Table 24
This file corresponds to Cases 2a - 2d in Roark's Formulas for Stress and Strain.
Annular plate with a uniformly distributed pressure q over the portion from r o to a
Outer edge simply supported, inner edge free
Outer edge simply supported, inner edge guided
Outer edge simply supported, inner edge simply supported
Outer edge simply supported, inner edge fixed
Notation file
Provides a description of Table 24 and the notation used.
Enter dimensions, properties and loading:
Plate dimensions:
thickness:
outer radius:
inner radius:
Applied pressure:
Modulus of elasticity:
Poisson's ratio:
Radial location of applied load:
Constants:
Shear modulus:
D is a plate constant used in determining boundary values; it is also used in the general equations for deflection, slope, moment and shear. Ksb and Ksro are tangential shear constants used in determining the deflection due to shear:
General formulas and graphs for deflection, slope, moment, shear and stress as a function of r:
Define r, the range of the radius and i, the vector index:
Deflection:
The following values are listed in order of inner edge:
free (i = 0)
guided (i = 1)
simply supported (i = 2)
fixed (i = 3)
Deflection at points b and a (inner and outer radius) due to bending:
Deflection at points b and ro due to shear:
Maximum deflection (magnitude):
Large deflection condition check:
Check to verify that the absolute value of the maximum deflection is less than one-half the plate thickness (an assumption stated in the Notation file which must hold true):
The above values are listed in order of inner edge.
free (i = 0)
guided (i = 1)
simply supported (i = 2)
fixed (i = 3)
If |ymax| is greater than t/2 (i.e., check = 0), the equations in this table are subject to large errors. For large deflections, use the equations provided in Table 24a to obtain stress and deflection. Read the Notation file for more specific information. Other values are not available.
Table 24a
Notation file
Slope:
The following values are listed in order of inner edge:
free (i = 0)
guided (i = 1)
simply supported (i = 2)
fixed (i = 3)
Slope at points b and a (inner and outer radius):
Maximum slope (magnitude):
Radial m oment :
The following values are listed in order of inner edge:
free (i = 0)
guided (i = 1)
simply supported (i = 2)
fixed (i = 3)
Moment at points b and a (inner and outer radius):
Maximum radial moment (magnitude):
Transverse moment:
The following values are listed in order of inner edge:
free (i = 0)
guided (i = 1)
simply supported (i = 2)
fixed (i = 3)
Transverse moment at points b and a (inner and outer radius) due to bending:
Maximum tangential moment (magnitude):
Shear:
The following values are listed in order of inner edge:
free (i = 0)
guided (i = 1)
simply supported (i = 2)
fixed (i = 3)
Shear at points b and a (inner and outer radius):
Maximum shear (magnitude):
Radial b ending stress:
The following values are listed in order of inner edge:
free (i = 0)
guided (i = 1)
simply supported (i = 2)
fixed (i = 3)
Radial bending stress at points b and a (inner and outer radius):
Maximum radial bending stress (magnitude):
Transverse bending stress:
The following values are listed in order of inner edge:
free (i = 0)
guided (i = 1)
simply supported (i = 2)
fixed (i = 3)
Radial bending stress at points b and a (inner and outer radius):
Maximum radial bending stress (magnitude):
Review the maximum values
for deflection, slope, moment, shear and stress:
Total deflection of plate (bending induced plus shear induced):
At b (inner radius):
At ro (loading point):
The remainder of the document displays the general plate functions and constants used in the equations above.
Boundary values due to bending:
At the inner edge of the plate:
At the outer edge of the plate:
Due to tangential shear stresses:
End of Section