The FEM is based on the element's full bodies and it needs a set of additional definitions and subfunctions to display these complex FEM results. Usually, the integral results for the full overall cross-section are automatically created and Lines could be computed on each side of the Shell elements. Therefore, in general, it would be not necessary to specifically generate any Line or Area Integrals.
Though these two functions are provided, Line and Area Integrals are to be used for different purposes that allow users to enhance the ability to get significant local results with RM Bridge FEM analysis:
- Area Integrals: integrated over a set of selected cross-section elements (for example the web of a slab part of a hollow box cross-section) resulting in forces (top of the picture below);
RM Notation Shell Theory Description Nx ∫∫σx dydz Normal force in x-direction Qy ∫∫τxy dydz Shear force in xy plane Qz ∫∫τxz dydz Shear force in xz plane Mx ∫∫z× τxy dydz +∫∫y× τxz dydz Torsion moment My ∫∫z×σx dydz Bending moment around y-direction Mz ∫∫y×σx dydz Bending moment around z-direction - Line Integrals: integrated per a linear set resulting in per meter values (bottom of the picture below).
RM Notation Shell Theory Description Nx ∫σx dz Normal force in x-direction Qy ∫σy dz Normal force in y-direction Qz ∫τxy dz Shear force in plane of shell element Mx ∫z×σx dz Bending moment around x-direction My ∫z×σy dz Bending moment around y-direction Mz ∫z×τxy dz Torsional moment (in element plane)
Sort longitudinal or Transversal is the option that allows for searching for a sequence of transversal results in a diagram line of different body series. A much more detailed explanation can be found at the document RM Bridge FEM Application Guide and the Training Example 08. FEM.