Shape factor and Poisson’s ratio in SOM

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Shape factor is the ratio of a plastic moment(Mp) to elastic moment(Me) OR we can say that it is the ratio of plastic section modulus(Zp) to elastic section modulus(Ze). Shape factor shows the extra strength or moment possessed by a section, that is the strength or moment beyond yield point. It is a dimensionless value.

Now, shape factors for different sections:

  • I- section:                      1.12
  • Rectangular section:      1.5
  • Circular section:            1.7
  • T- section:                     1.8
  • Triangular section:        2.34
Higher shape factor represents higher ductility, means more deflection and hence gives warning before the collapse of a section.
-The cross-section reduces for higher shape factor, hence less material is in demand.
-Shape factor depends upon geometry of the sections.

Poisson’s ratio in SOM

This topic is important from the point of view of examination. So, Poisson’s ratio is the ratio of lateral strain(contraction) to longitudinal strain ( expansion), when material is stressed axially. Hence, the material in both axis (perpendical to each other) shows strain values in both directions.

µ = -(lateral strain) / longitudinal strain

(-)sign indicates contraction.

Poisson’s ratio mainly tells the elasticity of that material because material is stressed axially and plasticity when value is less or near to zero. Different materials have different Poisson’s ratio. It is a dimensionless value.

The Poisson’s ratio value is equal to or in between 0 and 0.5.

 

    • If value is less, the material is hard i.e. for concrete it is 0.1.

 

    • If value is more the material is elastic i.e. for rubber it is 0.5.

 

Value of Poisson ratio for various materials are

aluminium – 0.330

brass – 0.340

copper-0.344

concrete – 0.200

bronze-0.350

cast iron-0.288

Poisson’s ratio cannot be negative or greater than 0.5.

But also said that Poisson’s ratio can also be negative for some materials like colloids, neutron stars and genetic materials(http://sdpha2.ucsd.edu/pdf_files/Science_2000.pdf).

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Arbaj Demrot is the founder of VideRime Online Learning, a leading engineering website. He did his BE Civil and M.Tech Structure from RGPV University, Bhopal and has been working as an Assistant Professor in a reputed college.

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