3 Sides supported beam
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Re: 3 Sides supported beam
Re: 3 Sides supported beam -- naveen_guntur	Post Reply	Top of thread	Forum

Posted by: ChrisMEngr ® 01/08/2006, 13:17:05 Author Profile eMail author Edit

Sounds like a Plates and Shells book would be helpfull. They deal with deformation of materials with more complex constraints than just a bending beam.

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Re: 3 Sides supported beam
Re: 3 Sides supported beam -- naveen_guntur	Post Reply	Top of thread	Forum

Posted by: Kelly_Bramble ® 01/07/2006, 17:22:40 Author Profile eMail author Edit

The following webpage /Calulators_Online.htm has a selection of beam bending calculation / equation webpages. If you don't see your exact case, post a picture of this forum.

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Re: 3 Sides supported beam
Re: Re: 3 Sides supported beam -- Kelly_Bramble	Post Reply	Top of thread	Forum

Posted by: akhan ® 01/08/2006, 05:48:54 Author Profile eMail author Edit

How much loading will you be talking about? A small loading on this would have a negligible effect since the beam is fixed at the back and also supported. A sketch of the arrangement would be more helpful in understanding your situation!!

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Re: 3 Sides supported beam
Re: Re: 3 Sides supported beam -- akhan	Post Reply	Top of thread	Forum

Posted by: naveen_guntur ® 01/09/2006, 11:41:07 Author Profile eMail author Edit

Thanks For the Reply. pl. find the attached document showing the representation of the loading on the beam. I am interested finding out the Maximum deflection for this kind of loading.

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Re: 3 Sides supported beam
Re: Re: 3 Sides supported beam -- naveen_guntur	Post Reply	Top of thread	Forum

Posted by: zekeman ® 01/10/2006, 20:13:55 Author Profile eMail author Edit

The solution to your problem is in any book on plates and shells. Timoshenko's famous book with that name has a solution in tabular form for the boundary conditions you have. However, it has solutions for b/a ratios of width to length ( your 22" by 120") or 22/120= 0.18. He has solutions for b/a= .33 and b/a =0 as follows: For b/a=.33: deflection=0.094qb^4/D For b/a= 0 : deflection=0.125qb^4/D where the maximum deflection is in the center of the unsupported edge and D=EI/(1-nu^2) I =inertia of a crossection 1 inch wide nu= Poisson's ratio q= loading density, psi For your case the solution is betwen these . Conservatively, take the worst case of the 0.125 coefficient. AS an example, suppose the beam is 3/4 inch yellow pine and the load is 200 lbs, then E= 1.4*10^6 psi from mechanical properties For a rectangular beam 1 inch wide I=h^3/12 D=1.48*10^6*.75^3/12=5.2*10^4 , assuming small nu(I was unable to get precise values for this number, but it is has a negligible affect on the result). And q=200/(22*120)=.0757. Evaluating the eq for maximum displacement I get .125*q*b^4/D=.125*.0757*22^4/5.2*10^4= .341 inches.

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Re: 3 Sides supported beam
Re: Re: 3 Sides supported beam -- zekeman	Post Reply	Top of thread	Forum

Posted by: naveen_guntur ® 01/11/2006, 09:35:25 Author Profile eMail author Edit

Dear Zekeman, Really It helped me a lot to solve this problem. I am glad that I have solved this with your valuable references. Thanks for the help.

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