Material properties
Material: Titanium, 6AL-4V
Modulus of elasticity:
Material density:
Poisson's ratio:
Yield Stress:
Shear stress:
Bearing yield stress:
Shear Modulus:
Design Dimensions
Factors of Safety
Table 28
Cylindrical shell
Shell thickness:
Height:
Mean radius:
Uniform internal or external pressure:
Note:
Meridional stress:
Circumferential stress:
Von Mises Stress:
Radial displacement of circumference:
Change in height:
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)
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
Notation file
Provides a description of Table 24 and the notation used.
Outer edge simply supported, inner edge free
Outer edge simply supported, inner edge guided
inner radius:
outer radius:
Radial location of applied load:
Outer edge simply supported, inner edge fixed
Plate dimensions:
Outer edge simply supported, inner edge simply supported
thickness:
Applied pressure:
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:
Define r, the range of the radius and i, the vector index:
General formulas and graphs for deflection, slope, moment, shear and stress as a function of r:
Slope:
The following values are listed in order of inner edge:
free (i = 0)
Shear:
The following values are listed in order of inner edge:
Radial bending stress at points b and a (inner and outer radius):
Radial m oment :
Radial b ending stress:
The following values are listed in order of inner edge:
Transverse bending stress:
Deflection:
Transverse moment:
The following values are listed in order of inner edge:
free (i = 0)
guided (i = 1)
free (i = 0)
guided (i = 1)
simply supported (i = 2)
free (i = 0)
Radial bending stress at points b and a (inner and outer radius):
guided (i = 1)
simply supported (i = 2)
fixed (i = 3)
guided (i = 1)
simply supported (i = 2)
fixed (i = 3)
simply supported (i = 2)
Moment at points b and a (inner and outer radius):
fixed (i = 3)
fixed (i = 3)
Shear at points b and a (inner and outer radius):
Deflection at points b and ro due to shear:
The above values are listed in order of inner edge.
free (i = 0)
Maximum radial bending stress (magnitude):
guided (i = 1)
simply supported (i = 2)
Maximum radial moment (magnitude):
Maximum shear (magnitude):
fixed (i = 3)
Maximum radial bending stress (magnitude):
The following values are listed in order of inner edge:
free (i = 0)
Maximum deflection (magnitude):
guided (i = 1)
simply supported (i = 2)
fixed (i = 3)
Transverse moment at points b and a (inner and outer radius) due to bending:
The following values are listed in order of inner edge:
Slope at points b and a (inner and outer radius):
Deflection at points b and a (inner and outer radius) due to bending:
free (i = 0)
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):
guided (i = 1)
simply supported (i = 2)
The following values are listed in order of inner edge:
Maximum slope (magnitude):
fixed (i = 3)
free (i = 0)
Table 24a
Notation file
Maximum tangential moment (magnitude):
guided (i = 1)
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.
simply supported (i = 2)
fixed (i = 3)
The remainder of the document displays the general plate functions and constants used in the equations above.
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):
Boundary values due to bending:
At the inner edge of the plate:
At the outer edge of the plate:
Due to tangential shear stresses: