Bi-pantographic fabrics are materials that are composed of two families of fibers with a micro-structure. The micro-structure of a straight fiber is given by a periodic arrangement of cells that resembles an expanding barrier. The planar behavior of such a fabric is captured at a macroscopic scale by a second gradient continuum. The corresponding strain energy function depends upon the fiber stretches, as well as upon the gradients in fiber direction of the stretches and inclination angles. In this brief communication, we present the equilibrium equations, which must be satisfied in the bulk of the continuum.