Table 26
Table 28
Sphere volume:
Rectangular plate, all edges simply supported
Cylinder volume:
Spherical shell
Uniform internal or external pressure, q (force per unit area), tangential edge support
Notation file
Provides a description of Table 26 and the notation used.
Enter dimensions, properties and loading:
Enter dimensions, properties and loading:
Shell thickness:
Table 35 Formulas for elastic stability of plates and shells
Plate dimensions:
length:
Angle from centerline to edge:
width:
Mean radius:
thickness:
Modulus of elasticity:
Distributed load over circle:
Poisson's ratio:
Modulus of elasticity:
Thin sphere under uniform external pressure
Internal or external pressure (positive denotes internal):
Distance from centerline to edge measured perpendicular to centerline:
Height of section:
Note : For these equations to be valid, R2/t>10.
Calculation procedure:
Meridional stress:
Enter dimensions and properties:
Calculation procedure:
Sphere dimensions:
radius:
Circumferential stress:
For a plate material with
thickness:
Von Mises Stress calculation:
Conditions:
For the expressions in the Case to be valid, the following condition must be true (i.e., condition = 1):
Radial displacement of circumference in R direction:
Critical pressure:
For ideal case,
Radial displacement of circumference in R2 direction:
However, the probable actual minimum value of q' is
The above stress and deflection occur at the center of the plate.
Change in height:
The above reaction force occurs at the center of the long sides.
References:
Ref. 1.
Ref. 37.
Ref. 43.
Interpolate data values:
End of Section
End of Section
Table 3
2
Spherical
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):
If ymax is greater than t/2 (large deflection), the equations in this table are subject to large errors. For large deflections, use the equations provided in Table 26a. Read the Notation file for more specific information.
Table 26a
Enter dimensions, properties and loading:
Outer radius:
Notation file
Inner radius:
Formulas for change in outer and inner radii, and change in length:
References:
Ref. 21.
Outer radius:
Inner radius:
(See Ref. 3)
End of Section
Formulas and graphs for normal stresses as a function of radial thickness, r:
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.
radius range variable
point of interest along range
Longitudinal stress:
Circumferential stress:
Radial stress:
Maximum shear stress (at inner radius, r=b):
References:
Ref. 3.
Societies Monograph, McGraw-Hill Book Company.
End of Section