Section Modulus calculation and optimization

Ans:

Section modulus is ratio of moment of inertia about neutral axis upon the farthest point of section from neutral axis.

The section modulus is denoted by S. To calculate S, the distance (y) to extreme structure of boundary from the centroid.

The maximum stress could cause failure.

Formula of section modulus is : S=I/Y

Where I is moment of inertia (MOI) & Y is the distance from neutral axis to the outer most boundary.

Calculation for section modulus of hood.

Initial hood design and it's moment of inertia as shown in fig 1

Fig:1

In this hood design minimum Moment of inertia is 2.722073569e+05[mm^4]

To find out section modulus S=I/Y

Here I is moment of inertia and Y is distance from neutral axis.

unit of section modulus is mm^3

as we know that section modulus is directly proportional to Moment of inertia.

so,

For unit Y distance s= 2.722073569e+05mm^3

Modified section of hood as shown in fig 2

after offset inner pannel by 1.5mm

Fig: 2

after offset inner pannel by 1.5mm outward, minimum moment of inertia is 3.084531862e+05[mm^4] as we see in above image.

for unit Y distance, s= 3.084531862e+05mm^3

CONCLUSION-

Therefore a small modificcation in the sectional area results in a variation of the section modulus

between the initial and new hood design is 0.362458293e+05mm^3

OR

Y= 877.3950 as per attached picture

So we can also write S=I/Y

i.e. S= 0.362458293e+05mm^3/877.3950.