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Steel Pan Stairs

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Does anyone have any insight on steel pan stair design. I have trouble with an analytical design for such a structure. For instance an 1 1/4" diameter post supporting a handrail/guardrail with the prescribed load of 100plf vert. and 50plf lateral at 36" centers can have a cantilevered load of somewhere between 150lbs to 260lbs at a height of 42" (at the landing). This will cause a load well in excess of the strength of the pipe. Then there's the question of how you resolve the weak axis bending in the stringer. It seems to me that from most stair systems I've seen that there more empirically designed than analytically design.
 
Any input would greatly be appreciated.