Section Modulus calculation and optimization

SECTION MODULUS:
Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in the design include an area for tension, the radius of gyration for compression, and the moment of inertia for stiffness. Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below. There are two types of section moduli, the elastic section modulus (S) and the plastic section modulus (Z). For general design, the elastic section modulus is used, applying up to the yield point for most metals and other common materials.
The elastic section modulus is defined as S = I / y

where,

I- is the second moment of area (or moment of inertia) and

y- is the distance from the neutral axis to any given fiber.

It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fiber

moment of inertia:-

Moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion. It appears in the relationships for the dynamics of rotational motion. The moment of inertia must be specified with respect to a chosen axis of rotation. For a point mass, the moment of inertia is just the mass times the square of the perpendicular distance to the rotation axis, I = mr². That point mass relationship becomes the basis for all other moments of inertia since any object can be built up from a collection of point masses.

common moment of inertia

Section Modulus calculation of the Hood Design:

In CATIA intersect the inner panel and outer panel to the plane.

CASE 1: Initial Hood Design

 

I min:-7.046X10^5 mm^4
I max:-1.554x10^8 mm^4

For Calculation, considering the minimum value

 Then

The total length of the model value was 481.354mm
So, at the neutral axis, we need 'Y' value:-total length/2=481.354/2=240.677mm
1)Section modulus(S):-I/Y=7.046X10^5 mm^4 /240.677mm
=2.927X10^3mm^4.

CASE 2: Modified Hood Design

I min:-7.376X10^5 mm^4
I max:-1.601x10^8 mm^4

For Calculation, considering the minimum value

 Then

The total length of the model value was 481.354mm
So, at the neutral axis, we need 'Y' value:-total length/2=481.354/2=240.677mm
1)Section modulus(S):-I/Y=7.376X10^5 mm^4 /240.677mm
=3.064X10^3mm^4.