The force distribution in multi-legged robots is a constrained, optimization problem. The solution to the problem is the set points of the leg contact forces for a particular system task. In this paper, an efficient and general formulation of the force distribution problem is developed using linear programming. The considered walking robot is a quadruped robot with a locked-joint failure, i.e., a joint of the failed leg is locked at a known place. For overcoming the drawback of marginal stability in fault-tolerant gaits, we define safety margin on friction constraints as the objective function to be maximized. Dynamic features of locked-joint failure are represented by equality and inequality constraints of linear programming. Unlike the former study, our result can be applied to various forms of walking such as crab and turning gaits. Simulation results show the validity of the proposed scheme.