Beams with held ends: notes
This form uses the theory of beams in bending under transverse loads and in tension under an axial load generated by the ends being not allowed to get closer when loads are applied. The behaviour is no more linear under such conditions, and the principle of superposition does not apply: that's why a uniform load is allowed to be superimposed to the main loading.
The solution is based onto a polynomial approximation formula obtained from strain energy minimization ('Options'->'Show formulae' in the menu to see, relationships enforcing boundary conditions not shown).
When the area of beam's cross section is zero, the elementary solution for a beam in bending is obtained.
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.