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Re: Deflection of Cantilever Beam with Moment at Free End
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- Subject: Re: Deflection of Cantilever Beam with Moment at Free End
- From: "Rand Holtham, P.E." <rand(--nospam--at)sigmaengineers.com>
- Date: Fri, 25 Mar 2005 10:00:52 -0600
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 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 loading on the conjugate beam is a uniform load 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 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__________________________________ Do you Yahoo!? Yahoo! Small Business - Try our new resources site! http://smallbusiness.yahoo.com/resources/ ******* ****** ******* ******** ******* ******* ******* *** * Read list FAQ at: http://www.seaint.org/list_FAQ.asp * * This email was sent to you via Structural Engineers * Association of Southern California (SEAOSC) server. To * subscribe (no fee) or UnSubscribe, please go to: * * http://www.seaint.org/sealist1.asp * * Questions to seaint-ad(--nospam--at)seaint.org. Remember, any email you * send to the list is public domain and may be re-posted * without your permission. Make sure you visit our web * site at: http://www.seaint.org ******* ****** ****** ****** ******* ****** ****** ********
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