EK223

Theorems for plastic analysis:

1. Lower bound theorem: if only the structure is in equilibrium, that is, the forces and moments, externally and internally, balance, and no bending moment exceeds the plastic moment of resistance of a member then the solution is less than or equal to the collapse load.
2. Upper bound theorem: if only the structure is in equilibrium, that is, the forces and moments, externally and internally, balance, and there are sufficient number of hinges to form a collapse mechanism then solution is greater than or equal to the collapse load.
3. Uniqueness theorem: if the structure is in equilibrium, that is, the forces and moments, externally and internally, balance, and no bending moment exceeds the plastic moment of resistance of a member and there are sufficient number of hinges to form a collapse mechanism then the solution is equal to the collapse load.