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Boundary conditions 
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#1
Jun2308, 10:23 AM

P: 40

Hey people can u please tell me what will be the boundary conditions for a circular plate with a central hole clamped at the circumference... Plate is axis symmetric and is under uniform load..



#2
Jun2308, 12:49 PM

Sci Advisor
P: 5,095

You'll obviously have no displacements at the outer edge. There should also be a zero slope at the edge. At the center there are similarities for the conditions of a beam's free end. Can you think of what those would be?



#3
Jun2308, 12:59 PM

P: 40

These two were known to me.. I was encountring problem with the inner edge only..



#4
Jun2308, 01:32 PM

Sci Advisor
P: 5,095

Boundary conditions
Well, if you have a cantilevered beam, what can you say about the moment at the free end?



#5
Jun2308, 01:38 PM

P: 40

I guess moment will b zero there



#6
Jun2308, 01:44 PM

P: 40

But then also i will be needing 1 more condition coz i have 4 constants to be determined in my equation..



#7
Jun2308, 02:21 PM

Sci Advisor
PF Gold
P: 2,241

Is the shear force defined at the fixed edge of the plate, perhaps by calculating the resultant reaction at that edge?



#8
Jun2308, 02:26 PM

P: 40

Will there be any shear force at the fixed edge??



#9
Jun2308, 02:43 PM

Sci Advisor
PF Gold
P: 2,241

On a uniformly loaded a cantilever beam, the shear force will be maximum at the fixed end of the beam, and equal to the reaction force at that end. Additionally, since the beam is only supported by one end, the shear force is zero at the free end of the beam.



#10
Jun2308, 02:53 PM

Sci Advisor
PF Gold
P: 2,241

According to Roark's Table 11.2 Case 2e (Annular plate, outer edge fixed, inned edge free), the following boundary conditions apply:
They also have a definition of the shear force at the fixed edge (enge "a") that is basically a calculation of the reaction force along that edge. [tex]Q_{a}=\frac{q}{2a}(a^2r_{o}^2)[/tex] 


#11
Jun2308, 03:04 PM

P: 40

Thanx a lot.. can u plz send me that link??



#12
Jun2308, 03:17 PM

Sci Advisor
PF Gold
P: 2,241



#13
Jun2308, 03:19 PM

P: 40

Ok.. Do u have ebook or hard copy??



#14
Jun2308, 03:35 PM

P: 40

Can u please check wat r d conditions if inner edge is simply supported and outer edge clamped..



#15
Jun2308, 03:58 PM

Sci Advisor
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#16
Jun2308, 04:03 PM

P: 40

Thanx a lot sir for helping me that way..



#17
Jun2308, 05:17 PM

Sci Advisor
PF Gold
P: 2,241




#18
Jun2308, 05:20 PM

P: 40

sorry but i got stuck once more.. I am not being able to integrate dw/rdr w.r.t dr



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