Previous posts on the new Narrows Bridge:

- History of the Tacoma Narrows Bridges
- The Two Towers I: Intro
- The Two Towers II: Concrete Thinking
- The Two Towers III: Anchor Management Classes
- The Two Towers IV: Out & Down
- The Two Towers V: The Struts
- The Two Towers VI: To the Top
- The Two Towers VII: Stairway to Heaven
- The Two Towers VIII: Spinning Beginning
- The Two Towers IX: Wheels Over Water
- The New Bridge at Christmas
- The Two Towers X: Compacting the Cable
- The Two Towers XI: Cable Banding
- The Two Towers XII: The Cranes
- The Two Towers XIII: Life on the Bridge

*For those who may be new to this series, I have been blogging the construction of the new Tacoma Narrows Bridge. See the above posts for more information on the Narrows Bridges, the engineering challenges, and a first-hand tour taken of the construction site.*

The towers are completed, the cables strung, the gantry cranes are in place–now it’s time for the big show: building the bridge deck.

Two shipments of bridge deck sections (of three total) have arrived from South Korea, and are waiting on the deck of specialized transport ships. One of these is moored just under the west end of the new bridge; the other waits in the Port of Tacoma until the first has been relieved of its load.

Several weeks passed after the gantry cranes were constructed on the cables. They moved around a bit–and were seen with odd-looking orange bags hanging from their cables:

Just before the first section lift, their purpose became apparent: they were for testing the cranes under load. The bags–12 on each crane, holding 9000 gallons of water–cumulatively weight over 450 tons.

Man, I haven’t seen water bags *that *big since my plastic surgery rotation…

Since the heaviest deck section weighs about 600 tons–and is lifted by two gantries–this test far exceeded the weight loads required to lift the deck sections.

Having passed the weight test, it was time for the first section lift.

The gantry cranes can move along the cables–albeit very slowly–but cannot move under the load of a deck section. So the cranes can be used to lift the sections *vertically*, but cannot position them *horizontally *after they are lifted. The transport ship is far too large and cumbersome to move around under the cables, so the sections must be moved to more mobile barges. Special barges are used which have lateral thrusters to stabilize and fine-tune their position under the cables in the rapid, ever-changing currents of the Narrows. But there’s one more problem: how are you going to get the sections from the transport ship to the barge, since the cranes can’t move the sections horizontally?

The answer is rather ingenious and surprising: move the transport ship–*laterally*.

The transport ship is equipped with a dozen large winches along its sides and ends, just above the water line, which are attached to fixed anchors. The cranes position themselves over the transport, lift a section vertically–then the winches pull the transport ship *to the side*, allowing tugs to move the barge under the bridge section. This is quite a treat to watch–take a gander at the time-lapse video below, which recorded the lift of the first section off the ship and onto the barge:

Tacoma Narrows Bridge Deck Build Time Lapse from CurrentCom on Vimeo.

The first sections were then lifted to center span, where their uncompensated weight caused the cables to drop nearly 12 feet–resulting in a shape more like a V than a gentle parabola between the two towers.

The degree of this dip can be appreciated by following the curve formed by the free suspension cables hanging from the main cables. Prior to lifting the center deck sections, they formed a gentle parabola upwards toward mid span; after the deck sections are in place, they gradually slope *downwards *from the towers to mid-span.

The sections are held in place by the gantry cranes as workers prepare them to be connected to the suspension cables and to one another.

One might think that the deck sections would simply be placed end-to-end, starting at the anchors or mid-span. But instead, they are placed in seemingly random fashion–as is this section between the Gig Harbor anchor and the West tower.

This is done to balance the weight load on the cables, preventing excessive stretch or unequal tension which could cause alignment problems later. The engineering math involved in calculating these loads is exceedingly complex. While I know my readers are well-aware of the formulas used to calculate these stresses and the resulting length of the suspension stringers (and have already worked most of these formulas out in their heads), I have provided them here for the less enlightened–and for graduates of the Washington State public school system:

Well, that’s all for now–next time we’ll take a little swing on a trapeze…

Incidentally, the shape of cables before the decking is lifted into place is a bit sharper than that of a parabola. That is because the weight of the cabling changes how the whole length hangs, and that form is called a catenary. (Once all of the decking is in place, the cables will once again form something close to a catenary, but it will probably be slightly different due to some of the decking weight being taken by the towers.)

The reason I mention this is because an inverted catenary (aka catenary arch) is the strongest arch you can build, literally. The pressure is equally distributed along all points. When I took ceramics, our teacher showed us pictures of a kiln they had built that was a catenary kiln; they’d laid the bricks over the form and removed the form, then had someone sit on it to demonstrate its strengthâ€” before they’d put any kind of mortar in it. In other words, loose bricks. Very cool.

*cough*

I just think that catenaries are cool…

See, I just

knewmy readers could figure this stuff out in their heads… thanks for the clarification, Durb.Fascinating story. And your pictures are marvelous.

Say, I was told that cables hanging freely in the way you described would follow a curve called a “hyperbolic cosine”. (At least, called that by mathematicians.)

However, the description I was given matches the description of a catenary.

If you know what the natural number

eis, you get the hyperbolic cosine by calculating the following:(1/2)(

ex+e-x)Of course, I think the hyperbolic cosine is cool…it’s got an elegance to it that not many math functions have.