Integration over the area of cross-section would have to include one of the larger dimensions and would lead to a model that is too simple for practical calculations. For this reason the stresses are only integrated through the thickness and the stress resultants are typically expressed in units of force "per unit length" (or moment "per unit length") instead of the true force and moment as is the case for beams. For plates and shells we have to consider two cross-sections. The first is perpendicular to the "x"1 axis and the second is perpendicular to the "x"2 axis. Following the same procedure as for beams, and keeping in mind that the resultants are now per unit length, we have We can write the above as where the membrane forces are defined as and the shear forces are defined as  For the bending moment resultants, we have where r = "x"3 e3. Expanding these expressions we have, Define the bending moment resultants such that Then, the bending moment resultants are given by These are the resultants that are often found in the literature but care has to be taken to make sure that the signs are correctly interpreted.