Continuous beams in simple bending: notes
This form uses the classical theory of beams in simple bending as represented by the equation M=-EJy''
The solution is based onto a polynomial (exact) formula obtained from strain energy V minimization ('Options'->'Show formulae' in the menu to see, relationships enforcing boundary conditions not shown).
The formulae shown in the sheet for deflections, in the order 1,2,3,... , apply to successive fields of the beam, where the fields are divided by supports and by loads.
The tabulated stresses are the maximum absolute value of the stress at upper and lower fibers in the section. Use bending moment values to separate the two.
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.
The solution is based onto a polynomial (exact) formula obtained from strain energy V minimization ('Options'->'Show formulae' in the menu to see, relationships enforcing boundary conditions not shown).
The formulae shown in the sheet for deflections, in the order 1,2,3,... , apply to successive fields of the beam, where the fields are divided by supports and by loads.
The tabulated stresses are the maximum absolute value of the stress at upper and lower fibers in the section. Use bending moment values to separate the two.
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.