The correct answer is: A. Equilibrium and mechanism conditions.
The statical method of plastic analysis is a method of structural analysis that uses the concept of plastic hinges to determine the load-carrying capacity of a structure. A plastic hinge is a point in a structure where the bending moment is equal to the plastic moment of the material. When a structure reaches its plastic collapse load, all of the members in the structure will have at least one plastic hinge.
The statical method of plastic analysis satisfies the equilibrium and mechanism conditions. The equilibrium condition states that the sum of the forces acting on a structure must be equal to zero. The mechanism condition states that the structure must have at least one mechanism, which is a kinematically admissible set of displacements that satisfies the equilibrium conditions.
The other options are incorrect because they do not satisfy both the equilibrium and mechanism conditions. Option B only satisfies the equilibrium condition, while Option C only satisfies the mechanism condition. Option D does not satisfy either the equilibrium or mechanism condition.