The disparity of numbers for the minimum breaking strength (MBS) of webbing anchors between some authors and instructors of rope rescue, and that of some published test data has led me to seek out the correct answer as to what the true MBS of webbing anchors is. For a brief rundown of what I am referring to, I will explain.
I have heard during rope rescue training, and also read in books that the MBS of 1 inch flat tubular webbing anchors is around 4000 pounds per strand. What this means is that for a wrap 3 pull 2 anchor you would have 4 strands times 4000 pounds for a total of 16,000 pounds. In the wrap 3 pull 2 the water knot is removed from the equation.
Now, published test results have put the MBS of the wrap 3 pull 2 to be about half of the mentioned above or 8000 pounds.
After some searching, reading, figuring, and computing I think I may know where these webbing anchor numbers have skewed from real world numbers.
For this discussion, refer to figure 1. To understand where the 4000 pound per strand comes from, we need to look at the pulley. Ignoring friction, a pulley as shown in figure 1 will have a mechanical advantage of 1:1, therefore; whatever weight is on the load end of the pulley will require an equal force on the other end to lift the load. The resulting force is doubled at the anchor point of the pulley. The web anchor uses the same concept, but now the load can be viewed as the anchor point thus distributing the weight equally between the two halves. It should be noted that in the case of the pulley; for the numbers to work, there is a 0 degree angle between each leg of the pulley, and this will be significant when looking at anchors.
Figure 1
With webbing anchors, understanding how angles have impact on anchor strength may be difficult to grasp at first. You might try visualizing to aid in understanding this concept. As a web anchor angle is increased, it becomes more akin to a straight piece of webbing, and thus a reduction in load distribution. See Figure 2.
Figure 2
One can see from figure 2 that with increase in angle, load distribution decreases, that is to say, at larger angles, the load on strand 1 or strand 2 equals the load.
So, the 16,000 pound load on a wrap3 pull 2 (W3P2) web anchor only works at a 0 degree angle. Once angle is introduced the MBS of the W3P2 decreases per leg. This can be realized in figure 3. For a 1000 pound load on a single loop web anchor, at 0 degree angle you will have a equal distribution of the load or 500 pounds per anchor strand. Now, as the angle increases, the load on 1 strand approaches the weight of the load until it reaches 1.
Note: In this discussion, the angles discussed are per strand, so in figure 3, the angle is illustrated for 1 strand. When looking at the webbing anchor, you are looking at two angles if you bisect the anchor at its center line since we are calculating per strand. The formula used in calculations was as follows:
Note: If using calculator use Degree mode, not Radian.
MBS per Strand = (load/ # strands) / cos of strand. See example:
Example 1:
We have a W3P2 anchor with an 8,000 pound load, and an interior angle of 120 deg. This is a 4 strand anchor, so we have:
MBS per Strand = (8,000/4) / 60 = 4,000 lbs.
Remember we are calculating per strand so we half the angle of 120 for the anchor, refer to figure 2. Using these math calculations we come much closer to published test data. Also worthy of mentioning, note how the MBS does not increase in a linear fashion, almost exponential after 30 degree.
I am not a scientist, so my numbers may be wrong, and I welcome any corrections.
Bottom line here is; 4,000 pound per strand for a W3P2 anchor is unrealistic when you account for angles.
When constructing an anchor, keep your angle as small as possible. This may require a longer piece of webbing.
Figure 3
If you would like a copy of this post in word format along with Excel spreadsheet, send me a PM.
Thanks
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12282012, 01:38 AM #1
The 4,000 lbs per strand web anchor myth
Last edited by MichaelXYZ; 12282012 at 01:56 AM.

12282012, 10:12 AM #2
 Join Date
 Oct 2002
 Location
 Port Allen, LA
 Posts
 148
Good morning Michael,
This is a pretty common misconception. If you have an equal force on each side of the pulley the load doesn't move. The system has to be unbalanced to make it work. Apply more force to the end and the load moves up......apply less force and the load moves down.
As far as the rest of it goes, you are on the right track. It is always important to remember that fires, haz mat incidents, technical rescues, etc., don't happen under laboratory conditions. Any figures you find in a text book, msds, etc., may be much different in a realworld setting. Everyone should do some testing to increase their understanding and play it conservatively in an emergency.
Mike Dunn

12282012, 08:06 PM #3
Hi Mike, thanks for your input. I did mention the pulley system was frictionless (not real I know), so in that case the 1:1 pulley I mentioned would behave as I described as the forces of gravity would force the system to reach equilibrium. An example is shown in diagram.
From a paper on pulley's.
Fundamental Concept 1: In a theoretical, frictionless system (Fig. 3), a pulley equalizes the
tension in both legs of the rope that passes through it. In the real world, the same principle
applies, minus the effect of friction within the workings of the pulley in question.
http://www.ncstaff.net/oed/Pulley%20MA%20Systems.pdf
You can give it a try with this online pulley simulator.
http://www.compassproject.net/sims/pulley.html
I know it may seem silly for me trifle with this, but for some reason I just had to try and understand this?Last edited by MichaelXYZ; 12292012 at 03:44 AM.

01022013, 06:36 PM #4
 Join Date
 Mar 2010
 Location
 eastern WA
 Posts
 93
Attached is a tutorial on anchor physics that I created; don't know how helpful it'll be....Let me know if elaboration is necessary or if it just stinks. I tried to show where the T = L /[2cos(half angle)] equation comes from.
The attached calculations are useful for estimating the webbing tension but are NOT useful for predicting the load at which failure occurs. As has been mentioned a few times before, failure due to melting of the webbing where it pinches between the connection biner and the other strand of webbing occurs well below the load one would predict using T = L/[2cos(half angle)].

01022013, 06:47 PM #5
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 Mar 2010
 Location
 eastern WA
 Posts
 93
...and, I forgot to mention that your conjecture about dependence on angle is indeed correct.

01022013, 08:27 PM #6
Thanks for posting that. I like the way your formula takes into account both halves of the webbing anchor where mine only works for half the anchor. I graphed your equation and mine. The curve fit is the same only mine is higher on the Y scale due to not doing the divide/2. My equation in red.
I will use your formula next time I have a need.
Thanks and Happy New Year

01032013, 11:39 AM #7
 Join Date
 Mar 2010
 Location
 eastern WA
 Posts
 93
You're welcome.
One might notice on your graph that there's not much change in the tension between a half angle of 0 to 45 degrees (full angle 0 to 90 degrees) and then the tension starts taking off above 45 degrees (full angle 90 degrees). That's why we're told in training to try to keep the full angle to less than 90 degrees.
Moral: If the full angle is less than 90 degrees, you don't gain much by lengthening the webbing.

01032013, 01:31 PM #8
 Join Date
 Mar 2010
 Location
 eastern WA
 Posts
 93
Also, to clarify, the equation I "derived" is for one strand of webbing on each side i.e. for a "wrap one pull one". For a W3P2, you'll need to divide the T you calculate by 2 since each side has two strands of webbing that support the load (each strand supports L/4 instead of L/2).

01032013, 05:13 PM #9
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 Mar 2010
 Location
 eastern WA
 Posts
 93
1st file reposted with correction of small error. Apparently I don't know how to divide 180 by 2.

01132013, 09:13 AM #10
 Join Date
 Apr 2001
 Posts
 169
What a talented group of guys on this forum!!
There are a few reasons you don't see these "physics" calculations in training manuals.. First, the audience of the manual will make a big impact on what the content is. When I developed my book, we had to work with the publisher to determine their sales focus. My book has predominately been sold to academia; state programs, tech schools, and fire academy's. This makes it difficult to include the more difficult math functions. Not every State instructor has a grasp on technical concepts like you guys. When schools see this technical information, it also turns them off to the product all together.
The other reason is it simply is a fading art. We are in the mode of preRiggs and anchor straps that will hold 40kN easily. Our forefathers ( Larson, Smith, Mothner) didn't have the same equipment back then. They were forced to learn advanced rigging concepts. See Mike's thread Reluctance to Change. I consider myself pretty proficient, but even I have a hard time with the math. Some formulas work great, others have been way off the mark when put a Dyno in the system.
I have been considering putting together a Physics of Rope Rescue Program and bringing in a "Guest Speaker" who knows this stuff inside and out. Do you guys think this something worth investigating?

01132013, 02:21 PM #11
Third reason is that in Rope Rescue we are not hanging more than 600# on the anchor. That is why the equipment is built strong, so you can rapidly make patient contact and remove the patient from the enviorment. If you are rigging for structural collapse, than you need to keep weights in mind, but then we'd be using some heavy rigger equipment, bolts and/or air bags at that point.
All the theory is great practice, but lets face it; a single strand of webbing would hold the weight of you and a patient with a lot to spare.~Drew
Firefighter/EMT/Technical Rescue
USAR TF Rescue Specialist

01142013, 09:06 AM #12
 Join Date
 Jan 2012
 Posts
 76

01142013, 12:27 PM #13
No I agree completely, just couldn't stand to look at graphs and charts anymore. Better than knowing what the webbing strands each will hold would be understanding critical angles, forces applies to both anchors or changes of directions, and understanding limitations.
I see the need for this understanding, and a lot of good research like this is shown at International Technical Rescue Symposium, NCRC and the such. We use this data to set the systems we use and at a higher level understand them. When called into a technical rescue we build a system quickly, using principles that are taught in the many classes we have taken or instructed over the years. While the data shown here reflects in what we build, we generally over engineer our systems to negate these higher level mathamatics. As long as we are using suitable anchors, proven systems, rated software and hardware and keep in mind the forces applied by loads and angles to our equipment, the rescue works.
I have wrapped myself around the axel many times figuring out simular problems like Micheal has here. I then laugh at myself at the ammount of work I have put into all the math and science because it has not changed anything we do. I still wrap an anchor with a piece of rope or webbing in various configurations, attach a haul system or DCD to it and get the job done.
Becoming a bigger fan of KISS (keep it simple ****head).~Drew
Firefighter/EMT/Technical Rescue
USAR TF Rescue Specialist

01142013, 02:36 PM #14
 Join Date
 Mar 2010
 Location
 eastern WA
 Posts
 93
Jeff
The understanding is what keeps our systems simple, efficient, and safe.
There's definitely a place for this; at least two rope rescue schools have been incorporating physics in their instruction for quite awhile.
It's a matter of finding rope rescue practitioners who enjoy, understand, and can teach the relevant physics.
I emailed you...

01152013, 02:08 AM #15
I like to know how things work, it helps me remember and understand why we do things, but that is just me. I am not the type that just see's and remembers. I think this would be a good webinar, just make sure to accept Paypal
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