The bending stiffness of the sandwich beam is given by From the expression for the total bending moment in the beam, we have For small shear deformations, the above expression can be written as Therefore, the bending stiffness of the sandwich beam (with formula_19) is given by  and that of the facesheets is  The shear stiffness of the beam is given by Therefore, the shear stiffness of the beam, which is equal to the shear stiffness of the core, is  A relation can be obtained between the bending and shear deflections by using the continuity of tractions between the core and the facesheets. If we equate the tractions directly we get At both the facesheet-core interfaces formula_70 but at the top of the core formula_71 and at the bottom of the core formula_72. Therefore, traction continuity at formula_73 leads to The above relation is rarely used because of the presence of second derivatives of the shear deflection. Instead it is assumed that  which implies that  Using the above definitions, the governing balance equations for the bending moment and shear force are We can alternatively express the above as two equations that can be solved for formula_31 and formula_33 as Using the approximations where formula_82 is the intensity of the applied load on the beam, we have  Several techniques may be used to solve this system of two coupled ordinary differential equations given the applied load and the applied bending moment and displacement boundary conditions. Assuming that each partial cross section fulfills Bernoulli's hypothesis, the balance of forces and moments on the deformed sandwich beam element can be used to deduce the bending equation for the sandwich beam. The stress resultants and the corresponding deformations of the beam and of the cross section can be seen in Figure 1. The following relationships can be derived using the theory of linear elasticity: where  Superposition of the equations for the facesheets and the core leads to the following equations for the total shear force formula_30 and the total bending moment formula_29: We can alternatively express the above as two equations that can be solved for formula_31 and formula_35, i.e., The bending behavior and stresses in a continuous sandwich beam can be computed by solving the two governing differential equations. For simple geometries such as double span beams under uniformly distributed loads, the governing equations can be solved by using appropriate boundary conditions and using the superposition principle. Such results are listed in the standard DIN EN 14509:2006(Table E10.1).