FEM Line Integrals & Area Integrals

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.