A cantilever beam of length $$L$$ and a cross section with shape factor $$'f'$$ supports a concentrated load $$P$$ as shown below:

The length $${L_P}$$ of the plastic zone, when the maximum bending moment, equals the plastic moment $${M_P}$$, given by

The shape factor of the section shown in fig. is

The plastic modulus of a section is $$4.8 \times {10^{ - 4}}\,\,{m^3}.$$ The shape factor is $$1.2$$. The plastic moment capacity of the section is $$120$$ $$kN$$-$$m.$$ The yield stress of the material is

The fixed beam $$AB$$ has a span of $$3000$$ $$mm$$ and is of uniform cross-section. The plastic moment capacity $$({M_P})$$ of the beam's cross-section is $$1.5 \times {10^8}\,\,N$$-$$mm.$$

The beam will have like a simply supported beam when the magnitude of distributed load $$P$$ attains a value equal to: