++++ ++++ ++++ ++++ ++++ Concept Question ++++ ++++ ++++ ++++ ++++ How can the paradox with the spring be ex- plained ? In other words, which of the following statements is true? 1. Equilibrium can be derived from the equiv- alence of the external and the internal work. 2. Equilibrium is an artifact of our imagina- tion. 3. Equilibrium only considers the ?nal state and not the process by which it has been reached. Intermediate states are ignored and may violate equilibrium. 4. Equilibrium can be derived from the mini- mization of potential energy. 1. ++++ Statements (3) and (4). 2. ++++ Statements (1) and (2). 3. ++++ All of the above. 4. ++++ None of the above. 5. ++++ DKDU The right answer is (1) ++++ . ? Eqn. (??) is wrong because σ 22 negationslash= 0 due to Poisson’s e?ect. ? Eqn. (??) is correct, ? 33 negationslash= 0 due to the imposed displacement, ? 11 negationslash= 0 due to Pois- son’s e?ect and ? 22 = 0 because of the plane strain condition. ? Eqn. (??) is wrong, it contradicts Eqn. (??). ? Eqn. (??) is correct, the plane strain condi- tions are actually materialized via u 2 = 0.