Impact on steel ropes

[gtsolid]

hello
i'm going to buy a climbing nut and i see that the maximum sustainable force is 9000N. this is insignificant for me because safety depends on body weight, temperature, fall height...
i think the rope is submitted to a strike and the intensity is given by the first and the third causes i wrote before.
if my weight is 70kg and i fall from and height of 3 meters, i will have an energy of about 280J. how can i link this energy with the sustainable force of the rope? maybe knowing the energy stored in the material?

 

[drawoh]

gtsolid,

If you lift a mass of 70kg by 3m, it takes approximately 2100N.m of energy, all of which will be recovered when you drop it. Where are you getting 280J from?

--
JHG

 

[desertfox]

Hi

You could calculate the force from the energy generated by the fall and equate it to the stored energy in the rope, in order to do this you need the modulus of elasticity and area of the rope.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[Sparweb]

gtsolid Falls are only dangerous when they occur in a gravity field, especially the local 9.81 m/s/s experienced locally on the surface of this planet.

desertfox...You could calculate the force from the energy generated by the fall and equate it to the stored energy in the rope, in order to do this you need the modulus of elasticity and area of the rope...

...and you will get a very interesting answer if you vary the assumed fall height!
I hope the OP does this calculation, because it will illuminate just where the load ratings come from on this hardware!

STF

 

[pylfrm]

gtsolid,

Manufacturers typically provide impact force ratings for dynamic climbing ropes in accordance with EN 892.


pylfrm

 

[chicopee]

It seems to me that the title is about steel rope, therefore, is the OP thinking about a steel cable for scaffolds or about independent safety steel cables to which workers on scaffolds are attached. An explanation would be helpful.

 

[gtsolid]

Hi, i did not remember the formula with modulus of elasticity and area of the rope. this should be the stored energy in elastic conditions?

 

[desertfox]

Hi

The formula for stored energy in a spring = 0.5*k*x^2

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[gtsolid]

the problem is not solved: i could obtain the "k" using "E" and "sigma" data, but wich value of "x" should i use?

 

[desertfox]

determine your rope length and x will fallout of the equations

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[gtsolid]

"x" i think is an elongation, not a simple robe length

 

[desertfox]

Hi it is the elongation but you haven't mentioned a rope length:-

k= A*E/l

energy = 0.5*k*x^2

so decide how long your cable is then determine its stiffness k knowing the area and modulus of elasticity of the rope.
The energy comes from the m*g*h, then transpose to find x the elongation. From this you can find the force but only when you decide on rope length.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[gtsolid]

hi
by doing this i obtain an elongation of 4,1%. i remember that materials have a proper limit of elongation in %, for example building steels of about 20%.
i also think this is stranded steel. how can i judge this result?

 

[desertfox]

Hi
Well in the case of the fall the force due to the energy wants to be less than the maximum specified by the rope manufacturer, percentage elongation is a specified limit for a certain gauge length see this site:-

http://www.engineersedge.com/material_science/ductility.htm

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[pylfrm]

gtsolid,

When you said "climbing nut", I assumed you meant something like these, most of which appear to be rated at 10 kN. Is that the case? Also, how will you be connected to the nut during the fall? I suppose it doesn't really matter for discussing the theory, but I am curious.

Anyway, the impact force should depend only on the falling weight, the rope properties, and the fall factor. The equation involving elastic modulus and cross section area given here appears to be correct.


pylfrm

 

[chicopee]

pylfrm is that link of yours showing these devices for rock climbing?

 

[zeusfaber]

Dynamic climbing rope (which is what I hope you will be clipping into your nuts) is constructed in such a way that, in a fall, it absorbs quite a lot of energy inelastically. For that reason, you're best off using either the curves provided by the rope manufacturer, or those in the standards that the rope claims compliance with.

There are essentially three things that determine the peak forces when you fall onto a system (either that, or just one). If you're fortunate, the three are:

1. The mass that falls

2. The nature of the stretchiest part of the system (in most properly designed systems, this will be a dynamic rope, or an energy absorbing lanyard)

3. The fall factor - divide the distance fallen by the length of that energy absorbing rope/lanyard.

and climbing ropes are specified in terms of the number of factor 2 falls they can absorb from a given mass before the peak force exceeds a given value. The remaining components in the system can then be designed to survive this peak force. Because the energy absorption is inelastic, successive falls generate higher peak forces as the rope properties change.

(If you're unfortunate, the peak force is determined solely by the strength of the weakest component in the system).

Some relevant demonstrations at [URL unfurl="true"]http://dmmclimbing.com/knowledge/how-to-break-nylon-dyneema-slings/[/url] and nearby on the same site.

Clipping direct into the steel wire on a nut would be even more scary than using a slack sling in place of a fall-arrest lanyard and would result in even higher forces. This is the only scenario where the elongation of the wire itself would be at all relevant (and even then, deformation of the harness and of the body of the climber would become significant).

Two bits of digressionary food for thought:

A falling climber is hurt as much by the deceleration as by the peak force; a lightweight climber or a child taking a big fall onto a standard Single rope is going to come to a much more sudden stop than somebody of average weight.

It is possible to achieve fall factors greater than two by shortening the belay as your partner falls past you. It's really tempting, but quite unwise, to do this.

A.

 

[SwinnyGG]

It seems to me that the title is about steel rope, therefore, is the OP thinking about a steel cable for scaffolds or about independent safety steel cables to which workers on scaffolds are attached. An explanation would be helpful.

OP is asking about steel rope because he's talking about a climbing nut.

For those not in the know: a climbing nut is a fall protection device which usually consists of an aluminum 'nut', which is a trapezoidal block which comes in many many sizes and specific shapes, which has been crimped around a loop of steel wire rope, to which a carabiner is attached.

The nut is used in a matching sized crack in a rock wall, and protects the climber by simple mechanical wedge action.

What is your exact concern here, OP? It sounds like you're calling into question how climbing nuts are rated, or something..

There are mountains of literature on the topic of climbing gear design, construction, and use- and any gear you can buy in a store is rated to various standards of safety. You should familiarize yourself with all of them before you attempt to engineer any climbing equipment that will be used in a life critical application.

 

[pylfrm]

chicopee,

Yes, the devices in the photo at my first link are for rock climbing as zeusfaber and jgKRI described, and the second link discusses fall factors and impact forces in that context.


Regarding the equation I mentioned, I should have clarified that it's correct for the perfect linear elasticity simplification (as claimed in the article), not necessarily for nonlinear inelastic reality.


pylfrm