The issue of turbulent pinches induced by inhomogeneities in the magnetic field confining tokamak plasmas is studied in the framework of the self-consistent action-angle transport theory. It is found that, in magnetic turbulence, electron particle and energy fluxes proportional to the magnetic shear and originating from the toroidal frequency of the particle motion are different from zero only if the electron temperature is different from the ion temperature, independent of whether the electrons are trapped or untrapped. Restricting to passing electrons, it is shown that both the magnitude and the sign of these fluxes depend crucially on the ratio Ti/Te.