Why does the NCARB solution (as I also show) has the ramp segments width at 60" throughout? Why is it not reduced to 44", as shown in other solutions?
I think this is because your landings need to be 60" x 60" anyways. With this configuration you'd end up with dead space between the ramps. You could possibly make the lowest 2 runs 44".
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The least dimension in the direction of travel shall be 60 inches. If ramps change direction at landings, the least dimension shall be 60 inches." - NCARB program.
Also, is there a minimum clearance between the end of the handrail extension at the bottom of the stair and the wall?
This confuses me also. Presumably it needs to be 44", but it makes a mention of handrail projections. I assume that the handrail projection doesn't apply when it is an extension protruding perpendicularly into the clearance. On the other hand you might be able to get away with a 4" encroachment; reducing your minimum clearance to 40"? I'd stick with 44" to be safe.
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Maneuvering Clearances
1. The minimum width of an exit route shall not be less than 44 inches.
Projections into a required exit route width are prohibited, except for handrail projections"
Also, I believe you need to provide a rail on the open side of the smallest ramp. Even though it is only 3" rise (so a handrail isn't necessary) it is an "open side" so you need a guardrail. Since handrails and guardrails are the same in this vignette, you need the handrail.
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Open sides of landings, floor surfaces, ramps, and stairways shall be protected by a continuous guardrail." - NCARB program
The only time you wouldn't need a handrail is if your ramp was up against a wall or a higher ramp (with a guardrail) and was less than 6" rise. (So probably you are right in not needing one on the opposite side of the 3" ramp). My philosophy on this, though, is that if it doesn't encroach on other requirements, you may as well show a handrail.