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

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• To: seaint(--nospam--at)seaint.org
• Subject: Re: Deflection of Cantilever Beam with Moment at Free End
• From: BCainse(--nospam--at)aol.com
• Date: Sat, 26 Mar 2005 11:43:15 EST

 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.>>Checked by AVG Anti-Virus.>>Version: 7.0.308 / Virus Database: 266.8.1 - Release Date: 3/23/2005>>>M x L^2>_______   = deflection @ free end>>    2EI>>According to Roark, 6th ed, Table 3, case 3a, pg 105.>>******* ****** ******* ******** ******* ******* ******* ***>*   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 >******* ****** ****** ****** ******* ****** ****** ********Regards  Gil BrockPrestressed Concrete Design Consultants Pty. Ltd. (ABN 84 003 163 586)5 Cameron Street Beenleigh Qld 4207 AustraliaPh +61 7 3807 8022              Fax +61 7 3807 8422email:          gil(--nospam--at)raptsoftware.comemail:          sales(--nospam--at)raptsoftware.comemail:          support(--nospam--at)raptsoftware.comwebpage:        http://www.raptsoftware.com******* ****** ******* ******** ******* ******* ******* ****   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 ******* ****** ****** ****** ******* ****** ****** ********   Regards,Bill Cain, S.E.Berkeley CA