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.

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