We study the influence of solid friction on the structure of the force network sustaining a regular bidimensional granular piling. We show how the mechanical equations describing local equilibrium may couple naturally with a stochastic variable. A Monte Carlo method is designed to extract the force networks satisfying static equilibrium conditions. A statistical ensemble is constructed and we study some of its structural and stochastic properties. We address, in particular, the question of the vertical load transfer in two different cases i.e. the response to a localized force excess at the top of an horizontal piling and the distribution of forces under a sand pile. Using this very simple mechanical model, we test the validity of the passage to various stochastic descriptions as well as the existence of macroscopic constitutive relations. We also address the question of the influence of a local friction bias on the macroscopic static equilibrium conditions.