The 4,000 lbs per strand web anchor myth
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.
Attachment 22650Figure 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.
Attachment 22651Figure 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:
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.
Attachment 22652Figure 3
If you would like a copy of this post in word format along with Excel spreadsheet, send me a PM.