. The drawn bend is exaggerated so it can be seen.

Real bridges stand on strong supports.

The supports carry the bridge's weight down into the ground.

The beam bridge is the most common kind of bridge. Real bridges rest on supports, such as abutments and piers, that carry the weight down to foundations in the ground.

Engineers design every bridge to hold its own weight and the weight of the traffic on it. They also choose materials carefully. Concrete is strong when squeezed but weak when stretched, so in our model a plain concrete beam with no steel inside would crack under the truck.

Britannica describes the beam bridge as the most common type, carrying vertical loads by bending, with compression on top and tension below. Supports such as piers and abutments transfer loads to foundations, which resist settling and sliding. Bridges are designed for their permanent dead load and for the live load of traffic.

Concrete is strong in compression but weak in tension. In the model, a plain 30 MPa concrete beam of the same size reaches a safety factor of only 0.18 under the truck, which is why concrete beams are reinforced with steel bars, as Britannica explains.