how to account for curve in radial steel stair design

huangyhg

how to account for curve in radial steel stair design?
hello,
question:
i am attempting to design a curved steel staircase, but i am unsure of how to calculate the effect of the curve.
given:
the inside radius is 15'-9" and the outside radius is 19'-7".
the stair stringers span approximate 16.5'.  
the strair treads are 14 ga steel and 11" long, and the strain risers are 14 ga steel and 7" high.  the treads and risers have 1" overlaps and are stitch welded.
the stair stringers are 1/2"x12" steel plate, and the treads and risers are located mid-depth of the diagonal (and curved) stringers such that there is about 2.5" of stringer above and below the tread/riser.
solution?
so, here's my train of thought:
1.  the curved stringer essentially is equivalent to an eccentrically-loaded straight stringer.
2.  the moment from that eccentric load is resisted by the combined s of treads and risers.
3.  since there is a stringer on both sides of the tread/risers, the tread/risers are put into double-curvature moments, like a shear wall between two stiff diaphragms
4. the double-moment is resisted by a vertical coupled-force,
5. the vertical coupled-force pushes up on the inside tread and down on the outside tread, thereby amplifying the load in the outside tread.
how does that sound?
now to put some numbers to it...
thank you for your input!
mike
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this sounds similar to how they design curved bridge girders, see if you can get a reference on that
search eng-tips using keyword   "stair" and "stairs"
lots of hits.
the torsional moment (eccentricity) will be maximum near the mid span of the stringer and you might consider taking this back into 3 or 4 of the treads/risers in the immediate area and design all treads/risers to be the same.  a month back, i had a similar design; my concern was the 'bounce' due to impact from walking down stairs.  also the stair guard was glass.
dik
you will have near the two edges of the stair high tension stresses so u need to provide extra top and bottom bars all over its lenght at the ends alos reinforcment on the transverse direction should be top and bottom, both having u-shape