Steel cables for lateral stability - pre-tension force? 1

[nivoo_boss]

Hey everyone!

Let's say I design a steel frame building and I would like to use cables for lateral stability. How should I determine the required pre-tension in the cables?

 

[centondollar]

"I may be misunderstanding you but I don't see the pre-tensioning force reducing the ultimate strength of the brace. I think of it like this. A brace member pre-tensioned to 50 kips would see no additional stress from an externally applied load beyond it's pre-tensioning stress until that external load exceeds the pretension force. Even then, they are not additive."
After the external tension exceeds the prestressing in the rod, the tensile force increases and the capacity is achieved much sooner. The forces are additive once pretensioning is overcome by the external load.

Initial force due to pretension (after losses, say)
F_i = deltaL*E)/(L0*A)
where deltaL = measured length change of the pretensioned rod, L0 = rod original length, A = rod area, E = rod young's modulus.

Total force after pretension is overcome:
F_total = F_i + F_external

Maximum force:
F_max = (F_ultimate)/A

The maximum additional tensile force after prestress is lost is less than or equal to
(F_ultimate-F_i)/A

Thus, the force that can be added after pretensioning is lost (F_external > F_i) is limited. The capacity of the rod does not increase by pretensioning, and the available capacity after tensioning is lost is the difference of ultimate force capacity and prestressing force after losses.

 

[azcats]

I don't think I've seen it mentioned here yet, but there's an initial stretch on new cables that isn't elastic but permanent. The tower code requires that new cables be pre-stretched to almost have the rated breaking strength.

 

[dik]

Preloading the cables with any useful load, only puts an added load into the system.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[Brad805]

If we take the general case in the OP, is anyone doing any of this for these buildings? I am not sure I recall a tension spec on the PEMB dwgs I have, but it has been a while.

 

[bones206]

I've seen some permanent wire rope bracing at my local indoor soccer arena, which has huge clearspan trusses. But I haven't really seen it in a typical PEMB, aside from temporary erection bracing.

That got me thinking, and I dug out my copy of AISC Design Guide 10 Erection Bracing of Low-Rise Structural Steel Buildings (Second Edition). Turns out there is a wealth of really good info on wire rope bracing, including recommended preload to remove "constructional elongation", which is what azcats was referring to. Check it out starting on pg. 53.

 

[BridgeSmith]

I had to go back to basics and draw a free body diagram, but once I did it looked obvious that STrctPono, Ingenuity, and human909 were correct. Then I read what steveh49 wrote, and I had to reconsider - the FBD doesn't account for the deformation that has to occur in order to transfer the force from one cable to the other. If the frame is braced by compression struts, which will by necessity be of a much larger cross section that the tension cables, the compression struts can be assumed not to deform (change length). Therefore, in order for load to be reduced in one of the cables, it has to get shorter and the opposite diagonal cable has to get longer, which means, unless it's already yielded, there has to be an increase in stress that corresponds to the increase in strain.

Also, each cable pair and corresponding compression struts are part of a larger system, where the pretensioned members produce a stiffer 'diaphragm' in the structure, which will result in the pretensioned members resisting more than their 'share' of the externally applied loads.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[human909]

I had to go back to basics and draw a free body diagram, but once I did it looked obvious that STrctPono, Ingenuity, and human909 were correct. Then I read what steveh49 wrote, and I had to reconsider - the FBD doesn't account for the deformation that has to occur in order to transfer the force from one cable to the other. If the frame is braced by compression struts, which will by necessity be of a much larger cross section that the tension cables, the compression struts can be assumed not to deform (change length). Therefore, in order for load to be reduced in one of the cables, it has to get shorter and the opposite diagonal cable has to get longer, which means, unless it's already yielded, there has to be an increase in stress that corresponds to the increase in strain.

I now agree. I was wrong and too hasty in my comments.

I was going to include a few weasel words in my post because in the back of my mind I was saying to myself don't post non-intuitive assumptions before checking them! But I didn't an I deserve a negative pink star!

It was true about the recent structure I analysed. On that one it took me a while to realise that the pretension wasn't additive in the circumstance I was dealing with. It becomes easier when you start thinking about things in term of a change in strain diagram.

 

[Brad805]

Thanks for pointing that out Bones.

 

[STrctPono]

I too apologize for posting that comment. I was rationalizing it incorrectly with a pretensioned element locked off on a rigid body not part of the system. If the pretensioning force were locked off at one of the nodes of the braced frame then statics would tell you that the additional stress in the brace would increase. I recently worked on two projects in the past month where we utilized a system very similar to the former and I incorrectly applied it here. My apologies to BridgeSmith and to human909 and Ingenuity. I will not edit my previous post but rather leave it there as my mark of shame.