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Re: railing design

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Presuming from the Q and A so far that the verticals are steel, and all
alike, and cantilever up from a moment connection at the stair stringer to a
steel flat bar at their top ends, to which all the verticals connect
rigidly, you have a classic "beam on elastic foundation".

The code horizontal load of 200 lbs. is a point load (isn't it) acting
horizontally on the top rail "beam", which spans horizontally. The
resistance is the whole array of verticals, each of which supports the beam
with a springy resistance, the amount of which depends on the deflection
imposed. The horizontal stiffness of the top rail, with respect to the
stiffness of each vertical against horizontal load at its top end, is the
basis of analysis.

Timoshenko presents a complete solution in his texts on Strength of
Materials, Part II, dating from 1930 and still in use at least into the
1960's. His solution also covers the case where the applied load is
distributed over a certain length of the "beam", or there are multiple point
loads. There are formulas, curves, and tables.

If an approximate solution is adequate, it could be done by trial and error
as Richard Lewis suggested, keeping in mind the basic principle.

There are code limits for stairway handrail dimensions that relate to a
person being able to grasp and hang on. Lateral stiffness wants to be enough
that subjective confidence in the sturdiness of the thing is not impaired.  

Charles O. Greenlaw, SE   Sacramento CA
********************************************

Original question:
>i have a handrail that has 1/2" X 1/2" verticals at 4" o.c. with a
>nominal flat stock top horizontal.  in applying the code required 200 #
>horizontal load what effective width is allowed.  another words how many
>verticals can contribute?
>
>another question is, what is the codefied deflection criteria?