The correct answer is A. Equilibrium condition.
Equilibrium condition is the most fundamental condition that must be satisfied in any analysis, whether it is elastic or plastic. It states that the sum of all the forces acting on a body must be equal to zero, and the sum of all the moments acting on a body must be equal to zero.
Yield condition is a condition that must be satisfied in plastic analysis. It states that the stress at any point in a body must not exceed the yield stress of the material.
Plastic moment condition is a condition that must be satisfied in plastic analysis of beams. It states that the plastic moment of the beam must be greater than the bending moment at the critical section.
Mechanism condition is a condition that must be satisfied in plastic analysis of frames. It states that the structure must have at least one mechanism, i.e., a set of kinematically independent collapse mechanisms.
In conclusion, the equilibrium condition is the most fundamental condition that must be satisfied in any analysis, whether it is elastic or plastic. The yield condition, plastic moment condition, and mechanism condition are conditions that must be satisfied in plastic analysis.