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Preventing Ship Allisions of Bridges

Baltimore 2024 Allision

Francis Scott Key Bridge

On the 26th of March, 2024, the Outer Harbor Bridge in Baltimore, Maryland, officially called the Francis Scott Key Bridge, collapsed after being struck by a large container cargo ship. The ship was reported to be drifting without power after leaving the nearby inland Port of Baltimore.

The alliding ship was not escorted by tugboats, and the bridge had many design errors. Both factors caused the bridge collapse, resulting in renewed calls for the United States to improve its bridge designs and require use of tugboats in its inland waterways.

The ship struck a bridge pier on the side of the ship channel (waterway) that passed under the main bridge span, knocking down the two bridge spans that were supported by that bridge pier, which in turn knocked down additional spans on the other side of the main span due to the seesaw effect and lack of arm-to-pier bracing.

Figure 1:  View of bridge, approaching from the inland port. The shipping channel and main bridge span are between the triangle bridge piers. Allision was with pier on the right side of the channel. Six bridge spans collapsed: all three truss spans (right); and three girder spans (left). [Fvasconcellos]

The length of the alliding cargo ship was 299 meters, while the bridge span was only 366 m, violating a basic rule of thumb of bridge design, which states that a bridge span should be at least 2 or 3 times longer than the length of the longest ship that will pass under it.

Weak Piers

The two main bridge piers, holding up the main bridge span over the shipping channel, were pairs of inclined hollow rectangtes tilting into each other, forming hollow triangle ends.

Each pier column was tilted into another tilted column, for the columns to hold each other up, instead of only holding up the bridge.

Figure 2:  A different ship, under the same bridge, December 2012. Notice that the bow overhang of the ship is much higher than the bridge pier fender. [ArtondraHall]
Figure 3:  One of the two bridge piers that held up the main span of the Baltimore bridge. Allision of this bridge pier caused the bridge to collapse. [LarrySyverson]

Concrete is stronger in compression than in tension, and designing a concrete column to lean into an oppositely leaning concrete column will cause both columns to fail if either one fails.

The columns should have been vertical, and spaced further apart. Boxes of steel trussing above separate vertical columns could have temporarily held the bridge up in the event of a limited number of columns being removed by allision (giving time to evacuate the bridge).

Seesaw Effect

The hollow concrete triangle shape, of the main bridge piers, converges to a fulcrum, at the apex of the triangle, where the contact interface between the pier and the bridge is only a line (one dimensional), causing the bridge to seesaw, with the pier as a fulcrum, if the other pier fails. That is what happened (viewed from the other side of the bridge):

On the right in this view, notice the end of the truss bridge initially lifted up in the air, then came back down like a seesaw, destroying that girder span pier.

Collapse of the girder pier and span could have been avoided if the seesaw effect had been reduced.

Forth Railroad Bridge

The seesaw effect could have been reduced by having a multidimensional contact interface between the bridge and the shipping channel piers. If that interface was planar instead of a line (2-dimensional instead of 1-D), less seesaw effect would have happened.

One way to make the interface two-dimensional is having four or six columns instead of two columns on the side of the waterway. Earlier we mentioned an advantage of extra columns was to make the bridge take longer to fail (allowing more time to evacuate people to safety). Now we mention another advantage of extra columns: to reduce the seesaw effect.

The topic of extra columns for truss bridge piers was brought up during the late 1800s, in the design of the Firth of Forth Railroad Bridge.

The original design called for linear contact interface at the anchor-to-cantilever piers. However, that plan was rejected by independent engineers that vetted the design, causing the design to be changed as follows:

Figure 4:  Firth of Forth Railroad Bridge, original design (top) and adopted design (bottom). The two-column seesaw design was replaced with four piers and box trussing. The updated design was constructed and still stands today. [Wiki]

The reason for replacing the seesaw design with four columns in the Forth bridge design was to reduce deflection of the bridge deck when two trains approach from opposite directions.

That same spreading of load transfer would reduce the seesaw effect.

Moment of Inertia

Another design error, worsening the seesaw effect during failure, was to have the bridge deck (anchor and cantilever arms) vertically offset, up from the seesaw fulcrum.

Figure 5:  The bridge deck (top of green arrow) was vertically offset upward from the seesaw fulcrum. Drawn by Arc Math Software staff over an independent photo. [BruceEmmerling]

If a seesaw had to be used (as was done), the pier should have extended to the bridge deck, with fulcrum at the bridge deck (top of green arrow). The diagonal bracing below the deck would still be used, connecting to the pier below the fulcrum, not at the fulcrum.

Having the pier too short created a moment arm that worsened the collapse. We explain by considering classic seesaws.

A seesaw is a straight beam with a seat at each end. The beam rests on a fulcrum below the middle of the beam. Children sit at each end balancing the beam.

Figure 6:  Children playing on a seesaw. The fulcrum holding up the seesaw beam is a horizontal pipe transverse to the beam. A child who weighs less can sit further out on the beam to gain leverage. [Wiki]
Figure 7:  Conceptual diagram of a seesaw. The beam rests on a fulcrum, with half of the beam on each side of the fulcrum.

Each half of the seesaw beam is a moment arm (lever). To get more leverage, sit further out on the beam.

Half of the beam is always on one side of the fulcrum, regardless of whether the beam is horizontal or not. In the photograph above, the beams of unused seesaws in the background are not horizontal, but still have half of each beam on one side of the fulcrum (and the other half on the other side).

Pushing the beam up and down moves the beam up and down, as the beam rotates around the fulcrum.

Pushing the beam toward the fulcrum, instead of up and down, does not move the beam, because it is fixed at the fulcrum.

Now, consider if the seesaw beam was vertically offset upward from the fulcrum:

Figure 8:  Conceptual diagram of a seesaw with beam vertically displaced upward from the fulcrum. The vertical displacement is an additional lever (moment arm).

The axis of rotation is now away from the beam, instead of at the beam. The beam will rotate around an axis that is far away instead of at the beam.

Each half of the beam will be on opposite sides of the fulcrum only if the beam is horizontal, as shown above.

If the beam is not horizontal, more than half of the beam will be on one side of the fulcrum, and less than half on the other side:

Figure 9:  Tilted beam on a seesaw with fulcrum displacement lever.

Tilting the beam makes one side of this type of seesaw heavier than the other side of the seesaw, taking extra force to push or stop rotation around the fulcrum.

This extra force is called moment of inertia.

In the bridge failure, it took extra force to raise the anchor arm above its girder pier, in turn releasing that force downward on the girder pier.

Hypotenuse Spreading

Not only does having a displacement lever create additional collapse force, it also creates a hypotenuse that causes the anchor arm to dig into its girder pier, causing the pier to bend and break.

Superimposing this bridge design on the displacement lever seesaw diagram:

Figure 10:  Orange indicates the vertical displacement from the fulcrum to the bridge deck. Blue denotes the horizontal bridge deck span (the anchor arm) from the seesaw fulcrum pier toward the girder spans (to the left).
Figure 11:  The vertical purple line on the left indicates the girder pier that the anchor was arm attached to.
Figure 12:  The red line is the distance from the fulcrum to the end of the anchor arm (to where the anchor arm span meets the girder pier). Due to the Cauchy-Schwarz Inequality, this distance (red) is longer than the length of the anchor arm (blue), because the vertical displacement (orange) is nonzero.
Figure 13:  As the anchor arm rotates downward, the horizontal distance from the fulcrum pier to the end of the anchor arm increases, becoming the longer red distance instead of the blue distance, causing the girder pier to be pushed away and break.

References

What is a Moment
MIT lecture notes

NTSB Hearing, 10 April 2024
Bridge design advocacy