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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: "M. David Finley, P.E." <pec(--nospam--at)isgroup.net>
• Date: Fri, 25 Mar 2005 11:04:58 -0500

Yes, I've used that method in the past. I was just a little "integration challenged" first thing this morning when I was trying to verify the other loading cases before doing the moment case, so I thought I would use the list as a check.
```
Thanks,

David Finley

```
----- Original Message ----- From: "Rand Holtham, P.E." <rand(--nospam--at)sigmaengineers.com>
```To: <seaint(--nospam--at)seaint.org>
Sent: Friday, March 25, 2005 11:00 AM
Subject: Re: Deflection of Cantilever Beam with Moment at Free End

```
I use the graphical method...draw beam loading,draw shear diagram (it's zero since there is no other load since there's only the external moment), draw moment diagram (area under the shear diag + external applied moments), draw rotation diagram (triangular with max at end of beam = to area under moment diagram {MxL}divided by EI, draw the deflection diagram (first order parab with max equal to area under rotation diag {ML^2/2EI}).
```
It took me longer to type the procedure than to perform it ;o)
HTH

Rand

```
----- Original Message ----- From: "Padmanabhan Rajendran" <rakamaka(--nospam--at)yahoo.com>
```To: <seaint(--nospam--at)seaint.org>
Sent: Friday, March 25, 2005 9:26 AM
Subject: Re: Deflection of Cantilever Beam with Moment at Free End

```
```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
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

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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