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Re: Deflection Criteria

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Mark:

I will dicker slightly with you...I believe that L/240 places a limit on
deflection not slope.

And code provision does work cause it is based upon some rational
structural theories.  If one takes L1 as the length of a cantilever and L2
as the length of a simple span beam, and then defines L1=0.5*L2 and plugs
that information into the typical equations for either simple beams or
cantilever beams, it all works out rather close.

For a uniform load, if you plug L1=0.5*L2 into the cantilever maximum
moment equation one gets w*L2^2/8 which is the maximum momment for a
simple span beam of L2.  If you plug L1=0.5*L2 into the cantilever maximum
deflection at the tip equation (i.e. w*L1^4/[**E*I]), then one gets
w*L2*4/[128*E*I] which is rather close to 5*w*L2^4/[384*E*I] which is
basically w*L2^4/[76.8*E*I].  Thus, the "equivalent" cantilever deflection
is actually LESS than the simple span beam deflection, which thus makes
using the same limitation more conservative in theory.  I would assume
that you would get similar results for different types of loads (i.e. a
point load).

The point is that the code provision IS based in some valid reasoning,
even though the two situations don't result in the exact same performance.

Regards,

Scott
Adrian, MI


On Fri, 24 Mar 2006, Mark Gilligan wrote:

> There seems to be a mistaken impression that the
> deflection criteria of L/240 is related to curvature.
> If we wanted to control the curvature the criteria
> would be based on L*L.  For bending members L/240
> simply places a limit on the slope at the end of a
> simply supported beam.  This can be seen if you
> differentiate the equation for the deflection of a
> beam.
>
> The code criteria seems to "work" for typical spans,
> but is lacking in rigor.
>
> Mark Gilligan
>
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