Table 24
Solid circular plate
Uniformly distributed pressure from r o to a
Notation file
Provides a description of Table 24 and the notation used.
Enter dimensions, properties and loading:
Plate dimensions:
thickness:
radius:
Applied uniform 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. Ksro is the tangential shear constant used in determining the deflection due to shear.
Boundary values:
The G n and L n functions used in the equations below are defined at the end of this document.
Mr is radial moment, Q is shear, y is deflection and
Due to bending:
At the edge of the plate (a):
At the center of the plate (c):
Due to tangential shear stresses:
General formulas and graphs for deflection, slope, moment, shear and stress
Define r, the range of the radius:
Deflection:
Deflections at the center and outer radius:
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). If |ymax| is greater than t/2 (large deflection), the equations in this table used for plates with small deflections are subject to large errors.
If |ymax| is greater than t/2 (i.e., check = 0), only max y and
If |ymax| is not greater than t/2 (i.e., check = 1), hit Shift-PageDown twice to continue with the Table 24 solution of plates without large deflections.
The large deflection equations are
where
Make guesses for max y and
Solution for y:
Solution for
If your deflection was a large deflection, stop here. The remainder of the document only calculates values for plates without large deflections.
Slope:
Slope at center and outer radius:
Maximum slope (magnitude):
Moment; radial and tangential:
Radial and tangential moment at center and outer radius:
Maximum radial and tangential moment (magnitude):
Shear:
Shear at center and outer radius:
Maximum shear (magnitude):
Bending stresses; radial and tangential:
Radial and tangential stress at center and outer radius:
Maximum radial and tangential stresses:
Review the maximum values for deflection, slope, moment, stress and shear:
Total deflection of plate (bending induced plus shear induced):
The remainder of the document displays the general plate functions and constants used in the equations above.
End of Section