Book-inspired Suspension Bridge in Virginia

We were delighted to finally receive photos of a suspension bridge that was inspired by our book, Building a Small Cable Suspension Bridge With the Cable Locking System.

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According to the builder, Mo Goldman, the bridge is just under 40′ feet in length and 4′ wide (basically half the length of our bridge) and is located in Virginia just outside of Charlottesville.

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The posts are aluminum, 13′ in length, 6″ round with 1/4″ thick side walls, easy for two guys to carry. The post holes are 3′ deep and about 2′ around; the posts are placed on a concrete footer prior to pouring around them. Everything was hand-dug and poured because they were limited to access with a Polaris on one side.

It was fun to see that Mo set up a temporary cable to move materials across. That’s how we moved our gravel for the opposite side, one bucket at a time. But Mo took it further and carried the posts, other materials, plus wheelbarrow and even himself across their “zip line.”

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Mo also followed the idea of setting up the catenary curve between two trees/structures located away from the creek to plan and build the cables and stringers on dry ground.

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Mo didn’t use our cable-locking system, but instead used a system often used for this type bridge – an appropriate length “eye” bolt placed in a drilled hole in the beam. The suspenders were then connected with a chain connecting link, which uses a threaded portion mating to a free spinning nut to open or close it.

He wrote to us about the bounce in his bridge which was more than he expected, though not a big deal. I noticed that he paid attention to harmonic resonance in the arrangement of the stringers so they were assumed off the “nodes,” so wondered if the decking material he used could be partly responsible (a suspension bridge is going to bounce, that’s a given). He used a material called Trex, which is a deck material made from recycled plastic and wood fiber. Trex tends to flex more than standard lumber does. We concluded that he needed to stiffen the deck, so now he is working on some ideas.

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Mo even put up a sign on his bridge similar to ours and inspired us to remake our sign so that it names the creek, too. We hope others who build a bridge based on what we did will also send us photos and notes about their building experience.

Meanwhile our book is available in paperback and as an ebook via Amazon.com.

 

To Gallop or Not to Gallop?

Another consideration when building my suspension bridge was harmonic resonance. While harmonic resonance was not completely to blame for the failure of Galloping Gertie (http://www.wsdot.wa.gov/tnbhistory/Connections/connections3.htm), I decided to address the problem because it could be an issue. After all, the bridge was bound to be a little bouncy, so why make it worse?

All objects have a frequency or a set of frequencies with which they will naturally resonate when disturbed in some way – be it plucking a guitar or stepping on a bridge deck. Each of these natural frequencies is associated with a wave pattern. When the object resonates at one of its natural frequencies, it vibrates in a manner so that a standing wave is formed within the confines of the object.

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A set of standing waves, in a “container” of a specific length. This set of waves is called a harmonic series, the grey dots are the nodes. (illustration by Marvin Denmark)

Harmonic resonance refers to the multiples of the strongest resonance of, in this case, a mechanical system. Resonance is the tendency of the system to absorb more energy when its oscillations match the system’s natural frequency of vibration. Resonance can cause swaying motions, but there are ways to reduce those motions. Since this was just an 80-foot long bridge, resonance was not a serious concern, but I decided to use one trick to prevent it from waving “on its nodes.”

In the case of resonance for this bridge, the waves will bounce back and forth between two boundaries: the posts. Nodes are always at equally spaced intervals where the wave amplitude (motion) is zero. The points where the cable connects to the post are two nodes. There is a possibility for one node in the middle, at third points, at quarter points, and so on, as seen in the previous drawing showing standing waves. The more excitation, the more nodes will potentially form.

I decided to space the suspenders so that they were not positioned on the nodes of the bridge span. I determined the exact points on my string model, then just moved the suspenders a couple of inches over to avoid the nodes.

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Drawing of the suspenders with measurements. (illustration by Marvin Denmark)

I assembled everything on dry land according to my plan so that I could tweek things fairly easily. The final product doesn’t bounce much, unless two people and a dog are all walking on it at the same time. Or maybe a bobcat. But at least my bridge doesn’t gallop!

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You can read more in my book, Building a Small Cable Suspension Bridge. There is a link to purchase it on my website: http://www.wildcatman.com.

Images, diagrams, and text copyright 2013 by Marvin Denmark unless otherwise noted. Please do not copy and post my content anywhere without my permission. Thank you.