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Re: Stacked Floor Joists

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Title: Stacked Floor Joists
Jordan,
 
        Actually, I believe Jim Lutz is correct.  If you take this curvature to the extreme the two beams will form a wheel with one beam inside of the other, hence, they can not have exactly the same radius of curvature.  I don't want to be bothered doing the arithemetic; but I would estimate that the ratio
 
R(bot)/R(top) is probably about 1.001
 
(just a guess) for beams deflecting about L/360, therefore, the stresses and deflections of the two beams are equal for most practical purposes.
 
Respectfully presented,
 
H. Daryl Richardson
----- Original Message -----
Sent: Tuesday, March 27, 2007 10:09 AM
Subject: Re: Stacked Floor Joists

You're considering that the ends don't move in your paradoxical case. By allowing the ends freedom of motion (rotation and lateral deflection), the curvature radii will be the same.
Jordan


Jim Lutz wrote:

I have been on vacation and just read this thread and offer the following paradox.

Stacked members may share the same deflection, but does this mean they share the same bending moment? If the members stay in contact, then the member on the concave side necessarily has a smaller radius of curvature and should have slightly higher bending moment than the lower member. (Remember 1/R = M/EI from basic mechanics?) So if the moments aren?t the same, how can the deflections be the same? That?s the paradox.

Jim Lutz, P.E., S.E.

720 3rd Avenue, Suite 1200

Seattle, WA 98104-1820

206 505 3400 Ext 126

206 505 3406 (Fax)

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