Post-tension 7 wire strand bending stress

[Baffled Engineer]

I am designing a new post-tension system for an existing timber truss. A requirement from the stay cable design guide (PTI DC45.1) is I include local bending stresses from the turning points of the post-tension wire in addition to the axial stress.

When I calculate the bending stress per the equation provided (see below), I am getting 6200 mPa of stress which is way above the specified tensile strength of the new 7 wire strand I plan on using (fs'= 1860 mPa).

I find the radius of curvature of the turn is too tight but the existing post-tension system on the timber trusses have a tighter radius of curvature which clearly works. I was wondering if anyone can provide me comments on how this works and how I can make it work with the same turning point. Thank you.

This is a picture of the existing turning point.

This is the formula from PTI.

radius of curvature of the turn = 130mm
7 wire strand dia. = 12.9mm
X = 130 + 12.9/2 = 136.5mm
E = 197000 mPa
r = c/c of king strand to outer strand (per PTI) = 4.3mm

f,bending = (1/x)Er = (1/136.5) * 197000 * 4.3 = 6205 mPa

 

[IDS]

What we can see on the above pictures is not allowed.....regadless of formulas

The question is how to avoid it. Quoting from Agent666's link:
"Figure 1.4 shows a graph of the D/d ratio versus the reduction in breaking strength thisformula leads to. As can be seen, small D/d ratios give a large reduction in the capacity of the wire rope. While this reduction factor is used in almost every engineering application
where wire rope is bent, it is unclear how this formula is derived or what it is based on. Therefore the main research question of this paper is:
How does the forced bending of a steel wire rope around a shackle aect the break load of the wire rope?"

Note that the paper relates to wire rope rather than 7 wire strand.

Practice in use of deflected strand in precast pretensioned beams should be relevant, but this seems to be treated as precasters business, and I couldn't find any specific limits on minimum radius.

The link below is a Portuguese (English language) paper on external prestressing:
External prestressing as a strengthening technique

"For the purpose of avoiding damage of the prestressing cables and of the protective ducts, due to excessive stresses, the radius of the external prestressing cables in the deviation areas should be limited. When using smooth polyethylene ducts, the minimum value should be calculated using the following expression [8]:" see link for the equation (minimum radius = 2.0 m)

So in summary:

1) Clearly the detail used in the existing structures produces unsatisfactory results (both in the strand and the highly loaded timber).
2) If there are any well defined limits for this sort of structure they are not easy to find (but timber building structures is not my area, so there may well be information out there).
3) It seems likely that a much greater radius of curvature will be required.
4) Ensuring effective long term durability of the strand needs to be considered, which will require considerations other than stress in the strand.


Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/