Non-shakedown collapse of a doubly-reinforced rectangular plate under cyclic loads

A typical doubly-reinforced concrete rectangular plate is subjected to quasi-static (and more general quasiperiodic dynamic) transverse loads. The amount of reinforcements can be different in the upper and lower layers, in the central and rear parts of the plate, and in different directions, as usually designed in practice. An upper bound kinematic approach, which involves construction of potential collapse kinematic fields with plastic hinge lines, is developed to evaluate the non-shakedown loads corresponding to the respective collapse modes. The relations between the non-shakedown load parameters (frequency, amplitude limits) and the reinforcement parameters are derived for practical use. The kinematic assumptions with plastic hinge lines reduce the set of admissible kinematic fields for our upper bound approach, however the procedure appears relatively simple, visual, and can be developed to investigate the behaviour of other plates in various loading and reinforcement schemes, like the respective approach of plastic limit analysis, which was restricted to static loading.