When the reactions have been determined for an arch (Arts. 4.1 to 4.3), the principal forces acting on any cross section can be found by applying the equilibrium laws. Suppose, for example, the forces H, V, and M acting at the elastic center of a fixed arch have been computed, and the moment Mx , shear Sx , and axial thrust Nx normal to a section at X (Fig. 4.4) are to be determined. H, V, and the load P may be resolved into components parallel to the thrust and shear, as indicated in Fig. 4.4. Then, equating the sum of the forces in each direction to zero gives
Equating moments about X to zero yields
