The two‐nonlinearity model of dissipative trapped‐electron drift wave turbulence [Y.‐M. Liangetal., Phys. Fluids B5, 1128 (1993)] is generalized to include the effects of a sheared magnetic field. Because of the coupling of drift waves with the damped ion‐acoustic modes, the eigenmodekhas a radial structure centered on its rational surface characterized by a mode width &Dgr;k. In this work, both the linear properties of the model, and the multiple‐helicity nonlinear dynamics, including the interactions of the two nonlinearities, i.e., theE×Bdrift and the polarization drift nonlinearities, are analyzed in detail. In particular, a one‐point renormalization is performed to investigate the nonlinear eigenmode properties and the saturation of the system in the multiple‐helicity limit. It is shown that, for the ultrastrong magnetic shear limit where &Dgr;k≤2&rgr;s, the polarization drift nonlinearity is the dominant nonlinear transfer mechanism. However, for the moderate‐to‐weak magnetic shear limit where &Dgr;k≫2&rgr;s, both nonlinearities and cross‐coupling effects will affect the nonlinear transfer processes. An analytic explanation of previous computational observation of the suppression of magnetic shear damping by turbulence [D. Biskamp and M. Walter, Phys. Lett. A109, 34 (1985)] is also given.