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I have a steel single speed bike and want to add a rear brake. All is good expect there is no cable stops on the top tube. I want to bond two cable stops to the under side of the top tube.

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Don't use cable stops. The biggest load those stops will ever see is when you grab your brakes hard for an emergency stop. So you're likely to find out that whatever you did to bond the stops to the frame wasn't strong enough or fatigue-resistant enough at the absolute worst possible time.

And you'll never be able to know if your work is fatigue-resistant enough. You can only find out that it wasn't - and you'll know that only after it fails.

Run the outer housing the entire length of the cable. All you need then is a few tie wraps to hold the cable near the frame.

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    If you want something that looks more finished than zip-ties, you can get old-school clamp-on cable guides, but they're functionally identical. – Adam Rice Aug 4 at 19:02
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    Unless the bonding technique is 'welding' or 'brazing'. Then you can be pretty sure the bonds are strong enough. – Argenti Apparatus Aug 4 at 20:08
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    @ArgentiApparatus If you're practiced at doing that... – Andrew Henle Aug 4 at 20:28
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    +1 for just running the outer housing the whole length. However, I would contradict your assertion that the biggest brake-load is at an emergency stop. A properly working brake system should lock the wheels and/or throw you over the bars if you ever put maximum force on it, and it's part of the essential skills of cycling to regularly practice going to the maximum safe brake pressure, so you can get that pressure right even at an emergency. So, the brake stops should fail during one of these practice sessions (and then you'll still have the front brake left), if there really is a weakness. – leftaroundabout Aug 5 at 11:24
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    @leftaroundabout But no one practices modulating the rear brake. – Andrew Henle Aug 5 at 15:23
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Beside a professionally done welding, clamp-on cable stops should be a reasonably reliable solution.

Problem solvers

Origin8

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1

Do you already have the cable stops? If not, then you might consider looking for ones that are attached by rivets. That will reduce the amount of skill and tools you'll need and will still give you a pretty strong bond (although it probably won't be the strongest as per your question, that is still probably welding or brazing). You'll need to make sure the rivets are the right size for the depth and diameter of the hole, as well as being thick enough to withstand the shear forces.

The ones sold here have holes for two 1/8" rivets. enter image description here

If you go this route, I strongly encourage you do your own calculations, but as a rough guide according to NASA the 95 percentile maximum grip strength for males is 729N. On my bike the brakes have a lever ratio of roughly 1:3, which says we can assume a conservative estimate of 2200N of maximum force applied to the cable stop (if you're a 95th percentile male, squeezing at maximum grip strength in test settings that is!). I'm pretty sure this is within the capabilities of commercially available rivets (the fact that these things are even available for sale, not to mention being commonly used on carbon road bikes is testament to that!).

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