Circular rings: notes
This form uses the theory of circular arches under bending, normal stress and shear to calculate the behavior of circular rings subject to various loads.
The ring is in all cases taken as supported on bottom line. You may use the combination sheet to combine different loadings: if these are in equilibrium, the support reaction will disappear.
The solution is based onto a sinusoidal formula (exact) obtained from strain energy U minimization ('Options'->'Show formulae' in the menu to see, relationships enforcing boundary conditions not shown).
You may force the value of α to zero and/or the value of β to zero to remove the contribution of normal stress and/or of shear deformation.
When present, the button 'Data' will download the vectors of coefficients (without dimensions) a,b,c,...,A,B,C,... as defined in sheet's formulae. Note that it is up to the user to link the downloaded vectors to the input data: when you download it, the vectors correspond to the data in the sheet as you view it.