Section Modulus calculation and optimization

SECTION MODULUS

INTRODUCTION

Section Modulus is a geometric property used to calculate the bending stresses in a structural member. Mathematically, It is defined as the ratio of the moment of inertia of a section about its centroidal axis and to the distance of the extreme layer from the neutral axis.

FORMULA:

S = I/y

S = Section Modulus

I = Moment of Inertia

y = distance between the neutral axis and the extreme end of the object.

CONCEPT OF SECTION MODULES

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 design include area for tension, radius of gyration for compression, and 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 = 1/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, as seen in the table below. It is also often used to determine the yield moment (My) such that My = 5 x ay, where ay is the yield strength of the material.

SECTION MODULES CALCULATION IN HOOD DESIGN

Hear we are going to calculate the section modulus of the BIW hood by applying the formula,

Example-1(previous section):

(fig-1.0) (fig-1.1) (fig-1.2)

from the fig 1.0 we get the of maximum and minum value Moment of Inertia

MOI(MAX)=8.981

MOM(MIN)=2.988

Sction modulus (S) = I/Y

Hear we taken the MOM(MIN) valus as (I) and distance between the neutral axis and the extreme end of the hood section as (Y),

Then, I=2.988 & Y=438.402,

S=2.988/438.402=0.00681

section modulus (S)=0.00681.

Example-2(improved section)

(fig-2.0) (fig-2.1) (fig-2.2)

from the fig 2.0 we get the of maximum and minum value Moment of Inertia

MOI(MAX)=8.966

MOM(MIN)=3.031

Sction modulus (S) = I/Y

Hear we taken the MOM(MIN) valus as (I) and distance between the neutral axis and the extreme end of the hood section as (Y),

Then, I=2.988 & Y=438.402,

S=3.031/438.402=0.00681

section modulus (S)=0.00699.

RESULT:

SECTION MODULUS (S) (previous section) =0.00681

SECTION MODULUS (S) (improved section)=0.00699

CONCLUSION:

There for by increase distance in between the outer and inner that means by changing width of hood section the moment of ineria value get increased by increaing MOM value then section modulus value is also and there by stifnes value of an hood get increased.