# Boundary conditions

by harpreet singh
Tags: boundary, conditions
 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..
 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?
 P: 40 These two were known to me.. I was encountring problem with the inner edge only..
 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?
 P: 40 I guess moment will b zero there
 P: 40 But then also i will be needing 1 more condition coz i have 4 constants to be determined in my equation..
 Sci Advisor PF Gold P: 2,248 Is the shear force defined at the fixed edge of the plate, perhaps by calculating the resultant reaction at that edge?
 P: 40 Will there be any shear force at the fixed edge??
 Sci Advisor PF Gold P: 2,248 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.
 Sci Advisor PF Gold P: 2,248 According to Roark's Table 11.2 Case 2e (Annular plate, outer edge fixed, inned edge free), the following boundary conditions apply: Bending moment at the free end is zero. Shear force at the free end is zero. Displacement at the fixed end is zero. Slope at the fixed end is zero. 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. $$Q_{a}=\frac{-q}{2a}(a^2-r_{o}^2)$$
 P: 40 Thanx a lot.. can u plz send me that link??
 Sci Advisor PF Gold P: 2,248 It's not on the web, the equations are located in this book: Roark's Formulas for Stress and Strain
 P: 40 Ok.. Do u have ebook or hard copy??
 P: 40 Can u please check wat r d conditions if inner edge is simply supported and outer edge clamped..
P: 5,095
 Quote by Mech_Engineer According to Roark's Table 11.2 Case 2e (Annular plate, outer edge fixed, inned edge free), the following boundary conditions apply: Bending moment at the free end is zero. Shear force at the free end is zero. Displacement at the fixed end is zero. Slope at the fixed end is zero. 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. $$Q_{a}=\frac{-q}{2a}(a^2-r_{o}^2)$$
I was trying to not directly quote that to get the OP to think about the conditions on his own...Make him work!
 P: 40 Thanx a lot sir for helping me that way..
PF Gold
P: 2,248
 Quote by FredGarvin I was trying to not directly quote that to get the OP to think about the conditions on his own...Make him work!
Sorry about that Fred, I just get so excited!

 Quote by harpreet singh Can u please check wat r d conditions if inner edge is simply supported and outer edge clamped..
Its quite easy to interpolate what you've "learned" on the case above to the simply supported case. Perhaps trying to sketch a rough shear force and bending moment diagram could help you... specifically looking at what a simple support's effect looks like on those diagrams.
 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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