East Campus has a long tradition of building large wooden structures and improving/ building off of previous years' large wooden structures. This past year, I set out to make a better way of building our rope bridges. This rope bridge project ended up being a small part of Elena's & my Clubhouse structure, itself a small part of the East Campus 2016 REX Fort. (she has a blog too!)
|Photo credit: Wesley Lau|
An issue we had with the 2015 East Campus rope bridges was that their nylon-webbing cables were directly tied to steel eyebolt anchors, and as the bridge bounced up and down the steel eyebolts would fray their cables. We had to conduct periodic maintenance on the rope bridge to replace cables that frayed too much. In addition, the bolts themselves would bend from the weight of the bridge and the people bouncing on it. It was impossible to observe the effects and extent of bolt bending until we removed the bolts during deconstruction, so I decided to devote my 2.671 (Measurement and Instrumentation class) experiment to bolt bending.
A short explanation of theory:
|Pulling on a rope|
Any amount of load present on a rope (including the rope's own weight) will cause the rope to sag. You can express what forces this rope imposes on its anchors with the equation
where each anchor supports half the load (vertical component) as well as opposing tension from the rope (horizontal component). The upwards force component applies a torque on the anchor scaled by the span of the bridge,
When a person walks across the bridge, the load shifts from being mostly supported by one anchor, to being equally supported by both anchors, to being unequally supported again.
Turns out bolts really don't like being pulled at anchors. In fact, eyebolt strength drastically decreases the greater the angle becomes.
graphic from http://farmallcub.com/phpBB2/viewtopic.php?p=208393
It's actually rather terrifying. Below are the manufacturer specifications for the bolts used in the 2015 EC Fort, my 2.671 project, and the eventual 2016 Fort/Clubhouse.
Manufacturer specifications for decrease in strength with angular loads
Bolts are optimized for strength in the axial direction. If not loaded along their axis, they lose all mechanical advantage from compressing the substrates and instead become just a simple rod of "bolt steel". Thus when loads pull at extreme angles, you can expect bolt strength to drop to as low as 25% of their advertised strength.
Not only that, but if you pull on things long enough with enough force you can weaken them even more. The hope for this rope bridge was that we wouldn't keep it running long enough to run into this problem, and luckily we didn't! But fatigue concerns still gave us some panic.
|Zhu, Y. "Fatigue Strength", Strength of Mechanical Components Course Notes|
I approached the problem by looking at stress-strain curves. For most materials, you need to put some amount of force into yanking on stuff for it to stretch. Both aluminum and nylon rope will behave like a spring - they will stretch linearly with force. But if you keep pulling with steadily increasing force, the material structure will get compromised and no longer behave like a spring (or return back to its original position!) For our rope bridge's sake, we treat this phenomenon as structural damage.
I fabricated a jig to anchor eyebolts 0°, 30°, and 45° offset from a vertical loop of webbing, and then conducted pulling experiments using the Instron machine.
Rope and eyebolt-jig set to fix the bolt at a predetermined angle
Different kind of fixture to characterize the bolt without including rope
I made a rough, but functional angle jig from a block of hexagonal aluminum stock
You can see the point where applying steadily increasing force suddenly makes the bolt stretch more than usual. At this point the bolt is damaged.
It turned out that while experimenting on bolts resulted in expected graphs, introducing another compliant object - rope bridge - produced weird graphs that were difficult to relate back to physics.
You can see the final paper here.
One thing was for sure - a rope bridge that didn't need to worry about angular loading was going to be a very nice bridge. Wesley introduced us to the idea of saddle joints - create a protrusion to move the location where the rope changes angles away from the eyebolt itself and on something more forgiving.
Critical design requirements of this saddle joint were to 1. ensure that the rope was in line with the eyebolt axis, 2. sustain high compressive forces without crushing its wooden frame, and 3. allow enough space to tie knots!
#2 in particular required a bunch of structural calculations. We also needed to calculate how much abuse our wooden towers could sustain in order to determine how many people could use the bridge at a time.
This particular saddlejoint used sch. 80 black steel pipe with a quarter-circle cut out. It sat ~1.75" above the wood, which provided enough vertical clearance to mount eyebolts and their washers. It just barely cleared enough horizontal space to allow knot tying and rope tensioning, which forced creative thinking when tying the bridge cables together. Future saddle joints should consider having more horizontal space.
As you can see in the video below, movement of the bridge is redirected by the saddle joint into just axial tension. Because the ropes do not rub against the eyebolt surface, we saw no visual damage even after a large dance party and subsequent week of near-constant use. Even better, this saddle joint performed ideally enough at allowing only angular displacement that we couldn't visually find any rope damage at all, which indicates very little allowed extension or side-side motion of the ropes.
The rope bridge itself consisted of two double-rope main cables of 4000-lb nylon webbing, woven through 2x6 foot planks. We relied heavily on Liz, Thomas, Maya, and SNP's ropes expertise to choose knots and provide the required amount of tension.
Polypropylene 3/8" rope strands were used for the railings. The upper hand railings consisted of three braided strands, in order to be thick enough to grab comfortably.
We had expected either the bolts or the rope to be the strength-limiting factor of the bridge, but in practice our bridge 2x8 spandrel was the weak link. With enough people (5 bouncing up and down) we saw the spandrel flexing. Future bridges would probably have better performance using a bridge spandrel consisting of two paired 2x8 beams bolted through the 4x4 columns and some 2x4 flexion bracing.
However, during operation we didn't have to actively limit the bridge occupancy at all. Our bridge was sufficiently creaky and scary-looking that rarely more than 4 people were on the bridge simultaneously, and no one tried to use it as a dance platform.
Photos of the completed rope bridge below!