Beams in bending with axial compression
This form uses the classical theory of beams in bending as represented by the equation M=-EJy''
with an added axial compressive load.
The solution is based onto a polynomial approximation formula obtained from strain energy V minimization ('Options'->'Show formulae' in the menu to see, relationships enforcing boundary conditions not shown).
Note also that the principle of superposition is only valid in a limited way for such beams: the axial load must be considered as if it was an element of the supporting scheme. In other words the effect of various transverse loadings may be combined by summation, but the same axial load must be present with the same value in all the single superimposed load conditions.
When present, the button 'Data' will download the vectors of the coefficients (without dimensions) ai,bi,ci 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 corresponds to the data in the sheet as you view it.
with an added axial compressive load.
The solution is based onto a polynomial approximation formula obtained from strain energy V minimization ('Options'->'Show formulae' in the menu to see, relationships enforcing boundary conditions not shown).
Note also that the principle of superposition is only valid in a limited way for such beams: the axial load must be considered as if it was an element of the supporting scheme. In other words the effect of various transverse loadings may be combined by summation, but the same axial load must be present with the same value in all the single superimposed load conditions.
When present, the button 'Data' will download the vectors of the coefficients (without dimensions) ai,bi,ci 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 corresponds to the data in the sheet as you view it.