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Re: Deflection of Cantilever Beam with Moment at Free End

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It really isn't much more difficult to include the back span effect.  You simply need to add the rigid body deflection, a*theta to the ML^2/2EI determined with the cantilever fixed.. Where a = the cantilever span length and theta is the rotation at the end of the back span adjacent to the cantilever.  theta = ML/(3EI) [p. 49, "Structural Engineering Formulas" by Ilya Mikhelson]. L = the backspan length, M= the cantilever moment and EI are for the backspan. 
 
deflection = ML^2/(2EI) + a*(ML/(3EI)) 
 
As gil@raptsoftware indicates, it will usually be significantly more than the fixed cantilever case. 
 
I'll leave the PDE solution for the problem to Humberto! :<)  That taxes my brain too much for a Saturday morning.
 
Regards,
Bill Cain, S.E.
Berkeley  CA
 
In a message dated 3/26/2005 12:19:37 A.M. Pacific Standard Time, gil(--nospam--at)raptsoftware.com writes:
This is the deflection assuming the cantilever is fixed at its connected
end. You also need to allow for rotation in the back span assuming you have
a continuous member. To do this is much more complex but could easily
result in much larger deflections for the cantilever, depending on the
length of the back span compared to the cantilever..

At 01:47 AM 26/03/2005, you wrote:
>M. David Finley, P.E. wrote:
>
>>The AISC manual conveniently gives the formula for the deflection of a
>>cantilever beam for a concentrated load, a uniformly varying load, and a
>>concentrated load.
>>
>>However, it does not provide the case of a cantilever beam with a moment
>>applied at the free end of the cantilever.  Can anyone provide me the
>>formula?  I can get the value from my frame analysis program, but I want
>>to be able to check it by hand.
>>
>>Thanks,
>>
>>David Finley
>>
>>
>>
>>
>>------------------------------------------------------------------------
>>
>>No virus found in this incoming message.
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>>
>M x L^2
>_______   = deflection @ free end
>
>    2EI
>
>According to Roark, 6th ed, Table 3, case 3a, pg 105.
>
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Regards  Gil Brock
Prestressed Concrete Design Consultants Pty. Ltd. (ABN 84 003 163 586)
5 Cameron Street Beenleigh Qld 4207 Australia
Ph +61 7 3807 8022              Fax +61 7 3807 8422
email:          gil(--nospam--at)raptsoftware.com
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Regards,
Bill Cain, S.E.
Berkeley CA