Break down the cable support reaction into its components (dead, live, wind), and factor up to LRFD to analyze the structure. Or analyze the structure with ASD combinations and capacities (if not concrete).

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The name is a long story -- just call me Lo.

but the cables to the structure are transmitted as axial tensions, those tensions for cables are analyzed non-linearly, that's my doubt

Non-linear analysis still results in reactions that can be expressed in Cartesian directions. I don't understand your concern.

You may not be able to model your cable and structure simultaneously, depending on the limitations of your software... But that just requires two models and good bookkeeping.

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The name is a long story -- just call me Lo.

Cable calculations are always nonlinear.... you cannot add up results from different load cases
Different load factors need to be considered for cable pretension
e.g. lower pretension and higher pretension

Lo is right; the tension in the cable has 3 components, horizontal perpendicular to the span (usually due to wind), vertical (usually gravity loads), and parallel to the span, due to the equilibrium forces resolved from the other 2, based on the deflection (sag) of the cable. For the span wire traffic signals structures I design, I factor the loads before applying them, so that the tension is automatically a factored load.

For example:

Combination 5 (ASD): D+0.6W , I get the maximum reaction = 3105 kgf this this would be the cable tension = T

In the analysis of the metallic steel structure the combinations used are those of LRFD, for the combination 2: 1.2D + 1.6L + 1.0T (because the tension is present) what tensión should apply? . The maximum I got that is combination 5 of the ASD (3105 kgf) or another?

I don't think I'm understanding your combination. The tension due to DL is the vector sum of the DL acting vertically (call it the Y direction) and the horizontal force acting parallel to the span (X direction) = DL / SIN of the angle of the cable from the horizontal (or technically a straight line between the end anchorages). If you add a horizontal wind load (in the Z direction) it will also produce a force in the X direction, again as a function of the angle of the wire from the X axis. The tension in the cable is the vector sum of the 3 orthogonal forces as the square root of X^2 + Y^2 + Z^2. As I said, if you use factored loads to calculate the forces, your tension is a factored force resultant, which you can check directly against the ultimate capacity of the cable.

How the ultimate capacity of the cable under LRFD is related to the breaking strength or working strength (which is all I've seen published for steel cables) is the part I'm not sure about. We'll probably have to come to a decision about that soon, since we're going to be moving to the AASHTO LRFD sign specifications for design soon.

While you might be using ASD for the cable design. For the LRFD reactions, how much extra effort is it to add in the LRFD load cases required to the cable model? I'd just do that as it seems the easiest way. While you are at it, why not use LRFD for the cables design and avoid the ASD conversion troubles?

Because in Standard Structural applications of steel cables for buildings, states cable must be design with ASD method.

That's fine if the code is inflexible in this situation, but just add LRFD cable cases purely for designing the building, rather than trying to factor after the analysis. I'd be checking the cables for the LRFD case as well even if the code does not strictly require it to close the design loop.

Remember for most design codes that ASD is basically a method of the past.

It isn't always easy to design something to LRFD if there haven't been established strength reduction factors (Φ) determined...so ASD may be the only option.

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