ABSTRACT
Limit theorems provide bounds to collapse loads. Collapse occurs when a plastic zone encompasses an area of interest. In a finite structure such as a pipe, collapse impends when a plastic zone extends through the pipe wall. Tunnel collapse may occur when a plastic zone encompasses a cross-section. Generally, when the elastic zone no longer contains the plastic zone, collapse impends. The starting point is the divergence theorem that is also a principle of virtual work and a principle of virtual power in solid mechanics application. Slipline solutions are upper-bound solutions when associated velocity fields are kinematically admissible. An example application is to the strip footing problem for which a lower bound to bearing capacity was found previously. One problem for which bounds were obtained relates to the height of a vertical bank. A lower bound is obtained when the stress at the bank bottom just reaches yield.
