Section Modulus calculation and optimization

AIM : Calculate the section modulus of Hood by using thee formula S = I/Y. And to improve the section of modulus come up with new Design with increase in section.

INTRODUCTION :

SECTION MODULUS :

Section modulus is a geometric property for a given cross section used in a design of a beamor flexural members, it is also reffered to as the Polar Modulus or Torsional Section Modulus.

Other Geometric Properties used in Design include area for tension and shear, radius of gyration for compression, and moment of inertia and polar moment of inertia for Stiffness.

Any reletionship between this properties is highly dependent on the in equation.

Equation for the section moduli of common shapes are given below,

S = I/Y ,

here,

S = Section modulus.

I = Moment of Inertia.

Y = Distance from Neutral axis to the extreme end.

MOMENT OF INERTIA (I) :

The moment of inertia (I) or Second moment of inertia is an a geometrical property of an area which reflects how its points are distributed with regards to arbitrary axis. The moment of Inertia is typically denoted by I.

RADIUS OF YRATION :

This is the another property of of a section and is also a function of the second moment of area.

The radius of gyration can be considered to be an indiaction of the stiffness of the section based on the shape of the shappe of the cross-section when used as compression member.

STIFFNESS :

It is the property of material which is resist the deformation.

SECTION MODULUS for the ORIGINAL DESIGN :

Moment of Inertia (Max) = 5.19*`10^4

Moment of Inertia (Max) = 1.73*`10^4`

Y = 908/2 = 454 mm

S = I/Y

S = 1.73*`10^4`/454

S = 39.39 `mm^3`

SECTION MODULUS for the IMPROVED DESIGN :

Moment of Inertia (Max) = 5.39*`10^4`

Moment of Inertia (Max) = 1.97*`10^4`

Y = 908/2 = 454 mm

S = I/Y

S = 1.97*`10^4`/454

S = 43.39 `mm^3`

CONCLUSION :

In this way, we can conclude that the increase in section modulus or area we can increase the strength of the part.