What if a truck stopped near the end of a bridge?

A bridge is like a long, strong plank. It rests on something at each end.

A heavy truck drives on and stops. Is the bridge working harder if the truck stops in the middle, or near one end?

A beam bridge is a long, strong beam held up at both ends. When a heavy truck drives onto it, the beam bends a tiny bit, like a ruler with a book on it.

Does it matter where the truck stops? If it stops right in the middle, or just past the start of the bridge, does the beam bend the same amount? This lab lets you park the truck anywhere and measure what happens inside the beam.

A simply supported beam carries a load by bending: the top fibers are squeezed, the bottom stretched, and the internal bending moment sets both the stress and the sag. That moment depends on where the load sits.

The question: for the same truck on the same beam, how much do the sag, the peak bending stress and the safety factor change when the truck moves from midspan to 10% of the span from one support?

Olly's truck stops right in the middle of the bridge.

The bridge bends down just a tiny bit, less than half a centimeter. It is still very safe.

The model's bridge is a solid steel beam 20 meters long, 1 meter deep and half a meter wide, held at both ends. A 20-tonne truck stops right in the middle. To see the truck's effect clearly, the lab starts with the beam's own weight switched off.

The beam sags 3.92 millimeters, and its biggest bending stress is 11.8 megapascals (MPa). The steel can take 250 MPa, so the safety factor is 21.2: the beam is far stronger than this truck needs.

Model setup: steel (E = 200 GPa, yield 250 MPa), span 20 m, solid 1 m × 0.5 m section, simply supported, a 20 t point load at midspan, self-weight off. The model gives a maximum deflection of 3.92 mm and a peak bending stress of 11.8 MPa, matching δ = PL³/48EI and M = PL/4, for a safety factor of 21.2.

Switch self-weight on and the 78.5 t beam's own load dominates: 13.6 mm and 34.9 MPa, safety factor 7.2.

Now the truck stops near the start of the bridge, close to where it rests on the ground.

The bridge hardly bends at all! The end of the bridge holds the truck up easily.

Now drive the same truck only 10 percent of the way across, 2 meters from the support, and stop. The sag drops from 3.92 to 1.19 millimeters, and the biggest bending stress drops from 11.8 to 4.24 MPa, about a third. The safety factor climbs to 59.0.

Press play to drive the truck all the way across. The graph shows the beam working hardest as the truck passes the middle, and easiest near each end.

At a = 0.1L the model gives a maximum deflection of 1.19 mm, a peak stress of 4.24 MPa and a safety factor of 59.0. The stress ratio 4.24/11.8 = 0.36 is exactly a(L − a)/L ÷ L/4 = 0.09/0.25.

Driving across, the safety factor is lowest at midspan, where the bending moment under the load peaks. At the support itself (0%), the beam carries no bending from the truck at all: the support takes the whole weight directly.

Near the end, the truck is very close to a support. That support holds up almost all of the truck.

In the middle, the beam has to hold up the truck all by itself, far from both supports. So it bends more.

The two supports share the truck's weight. When the truck is in the middle, each takes half, and the beam has to carry the load a long way, 10 meters, to reach either one. That long carry makes it bend.

Near one end, the close support takes most of the weight, and the beam only carries it a short way. A short carry means little bending. The bridge isn't stronger near the end; the job is easier.

Torque balance about each support splits the load: the near support carries P(L − a)/L, the far one Pa/L. With a = 0.1L, the near support takes 90% of the truck. The bending moment under the load, the near reaction times a, is P·a(L − a)/L, which peaks at a = L/2.

The model's limits matter here: it checks bending only, treats the truck as a single point load, and ignores dynamic effects. It does not check shear failure, the supports themselves, fatigue from many trucks, wind or vibration, so 'easier for bending' near the end does not mean 'no load'.

Real bridges rest on strong supports called piers.

The weight of the bridge pushes down on the piers. A truck can stop anywhere, so the bridge has to be strong everywhere.

PBS's Building Big series explains that a beam bridge rests on piers, and the weight of the beam pushes straight down on them. The farther apart the piers, the weaker the beam becomes, which is why simple beam bridges rarely span more than about 76 meters (250 feet).

In our model, the middle is the hardest spot for the beam, while a truck stopped right beside a support puts almost all its weight on that support. A real bridge has to cope with both.

The Institution of Civil Engineers calls the beam bridge, a horizontal beam held up at each end, one of the oldest and simplest bridge forms. PBS notes that the beam's weight pushes straight down on the piers and that wider pier spacing weakens the beam, keeping simple beam spans under about 250 feet.

In the model, the beam's critical load position for bending is midspan, while a load near a support transfers almost entirely to that support. Real bridge checks consider many load positions and effects (shear, supports, fatigue, dynamics) that this bending-only model leaves out.