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# Re: Deflection of Cantilever Beam with Moment at Free End

• To: seaint(--nospam--at)seaint.org
• Subject: Re: Deflection of Cantilever Beam with Moment at Free End
• From: Padmanabhan Rajendran <rakamaka(--nospam--at)yahoo.com>
• Date: Fri, 25 Mar 2005 07:26:07 -0800 (PST)
• Comment: DomainKeys? See http://antispam.yahoo.com/domainkeys

```Your question has been answered by Jordan. ML^2/(EI)
is correct. Remember, however, that it is easy to
derive formula for deflection of a cantilever using
the conjugate beam method. If you are not familiar,
here are the steps.

(i) Draw the bending moment diagram on a line
represented by the beam span. (ii) Assume that the
free end is fixed and the fixed end is free (iii)
Calculate the bending moment at the "new" fixed end
due to loading represnted by the bending moment
diagram divided by EI (iv) Incidentally, the slope at
any sectiont is given by the shear force at the
section of the conjugate beam. The method is,
particularly, useful for beams with varying moment of
inertia.

For example, with moment M at the free end, the
represented by "M/EI". Bending moment at the "new"
fixed end is:
(M/EI)*L*L/2=M*L^2/EI.

Rajendran

--- "M. David Finley, P.E." <pec(--nospam--at)isgroup.net> 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
>
> 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
>
>
>

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