3 Sides supported beam Question
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Posted by: naveen_guntur ®

01/07/2006, 10:03:20

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How to calculate the deflection of beam supported at two ends and fixed at the back side.







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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

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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

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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

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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

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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.


 

3_Sides_supported_Beam_deflection.jpg (21.6 KB)  






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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

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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

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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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