"For a given structure and loading, if there exists any distribution of bending moment throughout the section which is both safe and statically admissible with a set of loads W, the value of W must be less than or equal to the collapse load W_c."

The above theorem is known as

concept:

• Static Theorem (also known as the Lower Bound Theorem of Plasticity):
  • The static theorem states that for a given structure and loading, if there exists a statically admissible distribution of bending moments that is both safe (does not exceed the plastic moment capacity) and in equilibrium with the applied loads, then the applied load $W$ must be less than or equal to the collapse load $W_c$
  • In simpler terms, if you can find a moment distribution that satisfies equilibrium and does not exceed the material's yield criteria, then the structure will not collapse under that loading.

 Additional Information

• Kinematic Theorem (Upper Bound Theorem):

  • This theorem states that for any assumed failure mechanism, the load calculated by equating the internal and external work done during the mechanism is an upper bound to the actual collapse load.

• Uniqueness Theorem:

  • The uniqueness theorem asserts that if both a statically admissible stress distribution and a kinematically admissible mechanism predict the same collapse load, then that load is the true collapse load for the structure.