Which expression represents shape factor?

Concept:

Shape Factor:

• It represents the reserve of the strength of a section beyond the yield point.
• It doesn't show the reserve of the strength of the complete structure.
• It depends upon the geometry of the cross-section only.
• It is defined as the ratio of the plastic moment capacity of a beam section to its yield moment capacity.

Mathematically,

\({\rm{S}}{\rm{.F = }}\dfrac{{{{\rm{M}}_{\rm{p}}}}}{{{{\rm{M}}_{\rm{y}}}}}{\rm{ = }}\dfrac{{{{\rm{f}}_{\rm{y}}}{{\rm{Z}}_{\rm{p}}}}}{{{{\rm{f}}_{\rm{y}}}{\rm{Z}}}}{\rm{ = }}\dfrac{{{{\rm{Z}}_{\rm{p}}}}}{{\rm{Z}}}\)

Where,

fy = Yield stress.

Zp = Plastic modulus of a section.

Z = Elastic modulus of a section.

Zp is calculated about the equal area axis and Z is calculated about the centroidal axis.

It can also be defined in terms of the moment of resistance under plastic and elastic conditions:

Shape Factor = (MOB)p/(MOB)e

(MOB​)p​ = Plastic moment of resistance

(MOB​)e​ = Elastic moment of resistance

Additional Information

Shape Factor for the different section: