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Circular Plates
Stresses and Strains in loaded Circular Plates and Rings.
Contents
Circular Plates Symmetrically Loaded.
Consider a Diametral Section through a plate of thicknessMISSING IMAGE!
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Uniformly Loaded, Edge Freely Supported
and since
and
can not be infinite at the centre, then
from Equation (14) at
,
, and therefore
from equation (15). Using equations (9) and (14). At
,
therefore
Thus,Central Deflection =at
. Thus,
Eliminatingby substitution from Equation (10)
From Equation (7)And atFrom Equation (8)As above when,
. Therefore
Note: the Maximum Stresses occur at the centre.
Uniformly Loaded With The Edge Clamped
- As in the last case,
and
at
,
. Therefore
from equation(15)
Structural loads or actions are forces, deformations or accelerations applied to a structure or its components.Loads cause stresses, deformations and displacements in structures.
Central Load P, Edge Freely Supported (w=0)
- At
,
therefore from equation (14)
and
. From equation(15)
Note:
At
,
do from equation (9)
From which,Thus, Central deflection
From Equation (7)Note:And from equation (8),
These Stresses appear to become infinite at the centre, but it must be realised that the load can not be applied at a point but must extend over a finite area. If this area can be estimated then the maximum Stresses can be obtained.
Loaded Round A Circle, Edge Freely Supported
- Let a total load
be distributed around a circle of radius
.
It is necessary to divide the plate into two regions, one forMISSING IMAGE!
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and the other for
. At
the values of
,
and
must be the same for both regions.
- If
,
and
. And from Equation (15),
Since
and
are not infinite at
then
, and since
when
and
, then above equations reduce to:
And,
- If
and
And from Equation (15),
Equating the values ofand
at
gives the following equations:
And,at
gives: From Equations (16) to (17) the constants are found to be:
The Central Deflection is given by the value ofat
and by substitution equation (15) reduces to:
- For
Which has a maximum value atHence from equation (12)
Similarly: - If
Annular Ring , Loaded Around The Inner Edge
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