Design Dimensions
Material properties
Material: Titanium, 6AL-4V
Modulus of elasticity:
Material density:
Poisson's ratio:
Yield Stress:
Shear stress:
Bearing yield stress:
Shear Modulus:
Factors of Safety
Table 28
Closure Calculations
Cylindrical shell
Shell thickness:
Height:
Factor of Safety (lid shear stress)
Mean radius:
Factor of Safety (key shear stress)
Uniform internal or external pressure:
Note:
Meridional stress:
Factor of Safety (endcapCompressiveStress)
Factor of Safety (keyCompressiveStress)
Circumferential stress:
Von Mises Stress:
Radial displacement of circumference:
Change in height:
Factor of Safety (endcapCompressiveStress)
Factor of safety:
Table 3
2
Cylindrical disk or shell
Outer radius:
Inner radius:
Length:
radius range variable
Uniform external pressure:
Circumferential stress:
Note: To find the maximum and minimum values of a graphed function, simply click once on the graph and read the extreme values to the left of the plot.
Formulas and graphs for normal stresses as a function of radial thickness, r:
Longitudinal stress:
Radial stress:
Maximum shear stress (at inner radius, r=b):
Formulas for change in outer and inner radii, and change in length:
Outer radius:
Inner radius:
Length:
Factor of Safety (Von Mises stress)
Factor of Safety (Max. shear stress theory 0.5*Sy)
Outer edge simply supported, inner edge free
Table 24
This file corresponds to Cases 2a - 2d in Roark's Formulas for Stress and Strain.
Outer edge simply supported, inner edge guided
Annular plate with a uniformly distributed pressure q over the portion from r o to a
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:
inner radius:
outer radius:
thickness:
Radial location of applied load:
outer radius:
inner radius:
Plate dimensions:
thickness:
Applied pressure:
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